Since nature is a principle of motion and change, and since our inquiry is about nature, we must not overlook the question of what motion is. For without understanding motion, we could not understand nature.”




Second edition, revised and extended.


By Yuri N. Ivanov









Ivanov Yuri Nikolaevich.

Rhythmodynamics. – M:


ISBN 978-5-98420-018-9


Significance of scientific theory is determined by its ability not just to explain logically and clearly what and how happens, but also to show the ways and means of practical application of those ideas the theory expounds. That’s where rhythmodynamics beats all modern hypotheses, theories and paradigms as it reveals the essence, the mechanism of basic phenomena and shows how the new understanding can be applied in concrete areas.


The new revised and extended version of Yuri Ivanov’s book gives a definite model account as to: how systems self-organize; what inside-matter processes trigger and maintain the bodies’ motion by inertia; how bodies in gravitational field form their propensity to free fall; what energy flow is; what the speed of this flow is and what it depends on.


A new understanding of space dimensions is given; the notions of ‘amplitudeless’ and ‘frequency’ space have been introduced and defined; coordinate axes of these dimensions have been introduced too. A possible cause of red shift among distant objects in the Universe (Alice’s effect), and the cause of self-propulsion of isolated molecules are examined.


Besides, interpretation of the results of the famous Michelson’s interferometer experiment is given which is based on the ‘standing waves’ compression’ phenomenon. Application aspects concerning energy production and new ways of motion in space are inspected.


Rhythmodynamics surprising compatibility with other scientific approaches is explained by the absence of unfamiliar or vague notions and ideas in its foundation. Waves and wave sources are present more or less in all known theories of physics, therefore all the effects, phenomena and laws described y rhythmodynamics are automatically true in those theories.


The book is provided with a DVD containing films, a library of rare books, teaching materials and demonstration programs.


About the author: Yuri N. Ivanov, Doctor of Science, Academician of the Russian Academy of Natural Science, Director of the scientific-technical center STC "MIRIT"

(Rhythmodynamics site:


Publishing house ‘Energia’, Moscow


ISBN 978-5-98420-018-9

© Yu. Ivanov 2007





Table of Contents


Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

From the author . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Rhythmodynamics (RD) : its goals and tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Chapter 1. The Elements  (12)

§ 1.01 On dogmas, axioms and postulates in physics . . . . . . . . . . . . . . . . . . . . . . . .

§ 1.02 The choice of instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 1.03 Axiom of foundation-regularity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 1.04 Wave geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 1.05 The properties of the wave geometry objects . . . . . . . . . . . . . . . . . . . . . . . . .

§ 1.06 The wave geometry potentials  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 1.07 Rhythmodynamics: postulates  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 1.08 Establishing the tasks to be solved  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Chapter 2. Interference  (49)

§ 2.01 Is it possible to manage without the notion of wave medium? . . . . . . . . . . .

§ 2.02 Standing wave. The basic properties we know as well as new ones . . . . . .

§ 2.03 Oscillations, standing waves, and physical standards of measure. . . . . . . .

§ 2.04 Dimension’s contraction and Michelson’s experiment . . . . . . . . . . . . . . . . .

§ 2.05 RD interpretation of the results of Michelson’s experiment . . . . . . . . . . . . .

§ 2.06 The speed of light in one direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 2.07 RD transformations of coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 2.08 Lively standing wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 2.09 Frequency difference and the speed of energy flow . . . . . . . . . . . . . . . . . . .

§ 2.10 On nature of electric current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Chapter 3. Fundamentals of Self-organization (107)

§ 3.01 Energy as a measure of motion  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 3.02 Absolute and relative aspects of energies  . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 3.03 Self-organization of wave systems  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 3.04 Self-organization and phase displacement  . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 3.05 Kinetic energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 3.06 Wave model of elastic object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 3.07 Properties of artificial elastic bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 3.08 Inertia is the property of system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 3.09 Model view on self-propulsion of molecules . . . . . . . . . . . . . . . . . . . . . . . . .


Chapter 4Motion (135)

§ 4.01 Motion as a fundamental property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 4.02 Translational motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 4.03 The nature of the moving force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 4.04 Three states of quiescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 4.05 First state of quiescence  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 4.06 Second state of quiescence  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 4.07 Third state of quiescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 4.08 Specifics of RD modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Chapter 5.  Force, gravitation (153)

§ 5.01 Nature of force  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 5.02 Motion in gravitational field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 5.03 Equation to calculate acceleration in gravitational field . . . . . . . . . . . . . . . .

§ 5.04 Force of gravitation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 5.05 Comparing formulas  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

§ 5.06 Gravitation and frequency pulling (hypothesis) . . . . . . . . . . . . . . . . . . . . . . .


Supplement (166)

1.        Scientists’ opinions about this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.        Science: privatization of truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.        The number of space dimensions  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.        Space expansion and the Alice’s effect  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.        Comparison of the RD and classical mechanics formulas . . . . . . . . . . . . . . . .

6.        Action without counteraction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.        Rhythmodynamics and vibrational mechanics . . . . . . . . . . . . . . . . . . . . . . . . .

8.        Phase-frequency tension and gravitational metrics  . . . . . . . . . . . . . . . . . . . . .

9.        Black Holes (phase-frequency interpretation) . . . . . . . . . . . . . . . . . . . . . . . . . .

10.     About Louis de Broglie’s law of phase harmony . . . . . . . . . . . . . . . . . . . . . . .

11.     Rhythmodynamics’ place in physics  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Conclusion: results and perspectives  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Bibliography  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .













































































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Truth is one of the ways of distorting reality!


In 1980s lots of science fiction films usually began like this: “In the year 2015…” after which achievements  of the earth civilization were shown, namely ability of a free space travel, not just to the neighboring planets but to the far corners in the Universe. Conviction grew that this would become true. Unfortunately, the qualitative  breakthrough in science and technology has failed to materialize for several reasons. One of them is that there is still no reasonable explanation of fundamental natural phenomena, and there’s no knowledge of the nature of processes which form these phenomena. There are few of them: motion, inertia, force, gravitation, nature of the fields, nature of electricity and elementary particles.  These phenomena and their properties are still considered inherent and therefore require no explanation. But not all think so. May be for this reason opinion was circulated that discovery of the physics aspect of these phenomena  is beyond the ability of human mind, the same way understanding of the easiest technical appliance is beyond the mental abilities of a dog.


With such attitude to human capabilities one can hardly expect any qualitative breakthrough in science. Therefore dilemma emerges: either to quietly sanctify one’s own inaptitude, i.e. declare the modern view of the world final because any other views will never emerge, or to admit frankly one’s own inaptitude, and run the risk of being fired, or wait for a messiah who might clarify everything in science. This second coming is actually expected in science; they even revived the practice of fighting dissent there, the so-called committee against pseudo-science. But this is a different issue.


In 1997 a book called ‘Rhythmodynamics’ was published in which the author expounded the results of many years of research of fundamental problematic phenomena. Ten years since lots of additional experiments have been conducted which confirm the conclusions and predictions made in the book.


The new edition presents Rhythmodynamics as a method of examining the processes which form phenomena and their properties. The author would like to stress that Rhythmodynamics is not claming the role of a universal paradigm, but it can be quite useful instrument in solving complex tasks in theoretical and applied science. For example, the means of rhythmodynamics helped visualize the process of gravitation formation by the imposition on the elements which make up the body of the oscillators matching the elements in phase and frequency. Interference pattern in the form of a spider-effect has become an illustration of gravitational field impact on a system of two linked atoms. A way to achieve anti-gravitation has been predicted. An interesting formula was drawn up determining acceleration of material system in gravitational field at the expense of discordance of phase and frequency triggered by this field. Eureka!


Another example of rhythmodynamics effectiveness is visualization of assumed interatomic processes which form self-propulsion of isolated molecules, like Í2Î. This self-propulsion could well be the cause of Brownian motion.


Special attention was paid to the physical phenomenon which the author calls ‘compression of standing waves’. This phenomenon was discovered in 1981 after a theoretical analysis of interference processes in Michelson’s device. It was discovered that to explain the negative result in Michelson’s experiment one had to take into account the wave nature of matter and to base the change in interferometer’s dimensions on the property of standing waves to compress with speed increase, i.e. on actual physical phenomenon. Such approach makes unnecessary all speculations about invariancy, as well as the postulates of the constancy of the speed of light, of space filled with void, ether attraction and lots of others.


In author’s opinion, the achievements made in metrology could soon make it possible to stage an experiment in determining the speed of light in one direction, the results of which could help physics get rid of lots of ‘rubbish’ both in the sphere of theory and scientific ideology.

Mankind requires a clear-cut picture of the world, effective scientific instruments capable of solving practical high level tasks for the sake of well-being of all society.


Wave geometry, a separate branch of science in itself, was suggested as one of the instruments, with the help of which a number of physical phenomena were discovered and processes forming these phenomena were modeled. For example, a model was created of a system of oscillators which has no outward radiation; amplitudeless way of energy existence was shown; relation of speed and acceleration of the oscillating system to phase-frequency shift between the system’s elements was determined; the law of preservation of energy was examined and a new formula was drawn up as a sum of its manifest and non-manifest components.


The issue of multi-dimensional world possessing frequency depth was examined in this book. A concept of frequency space was suggested, i.e. in our usual system of coordinates a coordinate axis of frequency depth was introduced. Such approach strengthens the argument in favor of the so-called ‘parallel worlds’ existing side-by-side with us in our single space but in different frequency bands.


Rhythmodynamics has made it possible to re-write the formulas of classic mechanics in such a way that they acquired phase, frequency, speed of light and Planck’s constant parameters. Isn’t it a firm indication toward the way of unification of classical mechanics, elecrodynamics, and quantum mechanics? May be such approach could help us make the first steps toward creation of a single physics, in which macro- and micro-levels of matter organization, phenomena and processes won’t be artificially divided?



List of the main issues


On fundamental phenomena:


1.      How exactly is the uniform and rectilinear motion of a body in space (motion by inertia) is ensured?

2.      What is the origin of a body’s propensity to resist external impact (inertia)?

3.      What is the origin of force, centrifugal and gravitational? What processes trigger the emergence of centrifugal force during the body’s motion along curvilinear trajectory? What changes in bodies does gravitational field affect, and how exactly do these changes trigger attraction?

4.      Through what and how does interaction between ‘elementary particles’ and macro-bodies take place?

5.      Can the physical essence of electric and magnetic fields be comprehended? Can one understand the processes triggering the energy flow, including the flow of electricity?


General philosophical problems:


1.      What is container for everything possible which exists, and what is it precisely filled with?

2.      What is the origin of continuum? Has continuum a proto-element? Is continuum even and uninterrupted, or is it endlessly and inwardly discrete?

3.      Presuming continuum is even, inseparable, uninterrupted, how then can anything happen in it at all?

4.      Can anything exist in container provided continuum has no proto-elements?

5.      Can one create a satisfactory view of the universe without the notion of a ‘reality’?


The questions of researcher’s consciousness and spiritual level:


1.      Who is the ‘customer’, the recipient of information collected by the sense organs in the human body?

2.      In what form does the customer’s representative resides in the body, and where is the customer himself?

3.      What does the customer need information for?






From the author


‘Everything that exists is justified in its existence’



Any phenomenon or property is based on the processes which form them. It’s a general practice in science to regard phenomena and their properties inherent until a theory and instruments are created with the help of which such processes can be discovered. For example, until the emergence of rhythmodynamics the notion of ‘gravitation’ was explained by the curvature of space or the flow of ether toward matter. We understand that this could well be so, but we want explanations to the curvature of space and ether flow. If they cannot be explained, i.e. regarded as a ‘fact’, a hierarchy of hypotheses emerges in which the unknown is explained by something yet more unknown. Which, in science, is looked upon as a ‘mauvais ton’.


Another example is motion, i.e. the bodies’ ability to move in space by inertia. Such motion is regarded as inherent, i.e. something basic and preordained and therefore requiring no explanations. And how about matter as a philosophical category? How about physical fields as a special kind of matter, or rather special kind of philosophical category?


With the emergence of mathematics (all kinds of mathematics are based of arithmetic) it became possible to determine correlations between the facts of micro and macro worlds. Somehow this came to be regarded as a true physics. For example, the rectilinear motion by inertia is characterized by speed → speed is determined by a ratio of a distance passed in a unit of time. The question is what is the cause of motion? The answer is the cause of motion is in the force which has been applied to the body!


Such answer doesn’t reveal anything because the question referred not to the cause which triggered motion, but to the cause of motion as a process, i.e. thanks to what exactly the body moves in space in uniform and rectilinear way, what originates and facilitates such motion? The modern physics doesn’t answer this seemingly simple question.


In such case how should one treat the now fashionable physical hypotheses about creation of the universe, if we still do not know the origin of motion (there’s no matter without motion…)?


The modern interpretation of the main fundamental phenomena and properties sounds more like a system of ritual chants rather than scientific explanations. Many researchers are not content with this. They are forced to conduct their own independent research so as to solve the problems which physics avoids to solve. As a result of such research Rhythmodynamics emerged with the help of which model analogies were created of those phenomena under study. If anyone succeeds in creating a simpler way and means of explanation than I’ve created I’ll be much obliged to this man.



Yuri N. Ivanov







Rhythmodynamics (RD): its goals and tasks


No image – no understanding!


There is a problem in physics of explaining the processes which form the fundamental phenomena and their properties. The problem is due to axiomatic nature of fundamentals and, consequently, due to seeming absence of necessity of their in-depth understanding, to say nothing of their visualization.  But it’s the disclosure of these processes which is essential for a qualitatively new understanding of nature. Here Rhythmodynamics plays the role of an instrument for deeper penetration, which gives qualitatively new knowledge by making its visual presentation possible.


The term ‘Rhythmodynamics’ consists of two notions: ‘rhythm’ and ‘dynamics’.


RHYTHM (Gk.rhythmos). An ordered recurrent alternation of some processes, moments (acceleration and deceleration, tension and relaxation in motion or in the course of something).


DYNAMICS 1. A branch of mechanics with deals with the motion of bodies under the impact of forces applied to them. 2. A pattern or process of change of some phenomenon. 3. Motion, action, development.


In which case,


RHYTHMODYNAMICS (RD) is a branch of science studying the role of periodical processes in formation of natural phenomena and their properties.


Specifically, Rhythmodynamics, introducing in classical mechanics the notion of ‘wave medium’, ‘phase’ and ‘frequency’, using modeling and visualization of processes which form the phenomena and their properties, makes it possible to deepen our knowledge of them as well as discover so far unknown ties between the fundamental phenomena regarded until then independent.


RD’s goals and tasks



·        research of natural phenomena and their properties through creation of simple and illustrative means of their presentation;

·        reaching understanding of processes participating in formation of phenomena and their properties, starting from the stage of their inception;

·        determining the adequacy of the drafted models to the phenomena they are supposed to reflect;

·        a return to classical approach in physics, but at a qualitatively higher level.


Tasks outlined:

·        to form an illustrative user-friendly instrument on the basis of Euclid’s geometry, arithmetic, algebra and trigonometry to analyze and describe processes participating in the formation of phenomena and their properties.

·        to verify the effectiveness of the instrument in cases when the essence of mechanism of the most crucial notions, phenomena and properties traditionally viewed as inherent is revealed.


Expected result


To learn something new is particularly difficult, especially if you are past school age. So the best option is to introduce the RD elements into school text-books. For example, the teaching materials (see DVD) already created could significantly simplify the teaching and learning processes of some phenomena. Of course the rival forces would do their best to ignore and block such knowledge. But the book is already written! And it’s addressed to those who are not used in their relations with reality to rely totally to established authority, to those who at least tries to think independently, who sees that society as well as science and its system of views are in a state of disorder and conflict, to those who want to find out, understand and facilitate progress, i.e. make out life better.


Rhythmus: As if progress ever needed someone’s help!  I’m sure it will manage without any outside interference. The more so that instruments for this are abundant – Galileo-Newton’s mechanics, Einstein’s theory, quantum mechanics, a powerful calculus, brand new laboratories and technologies. Your attitude might be more appropriate in the Age of Romanticism.


Dynamicus:  Are you trying to convince all, myself including, that everything which exists in the world has already been discovered? Including the nature of inertia, gravitation, nature of electricity, and so on and so forth? I suspect you are simply trying to cover up the inability of modern science to explain comprehensibly the most usual things. I suspect the commission to fight the so-called pseudo-science was created exactly for this purpose of hiding incompetence of certain personalities in science.



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Chapter 1. The Elements


Nothing exists except the continuum and the illusion inside it!


Trying to understand the “elements of this world” from the position of sound reason and natural science, our minds are confronted with a paradox which is neither possible to fully define, nor grasp. In other words, one cannot understand it, but one can get used to it!


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§ 1.01 On dogmas, axioms and postulates in physics


What’s the world we are living in built with? What were the elements used? The modern physics cannot give a definite answer. Many scientists know this, some even openly admit it.


In this case, let’s put the question differently: Does the world really look the way the modern physics present it? Does the modern physics portray the world as it is, or does it portray the researches’ subjective notions of it?


The researches study and portray the real world, but within the limits of their own subjective abilities. Which means that the modern physics does not reflect the world as it really is, and therefore gives a subjective view of what objectively exists. The physical picture of the world is subjective because it’s based on the subjects’ ability, their inner means (their senses, consciousness) of reflecting the reality.


The absence of at least one sense organ, or possession of an extra one unknown to us, has a significant impact on our physical picture of the world. To understand it just imagine yourself possessing hearing in the world of the deaf, or having sight in the world of the blind.


Which implies that physics created by a group of subjects of the same mind and perception is in no way better than other physical concepts created by those subjects whose perception and thinking differ somewhat. In both cases their physical concepts will be subjective. Which means the society may have more than one school of scientific thought, alternative world outlooks and ways of world exploration.


Let’s examine the differing views on the issue of ‘continuum’ held by different groups of researches of varying world outlook.


·        Democritus and Aristotle stated that continuum consists of the continually dividable particles: “Continuum is what dividable in parts, which are, in turn, dividable again”.

·        The continuum of the Eleatic school represented by Xenophanes, Parmenides and Zeno is opposite to the continuum of Democritus and Aristotle. Their philosophy is based on the Single, or Absolute Being. Their main postulate: Being is eternal, and the continuum is endless, consisting of neither divisible or indivisible parts.


The modern science has adopted the Aristotle’s interpretation of the postulate-axiom of continuum. It’s easy to explain the mobility of the ‘whole’ as all endlessly dividable parts move one against the other. This is an easy and instinctively comprehensible option, though in this case the answer must be given to the question of the continuum’s proto-element.


It’s much harder to explain the mobility of the world we observe if we postulate the continuum as endless and indivisible. By definition, such continuum cannot afford even the slightest shift because it would imply the presence of parts there. One might think that it would be impossible to create the physics of motion under such conditions. But this is not so, and there are ways to do this, as there are real processes which can develop without triggering imbalance in the body of their agent.


Our modern notion of continuum is that of a continuous material environment whose properties are constantly changing in space. Whereas a continuum which consists of no parts never changes its properties in space. Which implies an entirely different approach, different physics and different original basis. It would be useful to know what processes and phenomena are lying hidden along this so far unexplored path.


It would be impossible to create either a proper world picture, or a good scientific school unless a deep understanding of science, natural philosophy foundations and primary problems is reached. And the foundation of science is based primarily on a seemingly natural assertion: “The World Is! And it’s material.” It’s a dogma, pure and simple, without accepting which one can forget about such material science as physics. To prove the validity of this dogma, i.e. the material nature of the World, one has to show the proto-element with which this World is built. An impossible mission because beside matter there’s always ‘something’, that’s why in such cases the argument is substituted by sensual beliefs, but in the majority of cases they use the notion of a ‘fact’.


But hasn’t the modern science accumulated too many things which are taken for granted, with attributes thought inherent? Let’s cite the notions and phenomena they derive from which in physics have so far received no scientific interpretation at the level of processes which form these phenomena: continuum, physical vacuum, ether, the speed of light, space curvature, various fields, motion, inertia, mass, force, gravitation, energy, electricity, invariance, elementary particles, expansion of space, singularity.


It’s apparent that the endlessly divisible continuum is infinite in depth, i.e. in theory it’s impossible to get to its root-cause. Nor one would try to dispute the infinity of the in-bound chain of the cause-and-effect relations which ensure the physical phenomena, processes and properties we observe. Which implies that any fact or inherent property is bound to have its root-cause. Motion, for instance, or rather, the object’s transfer in space (in continuum). For the body to move in continuum and relative to it, changes should emerge in the processes which ensure this motion. And if the speed of motion has changes, the processes have changed too. The reverse is also true: the changes in the nature of processes trigger the change in speed. One should bear in mind too that the absence of motion is also ensured by certain processes, and as the body and continuum are in constant interaction (the body being a manifestation of continuum) then any changes in the processes trigger the body reaction. But what are these processes, and what is the essence of their mechanism? And what if continuum is infinite and consists of no parts? What then? It’s not as if such continuum might have disturbed unstable  parts…


Rhythmus:  What do you mean ‘the essence of their mechanism’?


Dynamicus: Each process has its mechanism. Say, the field affects the body and makes it change the regime of movement. But what processes in the continuum determine the existence of the field as a phenomenon? How do these processes affect the body and in what way? How do these changes become transformed into motion? In other words, what’s the mechanism? Any talk about the force of the field being the actual cause of motion sounds more like ritual chants rather than physics. The mechanism is a supposed or specific chain of processes which ensure the phenomenon’s fact.



So, we’ve accepted the dogma ‘The World Is, and it’s Material!’  To begin the construction of a model of the universe (though the author sets a more modest task of constructing a model of the phenomena in the universe), we need such things as: container, continuum, the presence of processes, the observer. The construction begins with the latter. The observer’s presence in the model is crucial,  first of all, so as not miss the impact factor of the observer himself on the observed reality, and his perception of this reality.


Observer is the pivotal point there. Without observer, continuum and the developments there need no explanation, they exist as they are! Whereas the completeness of explanation depends on the instruments used by the observer, among which are the sense organs, the mind and technical devices extending the observer’s abilities. The process of building a picture of the world passes through numerous stages: the sense organs become stimulated by the incoming information the stimuli are transformed into signals entering the brain → the brain assesses the incoming information, classifies it and presents it in a form suitable for presentation  → after which the question rises about the user and his agent, i.e. some entity which directly receives this information.


We cannot fully describe the observer, though he’s actually the focal point of all knowledge about the surrounding reality.

As for this entity which plays the role of the information user’s agent, which we might call the Soul and take steps to find out what it actually is, we might run into another global problem which the rabid materialists are careful to side-step, saying there’s no soul because there’s no experimental proof of it. Whereas it’s precisely the soul, and every man feels it, which receives and assesses information. The issue of information ‘user’ is even more complex, besides it lies beyond the scope of this book.


Seeing the complexity of transformation of the input, coming from the outside, into the inner image, now we cannot assert that the surrounding world is actually the way we imagine it to be. In this sense our idea of the world and what’s going on in it is always subjective because the real world may differ strongly from our inner perception of it. A good point in question is a connection between the type of information (the form of its presence) on the computer’s hard disk and its outward presentation on the display: a nice picture on the display, and entirely different thing on the hard disk. The information received from the monitor in no way reflects its actual state on the hard disk. Which means that we do not know what we are actually dealing with, and what it all amounts to.





Fig.1 The object’s outward appearance in jpg. format (left), and a fragment of its computer presentation in the intermediary, between the hardware and display, doc. format (right).


Undoubtedly, the world we are studying does not match our notions of it. For example, the rainbow has no colors but signals of varying frequency; it’s our brain which colors these signals. For this reason lots of processes and phenomena natural in the real world may seem to us strange and illogical, sometimes completely beyond our grasp. This is also due to the fact that the researcher lacks perceptual abilities allowing him to receive fully the data coming from the surrounding reality. For the observer such information is latent: the processes and phenomena do exist but there’s no way to perceive or register them. In this sense the observer is always dealing with a limited notion of the object of his studies. That’s why the physical models he creates are often incomplete, and the yawning gaps emerging there are customarily filled with speculations in the form of axioms and postulates. Alas, there’s no other way for us to judge about the universe.  And lots of things exist and take place beyond our range of observation.



Container and continuum


Container and continuum which fills it pertain to the category of undefinable. The only thing we can do here is to philosophize, but we cannot penetrate into the physics and the logic of such entities. In essence, we do not know what exactly we are dealing with, but we feel that container and continuum do exist, though in a transcending reality, and we therefore accept them as a fact.  Besides, our choice is always limited: either materialism, or idealism. Let’s present our own view of container and continuum.


Container: endless and absolutely empty;  related to nothing and existing independently, possessing neither essence, nor content; logically incomprehensible and thereby without physical description, i.e. without rational explanation.


Role: to contain something.


Property: always filled.


If  absolute emptiness cannot exist by definition, and it’s not clear what the container is filled with, they speak of continuum. Its essence, too, is beyond physical description, or logical comprehension.


Continuum: continuous, incessant, uninterrupted, indivisible, consisting of nothing.


The logic of the latter assertion is that if continuality were measured by endless divisibility, such continuality would have no proto-element, nor could have it. And if the dividable continuum has no proto-element, the question arises about the continuum’s physical reality. Such paradox can only be solved through conditional agreement in which continuum is recognized as really existing.


The main role and the continuum’s feature: to be the proto-element of all.




We presume the elements of matter are the result of the disturbed state of continuum, and we know that this presumption is more artificial, than justified. Still, continuum has always been and will remain the carrier of disturbance, even if these disturbances are not linked with the ‘shiftsome’  nature of the carrier. (Later on we will reveal the cause of the doubt which emerged and describe the state of processes, real for the observer, in which the use of the disturbed continuum is unnecessary).


Outer and inner observers


One cannot separate the observer from the observation of a phenomenon. His observations are always subjective. The observer is always a part of continuum, and he’s always inside it. He cannot be an onlooker and observe the world under study from the outside. But he can create models in which he poses as an onlooker. So, the observer acquires a chance not just to assess the proceedings being outside the model he created, but to analyze them from the inside as if he were a part of the proceedings examined in his model. The simultaneous look from the outside and inside makes it possible to form a more comprehensive picture of subject under study. The observer’s most useful quality is his ability to go outside the limits of his model in which the phenomenon is examined, and assess the proceedings from the outside.


After a deep examination of the Elements one finds nothing which could justify their recognition as the foundation for the creation of the physical picture of the world. The observer’s idea of the elements is most likely to be based on his deep-rooted spiritual essence. ‘Something’ inside prescribes, and we therefore are obliged to accept such elements: being, on the one hand, unable to imagine and suggest something different, on the other, because of our deep certainty that we are right, it’s the only possible way, and there’s no other!


Rhythmus: What a surprise! The fundamentals of physics are nothing but our inner convictions? How about experiments, the ages-long experience, the accuracy of mathematics? Don’t they count for anything? You think the whole of physics, including the modern one, has no solid foundation?


Dynamicus: The modern physics is the knowledge for those who do not care for the root-cause: they have formulas; if they coincide with their calculations, they are therefore correct, and they actually show what the world is. Few are asking the question as to how come that the world seems real for us? And is it really real? The more so that its foundations are based entirely on speculations and sensual-experimental practice, beside which there simply cannot be anything else.





Postulate (Latin: postulatum), a hypothesis (a claim, presumption, regulation) advanced as an essential presupposition, condition, or premise of a train of reasoning. The latter often serves as a justification for the hypothesis’ acceptance.


The modern interpretation of postulate uses experimental fact as reasoning. The postulate of inertia could be cited as example: inertia manifests itself almost always.


In physics, experimentally discovered phenomena which have no explanation are often presented as postulates. Properties are usually regarded as innate, and therefore require no explanation. For example, the property of space to curve is a secondary postulate explained by the innate property of mass to curve space. The mass requires no explanation being experimentally proven fact, i.e. the initial postulate.


Many researches find any explanations of the innate properties through examination of processes superfluous because the physics’ calculus requires no additional entities. The modern physics in a way resembles a Lego set whose pieces are much like postulates. If this ‘Lego’ physics lack some connecting element, they first invent it then create a postulate-hypothesis of how this happened, like in the case of neutrino or gravitation waves when they made up for the absent after which intensive search was started for experimental proof.


Nonetheless, the number of postulates in physics can be significantly reduced. How? Take Lego for example, which presents every complex component through a number of small universal elements in such a way that a set of these elements can be used to assemble any complex component or structure. If earlier a score of complex components played a role of independent postulates, after the introduction of several types of the lesser sized basic elements the number of components-postulates may be reduced drastically. But the emergence of new, so far unknown,  elements is natural too.


To implement such reduction in physics one has to find something which the whole range of phenomena has in common, something which is responsible for the establishment of their characteristics. Thus we found that motion, inertia, mass, interactions of forces, self-organization, size reduction during motion and energy flow are explained from a single position, i.e. a single algorithm lies at the bottom of these phenomena and properties. This algorithm is presented in the form of familiar elementary phenomena and processes the combination of which produces different properties: motion, inertia, mass, interactions of forces, self-organization, size reduction during motion and energy flow.


Rhythmus: What’s this, another revolution? Curious. And at the same time you are suggesting that the World in which we exist may not exist?! So what’s the use of your dogma “The world simply is!”? Everyone knows this, and there’s no need to prove it!


Dynamicus: I cannot prove that the World really is. As for your proof, it’s of the carrot and stick grade. Scientific methods cannot prove anything in general. One can only accept this or that postulation on the nature of research. Otherwise you can forget about matter, and about science too.



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§ 1.02. The choice of instruments


Galileo introduced experiment in physics as a means of learning. At the time a revolutionary step which made it possible to separate science from fiction and elevate science to a new level of understanding of the essence of nature’s manifestations.


Traditionally, experiment has been regarded as the criterion of accuracy of a theory. But experiment is only the final phase of the research, the end result; the rest are our guesses, hypotheses about the processes which, in the observer’s opinion, ensure the fact of what’s taking place. For example, if the body falls on the surface of earth, its fall is described mathematically, and its cause is thought to be gravitational field. The fall is the fact, whereas gravitational field, at least initially, is an assumption.


Sure, the accuracy of mathematical description is tested by experiment, but neither mathematics, nor precise measurements of changing, during the fall, speed parameters say anything about the cause of the fall, nor about the nature of the existing force. Experiments only confirm the match of their mathematical description with the fact. For example,  - where’s the cause of the fall in this formula? If you say that the cause of the fall is force, then what’s its origin and how does it make the body move in space? If you say the space became curved, then say what curved, how and why? If you say we are dealing with the innate property, then you are talking about the incomprehensible reality, something which physics is bent on mathematizing.


The ignorance of the cause at the mechanism level is usually compensated by a hypothesis, which its author, as well as his followers are trying to validate mathematically. If arguments are strong enough, the hypothesis acquires a status of theory, in other words, theory is the same good old hypothesis stacked high with arguments. So, one has to be constantly aware that all our notions of the universe are subjective. If we had different sense organs, our notion of the world would be different too. Which means that any hypothesis is nothing but a subjective view of the reality. That’s why one hypothesis is always replaced by another.


Take gravitation for example. It’s became a universal habit to explain gravitation by the presence of gravitational field and its innate ability to affect the bodies present in it. This ability is called gravitation force. But what sort of force is this? Does it really exist? Or will it be more appropriate to say that gravitation force creates certain conditions in space which make the body, once in them, change? May be, it’s some processes in the body itself which make it self-propel toward the source of the field?


Such positioning of questions focuses attention on the cause-and-effect chain: massive body  → the field of gradient conditions (gravitational field) → small body  → field-imposed changes in the small body → broken balance of the inner forces in it  → reaction to disbalance, attempts to restore balance  → accelerated self-propulsion as a means of balance restoration.


In that case one should regard as the ultimate cause before the actual fall of a small body toward the big one not the field itself but those changes which are taking place in the small body, right? The logical chain built thereby allows us to conclude that if the body is not affected by the field, it won’t react to it, i.e. it won’t fall. With this link missing in the cause-and-effect chain you won’t see the final result, the fall.


Hardly anyone would deny the fact that ‘force is the essence of action, but not the action itself’. For example, one can apply with equal vigor a magnet to the bodies placed close together and made of dielectric and iron, but with evidently different effect. Therefore question arises: what parameters and processes has the magnetic field exactly changed in the iron body, and which it failed to change in the dielectric one?


Limited by stereotypes of thinking, few of us are aware that when the question arises about the cause-and-effect explanation of fundamental things the proof is often substituted by axioms and, literally speaking, ritual chanting. Here are examples: motion is an innate property of the material world; inertia and mass are innate properties of the material bodies; the speed of light is constant in inertial frames of reference due to the accuracy of the invariant theory; the force of action is equal to the force of counteraction; the physical vacuum which fills the space is expanding and creates the effect of moving apart galaxies. To this they add: “That’s how nature works”. And very few are trying to study the mechanism of  the very same motion, inertia, or invariant theory. Some researches sincerely believe the mathematical descriptions they have of this or that phenomenon as well as their correlation (mathematical, of course) with other phenomena are a sufficient enough proof. Mathematical description of phenomena and processes is not physics, but physics’ instrumentarium.


If opinion poll were conducted among physicists about the root-cause of the inertia of the body in motion the majority of them would maintain that the cause of the body’s movement in space is a force applied to it which gave this body a certain quantity of motion:


.                     (1.01)


Formally, correct. But the question was not about the cause of the beginning of body motion, but about the inner and outer processes which ensured the transfer of body after the force had been applied to it.


Many would regard such way of putting the question absurd because classical mechanics never examines any internal processes which ensure the fact of motion by inertia: the body moves uniformly and rectilinearly if there is no external force on it, or the net force on the body is zero. And the quantity of motion, once received by the body from external force, cannot be the cause of its subsequent motion because when moved to the reference frame of the moving body its quantity of motion becomes zero. They usually refer here to the invariant theory of Galileo and Newton’s relativity which prohibit to differentiate parameters of two equal bodies if there’s no relative motion between them. Here we encounter for the first time expression of pre-Einstein’s theory of relativity imposing a tacit ban on the study of absolute differences and recommending to examine only relative differences. Within the limits of the classical mechanics it’s correct because they are founded implicitly on the postulate of absolutely empty, filled with nothing container.


But no one has yet managed to imagine the absolute void; the absolute void in the volumetric container is beyond human imagination. Although the surrounding space seems to us empty, there is a sufficient number of physical effects, like interference and diffraction of light waves, indicating the presence of ‘something’ in this space which possesses the property of transferring the waves. This ‘something’ is in essence more akin to the wave nature rather than the absolute void. This is one of the reasons why in the early science they adopted the notion of ‘ether’: thin, imperceptible medium through which light is transmitted. Further on we will avoid this notion because of the large number of speculative models of ether: ether as a super-liquid quantum fluid; ether as a crystal; ether as gas; ether as densely packed ideal balls, etc.


We do not know what actually the luminiferous ether is; its only property that we know for sure is the speed of light rays’ (electromagnetic waves) transmission which equals 299792,5 km/sec. But even here we encounter a problem: how to establish the speed of light in one direction. This problem was indicated as far back as James C. Maxwell, in his famous work «A Treatise on Electricity and Magnetism».


Albert A. Michelson attempted to prove experimentally the existence of luminiferous ether. In 1881 his famous experiment was conducted in which he failed to detect the absolute motion of the Earth through ether. The scientific community was plunged into a crisis: by the time the existence of ether was a foregone conclusion. This crisis lasted for 24 years during which numerous attempts had been made to explain the experiment’s negative result. At the time the scientists were unable to understand the true cause of failure of Michelson’s experiment. In 1905 Albert Einstein published his paper "On the Electrodynamics of Moving Bodies" in which he suggested at the time irrational but a unique way of explaining electromagnetic phenomena without the use of ether. The scientific community worn out by the crisis gave a lukewarm reception to the Einstein’s work which they regarded  as interim until they discovered this dodgy phenomenon which canceled the expected result of A. Michelson’s experiment.


A hundred years later, in 1981, such phenomenon, indeed, was discovered theoretically, and in 1990 was proved experimentally. But by the time the Einstein’s theory has gained the status of the top leading paradigm. We are yet to return to this issue because now we have a unique possibility of not just explaining the cause of failure of the experiment which was to discover the absolute motion of the Earth, but also of going back to the old, pre-1881, classic-ether positions so as to continue the development of the scientific line which was first suspended in 1905 and later completely rejected. Hence the task: creation of a universal and conflict-free scientific instrument which anyone could use no matter what scientific prejudices he might choose to stick to.


In science, theory is such instrument. But the question always rises: Why do we need a new theory? What’s the new instrument for? We’ve more than enough of them as it is…”


To explain the motives which emerge due to dissatisfaction with, say, classical mechanics I’ll give several examples.


The classical mechanics is employing the invariant and relativity theories – which has certain advantages, but there are disadvantages too.


For example: Let object A and object B move in one direction with speed  and . Which of the objects, whose masses are equal, has greater quantity of motion?


If the problem’s condition had a reference frame in which and relative to which the objects’ speed parameters were to change, the solution would be simple:



The problem’s condition is incomplete, so the question has at least two correct answers:


1.      Relative to object À: ,  

2.      Relative to object Â: ,


Another example, showing the absurdity of the invariant theory.


The observer of the reference frame with mass m pushes a reference frame with mass M, with M >>m. The observer m notes that the force he exerts Fm  gave the object M   a momentum MV.  He also finds that his actions brought speed V  not just to object but to all visible objects in the universe. The observer m concludes that object M has some rigid link with all objects in the universe, and following the familiar formulas calculates the mass of the universe: ,  with the speed of the observer’s reference frame being zero (his reference frame the observer regards as the main one), the mass of the universe is M=0.


“Wait a minute”, an opponent would argue, “in the process of exerting force it’s the observer m who would feel more than M the inertia-born reaction to acceleration. So it’s he, m, who’s changed the speed, not the object M”.


Ok, let’s accept this. Suppose the reference frame m has changed the speed. But relatively to what?  Besides, the object M, too, has changed its speed relatively to the same thing. What’s to be done? Should one refer to the conservation of the center of mass? It’s relative as well… , only we cannot say for sure relative to what? In this respect, the mechanics of Galileo-Newton in its pure form is a theory of relativity!


Let’s examine another curious situation. Suppose we have a sailing boat with an electric fan firmly fixed in its stern (fig.2). The air from the electric fan flows in the sail. With what speed V is the sailing boat to move? Will it move at all? And if it moves, will its speed be relative?





Fig.2.  In some colleges students are asked to solve the problem: “Is it possible to propel a sailing boat by aiming at its sails the air flow from a powerful electric fan fixed in its stern?” The mediocrities are offered a standard answer: “No, the boat won’t sail because the force of pressure from the air flow is an internal force which cannot give a single joint momentum to the boat and electric fan in it.”




Fig.3.  The Fan Cart With Sail appliance showing the relation and direction of the thrust force to the form of the sail. Source:


There was little doubt that the sailing boat would move in the direction of the air flow produced by the electric fan, i.e. forward. And that’s how it turned out to be. The working model of such boat was made, and during its tests it reached the speed of 3 km/h.

The author invented and made this boat independently not just to demonstrate the shortfalls of school education, but as a toy to amuse both children and adults. But soon afterwards he found in the Internet an analogy, “Fan Cart with Sail”.


Let’s enumerate the forces acting on the boat: the reaction of the electric fan to the air flow it propels toward the sail; the reaction of the sail to the air flow from the electric fan; the reaction of the sail to the incoming air-flow which emerges as a result of the boat’s movement (the frontal resistance); the friction between the boat and water.


The cited factors split into two categories: those acting and counteracting. If action and counteraction moduluses are equal, the boat sails with constant speed, and in such cases they say that the force of action equals in modulus the force of counteraction. And if the opposite forces are equal, what’s the mysterious cause of its movement, with the zero net force on the boat?!


Guided by the definition “Force is the essence of action, but not the action itself”, one should raise the question: “What do the forces acting on the boat change in the boat’s body? And how do they make it move with the zero net force?” Are these changes real and pertain to the boat’s body, or they are of ‘relative’, fictitious, nature? And if these changes are real, what are they? At what level of matter organization do they take place and in relation to what?


Let’s take a look inside matter, what changes take place there? The bodies moving and resting in the continuum differ in parameters of the interacting elements. The external macro-movements are formed and sustained by asynchronization of processes at the micro-level. To understand this asynchronization one has to use some instrument. Whereas we have neither the methodology of analysis, nor equipment, nor any theory. The Rhythmodynamics suggests to use the wave geometry which differs from the Euclidean one by the use of the foundation axiom.


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§ 1.03 Axiom of foundation-regularity (introduction of the carrier of constructs in geometry)


Although science rests on its initial dogma ‘The world is! And it’s material!’, in its modern form it has lost its secure foundation, the proto-substratum. Instead, it has adopted other vague notions, like physical vacuum, independent field formations, space-time continuum, relativity.

For example, the ‘physical vacuum’ literally means the absence of something, which at the same has real physical properties. The time-space continuum curves, expands whenever it suits mathematicians, while relativity implies absence of absolute foundation, the basis. The main argument used there is ‘That’s the way nature is!’


But is it possible for the real world to exist without the proto-foundation, which our mind finds it convenient to consider as a carrier, environment? Many modern researchers think this carrier notion is superfluous, i.e. they’ve found a way to manage without it, replacing it with the void, fields (special kinds of matter) and math.


Two planes are flying parallel relative to air. The speed of one is 500 km./h., the speed of another is 600 km./h. If we need to find only the relative speed, do we need the speed of air relative to the planes? The air as the foundation for flying is present, i.e. without it the flight itself would be impossible, but it can be ignored in calculations. Nor does the speed relative to air has any impact on passengers which doesn’t mean it’s absent. The relative speed of planes is 100 km./h., and if we ignore the air, there’s no need to find the speed relative to it. Why increase entities without necessity? Of course, if the air were bursting in the portholes, it would be entirely different matter…


Relativity is present in Euclid’s geometry too. Because it has no carrier of constructs in the axioms of foundation (the word geo-metry indicates the carrier of constructs, but for some reason it was omitted from axioms). In practice such carrier could be: the surface of the Earth, school-board, a list of paper, computer display, etc. In geometry the carrier of constructs is always implied, but its importance is usually overshadowed by the conditions of the problem to be solved. If geometric constructs change in time, say, two dots move on the list of paper, then try as geometrician might to justify his logic by relativity, these dots, first of all, are moving relative to the material on which the constructs are made, i.e. relative to the carrier of constructs.


It’s to this carrier that the main reference frame should be tied to.


Let’s formulate the foundation axiom which Euclid’s geometry lacks. We call this axiom ‘foundation’ because without it we’re unable to define or construct anything.


The Foundation Axiom: There is foundation in the form of a carrier for constructing (presenting) dots, direct lines, planes, circles, two and three-dimensional figures. Dots, direct lines, circles, planes, two and three-dimensional figures cannot be constructed without the carrier, even if it’s an imaginary carrier.


Rhythmus: But why do we need this carrier of constructs? We’ve managed without it, haven’t we?


Dynamicus: Somehow we have, and until 1905 we didn’t need it much. May be, because we didn’t question its existence. By the way, physics still uses oblique synonyms to carrier: space, physical vacuum. But sooner or later, one has to define one’s position. If we recognize the carrier, then everything takes place in it and relative to it; which brings clarity and certainty. If the carrier is rejected, anarchy starts in physics where each is free to invent his  own foundations.


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§ 1.04 Wave geometry


In geometry the carrier of constructs plays the role of the absolute frame of reference (AFR).  It’s necessary in order to use the Euclid’s geometry in modeling the wave physical processes.

Without the carrier the modeling of wave processes is impossible, or it is possible but with additional opening conditions.


There are several kinds of geometries:


·        Static geometry with fixed points, lines, figures and relations between them. The static geometry has no notion of ‘time’.

·        Kinematic geometry in which the points, lines, figures move, and relations between them change, according to the set rules. Kinematic geometry is impossible without the notion of ‘time’.

·        Wave geometry – a branch of  kinematic geometry aimed at studying the periodic wave phenomena, processes and relations between them. The wave geometry is based on the axiom of the carrier of constructs, i.e. ‘wave medium’ All movements and transfers in wave geometry take place in, or on, the carrier of constructs, and therefore the parameters of those movements and transfers are measured in relation to the carrier. The carrier of the constructs is constant, never changes its form under any circumstances, i.e. serves only to display the movement of waves on it, as well as the movement of points, direct lines and figures.


In nature the role of wave carrier is played by the wave medium which transfers the wave disturbances always with the constant velocity through itself and in relation to itself. Having introduced the axiom of foundation, we thereby have brought the wave geometry closer to the real physical mediums and waves. The difference is that in wave geometry the carrier doesn’t become deformed under any circumstances, whereas in reality, for example, on the surface of water, or in acoustics, the waves are impossible without the deformation of the medium. As for the electromagnetics, we have no idea what happens with the medium when electromagnetic waves are transferred.


Rhythmus: Here’s again an implied return to ether.  Hasn’t Michelson proved that it doesn’t exist, nor can exist. Or your special opinion is just a reflection of nostalgia?


Dynamicus: This opinion is logically justified! The only way to prove the absence of the wave medium called ‘ether’ is to measure the speed of light in one direction. As long as there is no such experiment, there is no proof of ether’s absence! And the necessity of such experiment was stressed as far back as James Clark Maxwell. But the modern scientific clan driven by business interests is terribly unenthusiastic about it. Therefore they possibly either avoid any public experiments on this issue, or they may have done something and keep the results secret.  If this is so, one can hardly call what they do ‘science’.



Let’s take an example:

Suppose there’s a dot (oscillator) on a two-dimensional carrier of constructs which emits periodic waves in the form of circular fronts. Each point of the wave front is uniformly departing from the source of transmission, with the velocity of the front being tied to the carrier of constructs, not the source, which could be moving. A system of departing wave fronts emerged around the source. If transmission frequency is fixed and the source is stationary, the distance between the fronts is the same, and it equals the wave length. An even and rectilinear movement of the source  (V<c) shifts the position of the departing wave fronts in relation to each other. The fronts themselves remain always circular, with their center being in the place of their transmission on the carrier. After transmission the wave front is no longer tied to the moving source and other fronts, i.e. exists on its own. (fig.4).


The classic rule of adding velocities can be presented as


,                  (1.02)


The Doppler’s rule


.       (1.03)




Fig.4 . That’s the way the processes in way geometry look. The wave fronts spread in the medium with constant velocity. The speed of their sources doesn’t affect the propagation of waves they transmit.


The absence of carrier, i.e. wave medium, leads to ambiguity, particularly when the reference frames are required to be invariant.




Fig.5. If one is to use the geometry without the carrier one won’t be able to manage with one drawing only because each oscillator, depending on the desires of geometrician, may be regarded as the reference point. The absence of the carrier of constructs and the invariant principle lead to ambiguity, i.e. inability to construct a definite interference picture.


It’s interesting that Euclid’s geometry is incompatible with Galileo’s invariant theory. It’s impossible to construct a satisfactory interference pattern within the framework of absent carrier and at the same tine the declared invariance of the sources. For example: Suppose two equal in frequency sources are invariant. Suppose the velocity of one of them is zero, the other – V. One has to construct the changing in time interference of waves from the sources (fig.5). Obviously, it’s impossible without breaking the condition of invariance, because the waves are supposed to be circular due to the equality of the sources in relation to each other. In this sense the Euclid’s geometry and invariance contradict each other: even the simplest things cannot be constructed correctly because the modern physics and Euclid’s geometry are incompatible.


The wave geometry is the basis of rhythmodynamics. Its main postulates match the basics of wave geometry.


Wave geometry axioms

Rhythmodynamics postulates

1.        The dot is the oscillator, the source of spherical waves

2.        The waves spread in the carrier of constructs and in relation to it with constant speed

3.        There can be any number of dots-the sources of waves



1.        The oscillator of infinitely small size, possessing no properties, except being the source of periodic oscillations in the form of pulsations,

2.        Wave medium transforming the oscillator pulsations into spreading spherical waves and ensuring their constant speed of disturbance propagation in relation to itself.

3.       The emergence of any other oscillator creates a system.


The instrument of wave geometry makes it possible to model processes and calculate the experiments’ results. That’s how it predicted (later this was proved experimentally) the phenomena of standing wave compression, dependence of the speed of the system of oscillators on the phase shift between them, dependence of acceleration of the system of sources on the frequency difference, the speed of the energy flow, the zero-amplitude way of energy existence, etc.


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§ 1.05 The properties of the wave geometry objects


As instrument, the wave geometry allows to model the processes of self-organization of simple and complex systems without any specific calculations of the interacting forces. The modeling is based on the assessment of the state of medium around the examined oscillator with the subsequent transfer of this oscillator toward the area of the balance state. If this balance state area shifts, the oscillator obediently follows in its wake. But the moving oscillator now emits, due to the Doppler’s effect, the waves of a different length. These waves propagate in the medium and bring changes in the state of the wave field. After some time the waves which have changed their length reach the other oscillator and change the state of its surrounding environment. Such change leads to a transfer of the balance state area and, consequently, to the changed position of the second oscillator: now it starts emitting in space the waves of changed length. These changes  reach the first oscillator and it reacts by motion. Such process is repeated until the oscillators occupy stable positions in relation to each other.


The oscillator has no sense organs, and it knows nothing of any other, similar, oscillators. What the oscillator can do is to interact with the environment and, detecting any changes in its state, move in the direction of the area of its comfort.  The oscillators do have an impact on each other, not directly but through the wave medium, through changes in its state. It’s these changes which make the oscillator move, and it doesn’t care what caused them, how and why.


The most convincing examples to this could be the experiments conducted by Carl Bjerknes as well as by Ivanov and Didin.


Rhythmus: As far back as the middle of the 19th century the Norwegian physicist Carl A. Bjerknes (1825-1903) proved that two pulsating spheres, the radiuses of which are too small in comparison with the distance between them, when placed in liquid (which cannot be compressed), these spheres can trigger either mutual attraction or repulsion.


Dynamicus: By the end of the last millennium Y. Ivanov and A. Didin showed that two coherent sources of waves placed on the surface of water can attract, repulse or create an elastic wave connection between each other (form a system), as well as propel if the phase-frequency shift exists between them.



One should stress that in wave geometry the process of self-organization is witnessed by only one outside spectator, and the process itself doesn’t need the introduction of local, inner observers and the use of invariant principle the way they do it now in physics. Naturally, the observation procedures can be made more complex if we assign a local observer to each oscillator and remove the outside spectator. In which case the conflict between the eye-witnesses is inevitable because each of them has the right to regard his own oscillator as the main reference frame. Which can lead to nothing but confusion. The lucid picture which we could have is turned instead into squabbles at mathematical level.


There is a difference between the perception from the outside, and the perception taking place inside. If we take this into account we’ll see why our assessment of natural phenomena differs depending on our choice of the outer and inner ‘points of view’.




Fig.6. That’s how we see, for example, the ‘world’ from the outside (left), and that’s how – from the inside (right).


The semblance of the wave geometry foundations and the postulates of rhythmodynamics makes it possible to model the natural phenomena and observe the processes in their ideal, undistorted geometrical version. In effect, the outside observer acquires the ‘officially approved status’ which gives him the right not simply to judge impartially the proceedings, but also at his own discretion to set conditions and change parameters, and always stay outside the proceedings, i.e. to observe things as they are.


Rhythmus: Here we are: came back to what we’ve so painstakingly avoided: the absolute observer, the absolute reference frame, wave medium. Too many entities which we in the XX century worked so hard to get rid of.


Dynamicus: First of all, we are dealing with wave geometry in which you cannot manage without the geometrician as outside observer. If it’s more convenient for you to assess the developments from the inside, you are free to do it. Only I think certain things are better visible from the outside. For example, the difference between the depiction of the elephant made from the inside and outside is obvious. And if you prefer the inside look, I’d rather be outside. Both depictions are essential for the creation of a whole integrated picture. As for the seemingly superfluous entities, try to cook pilaf without water!


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§ 1.06 The wave geometry potentials


To assess potentials of wave geometry (WG) let’s imagine a simple 2D model experiment: two coherent oscillators at first stationary, then, with distance between them unchanged, moving at a certain constant speed.




Fig.7. Phase shift is absent. V = 0 – no transfer in the medium.  Interference field emerged, as well as the standing wave between the oscillators.




Fig.8. Phase shift is absent. Orientation to the transfer in the medium is perpendicular (). The speed of transfer V =0.75c. Direction of transfer is from left to right. Interference field is compressed. Additional anti-nodes and nodes areas have emerged . The distance between the standing wave nodes has diminished.




Fig.9 Phase shift is absent. The system moves to the right. The orientation angle toward the direction of movement . The speed of movement .




Fig.10. Phase shift is absent. Orientation to the movement direction () is parallel (oscillators move from left to right). Motion speed .


We can see without calculations that the interference pattern is changing: it depends not only on the speed, but also on the orientation of the oscillators’ system to the direction of motion. If the system’s speed and orientation could vary, similar patterns might show that the higher is the speed and the lesser is the angle of orientation, the closer the nodes and anti-nodes become to each other. If we set as condition the numerical preservation of nodes and anti-nodes between the oscillators, we would notice the lessening of distance. We would watch the standing waves compress, and the system’s size shrink. What’s notable is that these things were not calculated mathematically, but modeled by rhythmodynamics.


Let’s examine another example: an interference pattern of a couple of oscillators of different frequencies. This effect has received the name ‘spider-effect’ due to its resemblance to a spider.


Since moiré pictures first emerged the effect shown at fig.11 has repeatedly caught the eye of both ordinary people and serious researchers.


Still, no one happened to consider this interference effect remarkable, and this beautiful effect failed to receive the status of important physical phenomenon.





Fig.11. Spider effect.


And it’s the very same effect which emerges each time the waves from the sources of different frequencies start interacting (interfering). This phenomenon indicates concrete processes, including force and energy ones.


Another example:  Non-radiant systems. Few persons know that oscillators can be positioned in space in such a way that their net outwardly directed radiation would be zero. Normally, they say in such situations that all energy stays inside the system, but this opinion happens to be wrong. The energy is radiated in the so-called ‘non-manifest’ form.




Fig.12. The system of coherent oscillators on the plane. The outward wave radiation is practically absent. But this radiation may become manifest at a certain distance away from the system, which implies that unless you know about its source, the energy in wave medium will be emerging as if from ‘nowhere’.






The case when the source emits in one direction two waves of equal frequency, but each wave has its own velocity in the medium (such is the medium’s property: it’s two-lane). The interference of such waves produces a standing wave, i.e. stationary nodes and anti-nodes emerge in space. Inside every anti-node, a transfer of energy takes place away from the source, what is unclear is how the transferred energy behaves in the nodes. If we examine the process within the limits of one standing wave, i.e. from one node to the other, we would see that the energy emerges as if from nowhere (from vacuum, or ‘under-space’), travels some distance and disappears into nowhere.





The other option is no less exciting. Suppose, we had two coherent sources emitting energy in the form of rays in one direction, but at a very small angle. In some area of space the rays intersect in the strictly opposite phases and create a zone where they practically cancel out each other. Suppose this zone is sufficiently large and the observer cannot register the overall amplitude of radiations. The question: Is the energy present in this zone, and if so, in what state?







Fig.16 The arrow indicates a point where the manifest energy is zero, while the non-manifest energy is maximal


Of course, the energy is present, and the state in which it exists is called zero-amplitude. The zero-amplitude state of energy is noteworthy for its effect: the energy travels in the medium (by means of the medium) while the medium itself remains in a state of calm. Which means that the sources’ net energy may be in both manifest and non-manifest states.


Energy and zero-amplitude way of existence


Let’s examine a model: Suppose we had two separate independent coherent sources of monochromatic waves. The sources emit waves in one direction along axis x. Naturally, in the areas where the waves superimpose on each other their amplitudes may double or disappear. If the distance between the sources triggers the wave’s phase displacement of 180° , then along the hole length of the axis x we are to observe the disappearance of amplitude, i.e. the waves do exist, each of them carries energy, but the energy is in such a state which makes it impossible for the researcher and his instruments to register it. One might say there’s no transfer of energy there at all. But this is not so. To prove the reality of the energy transfer in the so-called zero-amplitude (non-manifest) state we should conduct another mental experiment.


Suppose two monochromatic waves from two coherent sources travel as rays in one direction at a very sharp angle (the minutest fraction of a second, say, nought point ten or more zeroes…). The area in which the energy is practically in a zero-amplitude state is large (the lesser is the angle, the larger is the area); and if we, being inside the area, know nothing of the experiment with the sources, our instruments would register no energy at all. But farther away, in the area of space for us inaccessible, the rays began to move apart. An observer in this area who also knows nothing of the experiment would regard as a miracle the appearance of energy as if from nowhere.


And suppose this observer must give a credible explanation to this ‘miracle’ and create a valid theory of the energy’s strange appearance out of the empty space. He can make such theory palatable only if he acknowledges the empty space’s inherent ability to produce energy. As for us, we know the real cause, and therefore we’ll have a different theory.


Rhythmus: I know what you are driving at. Now every mad inventor would have a chance to explain the unbelievable energy efficiency of his mechanisms by their ability to transform energy from its zero-amplitude state to amplitude state, i.e. to drag it out of zero, the vacuum.


Dynamicus: I used this example just to explain the meaning of zero-amplitude. I hope the hypothesis of the presence in space of real energy in its zero-amplitude state has received some rationalization. I think the presented explanation hides the key to obtaining any amount of energy anywhere in space. One only has to learn to transform it from its zero-amplitude state into amplitude one. To understand it we now have a model of the proceedings.



So, there’s no miracle there. If two rays intersect at a small angle , there will be no complete cancellation:





the result after subtraction




Complete zeroing is possible only if the angle between the rays . That’s why in the area of intersecting rays the wave doesn’t drop to complete zero! This is quite evident from the drawing. But neither the formulas nor the drawing can show in what strange state the energy near the zeroing area is and how it manages, having passed this area, to completely restore itself.





The interest to the non-manifest state of energy propagated by waves has emerged in connection with attempts made to understand the root-cause of continuum. If continuum is attributed with such properties as continuity, indivisibility and unbrokenness it turns into a complete mystery how on earth it can by itself transfer from one place in space to the other any disturbances?  Bearing in mind that any shift of one part of continuum’s body in relation to the other would imply its divisibility and brokenness?!


To overcome the predicament one might use a trick well-tested in science and say “That’s how nature is, and there’s nothing to do about it!” Quite often they resort to it.


Indeed, why should continuum change its state in order to transmit energy from one place in space to the other? This energy could well pass through (along) the body of continuum in the so-called zero-amplitude state while continuum would feel no need of relative shifts of its own parts. In this case the Eleatic school concept of continuum is quite justified.



Fig.18. Illustration of the issue of zero-amplitude state of energy.


It’s really difficult to imagine the zero-amplitude situation, likewise it’s difficult to answer the question about the state of energy propagated in real medium by waves in opposite phase. But now we at least understand that such quite real processes can be unobservable. In other words, the energy propagated by waves in real medium can be in two states: manifest (amplitude) one, and non-manifest. Formally, the situation can be described as:




This formula expands the understanding of the law of conservation of energy, i.e. it indicates that energy can be in any of the described states.


Rhythmus: With your non-manifest energy beyond any observation, for a researcher your equation would look like a violation of the law of conservation of energy. Naturally, having introduced such instrument in theory one can readily promise power stations producing energy out of ‘vacuum’.


Dynamicus: Yes, this is quite likely, and such generous and premature promises should be better tackled by the Commission on fighting pseudoscience.



The issue of transformation of non-manifest energy into manifest seems quite intriguing. It’s obvious that the non-manifest state of energy can be easily characterized by frequency. Which means that in space at the same time there can be non-manifest energies of different frequency. To obtain a manifest energy it would be sufficient to skillfully  transform the non-manifest energy of one frequency to the non-manifest state of a lower frequency. Formally, it would look like:


,                                (1.08)


i.e. a certain appliance, let’s call it a frequency transformer, seizes the non-manifest energy of high frequency and transforms it into the non-manifest low-frequency state. During which the energy difference could move into the manifest state.


Rhythmus: I guess I’d have to read Tesla once again on the issue of harvesting energy. Saying that “One has only to learn to transfer it from zero-amplitude to amplitude state” you apparently intend to make some appliance which could transmit energy from any space to the energy reservoir which could later be used as a source of electricity?


Dynamicus: The issue of transformation of energy from one state to the other is not so simple and requires additional clarification, laboratory experiments and demand on the part of society. As for the zero-amplitude transmission of energy from point A to point B it could be possible. As for harvesting energy directly from space, well, within the framework of the drafted model such space must be crammed with energy in zero-amplitude state at least because each radiating element of matter (provided this element represents a system of lesser radiating elements) acts as a kind of generator of such energy. Formally, nothing happens: ‘zero’ came – ‘zero’ went. In practice, a new sun comes to life.



The question of real state of processes which are registered by our sense organs and instruments poses quite a problem here. It’s quite possible that the world we are observing, our world with all its attributes is situated at one of the non-manifest levels of processes’ organization in continuum. Such levels could be numerous, and if we introduce an imaginary axis of coordinates to mark those imaginary zero-amplitude worlds, we will have another, strange as it is, dimension ().


Suppose our world were zero-amplitude one. But being inside it, we observe its amplitudes, i.e. its materialness; besides we have an opportunity to transform this or that energy process to a much deeper level of zero-amplitudeness.


Having accepted our world as the usual one among the zero-amplitude worlds, we are obliged to presume a possibility of ‘material-energy’ life in the worlds similar to ours. This picture of the world could explain a lot, say, where the elementary particles get the energy for their ‘recharge’ from – still, for science it’s nothing but a hypothesis which could be seriously exploited only in philosophy, esoterica or science fiction.


Of course, this hypothesis is a way below a theory status, but it has one unquestionable advantage: it makes possible to understand how the phenomena and processes which we consider real can happen without causing disturbances in its own carrier, the proto-basis, substratum. In this sense we have found a superconductor for processes.


One has also to admit that we have no prior experience in describing physical processes and phenomena within the zero-amplitude notions. Nor there any calculus for this.


Interference in supersonic regime is another little-known phenomenon. It’s difficult to imagine a situation in which the interference pattern moves in the wave medium faster than the waves in this medium do.





Fig.19 In a supersonic cone of a single oscillator a standing, relative to the source, field of wave energy emerges. The velocity of this field equals precisely the velocity of the source (), i.e. the field moves with the source. A picture made from space shows a running wave pattern in the boat’s wake.



Fig.20. That’s how the field of distribution of wave (interference) energy looks produced by two supersonic coherent oscillators. The velocity and direction of the field movement equal precisely the velocity and direction of the oscillators . The start of ‘Proton’ rocket. The energy nodes and anti-nodes are clearly visible in the supersonic jet stream.





Fig.20.a Distribution of wave energy from numerous sources (left model) moving at a supersonic speed (12 Max). Similar process also takes place in the supersonic jet streams.


Many scholars know that the existing calculuses cannot fully integrate those things which in wave geometry, and in nature even more so, occur easily and unobtrusively. For example, the self-organization of wave objects numbering over three. Such calculus requires a different approach, a different logic. The first such program already exists, but it’s still far from perfection.




Fig.21 a. Random initial arrangement of coherent oscillators on display.




Fig.21.b A short time later the oscillators created joint anti-nodes of the standing wave and became self-organized around it, forming a circle.




Fig.21 c Gradually the circular formation split into two lesser systems.


The potential of the wave geometry is not limited to this only. But even this is already something!


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§ 1.07 Rhythmodynamics: postulates


Postulates in modern physics


Many researchers still think experience is the only source and criterion of truth. If so, the foundation of the modern physical paradigm must rest on phenomena and properties which are amply proven and therefore thought fundamental. But if these phenomena and properties are not explained at the level of processes, i.e. there’s no idea what processes exactly generate these or those properties, then their proper place is among the phenomena of nature.


Note: One of the meanings of the word Phenomenon (Greek phainomenon – to appear) is a rare or significant fact or event.


Among the natural phenomena are: motion (there’s no explanation why bodies can freely move in space); inertia (no explanation has been given yet why bodies resist the impact); ability to interact (like gravitation, for instance, the cause of which hasn’t been amply determined although this issue was raised more then three centuries ago).


In other words, the phenomena and properties which lie at the foundation of the modern physical paradigm, although experimentally fully proved, can still be regarded as postulates because of the lack of understanding of their physical nature. Objections may be voiced to this but such objections could be justified only if the opponent were prepared to present a concrete model of formation of at least one of the cited properties and phenomena.



Rhythmodynamics’ postulates


Rhythmodynamics presents concrete means of illustrating natural phenomena through their geometric modeling in the form of wave processes. That’s what the ‘Wave Geometry’ has been created for: to discover and clarify a range of wave phenomena which form the mechanism of motion, inertia, interrelation ,etc.


One of the main criteria of any theory is the ability to predict certain events and phenomena which could be later verified in practice. The efficiency of wave geometry has been confirmed experimentally, when results proved to match predictions. Among such instances are: the experiment to determine compression of standing waves in acoustics; experiment to determine the dependence of the speed of motion of the oscillating system of sources on phase displacement between those source, and others.



Rhythmodynamics is based on the system of postulates:


1.      A hypothetical elementary object – a dot-size mass-free oscillator which possesses the property of vibration (or pulsation), exciting its environment and generating periodic waves in it.

2.      Medium which transforms oscillator vibrations into parting spherical waves, ensuring their constant velocity of disturbance transmission  relative to the stationary source (in relation to the reference frame, firmly fixed to the medium).

3.      Interaction, i.e. when at least yet another one oscillator emerges, a system of oscillators emerges.


Explanation of the choice of postulates:


·        The mass-free oscillator, in case of an outside impact, can without any inertia impediment pick up the speed of its motion in relation to medium. Inertia properties spring up among oscillating systems as a whole, but they are not attributed to single oscillators. We do not consider the properties of a single oscillator because in such case they would require explanations. Whereas a system of interacting oscillators develop a property of resistance, say, to a change in its velocity. If the property, absent before, appears with the system, it is attributed to the system, not to the elements of which it consists.

·        Medium is introduced without indicating its structure and organization. The dependence of amplitude on distance is not stated. One can even say the dependence of amplitude on distance is a property of oscillating system, not of isolated oscillators.

·        The emergence of a system makes it possible to speak of a stable form of its existence, as well as about localization of energy in a specific area of space. The system allows to distinguish the oscillators’ parameters (frequency difference, phase relations). Inertia is first discovered at the system level (such property is inherently absent in isolated oscillators) because of the finite speed of wave propagation (delay effect) between the elements of the self-organized system.

·        To build a potent geometry-physical model a number of auxiliary conditions are necessary. For example, each oscillator in the system is seeking to occupy the most suitable to it ‘energy-comfort’ area, a zone of durable balance, a potential hole and to always follow in its wake.

·        The presence of inertia in the case of isolated elements (wave sources) indicates their complex structure, i.e. the presence of a system consisting of component parts.


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§ 1.08 Establishing the tasks to be solved


Although the number of issues Rhythmodynamics is focused to solve is limited, they are of fundamental nature:


·        Dependence of standing waves parameters on the motion of sources in wave medium.

·        Energy flow and its dependence on frequency difference.

·        Interaction of wave sources. The basics of self-organization of systems.

·        Phase difference and its impact on the speed regime of propagation in the medium.

·        The cause of reaction to the external change of motion regime.

·        Propagation in the medium triggered by internal forces of propulsion.


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Chapter 2.  Interference


Things are not the way they seem to be…



§ 2.01 Is it possible to manage without the notion of wave medium?


It’s hard not to notice the fact that by the end of the XX century a curious situation emerged in science: matter has disappeared being substituted by equations. Long before it, the existence of such trend had been pointed out by Vladimir Lenin in one of his philosophical works but no one seems to have taken much notice. Now the modern scientists who regard themselves as materialists fancy an experimental-phenomenological cocktail in which physics is completely substituted by math and absolutely weird models. The supremacy of this type of fundamental physics lasted throughout the XX century and still continues.


Despite the acknowledgement of the wave nature of matter, of light, radio waves, the scholarly ideologists are still denying the existence of wave medium. A remarkable paradox: there are waves, but there’s no wave medium! Such unwillingness to consider the obvious leads to fragmentation of scientific outlook and, correspondingly, to inability to create a whole and full working model. To cover up one’s own intellectual disability one has to resort to such ‘potent’ explanations as “That’s the way nature is!” borrowed from Philistine arsenal of wisdom called “All live like that!” or resort to intellectual speculations of the type of: ‘fields as special forms of matter’, ‘mass as inherent property’, ‘curvature  of space-time’ and so on and so forth. All of them emphatically assert, none of then rationally explains.


As for the author and his rhythmodynamics model, here the wave medium not simply exists, it’s inseparable from the wave phenomena: without the notion of wave medium the model won’t be able to work, and implement its universal function.


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§ 2.02  Standing wave. The basic properties we know as well as new ones.


Standing waves are ubiquitous. The reason is the bodies’ ability to reflect. In other words, wherever you have waves and their reflection, standing waves are bound to emerge. Hydro-waves, acoustic waves, light (electromagnetic) waves being reflected by the surface are bound to create standing waves near it. Standing waves are widely used in radio, electrical technology and metrology (to create a standard of length, for example). Many chemists and crystallographers especially have already come to conclusion that the bodies themselves are the packages of standing waves, a kind of wave lattices in whose nodes atoms and molecules reside. The standing waves can play the role of a primary structure, and not just that. That’s why we attribute so much importance to this natural phenomenon.


Let’s sum up what we know about standing waves:


·        Standing wave emerges as a result of superimposition of two waves moving in opposite directions and meeting the following requirements: their wave frequencies are equal, their amplitudes are the equal functions of the coordinate system. Standing wave is one of the manifestations of the wave interference.

·        Standing wave emerges, for example, when the falling and reflected waves superimpose, when the angle of incidence is zero, and reflection factor is 1.

·        The amplitude of standing wave is a periodic function of the x coordinate and doesn’t depend on time.

·        The point in space where the net amplitude is always zero is called standing wave node. The areas between the nodes where the net amplitude is above zero are called the anti-nodes of the standing wave.

·        The standing wave’s length is a distance between the two neighboring nodes or between the two neighboring anti-nodes.

·        Unlike longitudinal wave, standing wave propagates no energy. This is evident from a fact that the position of nodes and anti-nodes in space doesn’t change in time – that’s why such waves are called ‘standing’. The absence of the energy propagation by the standing wave is due to the fact that the coming wave and its counter-wave carry energy in equal amount but in opposite directions.

·        Standing spherical wave emerges as a result of a superimposition of two harmonic spherical waves traveling in opposite directions.


The simplest case of emerging standing wave is the experiment with a string one end of which is firmly fixed to a solid wall, the other is attached  to an appliance performing vibratory movements. If the latter end of the string is moved continuously and made to perform harmonic vibrations, a sinusoidal wave is to run along the string. When it reaches the point where the string is fixed to the wall, the wave will bounce back and run in the opposite direction. The superimposition of those two waves produces a standing wave in the string (fig.22).





Now let’s talk about the standing wave properties discovered by rhythmodynamics.


Let’s complicate the experiment and replace the string with a thin elastic rubber tube (a hose). To make it clearer, let’s examine fig.23 and describe the appliance with the help of which we are to study one of the most unusual properties of the standing waves.





            a                                             b

Fig. 23 a) The rubber tube is filled with water, the tap is closed. The velocities of the wave and counter-wave are equal. b) The tap is open. The velocity of the water flowing in the tube is V. The velocities of the wave and counter-wave are different.  While in (a) case one can expect the emergence of a standing wave of the type shown at fig.22,  in (b) case such prospects are not clear because it’s the waves of different length which are to interfere! c) Counter-waves (left) produce the beat (right) in which one can hardly make out a standing wave (Fig. 24).


One end of the rubber tube passes through a hole in the wall and comes out on the other side. This end of the tube is attached to a tap, which in open position lets water in the tube. Some distance from its free end the tube is fixed to the vibrator appliance, while the free end is inserted into a reservoir for water drainage.


Let’s fill the tube with water, close the tap as well as the exit opening so that during experiment the water could stay inside the tube. Moving, the same way as with the string experiment, the free end of the tube with water we are to obtain the striking and counter-waves of equal length, the superimposition of which is to produce a standing wave.


Let’s change the experiment’s conditions. Let’s open the tap outside the wall so that water could flow in the tube with certain speed V. In the process of, say, a single vibration of the free end of the tube we are to find that the wave running to the wall is slowing down, while the speed of the same wave which bounced back from the wall actually increased. Then, if the free end of the tube is performing harmonic vibrations, we are to observe the superimposition of two waves which have the same frequencies but different velocities of propagation in the medium, and consequently, different lengths. This is explained by the fact that the speed of propagation of the waves of deformation in the tube with water depends on the speed and direction of movement of the water in the tube. The speed of the waves along the water flow is (), while the speed against the flow is (). Then, if the wave frequencies are equal, is the standing wave to emerge? Or interference is to produce something which has nothing to do with the standing wave?


At first glance, a beat should emerge which has nothing to do with the standing wave. The beat does emerge (fig.24), but the standing wave also takes place. It won’t be difficult to witness it either by solving the standing wave equation or through computer processes’ modeling, or by staging the experiment itself.




Fig.24 That’s how a computer model looks in which the oscillations’ source is presented as a speaker. The direct and counter-waves have equal frequencies but different velocities, and therefore different lengths. Addition of these waves results in the beat. If this process is examined as summed up in time, the nodes and anti-nodes will be visible which allows one to speak of a standing wave.


Solving  the equation or modeling, we inevitably encounter the dependency of the standing wave length on velocity V (2.02). This dependency differs from the previously known (2.01), and here we for the first time encounter the ‘magic’ factor in physics (). Such is the geometry of standing waves in which 2.01 is a special case of 2.02. The phenomenon discovered by rhythmodynamics was called ‘compression of standing waves’ (CSW).






But standing waves emerge in all wave mediums (electromagnetic wave medium is no exception). Standing waves have long been used in electromechanics, radio engineering, physics and metrology when, for example, the standard of length is determined. That’s why the CSW phenomenon is paid so much attention in rhythmodynamics.


It’s worth note that the compression of standing waves was first discovered in geometrical constructs in 1981 (the author conducted geometrical analysis of the wave phenomena related to Michelson’s experiment), then validated mathematically. Only nine years later, in 1990, an acoustic experiment was staged which confirmed this discovery.


Let’s dwell on this experiment more because in its course I discovered compression of standing waves not only with the lengthwise orientation of equipment, but with any orientation. In other words, the experiment fully confirmed theoretical forecasts.


Before we start describing the experiment, let’s ask a seemingly simple question: what is the nature of acoustic waves? There are at least two answers:


1.      Sound is a mechanical (displacement) disturbance propagated in elastic medium.

2.      Acoustic wave is a displacement interaction of molecules by means of their own electromagnetic fields, i.e. the nature of acoustic waves is electromagnetic.


I’ll describe the 1990 experiment so that everyone who wishes could repeat it. The goal of the experiment was to confirm the effect of the motion of medium or relative to medium on the metric parameters of standing waves.


The plan of the acoustic experiment (fig.25) doesn’t differ much from the experiment conducted by  Heinrich Hertz when he first obtained the electromagnetic standing wave.



Fig.25 a) direct and counter waves; b) wave superimposition: instantaneous show of resultant; c) developing in time the resultant outlines in space a picture with well-defined anti-nodes and nodes, i.e. the standing wave.





Fig.26 Hertz’ resonator


To create a standing wave in sound medium one has to have a source of harmonic oscillations and a reflector (acoustic mirror). As a source, one can use a speaker which receives via  an amplifier the signals from a generator. The speaker sends oscillations in acoustic medium in the form of displacement disturbances which the medium propagates in space through its own self in the form of waves. The velocity of waves’ propagation is determined by the medium properties, like elasticity, for instance. In the air such velocity varies, but at the earth’s surface it amounts approximately to 330 m/sec.


Spreading in the medium, the waves from the speaker hit the acoustic mirror, and bouncing off move backwards. The superimposition of two opposite waves between the source and the mirror results in a standing wave. This is in the ideal case when the waves’ amplitude is constant and doesn’t depend on the distance from the source. But in practice the amplitude decreases with distance which creates certain problems of purely technical nature.




Fig.27. The map of the area where the experiment was conducted (Russia’s western-most Kaliningrad region, the town of Luzhki. A view from space).


Fig.27 shows the area where the experiment was conducted and position of the main pieces of equipment (the source and mirror simulator) which helped realize the standing wave. The distance between the source and the mirror was 70 meters. Which means that the acoustic wave traveling back and forth covered 140 meters. The control node, the one the changes in position of which were registered, was near the source, therefore it was necessary to ensure in the node area that the amplitudes of the going and coming waves be equal. This problem was solved by the method of multiplication and division of frequencies.




Fig.28 Unit 1 consists of the sound generator, frequency multiplier, mixer, amplifier and speaker. Unit 2 consists of a microphone, frequency divider , signal restorer and low frequency (sound) amplifier and a speaker. The ruler was used to register position of the control node.


The driving generator was tuned to frequency 3.3 kHz. This signal went simultaneously to the amplifier and the multiplier, which increased its frequency four-fold (13.2 kHz). Two amplifiers and two emitters were used as a source. One of the emitters was low frequency, the other – high frequency. The power of the low frequency emitter wasn’t big, while the power of the high-frequency one was set so that its signal could be received by the microphone placed on the acoustic mirror.


The high-frequency signal received by the acoustic mirror was divided by four so as to restore the low-frequency component of the radiation. After its restoration the low-frequency signal was amplified and ‘re-emitted’ back to the source. The amplifier capacity was adjusted so that the amplitude of the incoming signal should be equal to the amplitude of the outgoing signal.





Fig.29 Pictures of the driving generator (a), and mirror simulator (b) as well as phonendoscope (c) where 1 – is a thin copper tube to search for the standing wave node.


These manipulations made it possible to register the standing wave nodes in close proximity to the source. The nodes’ position was determined with the help of an updated phonendoscope in which the capsule with membrane was replaced by a thin copper tube. The loose end of the tube was put in the standing wave, and by moving the tube one could find the spot in space where sound was absent. This spot corresponded to where the standing wave’s node was positioned in space.


The emitter and the acoustic mirror were always set at a fixed distance mounted on wooden marked with scales pillars dug into earth. To register position of the control node of the standing wave a wooden ruler was used on which marks were made by a pencil. The node’s position was determined manually with the help of the phonendoscope.


It must be stressed that had it not been for the acoustic mirror it would have been problematic to discover the compression of the package of standing waves, particularly with the wind directed along the appliance’s axis. Initially it was planned to set up two opposite emitters, coherent ones and therefore powered from a single sound generator. But analysis showed that emergence of wind would shift interference pattern so strongly that it would have been impossible to measure the expected result. So the solution was found in using the acoustic mirror which completely removed the ‘noxious’ shift of interference pattern.


During the experiment’s preparatory period calm windless weather set in (for three summer days). This gave a convincing chance to witness that at every installation of equipment with permanently adjusted parameters the control node was always registered on the ruler in one and the same spot. So the only thing left for us was to wait for the wind to appear.




Fig.30 Vane (left) Anemometer of revolving cups type (right).


A self-made vane was used to determine the direction of wind. An instrument measuring the wind speed (anemometer) was not installed due to its absence.


Two situations were of special interest: when the wind was blowing along the axis ‘source-mirror”, and perpendicular to it. According to the calculations made, the standing waves compression had to take place in both cases. To ascertain the fact of compression of the package of standing waves one had to register the shift of the control node toward the acoustic mirror. Below is the table of calculated relationship between the wind velocity, reduction of distance between the nodes of one standing wave and the shift of control node.


Wind velocity (km/h, m/sec) (along, across)

Calculated distance between the nodes (cm). ñ=330m/señ,

í =3,3êHz

Calculated shift of control node (cm) LL’. L=70m. ( pieces)

0,0km/h. 0,00m/señ



5,0km/h. 1,39m/señ


6999,87   0,13

10km/h. 2,78m/señ


6999,51   0,49

15km/h. 4,17m/señ


6998,88   1,12

20km/h. 5,56m/señ


6998,01   1,99

25km/h. 6,94m/señ


6996,91   3,09

30km/h. 8,33m/señ


6995,53   4,47


The best weather conditions for the planned experiment could be a pre-thunderstorm period which has a spell of quiet after which emerges the wind which gradually changes its direction. In the course of the following week such conditions emerged twice, and both were used for measurements. After processing the obtained results an unequivocal conclusion was made: whenever the wind emerged, no matter in what direction, the control node of the standing wave was always shifting toward the mirror – which testified to dependence in acoustics of the length of the standing wave in the system on its, the system’s, speed in the wave medium. Thereby the phenomenon predicted theoretically in 1981 was confirmed experimentally in 1990!


Here’s another experiment which could be staged in any ordinary school laboratory, or even at home. (fig. 31). It requires: sound generator, amplifier of 1 watt, a speaker, oscillograph, piezoelectric transducer and sufficiently powerful electric fan.




a)                                                                   b)

Fig.31. Emergence of an air-flow between the speaker and the wall (the air-flow is created by the electric fan) triggers deformation of interference pattern and a shift of the control node toward the wall. The package of standing waves is compressed.


Experiment procedures’ order:


1.      Have series connected sound generator, power amplifier and the speaker.


2.      Have sound generator frequency adjusted to, say, 3 kHz.


3.      Have the speaker firmly fixed at a distance of 2-2.5 meters from the concrete wall.


4.      After the speaker is switched on, make sure a standing wave has emerged between the speaker and the wall.


5.      Piezoelectric transducer is switched to the oscillograph. The transducer is used to determine the area of silence which corresponds to the standing  wave’s nodes.  The oscillograph would show the area of silence as a minimal surge of the running dot.


6.      After the node closest to the speaker is found by the transducer, the transducer is fixed in this spot.


7.      The amplitude of the running dot is marked on the oscillograph.


8.      The electric fan is set 1.5-2 meters from the shortest possible line between the speaker and the wall, aimed at it and switched on.


9.      After the electric fan is switched on the oscillograph’s readings increase.


10.  By moving the transducer carefully from the speaker to the wall a new position of the shifted node is found (due to the insignificance of the effect the transducer’s shift should be carried out with the help of a micrometric screw).


11.  The node’s shift toward the wall shows that the air-flow from the electric fan has changed the metric parameters of the standing wave.


12.  Conclusion: compression of standing waves’ has taken place!



The discovery  of this effect has an impact on lots of other important things, for example, the issue of establishing a fundamental standard of length. If, using interference method, a standard of length were created consisting exclusively of a set number of standing electromagnetic waves and this standard were compared with the platinum-iridium standard in Paris, an interesting picture would emerge: the matter behaves exactly the way the artificially created electromagnetic standing waves do. The root-cause lies in the matter’s structure, in its wave nature, the wave nature of ties existing between the matter’s elements.


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§ 2.03  Oscillations, standing waves, and physical standards of measure


Oscillations (pulsations) are one of the basic forms of motion. Any oscillation exists on its own,  related to nothing, and being without the observer has no quantitative parameters and measurements. It just exists! To determine those parameters and measurements the observer is required. But he cannot say anything about an oscillating source unless there are other oscillating sources around. What the observer can do is to calculate the number of oscillations. If he has other oscillators around he has a chance to compare. As a result of such comparisons, he may find that some sources oscillate faster than others, i.e. have higher frequency.


To systematize the observation results they choose the most stable of the sources, and, for example 1000 ‘pieces’ of its complete oscillations are acknowledged as the initial standard of duration, which is called  the unit of period (time).


The standard of period proves a useful instrument in systematization, allowing to assess any sources of oscillations from a single intuitively comprehensible position. Measurement: the ‘pieces’ (translator’s note: the author’s choice of term) of oscillations in a single period. Thus, the observer has developed the first measurement: ‘n’ pieces per 1000 pieces where ‘1000 pieces’ is the standard of period (time). Such measurement can be given any name you like, Hertz, for instance (pieces per second).




Fig.32. Unless extreme precision is required, a quartz generator of signals could be used to set a standard of time.


Understandably, any standard, including the standard of time, is no more than agreement based on the very same oscillations: the unit of time is determined by an ordinary number of oscillations of something. The initial measurement of a unit of time are pieces! But for the sake of convenience a certain number of pieces of oscillations of a certain, selected by consent, periodic process is called ‘one second’ – 1 sec.



Rhythmus: Cool! Hertz are pieces divided by pieces. Velocity are meters divided by pieces; acceleration – meters by pieces squared. If so, we can equally measure both meters and kilograms in pieces…  I wonder what fault you find with the existing systems of measurements?


Dynamicus: But that’s how it actually is: everything is in pieces! For example, the standard of time of 1 second is nothing more than the length of 9192631770 pieces of oscillations of emission of quantum transfer between the lines of the super-thin structure of 133Cs atom. As for the standard of length, it, too, is measured in pieces of oscillations and waves. A good proper measurement. ..



Establishment of length standard, the modern definition of which requires the notion of ‘wave’ proved a more complex issue. Metrology sets as the standard of 1 meter 1650763.73 pieces of wave lengths of 86Kr which, again, fill in a certain approved distance in space.




Fig.33. The draft of Michelson’s interferometer with a regulated mirror used to count the waves. M – micrometric screw; B – light-emitting diode used to measure light intensity.


The length of traveling waves depends on the frequency of oscillations and the ability of the wave medium to propagate waves with a certain speed in relation to itself. According to the Doppler effect, in a system moving in relation to a wave medium, the length of a traveling wave depends on the velocity of system, i.e. ; therefore it’s impossible to agree with a statement that  a distance accepted as 1 meter contains a constant number of the running waves of 86Êr emissions (transfer between the levels of 5d5 –> 2p10).


The assertion that the length of wave in the system doesn’t depend on the system’s speed is correct only within the framework of Newton’s and Einstein’s theories which deny the existence of wave medium as superfluous.


The issue of establishing the length of electromagnetic wave in vacuum is awkward one. We still do not know the direct way of measurement of the length of such wave in progress. Nor do we know if it is possible even in theory to measure the traveling wave directly.


Rhythmus: That’s cool! How about the calculations and the work of complex radio-electronic equipment? Do you really mean what you say? Using the waves, they learnt to measure the distances to various planets and operate space craft. To say nothing of the GPS navigation.


Dynamicus: The impressive achievements you are citing cannot confuse me. You’d better answer my question: when the system’s velocity changes do the sound standing waves compress, or not? And if they do, why shouldn’t the electromagnetic waves compress? If you are to say there’s no wave medium (ether), prove it.



The standing wave formed by the running direct and counter waves is quite the other matter. It was proved earlier that the doubled length of the standing wave matches the lengths of the traveling waves which form it only in one case: when the system in wave medium is motionless (, ). If the system is moving in the medium (), another relation would be correct:


,                                              (2.04)


which doesn’t indicate equality between the running waves and the doubled standing wave. Therefore, when one speaks of the standard of length one should speak of the number of standing waves in the space accepted as the standard of 1 meter. This number is 3301527.46 of standing waves of 86Êr emission.


But a problem emerges: when the system’s speed changes the behavior of the wave standard of length present in it would be ambiguous because:


.                          (2.05)


In other words, if you take the rigid platinum-iridium standard and count the number of standing waves fitting in the length of this standard when the system’s velocity in the wave medium is zero (), then count them again after the system’s velocity increased (), the number of standing waves fitting the standard’s length would increase too. Which is not observed in practice. In more than a century-long period of improvement of the means of realization of the standard of length no increase or decrease in the number of standing waves fitting 1 meter has been detected. Why?




Fig.34. Exterior view of the meter’s prototype (its full length is 102 centimeters).


The reason why it’s impossible to detect it can be explained by the dependence of the size of the moving bodies on their speed in wave medium, following the rule:




Body size


Standing wave length





The hypothesis becomes clear if the presumed compression of the body’s dimensions in the moving system is compared with the compression of the standing waves in the same system.




Fig.35. If the standard of length were matched with traveling and standing waves, the situation with the establishment of the length standard by counting traveling waves would become absurd. Another matter if standing waves were counted. But with changed orientation in space or changed velocity regime the standing waves compress. Had it not been for the material of the standard which compressed in exactly the same way the standing waves compress, the number of standing waves would change with the change of motion conditions. But this does not happen.


Such synchronization is possible only if the interatomic ties in a crystal lattice have a wave nature, and can be presented in the form of standing waves.




Fig.36. Crystals’ structure: a – halite NaCl; b – diamond; c- fluorite CaF2. Made up of different atoms, differently positioned, they all form a cube, i.e. relate to the same space group.


If the inner structure of matter were viewed in such a way, the distance between the atoms would be always measured by the length of the standing wave. When the speed of material bodies in a wave medium increases the standing waves shrink (compress), which leads to a reduction of distance between atoms and consequently to the reduction of the moving bodies’ dimensions.




Fig.37 Ties in a crystal (right) shown as a package of standing waves in the nodes of which atoms are set.



Rhythmus: And what’s wrong with the Fitzgerald-Lorentz contraction? What are the new contractions for if we have well-tested old ones? Are you going to turn the tables on all?


Dynamicus: The proposed model is based on a concrete phenomenon called ‘compression of standing waves’. Whereas the Lorentz-FitzGerald compression is based on a pure hypothesis which in modern physics became a simple mathematical proportionality coefficient of Einstein-Lorentz.



Don't we need to explain why the interatomic ties in matter should be presented as standing waves? And why should atoms be positioned precisely in the nodes of the package of standing waves and follow the nodes if these nodes, for some reason, change their position in space?


This could be done step-by-step: 1) examine the behavior of the model from positions of wave geometry; 2) justify with the help of familiar classic theories the feasibility of presenting the ties in matter as waves, and the matter itself as a package of standing waves; 3) conduct an experiment and compare the results.


Let’s examine the first step in which conditions are set from the start by wave geometry.


Suppose we had two coherent oscillators seeking, by condition, to occupy such a place against each other in wave space so that along the imaginary line which connects them the net emission would be totally absent. Such minimally possible relative position is equal to the length of a standing wave (fig.38). Suppose the conditions of stability were: oscillators set in the nodes of the standing wave created by them; along the line linking the oscillators the outward emission is absent; the number of standing waves (anti-nodes) between the oscillators is equal to any uneven integer. Additional variable is the phase displacement between the oscillators.




Fig.38. Along the line drawn between the oscillators the outward emission is absent (, ).


If such system, with its parameters unchanged, were moved in a wave medium with constant speed, the interference pattern would change, i.e. the conditions of inner balance would be broken (fig.39). We must find out by the change of which parameters we can restore the balance conditions of the moving system of oscillators.




Fig.39 Inner balance has been broken. Outward emission has emerged (,).


To fully restore the inner balance in the moving system one has to, first, change the distance between the oscillators in accordance with 2.06; second, create the necessary phase displacement between the oscillators (2.07)







Fig.40 Thanks to the changes made (, ) the inner balance of the system has been restored.






In which case



Which implies that in a freely moving system its parameters: velocity, length and phase displacement are closely related to each other, and must be mutually coordinated so as to restore the balance.


So, we’ve found that the motion of a system of oscillators in a wave medium leads not simply to the reduction of distance between the oscillators, but also requires correction of the phase displacement between the wave sources. The system’s velocity and oscillators’ phase displacement have a positive correlation. If the motion proceeds along the imaginary line linking the oscillators, then the distance between the oscillators changes according to the rule:



If the system of oscillators is oriented across the movement, then, with phase displacement absent due to its uselessness, the distance between the oscillators reduces according to the rule:



.                                       (2.11)


Conclusion: modeling the material body as a package of waves in the nodes of which the wave sources (atoms in material body) are set, we’ve pointed out the geometric cause which leads to the longitudinal and traversal reduction of measurements of the moving body, i.e. determined the algorithm of dimensions’ changes depending on the speed in the wave medium. Another important relation has emerged: between the system’s velocity (in cases of only two oscillators) and phase displacement of the wave sources in this system.


Let’s examine another step, which is more related to real dynamics. We are to examine the cause of oscillators’ preference to stay in the nodes of a standing wave in cases when some external influence is attempting to forcibly drive them out of the areas of stable balance.


According to classical electrodynamics, atoms and molecules are interacting mostly via electromagnetic forces. In solid objects the distance between atoms varies from 1 to 9 angstrom. Suppose, the ties were of electromagnetic-wave nature, and the minimally possible distance between atoms is determined by a standing wave. Let’s calculate the frequency at which this interaction is taking place.




which is by a factor of ten to the power of four higher than the wave frequency of light band (blue light frequency 6.3·1014 Hz) and corresponds to roentgen frequency band. Which could imply that solid objects are, in essence, localized clusters and sources of roentgen emission. In such case the question arises: Why are these emissions practically unobservable?


Their unobservability can be explained in the following way: all known ways of measuring are based on the principle of comparison of received information with a certain initial background standard which is accepted as mark ‘zero’; so if black background were accepted as mark ‘zero’, any deviation from black is observable; if the objects under study and the environment around them have the same temperature, it would be impossible in such conditions to measure the temperature of one object with the help of the other. The designed gadgets and sense organs, being themselves the clusters of roentgen radiation, are incapable of registering either the background state of space, or bodies of similar frequency the amplitude of emission of which is equal to the background amplitude but accepted as zero. In reality background level can be quite high, but for us and our devices this level remains just the same the initial zero reference point. That’s why we can observe only those objects whose emissions in amplitude and frequency are higher than background one. It’s amplitude excessive radiation which is registered by devices.


So, to detect the standing waves which are in the background, i.e. assumed as zero, corridor, band,  of amplitudes and frequencies is practically impossible. Intuitively, we understand that atoms, indeed, can form a primary structure made up of the very same standing waves but their frequencies and amplitudes are a ‘blind spot’ for devices. Everything which is going on in the background corridor can take place, but cannot be directly detected. But there is a situation in which two similar in chemical composition and structure objects can mutually register an increase or decrease in each other’s emission in roentgen frequency band. This is possible in gravitation field whose potential leads to a synchronized up or down shift in all frequency parameters of the body. But in the planet Earth conditions these shifts are extremely small, i.e. they are comparable with the gravitational red shift for sources of any emission.


Rhythmus: Does this mean we are the sources of roentgen radiation? And everything around us are the sources of roentgen waves as well? If so, why are we still alive?


Dynamicus: Yes, we and everything around us are the sources of roentgen waves. And our health almost immediately reacts to even insignificant above the norm increases in precisely roentgen and higher frequency radiations because all matter is made up of radiations of various frequency, saturated with these frequencies, and for this reason their balance can be broken only by the same or quite close in frequency excessive waves. If in isolated parts of balanced wave system  resonance emerges the system begins to change either through self-adjustment or through self-destruction. For a human being such resonance leads either to serious illness or death.


The matter is floating in a pool of zero-gradient (background) radiation, and therefore there’s no means to measure the level of such radiation.



The modern views about the nature of interatomic ties are quite vague and exist at the level of notions rather than models. The atom itself is no more than a convenient pivotal notion with an array of experimentally determined properties. With discovery of new properties the atom’s model changes (fig.41). There’s no definite answer to the questions how exactly the atoms bind each other in a crystal lattice, with what, by means of what processes?




Fig.41 Thomson regarded atom as electro-neutral system of spherical form with a radius of about ì. The atom’s positive charge is evenly distributed throughout the sphere’s volume, while negatively charged electrons are set inside it. Rutherford & Nagaoka model of the atom.


Suppose we had two pulsating coherent oscillators which excite the wave medium creating a standing wave between themselves. The oscillators are set in the nodes of this wave, which results in a simple, minimally possible, stable system. Attempts to bring the oscillators beyond the nodes areas trigger the reaction of a wave field aimed at restoring the oscillators in their initial positions. If action is aimed at only one oscillator, the whole system regroups and begins to move. The whole chapter of this book will be devoted to this issue.




Fig.42 Dipole, triangle and tetrahedron are the most stable systems because in-between the sources which form them only the integer ties in the form of standing waves exist.


There can be only three types of ideally stable wave systems with minimal dimensions: two oscillators and a standing wave between them; three oscillators forming an equilateral triangle with its side’s length equal to the length of a standing wave; four oscillators in the form of tetrahedron with its edge’s length equal the length of a standing wave (fig.43).




All other geometric figures linked by standing waves have intersecting fractional ties in the form of the very same standing waves. Fractional standing waves diminish the system’s stability (fig.44).







Fig.45 Energy distribution pattern: a) dipole b) triangle c) square. Fig.45c shows that oscillators are in the areas of unstable balance.


Let’s go back to the issue of length standard. If during the motion compression of electromagnetic standing waves takes place, then, comparing a certain number of these waves with the standard of length we won’t find any compression. The standing waves and the standard behave themselves in relation to each other as if nothing happened with them, and no compression existed. Such situation makes one think that interatomic ties of the standard and other bodies have electromagnetic waves nature similar to a standing wave. Which explains the inability to detect because both standing waves and the standard of length are subjected to equal compression.


One should bear in mind that both compression of electromagnetic standing waves as well as contraction of dimensions of material bodies are only hypotheses based on the established phenomenon of compression of standing waves in acoustics. The use of this acoustics phenomenon  as a direct analogy to electromagnetics is possible due to similarity of the nature of oscillatory processes, nevertheless, we are doing this only within the framework of developed models. The more so that Rhythmodynamics itself is based on oscillations, wave medium and waves.


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§ 2.04 Dimension’s contraction and Michelson’s experiment


Michelson’s experiment is a good illustration to the contraction of dimensions and the impact of this phenomenon on cancellation of expected results. Let’s examine it in detail.


As we presume, the interferometer’s size depends on its velocity in wave medium, according to the rule:




 is the angle of orientation of interferometer’s arm to the direction of motion





In these directions the standing waves change their dimensions in the same proportion:





where ‘n’ is the number of standing waves fitting in interferometer’s arms.


Fig.46 General view of Michelson’s first interferometer.


If now we were to repeat Michelson’s calculations, taking into account contraction of dimensions, no difference in the beams’ time in transit would be found.



Dimension contraction is absent, i.e. doesn’t depend on the system’s velocity V  in ether:




Fig.47. Interferometer’s general scheme


Let’s analyze this experiment.

Suppose the interferometer were positioned in such a way that beam 1 were moving along the Earth’s movement, while beam 2 perpendicular to it. In such case, unless ether is dragged by the Earth’s movement, the time the beam 1 travels its path is:


,                 (2.17)


while the time beam 2 travels its path is:


.                      (2.18)


So, beams 1 and 2 spend different time to travel distance 2L and the time difference is:




If we were to turn the device by 90°, then, vice versa, the time spent by beam 1 is:


,                      (2.20)


while the time spent by beam 2 is:


,                 (2.21)


their difference:





As a result the interference fringes should shift, and though this shift amounts to , it nonetheless is detectable. Consequently, having measured fringes shift one can determine velocity of the ether wind on the Earth.




Fig.48 The length of interferometer’s arms depends on the choice of type of dimensions’ contraction. Calculations are given for V=0,5c.


In Rhythmodynamics the dimensions contraction follows the rule:





.                                          (2.25)



Then the time of beam 1 in transit is:


,       (2.26)


whereas the time of beam 2


.                             (2.27)


So, the time in transit of beams 1 and 2 is equal, therefore





In other words, the time in transit (back and forth) of beams 1 and 2 depends neither on the interferometer’s orientation to movement, nor its speed in the wave medium, i.e. it’s always constant. It’s easy to show on the scheme used by supporters of a different approach in explaining the cause of a slowing down time.




Fig.49 The scheme for calculating time slow down.


Lorentz’ contraction of dimensions implies  that the traversal size doesn’t depend on velocity V (), therefore calculating the pace of time leads to a slow down of the clock pace in accordance with the rule , i.e. a second in the moving system lasts longer. In rhythmodynamics the traversal size changes according to the rule which removes the problem of dependence of the pace of clock on its velocity, i.e.  .


If the pace work of identical clocks doesn’t depend on their velocities in the wave medium such characteristic might be used to synchronize the clocks in different parts of space so as to, for example,  conduct experiment to determine the speed of light in one direction. But first let’s give a rhythmodynamics’ interpretation of the results of Michelson’s experiment.


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§ 2.05 Rhythmodynamics interpretation of the results of Michelson’s experiment


In this paragraph we give a rhythmodynamics’ interpretation of the results of Michelson’s experiment  due to the absence of a strict or at least logically backed up solution of the issue of electromagnetic ether as well as the Earth’s movement relative to this so far incomprehensible wave medium.


Maxwell was the first to raise the issue of a possibility of conducting an experiment which could give a definite answer as to which of the existing theories was correct: either an empty space of Galileo-Newton, or a space filled with luminiferous ether. In this experiment the speed of light coming from a terrestrial source on the moving Earth along its movement was first measured and then compared with the speed of light measured when it moved in opposite direction. Apparently, unless the Earth drags with its movement the ether around it, such speed in the first case is , in the second  , where V  is the speed of the Earth.  So, the difference of light velocity in the first and second cases is of the first order of smallness relative to .  Still, to conduct such experiment one has to be able to measure the time it takes light to travel a certain distance in certain direction, for example, in the direction of the Earth’s movement. The task which is experimentally unsolvable due to the problems of synchronizing clocks in various parts of space. Therefore in all experiments staged on the Earth to determine the velocity of light this velocity was  determined by the  time it takes light to travel forward and backward. Consequently, to determine the impact of the Earth’s movement on velocity of light one has only to compare the time the light travels, back and forth, a certain distance L one time along the Earth’s movement, the other, say, in direction perpendicular to it. But in this case the time difference in both the first and second cases would be of the second order of smallness relative to , i.e. the magnitude of order .



Fig.50 J.C. Maxwell


So, although experiment could help solve the issue of ether’s behavior during Earth’s movement, nonetheless smallness of the magnitude  makes the expected result extremely insignificant. In this connection Maxwell was rather skeptical about actual possibility of solving the issue with the help of such experiment. Nonetheless such experiment was soon, in 1881, staged by American physicist Albert Michelson. To compare the time in transit of light traveling both forward and backward along the Earth’s movement and perpendicular to it, Michelson used interference phenomenon. For this very purpose he invented interferometer which consisted of two mirrors N and M and a semi-silvered mirror O positioned as indicated in the picture. A beam of light from source S is split by plate O in two beams 1and 2 which after their reflection by mirrors M and N as well as reflection of beam 2 from plate O get into microscope K. The position of interference bars observed in the microscope is determined by the transit difference which beams 1and 2 acquire during time period when they travel the corresponding routes from plate O to mirrors N and M and backwards, which could be considered similar and equal to 2L.




Fig.51 A. Michelson


The objective of Michelson’s experiment was to turn the device by  90° and find the fringes’ shift indicating phase displacement and, thereby, the existence of motion in ether. In 1981, when a theoretical analysis of Michelson’s experiment was given, it was found that if the formation of the standing waves in OM and ON arms of Michelson’s interferometer (fig.52) were examined, their length must depend on the angle  of the device’s orientation relative to the direction of movement and on the velocity (V) relative to the wave medium (ether) in accordance with the formula:





 - distance between the closest nodes of a standing wave in case of interferometer’s movement;

 - distance between the closest nodes of a standing wave in case of interferometer’s immobility;



V – interferometer’s velocity;

c – speed of light;

 - angle of orientation between the arm in which the standing wave is measured and the direction of interferometer’s movement.




Fig.52. Michelson’s interferometer. N, M – mirrors, O – semi-silvered mirror, ÈÑ- light source, ÈÊdevice to observe interference pattern, c1 – speed of direct wave, c– speed of counter wave, c – speed of wave perpendicular to motion, V – interferometer’s velocity relative to ether,  LII è L – interferometer’s dimensions with V>0, L0 – interferometer’s dimensions with  V=0.


In other words, if Michelson’s interferometer changes speed or orientation relative to the direction of movement in ether, the quantitative relation of standing waves must change.


The correctness of this statement was proved in the experiment with sound standing waves: in 1990 a sound interferometer was built which registered, with the emergence of wind, both compression of standing waves, according to (2.29) and changes in their quantitative relation when the wind direction changed.


In Michelson’s interferometer experiment no such direct measurements were conducted, but when Michelson’s proposal about the length standard was implemented by interferometer means [7], it was exactly the count of a number of standing waves between the semi-transparent and reflecting mirrors which was mentioned. No changes in the number of waves were ever detected, which made possible any of the three options:


1.      Ether is dragged by bodies and it is completely immobile on the Earth’s surface.

2.      Ether is always immobile; bodies move through ether. Their dimensions change in such a way that the effect of motion through ether is always unobservable.

3.      Ether doesn’t exist (assertion of the special theory of relativity).


The correctness of these assertions has been debated for over 120 years. Neither of the participating sides has so far presented a convincing argument to back its position, though each thinks it is right.


It’s worth note that ether was originally assumed to be an immobile wave medium. Bodies were thought to go through ether, being its disturbed state, i.e. ether  freely passes through bodies moving in it. Ether was characterized as a luminiferous medium the speed of movement relative to which Michelson planned to determine with the help of his interferometer. The absence of the positive result of his experiment brought a justifiable question about the causes of inability to experimentally detect motion in ether.


The hypothesis of contraction of material bodies’ dimensions along the direction of movement made it possible to explain the absence of a positive result, but it proved insufficient because to be feasible it required introduction of another hypothesis about the slowing down of time. Lorentz tried to give a theoretical justification to this hypothesis but failed to find a phenomenon which could have demonstrated the nature of contraction.


Such phenomenon was found in 1981 following a theoretical analysis of the behavior of standing waves in the systems moving relative to a medium, and it was called “standing waves compression phenomenon”. In the light of the modern view on the wave nature of matter, the standing waves compression phenomenon was transferred to the electrodynamics of the moving bodies.




Fig. 53 Yuri Ivanov (1981 photo).


As a model, any solid body can be considered as a package of standing waves, with atoms in their nodes. Atoms are the sources of waves, and standing waves are the result of interference. Any displacement of a node is thought to provoke the inevitable shift of the appropriate atom.





Fig. 54 Velocity of a package of standing waves V=0 Dimensions of a package of standing waves with V=0,7ñ


If such package of standing waves is to change its speed relative to ether, the distance between the nodes is to change too according to (2.29). This would lead to contraction of the physical dimensions of the whole package, consequently the body itself along all coordinates:






, ,  – body dimensions with V=0


Now, calculating the expected change in the number of standing waves in the arms of Michelson’s interferometer, and taking into account contraction of its size, we find that the result will always be zero. Similar calculations of the difference of time of the beams in transit parallel and perpendicular to the arms when interferometer is turned gave equally zero result.


Hence, the contraction of interferometer’s dimensions is based on the physical phenomenon of compression of standing waves (2.29) which was transferred to material objects, assuming their wave nature.


The suggested approach differs from a formal FitzGerald-Lorentz hypothesis of length contraction by the fact that it’s based on the physical phenomenon: compression of standing waves.




Fig.55 Interferometer’s size change by Lorentz (left) and in accordance with compression of standing waves (right).





Fig.56 While the objects approaching the speed of light turn, according to Lorentz, into ‘flying pancakes’, according to Ivanov they turn into dots.


Lorentz hypothesis of length contraction was suggested exclusively for the sake of rescuing the idea of ether.


Ivanov’s contraction of dimensions along all coordinates is based on the physical phenomenon: compression of standing waves. Velocity increase triggers compression of an object.


The physical nature of the new explanation allows to talk about the special theory of relativity as an intermediary hypothesis advanced because of initial inability to explain the results of Michelson’s experiment within the framework of classic concepts. Now we have grounds to reject the Einstein’s principle of invariance of the speed of light and replace it with the principle of illusion of invariance of the speed of light (within the framework of new transformations of dimensions and coordinates such illusion is inescapable). The geometry of wave and inside-matter processes is such that the observer has no opportunity to detect through direct experiment violation of invariance theory due to a compensatory effect caused by compression of dimensions of moving objects.


Derivation of a formula describing the behavior of parameters of a standing wave in conditions of the system’s motion relative to a medium:


To substantiate the claim of discovery one has to observe a number of mathematical procedures, actually to solve the standing wave equation in the case when the emitter and reflector are moving in ether with equal speed V.




Fig.57 Emitters’ frequency is constant. With the device’s velocity increase relative to medium, and in accordance with Doppler’s rule, the direct and counter waves change their lengths ().  For the inside observer in the system which changed speed the frequencies of these waves will remain equal () but the nature of interference is to change, which is to lead to contraction of distance between the neighboring nodes, standing wave length change, and increased number of standing waves. The package of standing waves  compresses.


For the sake of better illustration the process of standing wave formation is split in three parts:


·        the upper draft shows direct and counter waves and dependence of their length on speed;

·        the middle draft shows the result of waves’ superimposition (resultant);

·        the lower draft shows the sum of resultants during the full period.


It was established that with the change of speed of the system ‘source-mirror’ the form of the resultant and the distance between nodes change too, which leads to compression of the package of standing waves according to the rule (2.29).



Derivation of a standing wave equation for the system moving in medium:





















   (see derivation below)


Putting  and  values in formulas (2.31) and (2.311) we obtain expression for  and  for any orientation of a standing wave in the moving system:






With  è     .           (2.33)

With   è    .       (2.34)


The time of the beam in transit forward and backward:




With  è         (2.35)

With   è        (2.36)


The time of the beam in transit forward and backward: .


Result:           (2.37)



Which means that:


1.      The moving object which constitutes a package of standing waves changes its longitudinal dimensions   times, traversal  times, which strictly matches compression of standing waves in these directions.


2.      The overall time of the beam in transit forward and backward along the arms of Michelson’s interferometer does not depend on the device’s velocity and orientation and is always equal to.


3.      The pace of time doesn’t depend on the system’s velocity and is equal in all identical systems, no matter whether they are moving relative to wave medium (ether), or stay put.


These formulas point directly to the solution of the problem linked with the negative results of Michelson’s experiment. Historically, it was the absence of a phenomenon which could have been used as explanation that made science adopt relativity theory which ends in a deadlock.



The scheme to calculate velocity of a wave front relative to moving source




Fig. 58


In which:


N – moving source

V – source velocity

Î – coordinate of the place where the wave front is emitted

ñ – velocity of wave front

ñ1 – velocity of wave front relative to N

ñ2 – velocity of wave front relative to N


Calculations of the wave front velocity relative to the moving source










Calculations results:






Let’s describe an acoustic experiment confirming validity of the discovered rules. There is a problem of transfer from the results obtained in acoustic experiments to electrodynamics. Had our predecessors (Michelson in particular) known about the compression of standing waves in acoustics they would have planned their experiments not to determine velocity in ether but to discover the compression of standing waves. In other words, the negative result would have been interpreted not as ether’s absence, but as confirmation of compression of interferometer’s dimensions. Now we know that experiment with the aim of discovering motion in luminiferous medium should be planned differently.


Experiment with the sound standing waves


In the summer of 1990 a series of experiments were conducted with the sound standing waves. The experiments proved beyond doubt that with the increase of wind speed relative to immobile emitter of sound oscillations and reflector (mirror) a compression of the package of standing waves takes place.



Fig.59 Calm weather (a) and strong wind (b). The sources of sound were powered from a single generator.


With the emergence of wind the lengths of sound waves and their velocities are changed according to the Doppler’s principle. The wave frequency in the system of sources remains constant.






The waves of different length but of equal frequency interfere, resulting in a standing wave the length of which




For ,




The waves of equal length and equal frequency interfere, resulting in a standing wave the length of which:






Fig.60 The key diagram of experiment with sound.


In calm weather a standing wave emerged between emitter 1 and mirror 3 (as a rule, experiments were conducted during a spell of quiet before a thunderstorm). With the help of indicator 2 a node of the standing wave, shown by unbroken line, was registered. With the emergence of wind the shift of control node toward mirror 3 was registered. The observed effect was interpreted as compression of the package of standing waves (the compressed package is shown by dots).




Fig.61. Block diagram of the device used in the experiment: 1 – sound generator; 2 – frequency multiplier (x4) serves to form a pilot-signal; 3 – mixer; 4,8 speakers; 5 – microphone to receive the pilot-signal; 6 – divider (); 7 restorer of the basic signal.


Mirror simulator made it possible to create a pseudo-coherent emitter and thereby extend the experiment’s base two-fold, which significantly increased sensitivity of the device.


The frequency magnitude of the driving generator was not important in the experiment. So it was set for the wave length to amount to 10 cm., while the distance between the speaker and mirror was 70 meters. With the emergence of wind a 5 cm. shift of the control node toward the mirror was registered which corresponded to wind velocity of 30 km/h. There were even greater shifts, but the main result of the series of experiments was the clear-cut rule: with the emergence of wind the package of standing waves compressed no matter whether the wind was blowing along or across the device.




Discovery of compression of standing waves and application of this phenomenon in electrodynamics of the moving objects in non-entrained ether has again raised the question of existence of ether as a wave medium.


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§ 2.06 The speed of light in one direction


Synchronization of the clocks’ pace


The task of synchronizing the running of the clocks A and B is limited to their start with the help of clock C moving with constant speed from A to B. The moment the running clock C draws level with the stopped clock A, the clock A is started in a way so that it should show exactly the same time the clock C shows. The moment the clock C reaches and draws level with clock B, the clock B is started in a way so that it should show exactly the same time the clock C shows. Thereby the synchronization is accomplished.






Fig.62 Synchronization with the help of the even transfer of the clock. Synchronization procedure for the clocks positioned in different parts of space is limited to the start of clock A and communication of its time reading to clock B via clock C by way of its even transfer.


Now, if synchronization has succeeded, one can begin determining the system’s velocity in ether.  To do this one has to register the signal’s time in transit from A to B by B clock which will be , after which from B to A by A clock which will be appropriately .







Equating the right parts




we’ll solve the equation relative to V




Having  assumed a random distance between the clocks A and B and measuring time of the signals in transit in accordance with the experiment conditions we can determine the system’s velocity in ether.


Thus one can solve more than a century old dispute about possibility of measuring the speed of light in one direction. Such experiment could either strengthen position of the theory of relativity regarding the existence of luminiferous ether or expose the theory’s faults.  It’s only experiment which is needed.


Experiment calculations


Solving this specific task we are to show that during synchronization of the readings of the clocks in different parts of space with the help of the third evenly going clock it doesn’t actually matter whether the pace of time in the moving clocks slows down or not.


Suppose the distance between clock A and clock B were 100 km.  Suppose the pace of time of the moving clock C depends on its speed following the rule , where . Suppose the speed of clock C transfer from A to B equals 100 km/h (0,02778 km/sec).


Then according to the clock C which moved from A to B clocks less time will pass: =3600 · 0,99999999999999571262= 3600,000000000015434568sec. Which means that clock B synchronized with the help of clock C will be behind clock A by


Suppose the velocity of the Earth were 30 km/h. and its vector were the same as the direction of imaginary lines between the clocks A and B.


Then the time in transit of the light signal from A to B by B clock would be =0,00033336667sec., and from B to A by A clock would be =0,00033330000 sec. If the clocks and combined with them sources of signals were orientated along the movement in ether, then with the Earth’s re-orientation in space due to its rotation along its axis and its movement around the Sun the  and  would change their values with the period of 12 hours.






The difference between the time of light passing distance AB with speed c-V  by clock B and distance BA with speed c+V  by clock A emerges in the 8th digit after dot – which is possible to register by modern instruments. It must be noted that clocks A and B have a presumed de-synchronization in the 11th digit after dot. This de-synchronization is too small to have a significant impact on the results of expected measurements.


Another option could be experiment without special synchronization of the readings of clocks A and B positions in different parts of space on condition that these clocks have maximally equal pace and thereby ensure the stability of frequency of the short impulses emitted by sources. The main task of the experiment is to detect the point (the spot) where impulses meet, being emitted by the source A to B and B to A. In the course of watching this point of impulses’ meeting its daily shift caused by the Earth’s rotation in ether is expected.









For example, with the Earth’s velocity in ether of 30 km/sec., the distance between the sources of 60 km and correspondence of the shortest possible line between the sources and velocity vector, the expected daily fluctuation of the point of the impulses meeting (crossing) would amount to ±3m. With the speed of solar system of 300 km/sec., velocity magnitude which some sources refer to, the expected daily fluctuations are to reach ±30m.



Fig.66. Experiments’ results depend on the Earth’s orientation to the motion in ether.


Conclusion. With existing theoretical possibility of detecting the system’s own motion in  electromagnetic wave medium (‘absolute speed’) it would be quite absurd to refuse the necessity of detecting such motion as well as deny the existence of the wave medium.


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§ 2.07 RD transformations of coordinates


According to Galileo


According to Einstein-Lorentz

According to Ivanov










One should make distinction between the contraction of dimensions and transformation of coordinates: dimensions refer to a real object, coordinate transformations – to mathematical manipulations to suit the principle of subjective invariance.


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§ 2.08 Lively standing wave


The ‘lively’ standing wave effect was discovered following the discovery of the standing waves compression.


While equality of frequencies is the main condition for the emergence of a standing wave, this equality is always realized when the falling and reflected waves are present. And it doesn’t matter whether the surface which reflects waves is moving or not.


For example, observer is placed between the two coherent sources. If his velocity is zero, he registers a regular standing wave. If the observer is moving in his reference frame the standing wave will be perceived as a beat (fig.71). But what is to happen if the wave reflector moves along with the observer?




Fig.67. Coherent emitters (). The standing wave moves along with screen; its parameters have changed. The standing wave with changed parameters exists only for the moving observer, that’s why we call it the ‘lively standing wave’. If the observer changes his speed, the parameters of the standing wave are to change too.





Fig.67.1 The standing wave also takes place when coherent sources are moving in wave medium. With the increase of the system’s velocity the distance between the nodes is to shrink and emergence of additional anti-nodes will be observed, i.e. a package of standing waves is to compress.




Phase displacement


Let’s examine the behavior of a standing wave emerging from wide-apart sources which are motionless in medium. A package of standing waves has emerged between the coherent sources. There’s no phase displacement between them too. In such situation the interference pattern will be symmetrical. Let’s mark the position of the central anti-node.


A phase displacement between the oscillations is created.  Apparently, the nodes and anti-nodes’ position is to shift relative to their initial position. (fig.68). With the growth of phase displacement nodes and anti-nodes of the standing wave are moving farther from their initial position, and with the phase displacement of 180° they’ll shift half of the standing wavelength. Further phase displacement will lead to further standing wave shift.




Fig.68 Phase displacement leads to the shift of nodes and anti-nodes.


If, by definition, the standing wave propagates no energy in space, then, changing the phase displacement, we organize such propagation: phase displacement between the sources leads to energy transfer in space between the two sources.


But constantly changing in time phase displacement between the sources means frequency difference




Which means that existence of frequency difference between the sources leads to the standing wave energy transfer from the source of higher frequency to the source of lower one. Energy transfer (flow) is taking place.


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§ 2.09 Frequency difference and the speed of energy flow


Watching the conduct of a standing wave in a situation when phase displacement changes in time, we found that increase in phase displacement leads to standing wave shift, while the constant phase displacement in time is nothing but frequency difference (2.48).


This relation shows that the more frequency difference the higher is the speed of standing wave shift. To determine this speed one has to find a moving system in which the standing wave shift will be absent. Which is only possible in a situation when in the moving system the waves coming from the sources have equal frequencies ().


Let’s explain it the following way.

Suppose we had two sources of waves with frequencies correspondingly  and . Suppose . One has to determine the speed of the system in which the frequencies  and  of waves coming from the sources are equal.




Fig.69 The observer has to move to implement the condition of frequency equality of the waves coming to him. In this case he registers the standing wave!


In the moving system we have





But , therefore




Let’s solve the equation relative to the speed of the system in which a genuine standing wave was observed:




The same is the speed of energy flow in the standing wave. But standing it is only for the observer who moves with the same speed as the wave does.


Rhythmus: Fig.69 shows different wavelengths. Which means different frequencies too?


Dynamicus: Relative to the moving observer the frequencies of direct and reflected waves are the same But we are dealing with the movement of the system in medium, which implies the Doppler effect. Hence these effects.




Fig.70 Frequency difference takes place (). The speed of energy flow and the speed of the car are equal. The passengers in the car observe a standing wave, and for them the energy transfer doesn’t exist. The observers outside see a complex wave picture which is not a standing wave.


Rhythmus: So, what you say is that there is a standing wave for those who are running or riding, and there is none for those who are standing or sitting?


Dynamicus: Yes, that’s the meaning of this phenomenon, and that’s what baffles everyone creating invariance illusion among moving observers, especially if they deal with electromagnetic waves. The significance of the illusion lies in the fact that nothing seems to change for the observer. Whereas actually all the phenomena and processes change, but in such coordinated way that it would be a real problem to detect those changes.


Rhythmus: But in electrodynamics we can measure the length of direct and reflected waves, and thereby detect changes…


Dynamicus: Unfortunately, I so far haven’t heard of experiments in which direct measurements were made of the length of traveling electromagnetic waves. We still estimate the length of the wave referring to the length of the standing wave, which is not the same, as you now know. The standing wave may emerge as a result of superimposition of waves of equal  frequency but of different, due to Doppler’s effect, length. So until now the general view of the standing wave should now be regarded as a specific case for V=0.



Now let’s go back this part of the standing wave definition which refers to the absence of energy propagation in the standing wave. And how electromagnetic standing wave is to behave? Will the energy flow inside the electromagnetic standing wave be in this case identical to the electric current in electricity cable? Let’s have a simulated experiment.




Fig.71 Frequency difference is absent. The flow of energy in the system of motionless observers is absent. In the system of moving observers relative to standing wave the energy flow exists. The of energy flow velocity equals in modulus the car velocity.  Could it be the source of de Broglie waves?


Suppose we had two sources of electromagnetic waves (300mHz) set wide apart in space. A standing wave emerges between the sources of equal frequency. The observer putting a neon indicator in the node would register absence of energy flow. Which means for us that the energy flow speed both relative the observer and wave medium is zero.


The position of neon indicator is fixed in the node. Let’s increase the frequency of one of the sources by 0.1 Hz. The standing wave would start moving slowly. Which will be visible from the increasing brightness of the neon indicator. Theoretically, the speed of such transfer will be:




The velocity magnitude is not big, so one can observe the node’s transfer by ‘catching’ manually the node with the neon indicator and following it. The speed of indicator following the node will be close to the calculated one, i.e. 5 cm/sec. If frequency difference were increased ten times, which is to amount to 1 Hz,  the speed of node transfer, as well as the whole interference process, will also increase ten times reaching 0.5 m/sec. For us it would mean that the speed of the energy flow in the standing wave equals 0.5 m/sec.


Suppose, the observer were moving in the same direction with the same speed (0.5 m/sec) with which the standing wave is moving. Relative to the moving observer the nodes and anti-nodes would be immobile, therefore he registers absence of energy flow. He also registers that the waves coming to him have equal frequencies, i.e. he doesn’t detect frequency difference.


Rhythmus: One can catch up with electric current in electricity cables, it seems, right? If the commuter train were moving with the speed of current in the cables, the commuter’s electric engines would stop running, right? And how about the alternating current? What is its speed?


Dynamicus: One shouldn’t mix up the electric current and the current created artificially by electromagnetic energy. The given example shows clearly how the energy flow is formed and why the speed of this flow can be different. As for the alternating current, it is the same old direct current moving in reciprocating fashion. To understand this one has to carefully examine the work of electric generator. Than it will become clear that it’s not the current but information signaling the start of the motion or the change of direction of the current in the medium which propagates with the speed of light.



Apparently, significant increase in frequency difference would lead to significant increase in the speed of the energy flow. For example, the two-fold frequency difference (, ) would produce the energy flow velocity of




If anti-nodes of the standing wave were rushing past us at such speed, the energy transferred by them would look to us like a continuous flow. But now we know that this flow has a definite speed and understand why this speed differs from the maximum possible magnitude which equals the speed of light. We also know why the energy flow always moves toward the source of lower frequency.


Here’s a real life example. “On Feb.14, 1996 an energy disagreement took place in the single energy system of Russia and Ukraine. Following a suspension in the work of atomic power station in southern Ukraine a frequency lowering took place in Ukrainian part of the energy system which triggered the influx of energy from Russia where frequency was higher. To preclude energy losses the Russian side was forced to switch itself off Ukraine.”


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§ 2.10 On nature of electric current


Let’s consider the content of this paragraph as a hypothesis based on the results of examining the issue of the speed of electromagnetic energy flow.


Assuming that direct electric current emerges due to natural frequency difference of materials used, say Cu-Zn, one may be tempted to determine the direction of movement in the circuit. But here the researcher may run into difficulties. First, the energy flow may be formed at various frequencies simultaneously which would lead to the energy flow with indefinite speed (its speed will be higher at some frequencies, but lower at others).


Here’s a simulated experiment. Suppose, we had two similar sheets of copper suspended on kapron strings near each other at the same height from the Earth. Let’s measure the difference of electric potentials between the sheets with the help of a sensitive device, for the purpose of which one has to connect the device preferably simultaneously to both sheets.

After which one of the sheets is replaced by a zinc one, and measurements are repeated.


The following results could be expected:


1.      In the first case when electric potential was measured between two sheets of copper no current was registered.

2.      When electric potential between copper and zinc sheets was measured the device registered a brief presence of current.


What’s the cause? Why is there no current between the sheets of similar material, and emerging current between the sheets of different, zinc and copper, materials?


To explain the absence of current in one case and its emergence in the other let’s go back to the previous paragraph where the cause of energy transfer is explained by the frequency difference between the sources. Which means that copper sheets at their atomic level have equal frequency parameters, while zinc-copper sheets have different frequencies.


The same method could be applied to test all elements of Mendeleyev periodic table.





We are paying much attention to standing waves because within the framework of rhythmodynamics’ methods they are the main link and measure during self-organization of systems. With their help we are to model the processes participating in formation of these systems’ transfers, emergence of inertia properties and force interactions between the elements of the system, and between the systems.




Rhythmodynamics helps create the models of phenomena. One of those phenomena is compression of standing waves which gave justification to renewed interpretation of the results of Michelson’s experiment. It was convincingly shown that rejection of the notion of wave medium (ether) proved unsubstantiated. A new model of Michelson’s experiment interpretation was proposed based on the system of oscillators in the wave medium.


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Chapter 3. Fundamentals of Self-organization


Self-organization is a way of the world’s existence. But what lies at its basis, what processes ensure self-organization, what’s its mechanism?


Any action understandably requires energy. Comparing those energies they talk of some measure, but so far no answer has been given to the question: what is energy, where’s its source and what are the source’ intentions?



§ 3.01 Energy as measure of motion


Energy is the universal measure of motion of matter, i.e. a certain magnitude showing how much motion is present in this or that object at a given moment, irrespective of the nature of motion. Any transfer in wave medium is regarded as motion.


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§ 3.02 Absolute and relative aspects of energies


The postulates of modern physics and theories based on them do not allow for absolute notions: energy, speed, time, frame of reference. The postulates of rhythmodynamics and wave geometry, on the contrary, suggest impossibility of creating a clear physical picture of the world without the carrier of constructs in geometry and wave medium in rhythmodynamics. The advantage of rhythmodynamics’ approach is in its ability to use both absolute and relative notions. For example, the objects’ speed in wave medium is absolute, the speed between the objects is relative. The same applies to energies: the higher is the  object’s speed, the greater is the absolute value of its kinetic energy; if another similar object were moving alongside it, we, comparing kinetic energies, could only speak of their difference. In that case kinetic energy is only relative. One should constantly remember that any relative magnitude is the result of the difference of two absolute magnitudes. For example, the relative speed of two planes 100 km/h. which means equation for a simple case  where V1 and V2 are velocities relative to air (for planes this velocity is the absolute parameter). The frame of reference linked with air is absolute for a plane, but if you are inside the plane and see no outside points of reference you cannot say anything about the plane’s absolute speed. It can be any.


We think the world around us exists in the form of electromagnetic waves. We cannot say with any certainty that at this level of its organization its phenomena are realized by continuum, so it would be more appropriate to speak of electromagnetic wave medium as the closest foundation. It’s this foundation which should be called absolute reference frame (ARF) because for material and other wave objects of our world it performs the same role of the air for the plane. Then all movement should be regarded as taking place in electromagnetic medium relative the reference frame linked to this medium. The tricky question of determining one’s own speed in wave medium emerges. The modern level of development of the standards of measures allows to solve this task, which is actually limited to determining the speed of light in one direction.


Rhythmodynamics regards energy as ‘capacity’. This capacity can be potential, hidden till the necessary moment, or kinetic. Kinetic energy is always linked with motion and in rhythmodynamics is divided into ‘absolute’ and relative. This is connected with wave medium which plays the role of the foundation for the objects present in it. The system of coordinates playing the role of absolute reference frame is linked to the medium.


To reveal the mechanism’s essence of kinetic energy, i.e. to transform of the notion of energy into model ideas at the level of processes, one has to solve two basic problems:

1)      to establish processes which trigger the self-organization of similar elements into objects;

2)      to establish parameters and their changes which self-organize the motion of objects.


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§ 3.03 Self-organization of wave systems


All objects in nature, just like the nature itself, are self-organizing systems. There are many examples of self-organization both in macro and micro worlds: self-formation of galaxies and planetary systems of the Sun type, crystals’ growth, chemical reactions, the growth of living organisms, social processes. But how exactly does self-organization proceed, what processes lie at its foundation, are there general algorithms?


For example, atoms in bodies have no direct contacts between each other being quite apart from each other and form space lattice. There’s only one possible explanation to such atomic ties: they are connected with each other by electromagnetic wave fields. The sources of those fields are atoms themselves and their nuclei.


But how does this tie between atoms emerge, on the one hand, capable of keeping them at a certain distance from each other, i.e. preventing their merger, on the other, preventing them from darting apart?


Before we begin examining this important issue, let’s clarify the meaning of the terms: wave source and oscillator. Oscillator in our view is a geometric object, a dot; a source of waves is an object of rhythmodynamics of the smallest possible dimensions. While with the help of dot-sized oscillator the researcher may detect position of potential’s hole in the carrier of constructs, i.e. while the oscillator, by condition, follows in the wake of the hole, the wave source, which has dimensions, acquires ability of assessing gradients which lead it to the nearest potential’s hole. It’s worth note that wave geometry is the basis of rhythmodynamics.


Here’s a typical example for detailed inspection.


Suppose, there were two sources of waves positioned within the range of each other’s emission with in phase oscillations. The waves are coherent, have no frequency beat, and form a standing wave between the sources. The sources have occupied stable positions in dynamic holes of potentials (areas of comfort) at a distance of one standing wave length. An elastic tie has emerged between the sources. Let’s examine the processes which take part in this tie formation.


Three objects are taking part in the process: two sources and wave medium (in wave geometry – two oscillators and carrier of constructs). The waves emitted by the sources after their departure become independent formations, i.e. have no link with the sources and exist on their own. The waves intersect and form a field of alternating amplitudes in the shape of nodes and anti-nodes, while along the imaginary line between the sources a standing wave emerges.


We presume that for a source the standing wave node becomes area of stable balance, a potential’s hole, the area of comfort. The source can react only to the wave field around it, and if this field has parameters’ gradient, the source starts moving toward the lesser magnitude parameter until it reaches the area of absent gradient. The source perceives this process as unequal wave pressure around it driving it to the potential’s hole.






Two sources of waves are in the nodes of the standing wave they’ve created. The nodes are areas of stable balance for the sources. In these areas the gradient of the wave field energy is absent.






Attempts to bring the wave sources closer, i.e. to take them out of potential’s holes, lead to the reaction of the standing wave aimed at bringing the sources apart. The reaction lasts till the sources are again in the balance areas.






Attempts to separate the sources, i.e. to forcibly bring them out of the balance area, lead to the emergence of the in-ward emission field which is seeking to bring the sources to their nodes.






The farther the wave sources from the potential’s holes the stronger is the impact of the wave field on them. The field is seeking to bring the sources to potential’s holes.






One has to exert effort to separate the sources. Which will take them to areas of unstable balance, i.e. on the crests of not fully formed standing waves. Beyond this border the sources will experience the pulling apart forces. At this moment attraction between the sources is replaced by separation.






Moving away from the center under the influence of the pulling apart forces, the sources will soon form another two standing waves and slide into new nodes, i.e. new areas of stable balance (potential’s holes).






Let’s go on pulling the sources apart – this would again lead to their unwillingness  to leave the potential holes expressed, as before, in emergence of external wave field and its resistance  to the effort.


That’s how self-organization process looks in which the minimally possible system consists of two sources and a wave field between them in the form of the standing wave anti-nodes. Such system can be called ‘RD-dipole’ (rhythmodynamics dipole).


Rhythmodynamics dipole is a system of two sources held together by the energy of the standing wave in the nearest areas of stable balance. RD dipole is the least possible in nature self-organizing system and presents the simplest model of a physical body.



Any two coherent sources are self-organized in the system. The distance between the sources is set according to the rule , i.e. there is always uneven number of standing waves between them. But the sources may be out of phase too.


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§ 3.04 Self-organization and phase displacement


Henceforward we are to use the term ‘oscillator’ attributing to it the properties of the wave source.


Let’s examine a system in which two coherent oscillators are set in the nodes of one standing wave. Let’s use the notion of ‘phase displacement’. The phase displacement between oscillators manifests itself in de-synchronization of their oscillations. If phase displacement is absent, oscillators’ work is synchronized, i.e. they emit simultaneously the waves of equal in magnitude amplitudes. Phase displacement implies that waves are emitted with certain fixed amplitude shift: lead or delay.




Fig.79 In phase oscillators




Fig.80 Out of phase oscillators. Phase displacement


Absence of phase displacement in the system implies absence of transfer of this system in wave medium. Phase displacement, on the contrary, makes the system move in the medium following the rule:




If the system moves (no outside force is exerted, i.e. supported by the phase displacement) the distance between oscillators diminishes:






,                                     (3.03)


i.e. the distance between oscillators depends on the speed of the system.


Which implies that with the change of the system’s velocity from zero to V the oscillators are influenced by the forces of interference nature: in motion, the standing wave shrinks, the distance between the nodes diminishes, and oscillators watching the nodes’ position follow in their wake.


Let’s examine relation of the phase displacement and speed. For the purpose of which we’ll choose a situation in which a phase displacement was made between the motionless oscillators (fig.82).




Fig.81. That’s how the system of oscillators looks (, ) in which the parameters of phase displacement and speed are interrelated according to the rule




Fig.82 Phase displacement between oscillators is  which made the standing wave move right.


Relative to oscillators the potential holes shifted right. The anti-node began exerting influence on the right source trying to move it toward the diminishing amplitude. On the left source influence is exerted by the emerging external field moving the oscillator into potential hole.






When such system () acquires a chance of free movement (with fixed distance between the sources), the system will start moving right with speed . The distance between the standing wave nodes will contract according to the rule  which will lead to difference in position of oscillators and the nodes. Forces have emerged seeking to place the oscillators in the moving potential holes.






If the distance between the oscillators becomes no more fixed, then, under the influence of external wave forces they are to move to potential holes, and the distance between the oscillators will equal precisely the length of the standing wave (fig.84).



The phase displacement leads to the shift of potential holes relative to the sources in such a way that the system’s motion with constant speed becomes its stable condition. Thus, the phase displacement breaks the inner balance of forces which can be restored only by motion. Such motion is even and rectilinear, and therefore looks like motion by inertia.


If for any reason the phase displacement between the oscillators changes, the system’s speed changes too. Evenly increasing phase displacement would result in speed growth, i.e. the system would self-propel with acceleration. It must be stressed that it doesn’t matter whether the phase displacement was caused by some external factor or the system developed some internal causes.




But phase displacement in time means frequency difference . Having transformed the 3.04 formula we have:




To get the notion with magnitudes of what order we are to deal with in practice, let’s calculate the frequency difference  between oscillators when: the system moves with acceleration , the speed of waves propagation .




Let’s also examine the case with absent phase displacement between the sources forcibly moved to the right with certain constant speed.




Fig.85 , .


Deformation of standing wave develops in such system: it moves left of the sources, and additional wave field emerges to the right. On the part of the anti-node and the wave field which emerged to the right the force appears applied to the sources and preventing the system’s transfer.


To transfer this system in wave medium is impossible without resistance. The system with no phase displacement would resist any transfer because it seeks to avoid any deformations which is possible only with zero velocity relative to medium. That’s how inertia emerges.


Its unwillingness to change the motion regime is due to the system’s inability to change phase relation. The emergence of phase displacement, on the contrary, would make the system move. As you can see, the speed of transfer and phase displacement are interrelated parameters:


,                                                   (3.06)




if ñ = 299792458 m/sec. and ð =180°, then





The correlation of the system’s speed and phase displacement between the oscillators  () is constant and equals the ratio of the speed of wave propagation in medium to a half-period ().


If the system resists action aimed at changing the speed regime, they refer to inertia as a measure of reaction to action. In the case herein examined the action applied to the system implies an impulse giving the system additional amount of motion.




The formula shows that the impulse is proportionate to the phase displacement, while the ratio  is a sort of coefficient which might be called a ‘mass quantum’ i.e. with m= 1



where the the minimally possible mass (mass quantum)




There’s incentive to introduce a notion of ‘rhythmodynamics mass’





measured in [kg·m(/sec·radian)]


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§ 3.05   Kinetic energy


Relation between speed and phase displacement allows us to take a different look at the ‘kinetic energy’ notion.


As energy is attributed with ability to do work, and work is linked with such notion as ‘force’, let’s examine the notion of ‘force’ as well.



















The 3.17  formula differs from the usual () in its right part which shows clearly the gradient-phase nature of kinetic energy (i.e. the inside system processes which provide this energy). The mass coefficient of proportionality (m) shows only the number of elementary systems which remains constant with all possible phase displacements and, consequently, with all velocities matching those displacements. Mass is a quantitative measure (expressed in ‘things’) of elementary systems in object and therefore, whatever velocity regime this object might have, its mass is always constant because the number of oscillators and systems they form cannot change without a cause.


The presence of phase displacement in 3.17 formula corresponding to a certain magnitude of speed V indicates the system’s intention to have precisely this speed. If the free movement is obstructed the system would exert constant pressure on the obstacle with a certain constant force. I.e. if this system is restrained its kinetic energy should be regarded as potential seeking to become kinetic. Such system has inner necessity to move, and the energy which provides this necessity is called potential. Potential energy is transformed into kinetic one if the system is no longer restrained.


Under condition ,  the energy is kinetic




Under condition ,  the same energy is potential




When 3.17 and classical  formulas are compared, the latter in no way indicates the root-cause of energy, whereas the rhythmodynamics approach  shows processes responsible for motion as well as kinetic energy notion. It shows a unified mechanism of kinetic and potential energies which is essentially the presence of internal phase displacements. These displacements, in cases when free movement is obstructed, become manifest in the form of the inner propulsion force (in the form of propensity to move).


 * * *


Now we have a model notion of the processes responsible both for kinetic and potential energies as well as motion. Which means one can test experimentally the correctness of rhythmodynamics approach to the means which provide motion. It’s obvious too that if wave medium doesn’t exist in real experiment we won’t be able to create a self-organizing system in space, to say nothing of making it propel by controlling the phase correlation between the active elements of the system.


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§ 3.06 Wave model of elastic object


Simple model and real experiments show that wave systems have a propensity to form (self-organize) in space lattice structures, similar to structures of physical objects.


For the self-organization to take place and the ties between the sources to acquire elasticity wave medium is required, as well as oscillating sources and emergence of standing waves between them.


The sources are in phase and form a model of artificially elastic body comprising numerous macroscopic elements positioned at macroscopic distances from each other and elastically tied together by wave fields. This is the most simple example of a system which is self-organized in time and space. This object has certain dimensions, it can move and undergo accelerations as any natural object. The wave fields and forces uniting the elements into a single object are not deeply hidden in the micro-world, so we have a chance to objectively examine such issues as: how and why do the object’s dimensions depend on its speed; how do the phase displacement and frequency difference trigger object propulsion and determine its speed.


Let’s start with the fact that every source (oscillator) reacts only to those changes which emerge in close proximity. The waves departing from the sources are objects of their own, i.e. at the moment of their emission and departure from the source they sever ties with it. Potential’s holes in the form of the standing wave nodes and areas of unstable balance in the form of the crests of anti-nodes emerge in interference field.


Stable balance is a state when after a small alteration of the object’s position forces emerge in the system seeking to bring the system back to balance, and the balance is not broken; the body returns to position of balance while disbalance is not increasing with time.


Unstable balance is a state when after a small alteration of the object’s position balance is broken, the object does not return to the position of balance and balance displacement is increasing with time.



If at the moment of interference field formation the sources are outside potential’s holes, the interference field drives them into the nearest potential’s holes. During their transfer the sources continue emitting waves, the interference field is changing in the wake of the moving sources. This happens with some lag due to the finite speed of waves in medium.  During this lag interval the position of potential’s holes changes as well.





Fig.86 Areas of stable (potential’s holes) and unstable balance.


A situation emerges in which several wave sources are seeking to find and occupy the nearest potential holes in their own constantly changing interference field. This process can end in formation of a stable system with elastic ties between the elements, or in disintegration of as yet unformed system.

I wonder if modern mathematics is able describe the process of the sources’ search of potential holes, as well as other transformations connected with the self-organization of numerous wave sources?


Nature is unaware of the man-made math. What is natural there can be extremely complicated in mathematics. But there’s other little known way of calculations. With its help one can describe behavior of numerous sources during their self-organization. Unfortunately, this method cannot be explained briefly; it demands special explication.


Suppose, self-organization took place of an artificial stable object the active elements of which became set in potential holes. Such object with initially set parameters () develops a problem with motion in wave medium. Potential holes in which active elements are set are formed by wave fields radiated by other object’s elements from other positions. The waves are moving with finite speed, therefore any changes in interference field are not instantaneous, but delayed. If the artificial object, i.e. all its active elements, were moved, the potential holes would be moving with some delay, i.e. they would be lagging behind the elements. The elements would be bumping into those potential potholes; thus forces emerge which impede progress. There will be no motion by inertia.


Until something changes, the work of restraining forces won’t stop, and the elements won’t move in holes and in agreement with them.  Until something changes, the object would be moving as long as external forces are applied to it; the fields (potential holes) would be always lagging behind the elements and forces would be active, pulling the elements back to stable positions.

To prevent these inhibitory forces from appearing the potential holes must emerge where elements are expected to be prior their movement. What changes should occur for this to take place, and how can these changes be organized?


As we already know there’s relation between velocity of movement and phase displacement. It’s this phase displacement which can secure the synchronized movement of the elements and potential holes. In such case the motion in wave medium will proceed without hindrance.  What is needed is a compulsory control over phase correlations, or self-synchronization of phase relations.




Fig.87  Phenomenon of mutual synchronization of auto-oscillations is well-known among radio engineers. Those who do not know this phenomenon can consult a mathematical equation which is not difficult to record for the simple generator scheme shown on the picture. An electric dipole in the form of two balls can be connected to the circuit as it’s shown on the picture, the coil can be screened, and we’ll have Hertz’ oscillator.


Self-organization would be complete and artificial object closer to natural if oscillations in the elements were autonomous and also subject to self-synchronization, i.e. automatic matching in frequency and current phase with other elements.

Such system could be created by means of radio engineering.


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§ 3.07 Properties of artificial elastic bodies


Velocity – phase displacement dependence


If artificial object is made on electromagnetic foundation, i.e. its elements are active resonators, the speed of motion of such object will depend on the phase displacement between the resonators. Let’s calculate phase displacement needed to provide the object’s velocity of, say, 1 km/sec.



Which doesn’t mean that our artificial object would immediately tear off the place picking the required speed; the forces of electromagnetic ties are not so big. But the object would have a propensity of picking the speed precisely due to the shift of electromagnetic potential holes ahead of resonators. Here the phase displacement would create a situation in which potential holes move first, while resonators and the object follow in their wake as a consequence. The problem of direct experimental testing is that the open space of cosmos is required where the impact of external forces is minimal.


The experiment could be also staged in some dense medium, say, water. Two options are possible there: on surface and underwater. Fig.75 shows experiment on surface with two oscillating floats with controlled phase displacement.






The experiment’s goal was to confirm theoretical conclusion about dependence of object’s motion velocity on phase displacement between its elements. The example of artificial body proved the correctness of conclusion: phase displacement was created between the elements of the system which brought it into motion.


In the second half of 19th century Carl Anton Bjerknes staged an experiment with pulsating under water drums. Later similar experiments were staged in air which proved that phase displacement does affect sources behavior.


In the middle of 19th century Norwegian physicist Carl Anton Bjerknes (1825-1903) proved that two pulsating balls with radiuses too small in comparison with the distance between them, being submerged into (non-compressible) liquid, can trigger either attraction (gravitation) or repulsion (anti-gravity) to each other. The balls were attracted with a force directly proportional to the product of pulsations’ amplitudes and inversely proportional to the squared distance between their centers in the case when frequency of pulsations and their phases coincide. If pulsations’ are in opposite phases attraction is replaced by repulsion. (V. Bjerknes. Lectures on hydro-dynamical long-distance forces according to theory of Carl A. Bjerknes, 1990). It should be emphasized that these are the same bodies but with different frequencies. The fact must be pointed out that the experiment was staged in practically non-compressible medium, liquid, i.e. in his experiment Bjerknes dealt not only with ideal conductors of waves and frequencies, but with objects which were in a state close to weightlessness.


According to Bjerknes, for attraction, balance or repulsion to become manifest, pulsation must take effect in the following cases:

·         pulsation of all particles must coincide in frequency and phase;

·         intensity of pulsations should be proportionate to their masses.


The effects of the drawn up hydrodynamics theory of gravitation at the level of  frequency-wave modulation were demonstrated by Bjerknes in 1861 at Paris electrical exhibition when two pulsating under-water drums attracted attention of some scientists. In 1885 another scientist Pierre Leahy found that in a compressible medium the work of two balloons pulsating with equal frequency and phase changes its character if the distance between them exceeds half of wavelength. Therefore to correctly explain gravitation through Bjerknes’ pulsation one had to assume ‘ether’ of cosmic space as absolutely non-compressible – which was difficult to imagine, regarding ‘ether’ as some kind of matter.


In 1898 positions of Bjerknes theory became much stronger after Wilhem Weber  found that all pulsating objects have a remarkable propensity for self-regulation: the forces which excite waves in medium quickly bring the pulsation of interacting masses to synchronism, even though such synchronism was absent before. Weber came to conclusion that the structural elements which made up the matter pulsate due to their own physical nature, and these pulsations automatically bring about synchronism, which leads to realization of Bjerknes’ second condition: direct proportionality of pulsations’ intensity to the magnitude of masses of pulsating objects. It must be noted that the physical cause of interaction (gravitational property of additivity) was comprehended at the level of mechanical notions.


Functionally, the hydrodynamic model of interaction (gravitation) at the level of frequency-wave processes was a perfect explanation of all at the time known gravitational effects, bringing them down from the level of interaction  of immeasurably large objects to actually microscopic level. Moreover, it amply explained not just the nature of gravitation or balance of interacting bodies, but also predicted possibility of repulsion, or anti-gravitation, which was unusual and revolutionary in its ramifications and surpassed the ideas of modern physics.


From these positions by the early 20th century  Bjerknes’ theory could be regarded the leading mechanistic theory of gravitation (mechanical ideas of Newton still have their grip on modern physics) which had unquestionable advantages over all other known at the time interpretations of physical nature of gravitation or interrelations in material world. Everything tapered down to experimental discovery of ‘ether’, material with properties which Bjerknes required, in particular, its absolute non-compressibility. Appropriately, the modern physics of the 20th century which unequivocally proved absence of any ‘ether’ – naturally, in its mechanistic interpretation of the notion – dealt a lethal blow to gravitational hydrodynamics.



There are analogies in the living world too: to propel in medium microorganisms can use their own vibrations. There are such among the hydrobionts: noviculae, oscillaria, pinnularia. Hydrobionts have attracted attention for two reasons: 1) absence of the means of propulsion in their environment 2) the mechanism of propulsion in their environment is not precisely clear.




Fig.89 Naviculae (left), oscillatoria (right).


Naviculae is an organism in the form of a quartz shell with cavities inside filled with live tissue.  The live tissue is supposed to generate electric potentials which the quartz shell transforms into high-frequency vibrations, which are transmitted to water in the form of waves.  A high-frequency acoustic interference field with two (according to the number of emitters) potential holes emerges around naviculae’s body. The emerging phase displacement between the shell’s ends shifts potential holes relative the emitters which triggers the noviculae’s propulsion. In other words, it’s a self-propelled organism.


Oscillatoria is an algae whose parts are self-propelled in its environment (water). Biologists are not unanimous about the mechanism of oscillatoria’s propulsion. The algae is thought to excrete a mucus in which it slides.


Object dimensions depend on velocity


Michelson’s experiment is still one of the key questions of science. There are several hypotheses explaining its results, but none of them have a model illustration, nor do they show precisely how the end result is nullified.


If one knows the relation between the standing wave length and velocity one can apply this phenomenon for the standards of measure and condensed objects. One can also create artificial elastic objects in various mediums to demonstrate dynamics of relation between these objects’ dimensions and velocity. The working model, which has no practical use, is quite complex to adjust, so we’d better limit ourselves to simulated experiments and computer modeling.


The distance between the standing wave nodes depends on velocity. In the artificial object the nodes play the role of potential holes, i.e. when motion in medium begins the distance between the holes shrinks and the object’s elements are affected by the forces of interference nature, which bring these elements together. Consequently, the object’s dimensions diminish. Such is the mechanism’s cause of reduction of dimensions of the moving objects.


One cannot discover directly the reduction of dimensions in Michelson’s experiment because all bodies and standards of measures change their dimensions synchronously and proportionately. This is the consequence of internal self-organization of all bodies in nature.


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§ 3.08 Inertia is the property of system


Definition of inertia: body propensity to resist the impact on it until its elements capable of self-synchronization enter a new regime of self-synchronicity.


How does it take place?


At the moment of the start of motion the active elements of the body shift relative to potential holes, i.e. potential holes drag behind the elements. Inertia, or resistance to impact, would continue until the elements’ phases become adjusted to the state of motion. Which takes time because waves in medium spread with finite speed.


The object has a ‘feel’ of inertia when force is applied not to all object’s elements at once, but to some of them. If it were applied to all at once as is the case with gravitation, the feeling of inertia would be absent.


Using the example of a simple system of oscillators we could describe the process of inertia formation the following way.


Let’s act on an oscillator with the aim of moving the system. The oscillator will shift, and the length of the wave it emits is to change too. The other oscillator in the system stays in place until it receives a signal from the first oscillator in the form of the wave which has changed its parameters. The altered wave which has reached the second oscillator will exert its influence by changing the position of its potential hole. The oscillator will shift in space and the waves it will be emitting during this period will be of different length. But the first oscillator continues resisting the impact on it. When the wave from the second oscillator comes back to it its potential hole will shift, and resistance will be over.


Conclusion: resistance to impact (force of inertia) on the first oscillator will last as long as it takes to transfer this oscillator and send a signal about the end of this transfer to the second oscillator and back, i.e.






 – time of impact on the system

 - number of standing waves between the extreme ends of the system.


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§ 3.09 Model view on self-propulsion of molecules


Because of their miniscule dimensions, no one has seen yet either the structure of molecule or atom. The hypothetical schemes of these formations are built on the basis of indirect, obtained by instruments, signs which disclose both behavior and properties of atoms and molecules. One of their properties is self-propulsion.


Let’s examine the cause of self-propulsion using the example of water molecule (Í2Î). Under normal conditions one might expect that the bonds of oxygen atom with two atoms of hydrogen in Í2Î molecule form at the central oxygen atom a very obtuse angle, close to 180°.  Surprisingly enough, this angle happens to be not 180°, but only 104°31'. Which makes the inner molecular forces not fully compensated and their excess manifests itself outside the molecule. Brownian motion is thought to be one of those manifestations.





Fig.90 Brownian motion, random fluctuations of tiny particles suspended in liquid or gas under the impact of  colliding molecules of environment, was discovered by Robert Brown.


Outwardly, the molecules which exert their influence on a particle seem to have a self-propulsion propensity. The motion is characterized by kinetic energy. But is it Í2Î internal energy? If so, where does it come from and how is it produced? Besides, can we speak of self-propulsion properties of a single molecule of water, being isolated from the rest of water molecules?


If self-propulsion is a forced reaction of the system to the contradictions between its elements, in this case they can be created and maintained artificially or can be the consequence of the system’s constructional peculiarity.


If the elements of a system are the sources of waves in wave medium, and their elastic ties are realized by standing waves, then any internal contradictions in the form of phase displacement and frequency difference violate synchronicity and consequently make the system liable to move.


Self-propulsion is an inner-motivated involuntary change of the system which is determined by its contradictions indirectly reflecting the impact of external factors and conditions. The conception of self-propulsion in dialectic materialism regards inner causes as the source of self-propulsion. They are, first of all, contradictions ascribed to all objects with systemic structure, or other forces, for example, interaction of isolated components of the system. The influence of external conditions on individual self-propelling system is brought indirectly through internal sources. Self-propulsion connected with direction, irreversible changes, presents a special kind of self-propulsion, self-development. On this issue the concept of Self-propulsion matches the general dialectic concept of development in which “…the main attention is paid to studying  the source of self-‘propulsion’” (V.Lenin. 5th edition, volume 29, p.317).



The RD modeling of Í2Î molecule as a system of active sources (oscillators) corresponding to two atoms of hydrogen and one atom of oxygen presumes that interaction of atoms-oscillators of different phase-frequency parameters is taking place. The combination of those phases and frequencies is such that emergence of a stable system becomes possible. Hydrogen atoms may be in phase, their frequency parameters are different from those of oxygen atom. That’s why building a model we ascribe equal frequencies to H-oscillators, and a different frequency to O-oscillator, which is proportionate to a distance between O-oscillator and any of H-oscillators.




Fig.91 The draft of the water molecule structure: molecule’s geometry and electrons’ orbits.


If H and O frequencies were equal, in space these atoms would occupy symmetrical positions.






Distribution of wave energy in a system of three in phase sources which are set in potential holes. The energy is localized symmetrically in the area between the sources.







Phase displacement between the sources triggers re-distribution of the wave field energy both inside and outside the system, violation of symmetry in relations (loss of synchronicity) and development of propensity to motion. The system with phase displacement has two options: either 1) to eliminate the phase displacement by auto-adjusting the oscillations of its sources to the oscillations of the system or 2) to neutralize through motion the internal tensions which emerged.  Both options trigger changes in the system’s motion regime.



The distance between oxygen atom and hydrogen atoms in a water molecule is 0,96Å, while the distance between two hydrogen atoms is 1,5Å.  If these distances were considered the standing waves lengths, then the wave linkage between two atoms of hydrogen is realized at the frequency of 1,0·1018Hz, while the oxygen-hydrogen linkage has the frequency of 1,56·1018Hz. To have a visual notion about the wave field, or rather about distribution of wave energy, one has to process this data by a special computer program. It produces a picture in which asymmetry is clearly visible.





Fig.94 RD model of wave energy distribution in a water molecule.


According to RD model, the distribution of energy in Í2Î molecule is always asymmetrical. Synchronicity is violated in its design, and therefore this violation can be neutralized only through motion.


The model of a water molecule indicates the inherent asymmetry of energy distribution, and therefore the ‘design’ disbalance of internal relations between the sources. The water molecule is destined to self-propel, i.e. self-propulsion is its natural state. What’s important is that this model allows us to at least have an idea as to why and how, through what internal contradictions and inconsistencies, such self-propulsion is implemented.





Fig.95 Model presentations of the energy distribution in Í2Î molecule


Lots of things in self-propulsion still remains unclear. The question arises, for example, how, if self-propulsion were recognized, should the law of preservation of energy be treated? * The system’s velocity increases without any visible cause, so where does the energy come from? The simple way of explaining a sustained motion in the micro-world is a phase displacement, or frequency difference, i.e. the so-called inherent energy notion is exploited. But let’s not forget that we are dealing with the model illustration of a hypothesis.


* In a closed system in which no forces of friction and resistance exist, the sum of kinetic and potential energy of all objects in the system remains constant. The full mechanical energy of the system of objects remains unchanged in the process of their motion if external and internal forces applied to the system of objects are potential.


The law of preservation of energy is one of the fundamental laws according to which the most important characteristic, energy, is preserved in a closed system. All known processes in nature obey this law. In a closed system energy can only be transformed from one state to the other, but its quantity remains the same.

In an open system energy can change with the same parallel change in the energy level of the objects around the system, or with a change of energy of system’s interaction with the surrounding objects. The energy change in the course of the system’s transfer from one state to the other does not depend on how (by what means and interactions) this transfer is implemented. The change of energy in the system occurs when work is performed, or when a certain amount of heat is transformed to the system.


If wave medium is an element of the system, as RD stipulates, no law is violated there. The model in question is, on the one hand, open, being inside of unlimited ‘reservoir’ of wave medium, on the other, being the element of a conditionally closed big system. Moving inside the reservoir the system passes some energy to it in the form of an impulse, which leads to the preservation of the common center of mass of the ‘reservoir’ and the system. As the size of the reservoir and the mass of wave medium are infinite, they can be ignored in calculations.


Even the existing definitions make one conclude that in the course of water molecule self-propulsion its potential energy diminishes while kinetic increases, i.e. the sum of energies remains constant.


* * *


In experiments with pulsating underwater spheres, on surface fluctuating cups, and with coherent acoustic emitters, gradients of wave pressure on the sources emerge during the period of broken synchronicity. The pressure disappears as soon as the sources again are set in potential holes. Any attempt by the source to leave the potential hole triggers counter-action in the form of wave pressure.


It becomes obvious that uniform rectilinear movement of an object as a system is actually made possible and maintained by the phase displacement between its active elements. Controlling phase displacement so that potential holes could be in their motion always ahead the object’s active elements located in them, we could accomplish a new way of propulsion.


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Chapter 4. Motion


Understanding of the cause of motion leads to understanding of nature!


At present virtually all fundamental properties of Nature are defined as inherent, inborn, in other words, the processes on which these properties of Nature are founded are thought to be beyond human comprehension.

A good point in question is the critical situation with ether (1881 – 2007), which hasn’t been solved yet in a consistent comprehensible way, as a result of which the luminiferous medium has been awkwardly rejected. The situations with the nature of gravitation, inertia and mass are no less embarrassing – these questions have been posing problem for over 300 years. As for the nature of motion in general and transfer of objects in particular, Aristotle tried to answer this question as far back as 2500 years ago.


It may seem that the problem of motion (we are referring here only to the transfer of objects in space) is in principle impossible to solve. But this is not so. At the level of model presentation the problem of motion was successfully solved as far back as 1996 [7], i.e. in the past millennium. And bearing in mind that any scientific theory is based on a system of postulates and actually is nothing but a subjective model of objective reality, the proposed and drafted methods of rhythmodynamics are in no way worse than any other which exist. The more so that rhythmodynamics in its potential development is focused on advancement and use of the new knowledge in solving technological, economic, social, humanitarian  and other problems.


There is a single universal algorithm, a sequence of rules which reveals not only the nature of motion, but also manifestations which accompany it: self-organization, inertia, force. But let’s not forget that rhythmodynamics is only a model presentation of the things cited, and one must constantly verify its accuracy by tallying it with natural phenomena.


Let’s examine a sequence of processes which form and sustain the motion of active elements in wave medium. I refer to the driving force without which motion (even by inertia) is impossible.


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§ 4.01 Motion as a fundamental property


To illustrate the problem of understanding the nature of motion in general, and mechanical motion (transfer) in particular, let’s have a look at the present definitions:


Motion 1. Form of matter existence, continuous process of material world development. There is no matter without motion, and no motion without matter. 2. Transfer of somebody or something along a definite path. Ex. Rotational motion.  3. Change in position of a body or its parts. 4. Transfer from one state, stage of development to the other state, or stage.


If motion and matter are inseparable, then to comprehend the essence of motion it would be worthwhile to learn what matter is.


Matter - is  a philosophical category which, within the framework of materialistic philosophy, is the conceptual foundation of science. According to materialistic dialectics, matter is objective reality, sensually perceived…


Within the framework of materialism motion was regarded as a form of existence of matter. Within the framework of modern science motion is regarded in context of its role in such phenomena as space, time and energy (special and general theories of relativity). In quantum mechanics, which examines phenomena inside atom as well as motion of elementary particles, there is a notion of transfer of wave packages, but it has never been linked to the motion of macro-bodies.


So, science has no notion of the mechanism of motion, i.e. motion is recognized as inherent quality which doesn’t need any explanation of its origin (one has to admit that the root-cause of motion is, indeed, impossible to find).


The mechanical motion (transfer) is also regarded inherent quality. When a body moves in space or relative to other bodies the main cause of its motion is thought to be force applied to it. As for the question ‘How exactly is the body transfer along a certain path made possible after the force has been applied to it?’, this question is generally thought inappropriate because motion (by inertia) is the usual phenomenon.


The RD models view motion as a means of solving contradictions between the qualitative transformation of the object itself and changes this transformation triggered in environment.


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§ 4.02 Translational motion


Translational motion is one of the forms of mechanical motion of bodies in space. Such motion can be uniform and accelerated.


Transfer is a more precise notion which comprises such applied questions as what’s transferred, where from and where to, in what and relative to what, by what means and at the expense of what, how fast and in what regime?


Transfer can be absolute, i.e. proceeding in a reference frame linked with wave medium, and relative.


To form a model notion about the processes which take part in organizing the translational motion let’s repeat the original conditions:

·        Oscillator (wave source) is always seeking to occupy a stable position in wave medium in which the overall influence on it from the wave field will be zero. Such place is called potential hole.

·        The motion of potential hole triggers the motion of the source, and if the source’s motion is impeded, the source exerts force on the obstacle.

·        If forcible transfer of the source does not trigger the transfer of potential hole, the source begins resisting the transfer due to the gradient action of the wave field.


Now let’s examine a simple wave system with two coherent sources. The distance between the sources equals one standing wave, while potential holes coincide with the nodes; the phase displacement between the sources is zero ().






Such  system (fig.96) has to reason to move in wave medium because positions of the sources and potential holes coincide. Here we can talk about the state of absolute rest characterized by the following parameters:


, , , .


Let’s call this state the first state of quiescence.


To create a situation in which the potential holes are to shift relative to the sources one has to create a phase displacement between the sources’ oscillations ().






Phase displacement triggers the shift of potential holes relative to their initial position, and appropriately, the shift of sources. The sources are influenced by the wave field so their natural reaction would be motion toward potential holes. If such motion is not obstructed the sources will be moving until they find themselves in the areas of stable balance.


For the sources to be again in potential holes with the standing wave anti-node between them, the system must pick a certain velocity V.






There is a correlation between the phase displacement, dimensions and system’s velocity, a correlation of parameters:


, , , .


The system is moving uniformly, the sources and potential holes occupy the same position, but phase displacement creates a lively standing wave between the sources. There’s no basis to speak of internal deformations inside the system because the moving system is in a state of internal balance. Let’s call this state the second state quiescence.


The third state of quiescence is a situation when phase displacement between the sources’ oscillations changes with time, which makes the system move with increasing speed, i.e. acceleration. The situation is remarkable because increase of its own speed triggers no counter-reaction on the part of the system, in other words it is neutral to it, being in a state of internal rest. The third state of quiescence can be realized artificially, and in reality it takes place in a free fall in gravitational field (the field, in the same way as was described, changes phase and frequency parameters of body elements).


Let’s give the usual examples of phase interpretation of motion.


Example 1. Two men in a boat are going to throw two stones of equal mass in opposite directions. If they are to throw them simultaneously the boat will remain still. But what is to happen, on condition friction between the boat and water is absent, if stones are thrown one at a time?




Fig.99 Illustration of example


In  a space of time between the throws the boat will shift, say, by 100 meters.  Will the boat return to its initial position after the second throw? No, it won’t; it will stop. If this procedure is repeated, the boat will move another 100 meters despite the fact that equal amount of stones (matter) has been thrown in both directions! And suppose such process were sufficiently prolonged and had wave nature, i.e. were invisible and proceeded without the loss of mass? Won’t the boat motion seem a miracle in such case?


In this example the boat transfer is linked with specific processes which have a phase-frequency component. It’s these processes which brought about transition without any outside action.


Example 2 Ivanov-Didin experiment.




Fig.100. System’s motion in medium brought about by phase displacement between the sources’ oscillations.


In both experiments, the first hypothetical and second real, motion is implemented through phase displacement between active elements of the system.


Example 3




Fig.101 A microorganism called naviculae moves in its environment (water)  through out-of-phase oscillations of its own quartz shell. The average length of naviculae’s body is 50 micrometers. Assuming that the length of the standing wave equals the length of naviculae’s body, then, using the magnitude of the speed of sound in water (1500 m/sec.) one can calculate the frequency generated by naviculae: about 15 mHz.


Conclusion: Motion is not necessarily started by some outside action, external force. There is another way found which doesn’t need such action:


The system of sources is moving in medium evenly and rectilinearly when certain facilitating relations have emerged between the active elements of the system and the medium; they are characterized by phase displacement and changes in the medium. Changes in the medium and constant phase displacement between the elements of the system (body) are not simply participating in formation of a uniform motion, they are also sustaining it.


Here’s a reverse order of phenomena participating in formation of conditions and implementation of transfer: sources motion → wave pressure on sources → potential holes shift relative to sources → phase displacement between the sources. The cause of the motion of the system’s elements here is the wave pressure brought on them which emerges due to the shift of potential holes which takes place because of the phase displacement between the elements.


With such approach the phase displacement is the root-cause which triggers such changes in relations between the elements of the system and wave medium which make the system move in this medium. The system’s motion is the consequence, or reaction to the changes which took place in its relations with the medium.


One should specifically stress that wave field linking the elements is an inseparable part of the system, therefore any changes in the wave field inevitably lead to reaction to those changes both on the part of the elements and the system as a whole.


Aristotle’s words come to mind in this connection “… the celestial matter (bodies) has a propensity to restore force which it needs to sustain the steadiness of motion”.


In the case of the described model it’s the phase displacement between the system’s elements which makes such propensity ‘to restore force’ possible. According to RD, there is no motion by inertia, but there’s illusion of it. The motion by inertia is maintained by the presence of phase displacement, proceeds with constant speed and in a state of inner quiescence (synchronicity). If phase displacement is eliminated (), the motion stops.


To implement sustained motion it is necessary that the speed and direction of transfer of active elements and potential holes should always coincide. For which one should ensure synchronicity (resonance) between the system’s motion, phase displacement of its elements and change in the wave field linking those elements. Achievement of synchronicity (resonance) in a simple system of sources with phase displacement between them is possible only if it moves according to the rule:


.                                                               (4.01)


When these conditions are not observed synchronicity is violated. Seeking to restore it, the system starts moving.


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§ 4.03  The nature of the moving force


Much has been spoken about the motion of bodies by inertia, but no one has indicated yet the cause which makes such motion possible. And such cause must exist: otherwise any motion may be regarded as almost a miracle. In which case motion should be referred to not as a physical process but as a God-given mystery. For example, Descartes thought that motion of bodies is always triggered by a push given to those bodies by other bodies. While the general cause of motion in his concept is God who created matter jointly with motion and quiescence and who preserves them.  Aristotle had a different approach to motion: “A rectilinear motion is implemented through the elements’ seeking their ‘natural places’”.







We got used to the idea that all uniform rectilinear motion starts with initial push, and afterwards is sustained by inertia. But inertia is a quality inherent in bodies, i.e. being the cause of any translational motion it, nonetheless, requires no explanation. Whereas we are interested in the root-cause of inertia thanks to which the body doesn’t stop after the push but keeps moving. In other words, there must be specific processes which sustain the body’s motion making it uniform and rectilinear. If such processes exist in nature, they are the driving force.


The driving force is usually linked with a difference of something. The usual analysis of the body’s motion by inertia does not reveal such difference. Of course, the researchers were not inclined to look for a driving force in what was initially and traditionally thought as inherent property.


The analysis of uniform and rectilinear motion of the system of sources (oscillators) in which the driving force is created and explained by the presence of phase displacement between the elements reveals a chain of processes: phase displacement between the elements leads to asynchronicity → propensity to shift and actual shift of potential holes in motion’s direction → motion of elements in the wake of potential holes until the speed is reached when synchronicity is restored. Here the rectilinear motion of artificial body (system) is implemented through its elements’ seeking their ‘natural places’, i.e. displaced potential holes.


Aristotle seemed to know what he was talking about! Now we know too!


So, the nature of the driving force which is hidden behind the notion ‘motion by inertia’ and which ensures motion without resistance has now become clear, at least in its model presentation. But the question rises: by what notions and what parameters should this driving force be formally presented?


In classical mechanics they use a tested and viable notion, the quantity of motion. Let’s use this notion for a formal and qualitative-quantitative presentation of the driving force:


.                                                (4.02)


Unlike classical mechanics in which the quantity of motion is relative, i.e. depends on the choice of reference frame, in rhythmodynamics the quantity of motion is absolute because all body motions are taking place in a medium.


Rhythmus:  A question of practical applicability: is it possible, using real equipment, to show that the driving force is, indeed, the consequence of phase displacement among active elements of the system?


Dynamicus: If such device were technically possible it would present a ‘simple’ way of almost direct transformation of electrical energy into translational motion. But I’m afraid at first the would-be machine might be compared to the first computer, being as bulky and ineffective.


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§ 4.04 Three states of quiescence


We’ve mentioned three regimes of motion in space during which the moving objects experience no internal tension and matched them with three states of quiescence.  For internal observer, his senses, these states of quiescence do not differ from each other, therefore it’s difficult for him to judge in what speed regime the moving system (body) is.


We are used to the idea that the change of speed regime inevitably manifests itself in the form of body reaction to the performed action. Speaking in the language of states of quiescence, during external action the balance of internal forces is broken and the body reacts by resisting.


Let’s imagine a hypothetical situation in which the change of speed regime has no bearing on the state of inner quiescence.


Here’s an example. The object under study is situated at a certain fixed distance from the source of gravitational field. Suppose, this field is absent, i.e. not emitted (switched off). There are no forces between the source of the field and the object  (), therefore the object, relative to the source, is in a state of stillness (), which corresponds to the first state of quiescence.






When the source is activated (switched on), the object under the impact of field () starts moving with increasing speed () toward the source of the field without any resistance, i.e. as if it felt no force applied to it. This is the situation of the third state of quiescence.


When the object picks some speed , gravitational field is switched off and the object is no longer influenced (). The moment the field is switched off the speed regime is switched from accelerated motion to motion by inertia with constant speed (). The third state of quiescence is transformed into second one.


Obviously all three states are different in their physical essence, but if judged by observers’ sensual perceptions or readings of instruments these states do not differ from each other. So the question arises: is it possible to tell these states apart without going beyond the limitations of the system, and will this moment of transfer from one speed regime to the other be felt?


Rhythmus: Here you are again, especially after your decision to cancel the law of inertia. Science knows no situations in which action would not be countered by reaction. Though I may have misunderstood you and something different was meant instead, so could you explain yourself?


Dynamicus: The body’s inertialess properties become manifest in the case when acceleration of the body exists, but reaction to this acceleration is absent! For example, we are falling in the elevator with acceleration, but we do not feel the action of force. If gravitational force should suddenly disappear, we wouldn’t even notice it, nor have it registered by our instruments, but at the same time our speed regime would change from accelerated to uniform motion. Moral: we should search more closely because Nature hides a lot, but few can see it…


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§ 4.05 First state of quiescence


Let’s examine this issue more closely. The system of immobile in medium coherent in-phase oscillators creates interference field in the areas of stable balance of which the oscillators occupy their position. Let’s choose the system of two oscillators as an example.




Fig.104 Analogy of Bjerknes’ experiment.


Two spherical oscillators (wave sources) are suspended on threads from a boat floating in a pool. The oscillators are controlled by an operator who can adjust their frequencies and create phase displacement between them.





Fig.105 If the sources’ frequency were increased or decreased synchronously the distance between them would decrease or increase too. Which is due to the fact that the sources are seeking to occupy positions of stable balance (potential holes) which are located in the standing waves’ nodes.





Fig.106 Absence of phase displacement between oscillators is crucial for the implementation of the first state of quiescence. Phase displacement leads to deformation of the interference field, and to the shift of potential holes relative to the sources. The system looses its equilibrium and acquires propensity to move. The non-equilibrium is compensated by motion.


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§ 4.06 Second state of quiescence


If oscillators, with phase displacement between them, were restrained from motion, the phase displacement would trigger deformation of the wave field and shifting of the nodes relative to oscillators.




                                              20°                    60°

Fig.107 The greater phase displacement is, the greater is the relative shift of oscillators and nodes.


The nodes (potential holes) depart from the oscillators, while the changed wave field exerts force making the oscillators move in the nodes’ wake. When restraining factor is removed the oscillators will be pushed by the field into potential holes, and the system will start moving. But, with fixed phase displacement, what speed should the system have so that position of oscillators and nodes were the same?




     à)                                                                                           b)


Fig.108 a) If the boat is restrained, force will be applied to it on the part of the system of the out of phase oscillators; b) if the boat is not restrained, under the influence of this force it will start moving with acceleration until it reaches certain speed.




Fig.109 This is how idealized situation looks (friction in medium is absent) in which the boat’s speed equals the speed of the moving oscillators and nodes.


Let’s solve the problem, starting with the analysis of the state of the field in the area between the oscillators, and find conditions in which coincidence of the moving sources and standing wave nodes is fulfilled.




l – distance between the sources


A general case solution:


,                                                 (4.03)


Solution in the case examined, where :


,                                             (4.04)


Let’s solve a reverse problem:


Suppose, we had two coherent with adjustable phases sources of electromagnetic waves between which electromagnetic standing wave emerged. What phase displacement between the sources should be for them to move with speed 8 km/sec. and 100 km/sec., and have at the same time their position coincide with the nodes?


We have:





We are to determine:











How much these values differ? You can see the illustration below.





Fig.110 The upper picture shows no phase displacement (), the lower picture shows  which corresponds to the system’s speed . A naked eye can hardly see the difference between them.


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§ 4.07  Third state of quiescence


Third state of quiescence is realized during a free fall under the influence of gravitational field. It’s the only case when the acting force gives body acceleration while the body does not react with inertia. How is it possible? Is there actually some external force which makes bodies fall with acceleration?


If the free fall were viewed as one of the regimes of motion in wave medium, then the following relation between the system’s acceleration and the phase displacement changing in time could be applied:






The distance between the sources of the falling system is changed according to the rule:







Fig.111 If frequency discordant system is restrained a spider-like interference pattern emerges. That’s why this phenomenon is called a ‘spider-effect’.


Gravitational field exerts influence on atoms’ frequency parameters, which (frequency discordance) explains the cause of free fall. Frequency discordance triggers deformation of internal connections which is followed by the body’s reaction in the form of self-propulsion with acceleration. If frequency discordance were absent, reaction to gravitational field would be absent too.


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§ 4.08 Specifics of RD modeling


Assumptions and consequences:


·        Each atom can be imagined as a pulsating oscillator of some frequency.

·        In solid bodies moving in wave medium the number of standing wave anti-nodes between the atoms of crystal lattice is always constant.

·        When body moves in wave medium the standing waves compress which triggers reduction of interatomic distance and consequently body dimensions.

·        To explain the effects of gravitation, motion, etc. a notion of phase displacement  between oscillators is introduced. Introduction of a gradient in the form of phase displacements makes it possible to explain motion, gravitation, inertia, interaction and other physical phenomena.

·        Controlling phase displacement one can control the speed of motion and modify gravitation (including its total neutralization).


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Chapter 5. Force, gravitation



We know only one universal force interaction between bodies – gravitation. The bodies react to gravitational field by moving in its source direction. But the immediate cause of emerging motion is not the field’s presence but changes which are taking place in the bodies under its impact.



Rhythmus: I didn’t get you… Explain, please, how can gravitational field be not the cause? What’s the cause then?


Dynamicus: We are talking about the cause of mutual motion which we call ‘interaction’, but we are not talking about the root-cause, the cause of all causes. Here’s example from our every-day life: a man became hospitalized with multiple fractures sustained in the road accident of which he was the cause as he’d jumped the lights. But what was the cause of this traffic violation? He just learned that his wife had not been loyal to him and became outraged. But this is not the ultimate cause either. Because two years before the man had committed adultery and badly humiliated his wife. But this is not the ultimate cause either…So what ultimate cause of the road accident do you think the court would examine?


Modern science regards gravitation mainly as curvature of space which can be presented as a model. The weak link of such notion is absence of understanding what exactly curves and why? The question of straightening space and thereby eliminating reaction of bodies to curvature, which is actually antigravitation, remains unanswered. No one knows how to do this, that’s why many researchers think antigravitation impossible.





Fig.112 a) Heavy ball in the center curves the fabric stretched on the hoop, thus creating conditions for smaller balls’ motion toward the center of curvature. b) Massive body curves space so that smaller bodies there ‘slide down’ into gravitational potential hole. ‘Sliding down’ is thought the natural reaction to curvature gradient.


Science has so far regarded any physical field (gravitational including) as a special form of matter, which is in a special state. But the essence of this special form of matter is unclear, so how can we talk about the cause of gravitation? Won’t it be more logical to clarify first what exactly changes in bodies under the influence of this special form of matter , what parameters change and how, then clarify what the field is and why body parameters change the way they do? In such case we would be talking about the mechanism cause of bodies’ reaction through motion, i.e. about processes which ensure this reaction in gravitational field.


The RD is talking about the cause of the body’s accelerated motion toward the Earth, not about gravitational field and its essence. The field’s essence and the way it influences parameters is the next stage of research. Whereas the cause of the fall is the discordance of phases and frequencies as if no field existed and this discordance had no cause, say it were inherent or created and maintained artificially. What remains is to define the mechanism of formation of this very motion. Which is quite simple: frequency discordance leads to potential holes shift and the sources’ drifting in the wake of those holes until synchronicity regime sets in.


Although lots of things remain unclear about gravitational field, its presence, no doubt, creates the force of attraction. Of course, such explanation is inadequate. Let’s recollect the situation with magnetic field when the field exerts strong impact on magnetic materials, and none on dielectric materials. Conclusion is obvious: the correlation of certain parameters in the body made of magnetic materials changes (is violated) so that this body starts reacting to these changes by motion, whereas the dielectric body is neutral to the field, i.e. the field failed to change those parameters. So, what’s important here is the effect of the field impact which manifests itself in the form of motion.


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§ 5.01 Nature of force


The processes which take part in formation of the notion ‘force’ have been described earlier, so some overlap is inevitable.


The majority of our contemporaries have no clear-cut view, nor the answer to the question as to what the nature of force is.


We’ll be guided by definitions:


Force is the essence of action, but not the action itself.

Force is the cause of the change of body’s velocity.


In rhythmodynamics force is the consequence of the phase displacement and frequency difference. The change of these parameters breaks the balance in the system of elements. And the system doesn’t care whether these phase and frequency correlations have changed due to internal causes or have been affected by some outside factor. It’s entirely different approach in which force which changes the body’s speed has the form of phase and frequency difference. Whereas the cause of the force as action lies in the system’s elements seeking to eliminate the emerging rift with their own potential holes. This rift is eliminated by wave pressure on the elements directed toward the shifting potential holes. In short, the force of motion emerges inside the body. If the elements have a possibility of free movement toward the shifted potential holes the system moves. If the system is restrained, the blockage comes under the influence of force. When phase displacement changes the amount of effort on the blockage changes too. One might find this description somewhat protracted, but it’s precise.


Rhythmus: What you mean is that the root-cause of motion and force lies in a simple phase displacement? But this displacement too must be realized somehow; some kind of action is required to effect it, an outside action too. Which means that the nature of force lies much deeper…


Dynamicus: You are right, this sequence of cause-and-effect is endless in nature. So we refer only to the closest cause, as if we were examining  everything in reverse order: action result → action itself → cause of action → the cause of cause → etc. For example, you get into a car, turn ignition key, press accelerator – the car starts. Can you name the precise cause of the car movement here? Whatever the cause is chosen it will always be the effect of something. Another matter is when you are using model presentation of a phenomenon which has no in-depth infinity because everything has been already stipulated in a precise manner.



Resistance to speed change or counter-force to blockage emerge if correspondence between the phase displacement and speed regime is not achieved, or it’s broken. If the system’s speed (acceleration) is higher than what the phase displacement  (frequency difference) allows, we are witnessing resistance to movement. If the speed  is behind the phase displacement (and acceleration is less then what frequency difference stipulates) a driving force emerges aimed at eliminating the lag. In both cases we are dealing with internal force which is applied to achieve synchronicity between the system’s parameters and the processes in wave medium.




Fig.113 The falling in gravitational field system seeks to compensate the lack of speed (acceleration) by force; and resists when speed (acceleration) is excessive.



The RD definition of the ‘driving force’ notion:


Driving force is the name of those changes inside the body which make it seek motion, and sustain continuity of this motion without any outside participation.


It was noted before that amount of motion is the measure of such force. Unlike classics case, rhythmodynamics regards amount of motion as absolute value.




If the system accelerates we are speaking about increase of its amount of motion and link this to the increasing in time phase displacement.




The driving force is an aggregate of concrete processes which either lead to motion and preservation of its continuity, or to action applied to blockage.


For a system which has a phase displacement the driving force is internal; for the blockage which the system is trying to overcome by its effort the driving force is external.


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§ 5.02 Motion in gravitational field


Depending on the free motion regime, one can judge the processes which ensure this motion.


In gravitational field the unrestrained bodies fall with acceleration. Gravitational field is the cause of this conduct. But its impact is indirect, it only provokes the bodies by changing then, triggering a chain of events leading to the fact of the free fall. Let’s examine the cause-and-effect sequence of events in their reverse order:

Accelerated motion (fall) → wave pressure on the system’s elements → shift of potential holes relative to the system’s elements → phase displacement between the system elements growing in time → gradient density (tension) of gravitational field → gravitational field → the source of gravitational field.


Assuming that gravitational field has a wave nature, i.e. results from aggregation of wave emissions of all elements of a massive body, we might explain the cause of this field’s influence on phase and frequency parameters of other bodies. The cause is well-known:  frequency pulling.


Obviously the first observation and description of synchronization phenomenon of oscillating objects was carried out by Christiaan Huygens who discovered as far back as the first half of 17th century that a couple of out of phase pendulum clocks became synchronized when mounted on a light beam, instead of the wall.


By the end of 19th century John W. Rayleigh observed that two organ pipes with vents nearby start sounding in unison, if closely tuned, i.e. mutual synchronization of vibrations takes place. Sometimes the pipes make each other almost ‘silent’. He observed similar phenomena in the case of two electric or mechanic tonometers linked with each other. By the end of the 19th, early 20th centuries synchronization in electric circuits and some electromechanical systems was discovered.


One of the most amazing phenomena of the examined type is self-synchronization of unbalanced rotors (rotors the axis of which doesn’t pass through the center of mass). Two or more rotors which are not linked with each other kinematically or electrically if mounted on a common movable support and powered by  independent asynchronous motors happen to rotate synchronously – with equal or divisible average angular velocity and with definite mutual phases. Rotors’ synchronicity emerges even despite difference between their partial angular velocities, i.e. those velocities with which they rotate when mounted on immovable support. (fig.114). The inclination to synchronous rotation in many cases is so strong that even switching off of one or several motors doesn’t break synchronicity: the powerless rotors can rotate endlessly. The energy required to maintain their rotation is supplied by the working motors thanks to the vibrating support on which the rotors are mounted. This vibration can be hardly noticeable so observer V might imagine that these rotors are linked somehow.



Fig.114 Self-synchronization of mechanical vibration exciters. Two or more unbalanced rotors powered by asynchronous motors on unmovable support have different rotation velocities w1 and w2 (à). If mounted on common movable support they rotate with equal general velocity w (b). Synchronicity may be preserved even if one of the motors is switched off (w1=0 or w2=0). Observer V may have an illusion that rotors are linked by a spring (c).


Analogy with vibration mechanics is apparent with the only modification that in rhythmodynamics wave sources have common movable, floating in wave medium foundation in the form of a standing wave which ensures the sources’ dynamic link through the wave medium itself. If this foundation (standing wave) shifts for some reason, the sources ‘mounted’ on it shift as well. This process may have a different description: if foundation, i.e. the standing wave linking the sources, cannot ensure synchronicity between the sources a driving force emerges shifting the foundation to such speed regime in which there won’t be any need to eliminate the phase displacement between the sources.


The same happens in the central gravitational field: the field imposes the phase displacement and thus breaks synchronicity of the system → foundation (standing wave) moves and ‘drags’ in its wake the sources → the trend to speed increase is due to phase shift increasing in time which is manifest until velocity is reached at which synchronicity of the system’s sources is possible. If the system is restrained from motion the standing wave passes efforts from a source to a source aimed at reaching synchronicity.


Synchronicity is possible either in the absence of phase displacement or in motion.  But the phase displacement is firmly secured by gravitational field which prevents nullification of the phase shift. As a result, the system is seeking synchronicity in motion.


One should distinguish motion-inspired synchronicity from synchronicity in a state of rest. The synchronicity of a motionless system is characterized by absence of phase shift; in a moving system synchronicity is characterized by the system’s motion thanks to which, according to Doppler’s effect, the sources have an illusion of absent phase shift, i.e. phase displacement is masked by motion. In both cases there’s no energy flow between the system’s elements, i.e. relative to its own energy carcass the system is in a state of inner balance which is the main condition of synchronicity. In other words, synchronicity is realized because the speed and direction of energy flow between the elements coincides with the speed and direction of the system.


An outward sign of broken synchronicity is emergence of outward emission. With absent phase displacement emission is practically absent (unless it’s uniform radiating in all directions), with emerging phase displacement emission emerges or changes the configuration of its distribution in space.





Fig.115 a) Oscillators (2-dimensional model) became self-organized in such fashion that a standing wave emerged inside, while outward emission is rapidly diminishing. Synchronicity as a sign of system stability has emerged. b) Emergence of phase  displacement leads to shifting anti-node of the standing wave and to broken synchronicity. Restoration of synchronicity is possible only in motion. The system of oscillators will seek to catch up with the shifting potential hole.


The force of gravitation is a complex phenomenon which triggers in bodies violation of inner balance (asynchronicity)  and leads to accelerated motion. The changes in body which participate in formation of the free fall in essence do not differ from the processes which form any other motion.


The motion in gravitational field is determined by phase displacement, and as potential holes in the system tend to be always ahead of the elements which created them, these elements are forced to constantly increase their speed so as to catch up with the runaway potential holes.




                      a                                             b                                              c


Fig.116 In gravitational field relative to the restrained system of wave sources, potential holes are shifted toward the field source (a). If restraining factor is removed the system starts moving because the sources will be seeking to catch up with the shifting nodes (b). Free fall in gravitational field is characterized by absence of internal deformations in the system (c).


There is only one way to cancel gravitation effect: to bring the phase displacement between the body elements to zero. Then the cause which makes the body react in gravitation field will disappear. But to keep phases in the necessary regime energy may possibly be required.


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§ 5.03  Equation to calculate acceleration in gravitational field


There are several ways to calculate the formula describing the mechanism of the bodies’ free fall in gravitational field. Here’s one the most curious of them stemming from familiar premises.


Phenomenon of gravitational red shift was predicted by Einstein. In earth conditions such shift is extremely small, nonetheless they managed to measure it with the help of Mossbauer effect




Fig.117 Shift of fringes, specifically of line A, toward red.


If photon with frequency   is emitted at the height H above the Earth toward the earth’s center, at the level of the earth’s surface its kinetic energy  increases at the expense of potential energy loss. According to the law of energy preservation:




We assume that photon’s mass  is constant. So, when photon reaches the receiver with frequency , which is different from the one it had when emitted by the source, and with H= 10 m








But what will be the phase displacement of atoms in the gravitational field of the Earth if we have a crystal of similar atoms in which interatomic distance along the crystal’s vertical axis is determined by one standing wave anti-node, i.e. ?





We’ll rewrite formula 5.05 relative to acceleration g:




   [m/ñ2]                                        (5.07)


Now we can determine what phase displacement between the body’s neighboring atoms should be for specific acceleration in gravitational field.




g = 9,81m/sec2, ,




Conclusion: The body reacts by motion to broken synchronicity in interatomic ties because in motion the body can restore synchronicity. That’s why during a free fall the body is not in a state of discomfort but in inner quiescence.



Rhythmus: So what’s curious about it?


Dynamicus: This conclusion could have been made long before rhythmodynamics’ emergence.


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§ 5.04 Force of gravitation


According to classical mechanics, in gravitational field the body m is influenced by force




Rhythmodynamics defines force through discordance of interatomic processes:


  [kg·m/señ2]                            (5.09)



m is a mass ratio of proportionality, quantitative measure of wave links in body’s crystal lattice [kg];

 is a frequency gradient in the system of two atoms linked to each other by a standing wave;

ñ is a velocity of light.


According to 5.09,  if frequency difference is artificially eliminated at the atomic level of matter organization  (). This conclusion is particularly important as it helps understand not only at the model level what’s to be changed in the bodies so as to reach antigravitational effects.


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§ 5.05 Comparing formulas


Let’s compare 5.09 formula with the formula of classical mechanics





Formula 5.08 reflects relation between three parameters. It doesn’t reveal the cause of the force, i.e. there’s no indication of the processes which form accelerated motion (free fall) of a small body toward the big one.


Formula 5.09 indicates the process which forms the driving force in bodies (gravitational force) and ensures their free fall.


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§ 5.06 Gravitation and frequency pulling (hypothesis)


What will the consequences be if phenomenon of frequency pulling is laid at the foundation of explanation of gravitation?


Frequency pulling is effective only in the case when interacting sources have close frequencies. If the sources’ frequency difference is sufficiently large, there’s no frequency pulling in its pure form. Which implies that the sources’ interaction would depend on the frequency difference between them. Frequency pulling is possible only until a certain frequency difference after which a break happens and the system enters a different regime.


There is a known relation () according to which frequency and mass are interrelated. Although the general line of the idea is correct, there are lots of questions about this relation, for example: it refers to the mass and frequency of what, of what state and level of matter organization? We won’t go into details, but we’ll agree that increasing mass of one of the interacting bodies will change its overall frequency parameter.


An interesting picture emerges: gravitational field force based on frequency pulling will increase until a certain limit after which the increase of mass of big body leads to a break of pulling. What happens then is not known. Will the big and small bodies interact gravitationally? But between big bodies of similar mass gravitation will remain due to proximity of their frequency characteristics. Let’s examine the situation using the hypothetical black holes example.


Suppose the black hole increased its mass so that frequency pulling break occurred between it and ordinary bodies. Suppose gravitational interaction has ceased after such break, i.e. for ordinary bodies the black hole has become gravitationally safe. If there’s another black hole of similar mass, frequency pulling will take place, and these objects will be gravitationally linked. To outside observer a picture emerges in which the black holes are interacting gravitationally, at the same time ordinary bodies do not react to the black holes’ proximity in any way. One might cite the analogy of magnetic field which has no impact on dielectrics.


A black hole ‘saturation effect’ is present in this situation when its mass increases until a certain limit after which for ordinary bodies the gravitational properties of the black hole switch into a new non-gravitational quality. If so, a strong suspicion emerges that gravitational, magnetic and electrical fields are identical in their mechanism essence, and their properties reflect only different frequency bands.



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1. Scientists’ opinions about this work


V.V. Bushuev, Doctor of Science, Director of the Institute of Energy Strategy: I share Yuri Ivanov’s hypothesis that driving force is caused by frequency (or phase) difference between two independent, but linked by waves, oscillators each of which reflects the essence of elementary material object. Whether these oscillations of magnetic or some other nature, in my view, it’s not important.


I.P. Kopylov, Doctor of Science, Faculty Head of Moscow Energy College: What’s new in it is that gravitational attraction, and any motion in general, is explained by the super small gradients of phase and frequency. The majority of researchers overlooked this aspect of the question.


V.A. Ilyin, Doctor of Science:  The author of rhythmodynamics succeeded in not simply giving the empirical formulas of classical mechanics the actual physical meaning, but in much more: in eliminating the dividing line between classical and quantum mechanics. This happened at the time when classic speed and acceleration were expressed in formulas through phase displacement and frequency gradient respectively.


A.I. Burenin, Professor: For the first time not just gravitation phenomenon, but of all natural phenomena of force have received coherent scientific explanation which doesn’t depend on questionable views on world organization. Undoubtedly, such approach is a discovery which by right claims the status of the law of nature.


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2. Science: privatization of truth


Natural phenomena do not require recognition: they simply are, like it or not. But their interpretation is prone to subjectivity, the interpreter’s talent as well as the condition of society which is the main customer of scientific interpretations. A society of feudal level of development requires appropriate interpretations, like existence of a philosopher’s stone with the help of which one can obtain lots of gold from lead. Capitalist society with more pragmatic collective mind requires a more businesslike concrete approach. So each time ‘scientists’ emerge to fulfill social order.


The men of reason know that although fundamental science may serve temporary interests of applied research it, nonetheless, has no communist, capitalist or national tinge. Science either is, or isn’t. But how can one tell science from fiction?


Modern views on objectivity of scientific knowledge are rather varying. For example, relativity theory which has mystified the minds of several generations of researchers. It is still not clear if time slows in the moving system, or it slows down in motionless one which moves relative to the moving system? The modern wise men are interested in such scientific mysticism: one can make a good profit answering allegedly vital questions posing mankind. Lots of these wise men are well aware that they are actually ordinary conmen. But such confession would mean their expulsion from ‘science’, the only source of these ‘wise men’s subsistence. So you can imagine what might happen should someone come to expose their ‘tricks’.  In short, the old saying that “the road to knowledge is measured by inquisition fires” still holds true.


Financing is the main factor in science. But what research receives money under capitalism? Only the work which brings quick returns and easy political dividends. Such are capitalist rules. All know this is wrong, and cannot go on forever.


So what’s to be done? Apply for foreign grants? Or plunge into business themselves so as to finance one’s own research?


One could also ask for private business donations, but there are few businessmen in Russia who want to know what our world really is.


* * *


Competition between scientific schools is really mind as well as science disturbing process, particularly if one speaks about formation of its fundamental elements. The modern world of science is affected not so much by the competition of ideas as by the fight for financing, a reflection of a general social scramble for better life. The winners are always those with stronger administrative power and media backing. Under such conditions any competition in the sphere of ideas is nipped in the bud. Sometime they simply steal those ideas. The fundamental science of the 3rd millennia is driven by the law of the jungle where might is right! Obviously for this very  reason, to preserve the status quo, a commission to fight pseudo science was created in 1998 under the auspices of the Russian Academy of Science.


But will this commission really protect science, or simply defend the cushy seats of bureaucrats in science?


Competition between various technologies and their creators is quite justifiable: these technologies are to improve peoples’ lives and accelerate the pace of progress. But how can one justify competition between those lines of research which are supposed to reveal the fundamental essence of our world and answer such seemingly simple questions as how the world was created, what proto-elements it consists of, what hidden processes form the basic properties of material bodies, like mass (inertia), motion (ability to move in space), force (ability to interact). All these properties are still thought inherent!


One should stress the fact that supporters and followers of quantum mechanics and relativity theory have been trying for over 50 years to convince the pubic that these theories and none other have reached the ultimate truth.


One should understand that people of Newton, Maxwell, Lorentz, Puancare, Einstein,  De Broile standing are not born every year; they are too few, while their followers are numerous. And these followers, especially those with bureaucratic background, are eager to reap the fruits of the glory which belongs not them, but the founding fathers. Trying to conceal their mental inaptitude they are doing their best to block the progress of new ideas by organizing struggle with the so-called pseudo-science or by falsifying the results of scientific research which they’d brought in and backed.


The current commercialization of fundamental science, in effect privatization of the right to announce truth is even a more bizarre phenomenon which might be viewed as the ‘enemy action of aliens’ seeking to fool the naïve mankind.


So what are independent researchers doing in such situation being excluded from privatized science? Surprisingly enough, instead of trying to unite in their common effort to survive as a species they are dying out, one by one.


Over the past two decades the majority of those who chose to stay in Russia, either have taken leave of their senses, or switched to business, or passed away. Those who are still alive and struggling is an interesting bunch to observe, especially their pathetic attempts to find a niche in the privatized science, hoping that bureaucrats would notice their efforts and give them some scraps from their dinner-table.


There is some logic in the current tragedy of the Russian science demise, so should one after all try to do something to stop it?


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3. The number of space dimensions


Human consciousness can grasp five (!) orthogonal dimensions in space + time as motion characteristic. Overall, six!


Orthogonality of properties – mutual statistical independence between parameters. The language of geometric models expresses each parameter as a vector, a correlation is a cosine of the angle formed by vectors. In this context independence is zero value of cosine reached with the angles of 90 and 270 decrees (mutual perpendicularity).


Perpendicularity is a sign of orthogonality, i.e. all listed coordinates must be perpendicular to each other. In clear geometrical form only three coordinates: x, y and z meet this condition. But there’s another sign of orthogonality.


If object moves precisely along one axis of coordinates, and the object’s coordinates in other axises do not change, this axis of coordinates is orthogonal.


Only in such case the axis of coordinates may be recognized as orthogonal and used for dimensional measurements. This condition is met by coordinate axises , where  is frequency axis of coordinates,  is a coordinate axis toward zero-amplitude states.




Fig.119 Referring to the question of frequency band: on infinite frequency scale our world seems imperceptible spectral line.


If object changes its frequency state, it or its parts are moving only along frequency axis of coordinates. The object’s coordinates in other axises remain unchanged.  Each object has its own frequency interval, frequency form and frequency depth. Space too has frequency depth ranging from infinity to zero (). Our world and every object in it is limited by frequency interval in frequency axis. Different frequency intervals coexist in a single space. It’s similar to different radio stations’ frequency bands: information broadcast by radio stations coexists in a single wave (ether) space and doesn’t interfere with each other.




Fig.120 The object’s shift in frequency or to zero amplitude may lead to interesting effects of materialization and dematerialization, i.e. the object is present, but its material part is present either in other frequency band, or in other amplitude (zero-amplitude for us) reality.


Coordinate toward zero-amplitude states is slightly more difficult for comprehension. If we superimpose waves in opposite phases and eliminate amplitude, the wave energy is transformed, for us, into zero-amplitude state, i.e. it exists but for observer it is situated in a different sphere of being, in other amplitude dimension. It’s this coordinate axis we are talking about.




Fig.121 There are no miracles, there is lack of knowledge and ignorance, which is unwillingness to learn!


Perhaps, there is depth of other amplitude realities, i.e. each zero-amplitude state in its reality is perceived as amplitude one, and can be transformed into a more zero-amplitude state.


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4. Space expansion and the Alice’s effect


“How do you know I’m mad?” said Alice.

“You must be,” said the Cat, “or you wouldn’t have come here”.


Alice’s Adventures in Wonderland by Lewis Carroll.


Let’s expound the RD hypothesis, according to which ‘space expansion effect’ and corresponding to it the ‘red shift’ of fringes are supposed to be explained not by space expansion but by synchronous shift along frequency coordinate of all visible objects (stars, galaxies) present in space.


According to the RD scenario, the Universe is not expanding, it’s the objects present in it which are synchronously shifting its frequency toward its rise. This leads to synchronous change of parameters of all instruments of measurement. For example, the standard of length after higher frequency shift becomes physically shorter, i.e. the observer with all his measuring attributes shrinks in size and therefore perceives the Universe increasing in size, i.e. expanding (Alice’s effect).


According to the hypothesis, in metrical space all objects remain in their place, whereas in frequency space they are ‘flying’, i.e. their material essence is moving with certain speed along frequency coordinate (the objects are ‘falling’ in high-frequency infinity). Should such frequency shift proceed at a higher speed, a situation might emerge in which now visible distant objects could become invisible, being shifted relative to the observer on the earth into radio frequencies band, while expansion would be perceived by the observer as proceeding with great speed.


The same dependency becomes the feature of Universe expansion at the expense of objects’ shift in frequency space: the farther the object from the observer, the stronger is the fringes’ shift toward the red due to the time delay of the incoming signals (photons). It’s easy to mistake such shift for Doppler’s effect and suggest a hypothesis of a big bang and running away galaxies. Some tend to regard as more logical the ideas of expansion of the space itself between the galaxies, also leading to the red shift.





Fig.122 Having drunk the magic potion Alice shrunk, and, therefore, the room in her perception became more spacious…


To this RD hypothesis I’d like to add information about one important consequence. Within this hypothesis there’s no need talking about photon’s ageing as photon remains exactly the same it was emitted at some time in the past. The answer is that during its (photon’s) ignifycant time in transit the system of the observer on earth has shifted its position on frequency axis of coordinates, and therefore the observer’s standards of measurement have changed too, by increasing their frequency. In such case we should talk not about Doppler’s effect which is always linked to speed, but about the shift of the standards of measurement toward the ultraviolet part of the spectrum. In effect, the observer is dealing with an illusion strongly resembling the Doppler’s effect. This is a different kind of effect and it requires some other name so as to tell them apart.


So, if all distant objects change synchronously their position only on the frequency axis of coordinates, i.e. shifting frequency toward its increase, a situation emerges in which the observer receives information from other objects with delay whereas its assessment is implemented by the frequency standards which have changed in the meantime. As a result, the observer either has the illusion of a big bang and running away galaxies, or ageing photons. But one can examine the situation in a reverse order: i.e. all visible objects in the Universe used to form a single body. This body, following the shift in high-frequency direction, split into parts, which, in their turn, became divided into galaxies, stars, and planets…


The term ‘Alice’s effect’ emerged from the context of the book Alice’s Adventures in Wonderland by Lewis Carroll in which his heroine Alice having taken a magic drink finds herself shrinking in size, and appropriately, in her perception the space around her grows, expands.


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5. Comparison of the rhythmodynamics and classical mechanics formulas






CM formulas



RD formulas






Quantum of mass






Centrifugal force


Kinetic energy



Standing wave length




Energy flow speed



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6. Action without counteraction


One can find support only in something which can resist!


Classical mechanics is based on Galileo-Newton’s laws which, though considered unbroken, fail to explain the main thing, the inner processes which form the essence of phenomena these laws describe. There is another line of science, quantum mechanics which seeks to explicate the essence of the inner processes. These two lines have a missing logical link which is supposed to bring them together and without which they exist separately despite the continuous talk about the necessity of unification of quantum and classical approaches.

I think such unification has practically been achieved because with rhythmodynamics the formulas of classical mechanics have acquired phase, frequency, the speed of light and Planck’s constant – the attributes without which quantum mechanics cannot exist. The phase-frequency means of presenting the old mechanics’ formulas fills with real physical sense both the formulas themselves as well as the notions which until now remained unclear: the cause of motion, force, speed, inertia, gravitation. In this aspect, the developing rhythmodynamics is rapidly bridging the rift between the two main lines in physics, bringing them closer together.  But let’s change the vector because the present article examines cases when Newton’s third law is not implemented directly.


Newton formulated the 3rd law of motion the following way:

‘To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts’.


Some of Newton’s followers interpret the third law literally: in nature there is no one-sided action of one body on the other, but there is always interaction! Does this imply there are no situations of action without opposite reaction?


It must be emphasized that Newton’s 3rd law applies only to the ideal closed systems where action and opposite reaction are not dissipated, but fully 100% realized. For example, when you affect an iron body with a magnet you find that the iron body too starts affecting the magnet, i.e. it starts attracting it with the same force. It happens because in the course of magnetic field action the iron object becomes itself a source of magnetic field (fig.123). Here the magnetic field, as a special state of surrounding environment, plays the role of a medium, i.e. between the body and magnet it exists on its own.




Fig.123 Interaction of a magnet and iron body M. Here action equals opposite reaction, i.e. Newton’s third law of motion is realized.


The magnetic field created by electric current is thought to propagate with the speed of light. If the current’s impulse is short, the magnetic field having separated from conductor keeps on traveling no matter if the conductor has at the moment electric current nor not.


If the distance to the body is big the magnetic field for the time being is situated between the source and the object and exerts no influence on the body. In this sense the portion of magnetic field en route from the source to the body can be regarded as independent moving ‘entity’, i.e. the space by itself transfers its changed state (magnetic) from one place to the other. During this period magnetic properties in their portion form can exert influence neither on the source from which this portion has already separated, nor on the object which it hasn’t reached yet.


Having reached the object magnetic field changes the object’s state. If this action results in the object’s turning into a source of magnetic field, part of the field is re-emitted toward the initial source, i.e. for the time being the object itself turns into a source and thereby can influence the initial source. In this situation the ‘action-reaction’ principle works because a back link exists.


If the back link does not emerge in the course of one body action on the other, the law of action-reaction doesn’t work in the system. Let’s show this on mechanical experiments in which the back link between the objects is absent.


Suppose, we had a device (fig 124) expelling two air jets in opposite directions in such a way that jet forces are fully neutralizing each other, while the downward expelled jet is neutralizing gravitational force as well. In such case our device would stay suspended in air, i.e. it would have zero weight.


Fig.124. The heavy ball suspended in the jet of air exerts no pressure on the source. This happens due to absent back relation between the ball and the source. If you had such device, you could hold the ball without feeling the ball’s weight. The reason: the ball is suspended at the expense of kinetic energy it receives from the jet, and it cannot affect the source through the jet. Even if you were applying downward pressure on the ball, i.e. significantly changed its position in the jet, even in this case the device wouldn’t feel any pressure. The picture shows the device connected with a hose to a powerful compressor.


For us the absence of the device’s weight is apparent, therefore we can freely move the device on condition of its initial (vertical) orientation in space.


Let’s change the situation and put a ball (a body of stable form for such kind of suspension) weighing 10 kg. in the upward air jet so that the jet could keep the ball suspended at a certain distance, say 5 centimeters. Would the device with zero weight react to a new situation, i.e. emergence of the ball? Would the device’s zero weight increase by the weight of the ball suspended in the air jet (0 + 10)?


No, it wouldn’t:




There’s no mistake about it. It’s only an illusion that the ball is propped by the jet and through it exerts pressure on the source. In effect, the ball is isolated from the system and suspended at the expense of kinetic energy passed to it by the jet. This is easy to check in home conditions if you stage your experiment in the bath-room:


Remove the spray from the shower hose, direct the jet upwards and, holding the hose with one hand, to measure weight try with the other hand to exert pressure through the jet on the hose. You might be surprised to find that the hand suspended by the jet or any other body suspended in it exerts no pressure on the source.


At first glance the situation seems paradoxical, but it’s this situation which illustrates possibility of application of force without incurring counterforce. Thereby action can be one-sided, i.e. it may not trigger opposite reaction in the form of pressure on the source of action.


In the same unusual way, provided the device had sufficient capacity, one can suspend the ball of a greater weight, say 100 kg., and freely move it with the device’s help at the same time experiencing no additional (100 kg.) weight in the jet. This is possible only if the back relation between the body and the source is absent, i.e. the body suspended in the jet has no possibility of influencing the source of power. Thus we are able to not just hold and transfer the heavy ball without any additional effort, but lift it to any height too. In effect, we are dealing with a new gravidynamics paradox.




Fig.125 One of the devices to demonstrate action without reaction is made in the form of a beam balance (published first time). The balls of steel of different weight placed in jets exert no influence on the beam balance.


I wonder how in such case one should solve the problem of this type: Suppose, a body weighing 10 kg. were suspended in a powerful air jet (fig.124) in such a way that it doesn’t affect the speed and direction of the jet expulsion from the source’s nozzle. How much energy should one spend to raise this body to the height of 20 meters? (What’s implied is that a person should take the device which keeps the ball in suspended state and climbing up the ladder should lift the body suspended in the jet to the height of 20 meters).

If this problem is solved correctly (the problem stipulates that the person with the device and the ball climbs the ladder himself), the solution is to show that the person will spend energy only to lift the device which creates the jet. The person moving upwards with the device won’t even notice the presence of the 10 kilo body in the jet (the essence of this paradox).


The situation only seems paradoxical, but it has its explanation.


The action without reaction effect can be organized in the ultrasound field of a powerful source. Such experiment was conducted in one of the secret laboratories. Water was used as acoustic medium. Heavy objects easily surfaced from the bottom of the pool, i.e. behaved as if they had no weight.


Similar phenomena, but of a different physical level, occur occasionally in nature. Incidentally, ‘phenomenon’ is called this way because it happens suddenly and cannot be studied in laboratory conditions.


“A globular lightening of a football size flew over Galtsovka village in Altai region at the height of twenty-thirty meters. The first obstacle in its progress, a shed with concrete poles was crushed and brought down. Passing over a house with slate roof-top the globular lightening tore off the slate  from the roof and lifting it in the air dragged it along, scattering it across the village.


Passing over a tractor station, the lightening crushed one of the steel covered with canvass carcasses, approaching the other carcass the lightening first dragged it on the ground, then when it overtook the carcass the lightening lifted it into the air and carried for 300 meters. The carcass itself remained intact. Its weight was no less than 100 kg”.


After which the author [20] examines situation trying to explain it by the laws of physics we know:


“The fields of the flying globular lightening carried the carcass weighing over 100 kg. And for some reason it flew in a strictly rectilinear fashion, totally unaware that some steel carcass got stuck to it. If globular lightening is really thought to have air’s density and weighs nothing, why did the carcass weighing no less than 100 kg. fail to alter to the slightest degree the trajectory of its flight?”


It’s worth note that in some cases the field of the globular lightening  repelled objects, and in others it attracted them. This can have only one explanation: in each specific case the field of the lightening had a specific impact on internal characteristics of the objects after which the objects reacted by this or that movement to their new state. Absence of the back relation (this happens differently between the magnet and iron object) allows the globular lightening to ignore the developments in its field. Had the objects themselves become the sources of similar field, i.e. re-emitted it, they would have altered the lightening’s trajectory. In this particular case we most likely have a situation when action was not met with reaction.






Within the framework of familiar laws of physics an isolated task of direct action without reverse relation has been formulated and solved. Solution of this task allows us to reach a deeper understanding of how weight characteristics of material bodies in open systems can be manipulated. As in the case with the jet example (which is only an illustration of more fundamental processes) we can ‘deceive’ nature provided we have a really deep understanding of the inner processes which form the phenomena under study.


In the case with the ultra-sound example we can see that there are field flows which can influence bodies without incurring the effect of reverse relation. Conditions and criteria for the bodies and means of influencing them have been defined in which direct realization of Newton’s third law of motion is absent (not to be published in this article).


What matters is not how much energy was spent to hold or transfer the body, but what parameters and how this energy managed to change in the body itself.  Sophisticated changes in the body would trigger the body’s equally sophisticated reaction.


One could call ‘pressure’ the type of influence cited above, but examining the proceedings at atomic and deeper level, i.e. from rhythmodynamics positions, we discover something different, of phase-frequency nature, which opens our eyes. This different gives us a clue as to what technologies of the near future we might have, and what flying machines we are to build soon. But not all are capable of seeing such fantastic perspectives.





In gravitational field, we have a balanced open system in which the emergence of a new body at first glance is supposed to trigger reaction of this system in the form of weight increase. But this is not so.


Such task is solved in two independent stages: 1) examination of interrelation of the source of the flow with the flow itself (jet effect which is compensated by reverse flow in the device); 2) examination of interrelation between the flow separated from the source and the body (impulse in a unit of time on a unit of area). One cannot examine interrelation between the source and the body because the flow has no rigidity. For example, the flow of water can be regarded as small drops with no tie between them. An interim flow split into drops cannot influence the source in any way, that’s why action-reaction principle applies in each particular stage, but not in overall case. If so, Newton’s third law of motion must be expanded:


In an open system with an intermediary between the bodies and 100% reverse relation the indirect actions of the two bodies on each other are equal and aimed in opposite directions; in the absence of reverse relation the indirect action of one body on the other triggers no opposite reaction, i.e. reaction doesn’t equal action.


Although this definition requires further clarification it signals entirely different approach!


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7.  Rhythmodynamics and vibrational mechanics


Let’s examine an example from vibrational mechanics [1]: self-synchronization of unbalanced rotors (rotors the axis of which doesn’t pass through the center of mass).


“…two or more rotors unlinked with each other kinematically and electrically mounted on a common movable support and powered by  independent asynchronous motors happen to rotate synchronously – with equal or divisible average angular velocity and with definite mutual phases. Rotors’ synchronicity emerges even despite difference between their partial angular velocities, i.e. those velocities with which they rotate when mounted on a fixed support. (fig.126). The inclination to synchronous rotation in many cases is so strong that even switching off of one or several motors doesn’t break synchronicity: the powerless rotors can rotate endlessly. The energy required to maintain their rotation is supplied by the working motors thanks to the vibrating support on which the rotors are mounted. This vibration can be hardly noticeable so observer V might imagine that these rotors are linked somehow.”




Fig.126  Self-synchronization of mechanical vibration exciters. Two or more unbalanced rotors powered by asynchronous motors on solid support have different rotation velocities w1 and w2 (à). If mounted on a common movable support they rotate with equal general velocity w (b). Synchronicity may be preserved even if one of the motors is switched off (w1=0 or w2=0). Observer V may have an illusion that rotors are linked by a spring (c).


Let’s stage an simulated experiment, and first change conditions: Suppose, the system of unbalanced rotors (fig.127) mounted on a fixed platform is situated in outer space, i.e. no external forces are applied to it. The system of rotors will create longitudinal oscillations (compression-expansion) in the platform’s body the material of which determines the speed of oscillations’ propagation. Suppose, between the two rotors , and a standing wave emerged in the platform’s body, in the nodes of which rotors are placed. In this case the sum of internal forces in the system equals zero.




Fig.127 A ‘mechanical’ standing wave has emerged in the platform’s body.  Phase displacement leads to the break of synchronicity and shift of nodes and anti-nodes (the standing wave energy is shifted to the left).


Suppose, a phase displacement  between the couples of rotors has been implemented by internal means, the displacement  which is firmly fixed and thereby prevents self-synchronization. How will this system behave itself in space? Will it develop a tendency to move in the form of internal force? The more so that the potential holes (nodes, the areas of energy comfort) are shifted relative to the sources, and one of them is even beyond the platform’s limits. How can such discordant system restore synchronicity? By its motion in wave medium?


If such motion is to take place in the experiment its speed is supposed to be insignificant because the link with wave medium via low-frequency mechanical vibrations is quite small. But one cannot give any definite answer until such experiment is staged.


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8. Phase-frequency tension and gravitational metrics


Is it possible to describe gravitational cause through the notion of ‘space curvature’? It is, at the same time one should understand that we are dealing with a mathematical expression which may have nothing to do with reality. The other matter is when we are talking about distribution in space of certain, say, frequency, characteristics which create in the course of bodies’ motion illusion of curvature. In such case the cause of gravitation could be more easily and gracefully described within the framework of classic logic without any use of ideas of the general theory of relativity.


For example, in rhythmodynamics all types of motion and interactions are expressed through phase displacement and frequency difference. The description is based on two simple formulas:  è . In such case force too () acquires phase-frequency expression:




This also applies to gravitational interrelation in which body M, say the Earth, creates such conditions in space around it in which, once a test body get there, its frequency parameters become asynchronized. The reason is gravitational red shift and experiments based on Mossbauer effect. As a result of such asynchronicity the so-called ‘spider-effect’ emerges, i.e. deformation and sliding of its own internal interference field toward the Earth. In other words, inside the test body the area of energy balance (comfort) moves in some direction and drags atoms in its wake. Outwardly, it looks like a free fall.


Frequency discordance is purely the system’s internal response to the emission created by the Earth’s presence and in which this material system finds itself. That was the reason why the notion of frequency gradient of space, or frequency tension, was introduced in describing the state of space:




In this sense Dn is a frequency gradient of space, frequency tension which depends on mass M and distance r. Now the tendency to gravitate can be expressed in Hz, the fact to which one has to get accustomed. (In case of the Earth on its surface )


Frequency gradient (tension) guarantees bodies a strictly definite in magnitude and direction discordance of internal phases and frequencies, and, correspondingly, concrete measure of disbalance  of their inner comfort. Emergence of frequency discomfort in bodies leads to their auto-reaction, i.e. to their self-propulsion toward increased frequency tension. In this sense the once-sided frequency discordance throughout the body is the nearest cause of the masses proclivity to gravitate toward each other.


Derivation of the formula:


 – rhythmodynamics expression

 – classic expression


, therefore



*If at the level of the Earth’s surface , at the level of the Moon’s orbit the frequency potential (frequency tension) will be equal . This corresponds to the acceleration of the free fall  (here and further on acceleration is described by formula ).


Let’s compile a comparative table of frequency tensions and accelerations which take place on the surface of the bodies of our solar system.


System’s object

acceleration [m/señ2]

tension Dn [Hz]


























Frequency tension at the level of orbits of the planets of solar system


System’s object

Radius [km]

Tension Dn [Hz]

Sun (on its surface)































*The tables and subsequent calculations cite estimated data.


Such approach allows us to draw a portrait of solar system’s frequency tension measured in Hz, and compile a computer chart varying relative to the planets’ position.


One should understand that the planets, too, bring in their alterations in the general picture. For example, Jupiter at the moment of opposition creates tension in the Earth’s area equal to

. This is 11.7 times less if compared with the Sun’s impact on Pluto, still it’s significant enough to alter the Earth’s trajectory. Such magnitude can create acceleration  and alter the Earth’s orbit by 1.3 km. in a single day, by 130 km. in ten days, and by 1166 km. in 30 days.


In a similar situation the frequency tension on the part of Venus equals  which corresponds to the Earth’s acceleration , and alteration of its orbit by 78 km. in ten days, and 700 km. in 30 days respectively. If the Earth is positioned between Venus and Jupiter, the Earth’s deviation from its orbit will diminish significantly.


At present the Earth’s frequency tension is also influenced by Saturn which is in opposition jointly with Jupiter. Saturn’s contribution equals , which corresponds to the Earth’s acceleration  and deviates the Earth from its orbit by 9.6 km. in ten days, by 87 km. in 30 days. As a result, the infinitesimal frequency gradients acting with surprising steadiness can bend the planets’ trajectories. But such alteration has nothing to do with the curvature of space.


The system’s response is, first of all, re-division of its internal energy relations which under the impact of frequency tension leads to the emergence of vector deformation. The system’s response is proportionate to the external impact of body M on the given area of space and inversely proportionate to the squared distance to M. Now we see that neutralization of gravitational field is possible only through elimination of the frequency shift in the test body, which is the task of antigravitational technology.


But what is the cause of the bodies’ displacement of their own inner frequencies, what’s its mechanism?


Rhythmodynamics has pointed out a possibility of existence of a zero-amplitude field, ideally made of waves without amplitudes (photons, gravitons). Amplitudelessness provides for high penetration capability of these waves, their weak interrelation with matter and other effects. But this is a separate serious topic for research.


As for gravitational waves which allegedly come to us every second from the depths of the Universe, and on detection of which huge sums are wasted in order to strengthen the entrenched misconceptions, well, to detect them a different system of views is needed, and, consequently, a different methodology: not by looking for space curvature, but by registering in concrete bodies concrete changes of phase-frequency parameters. A different, though equally uphill, task.


* * *


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9. Black Holes


Everyone in the 20th century knows about the Black Holes: “In keeping with the Newton’s laws and relativity theory, not even a quantum of light can escape a star compressed to gravitational radius. The space where the black hole emerged is curved and closes on itself” [14].



Fig.128. An artist’s view of the black hole. (Borrowed from [1]).


When black holes are discussed in scientific circles, the classic (diffuse) and ‘neoclassic’ (Burakan) concepts of cosmogonic process are thought to be main ones. The first originates from ideas and constructs of W. Herschel in late 18th century; the second was proposed by V. Ambartsumyan in late 1940s.


Unlike ‘classics’ who regard Black Holes a natural step in evolution of matter, the Burakan school postulate a hypothetical ‘pre-stellar matter’ as a relic heritage of cosmological singularity. Pre-stellar matter is supposed to be super-dense, being in a state beyond the influence of fundamental laws of modern physics. In this respect, the Burakan school avoids physical detail about the nature of hypothetical pre-stellar bodies which creates situation when unknown is explained through a greater unknown.


Although the black holes are regarded as exclusively theoretical(!) objects, representatives of competing concepts seriously acknowledge possibility of their presence in the Universe.


Academician Vitaliy Ginzburg, supporter of ‘diffuse cosmogony’, indicates that “black holes can exist within the framework of the general theory of relativity”.  Academician Ambartsumyan of Burakan school also thinks that “…existence of black holes in the Universe is quite possible, being predicted by the general theory of relativity”. Both schools regard the black hole a relativist object. But there are other opinions too. For example, A. Logunov who created his own version of relativity theory of gravitation thinks that black holes do not exist [13]. Still…


What is most interesting is the black holes’ matter which is concentrated in the central ‘no-single-point singularity’ the size of ~10-33   cm (Planck’s size). The fundamental laws of physics, including the general relativity theory and quantum mechanics, are presumed not to work there. There the black hole is regarded as an object which obeys the laws of physics unfamiliar  to us.

It’s the material part of the black hole which causes the most heated debates. Still, there are things in common, properties:


·        Super-powerful gravitational field;

·        Event horizon existence (Schwarzschild’s surface);

·        Unobservability of matter crossing horizon in the course of its collapse and continuing its movement toward central singularity.


These properties are recognized by all schools of research, and it is thought therefore that communication with the outside world for the collapsing object is impossible: any particles (even photons) emitted from the black hole would return to the black hole. Schwartzschild’s surface is a horizon beyond which an outside observer can see nothing. Which means that the body which got into the black hole becomes invisible after its crosses Schwartzschild’s surface. The general theory of relativity suggests a unique interpretation here: a changed geometry of space which became curved, closed on itself [1]. The presence of the super-powerful gravitational field is also explained by space curvature.


To give a full picture one should mention the ether concept which regards gravitation as a consequence of the ether flow into matter [5,6]. If the speed of the flow exceeds the speed of light, light is trapped inside.


So, there is a problem of the black hole and there are several hypotheses which offer their explanations. But is it possible, in keeping with scientific logic and operating only by the known physical phenomena and effects, to give a different explanation of the phenomenon’s properties? Let’s put questions:


·        What happens with the bodies between the distant observer and black hole surface?

·        Why do bodies which have passed the Schwarzschild’s surface become invisible?

·        Can one explain the super-powerful gravitation without resorting to hypothesis of space curvature type?

·        Does the Schwartzschild’s surface block electromagnetic waves?


Let’s give a comprehensive explanation to the phenomenon, and outline the sequence of examination of phenomena and effects by which we’ll be guided.


·        Gravitational red shift and

·        Wave concept of microstructure of matter;

·        Frequency pulling;

·        Deformation of interference field;

·        Gravitational drift;

·        Frequency horizon.


Gravitational red shift


Among gravitating masses the shift of frequency characteristics of matter takes place. Gravitational red shift and Mossbauer effect are known there. Experiments based on Mossbauer effect show that at atomic level a slow-down of oscillatory processes takes place which depends on the distance to gravitating body: the closer it is to the surface, the lesser is the frequency of oscillations [1,7]. In conditions of the Earth such difference is practically indistinguishable (the relative gradient 10-15 per 10 meters of height) but it can be registered by atomic clock. Such clock has a slower pace on the surface than at some distance from it. Another corroboration of dependence of the frequency state of material bodies on proximity to the gravitation source is the red shift of fringes of chemical elements on the surface of stars. By the size of the shift one can determine, for example, the mass of a distant star: the greater is the shift, the more massive or dense it is.


Let’s examine the mechanism of the shift of frequency characteristics.


Frequency pulling in amplitudeless field


By the end of 19th century John W. Rayleigh observed that two organ pipes with vents nearby start sounding in unison, if closely tuned, i.e. mutual synchronization of vibrations takes place. Sometimes the pipes make each other almost ‘silent’[4,8]. Here the competing source of vibrations impose on each other their own frequencies. The degree of such ‘imposition’ (pulling) depends on correlation of capacities and distance between them.


According to [1] matter has a wave origin and can be presented as a package of standing waves with atoms in their nodes (fig.2). Every element of matter (atom) is vibrating. If the minimal distance between atoms is determined by a single anti-node ( 1–10Å), then one can make a judgment about the level of frequency of these vibrations (1018Hz). In this sense matter is invisible for us because the range of visual perception is much smaller (1014Hz). What comes to rescue is the property of material bodies to reflect, or rather re-emit the waves necessary for our visual perception. If matter is in excited (plasma) state it starts emitting on its own the whole range of spectral lines and thereby shows its wave nature.


From the point of view of universality of world environment each atom of a chemical element forms inside and around itself its own frequency interval (frequency environment) within the ranger of which it is stable. When interacting with other chemical elements, or atoms, a different frequency environment is formed comfortable for the aggregation of these very elements and so on for any aggregation of elements. Chemical elements or their combination can exist comfortably only in frequency environments they formed and with any change in the elements or their combination formation of corresponding environment becomes condition of their stability. In other words, one cannot view matter separate from its frequency environment. This is obvious considering that various chemical elements consist of the same elementary particles, and what’s important here is combination which can be stable only in certain frequency interval. Acting on frequency interval leads to a reaction, or to the change of chemical elements if such reaction proves impossible.


Taking into account the above-said one can give a different  interpretation to D. Mendeleev’s table of chemical elements, which reflects only periodicity but gives no explanation to it.


There are interesting characteristics of frequency environment (field): density and amplitude. The field’s density (thickness, saturation) depends on the number of object’s oscillating elements and distance to it, i.e. diminishes with distance. Amplitude is a different matter. If the number of oscillating elements is big, any emitted traveling wave (quantum) can always be matched by identical one but in opposite phase. A situation of amplitude annulment emerges in which there are traveling waves but no resultant one. In this connection calculations were made and 3-D modeling performed [4]. A theoretical possibility of existence in nature of ‘non-emitting’ systems of oscillators and wave amplitudeless fields was discovered.


The absence of amplitude hinders possibility of registering wave characteristics of the field and creates an illusion of absence of anything in space. In such cases the field is referred to as a different kind of matter, but recognition of a model-based way of a zero-amplitude propagation of wave disturbances makes it possible to talk about the wave nature of the fields. Let’s dwell on gravitational field which, according to the rhythmodynamics approach represents a wave amplitudeless background of high frequency, ideally consisting of amplitudeless (non-manifest) quantums, gravitons.


Absence of amplitude makes it possible to talk about high penetration ability of gravitational field: there’s nothing in it, so ‘it’ can penetrate anything. OK, but isn’t there some way in which the bodies feel amplitudeless field? The energy transfer from non-manifest amplitudeless state to manifest one is presumed to take place in non-linear mediums. If non-linearity in the form of material body can displace phases part of the energy is released. Apparently, the release of this energy can be accounted for the emergence of frequency gradient in the bodies. And may be for this very reason in gravitational field the fringes of excited matter are shifted toward the red. Here’s analogy to this: If you have a mechanical pendulum clock, the period of its fluctuations in vacuum, air and water is different. The denser is the medium, the harder it is for the pendulum to swing. The clock has a slower pace in water then in vacuum, but faster then in liquid mercury. In this sense we can talk of gravitational medium which imposes on the bodies which got into it its own frequency rules of the game. In turn, the bodies too bring in changes – they deform the general field.


Deformation of interference field


One of the consequences of the body’s presence in gravitational field is discordance of its frequencies. The body is volumetric and discrete, i.e. consists of isolated atoms which are positioned at various distances from the massive object. For this reason the level of frequency pulling for each atom is different. Let’s examine this issue in greater detail.


Let’s consider the matter as a package of standing waves with atoms in its nodes (12).




Fig.129 Atoms are the sources of waves. Standing waves emerge between neighboring atoms and link the sources with each other. Wave crystal lattices emerge (packages of standing waves) with atoms in their nodes.




                         a                                                        b

Fig.130 a) Different distance between atoms and gravitation source makes the level of their frequency pulling different too. Frequency discordance takes place in the system; b) Frequency gradient leads to deformation of interference field and its sliding off the object. Outwardly the interference pattern resembles a spider, hence the name: spider effect, gravitational spider. To this sort of deformation the system reacts by motion.


Atoms are distanced differently from the surface. The space between the top and bottom parts of the crystal (fig.130a) is measured in just a few angstrom which is enough for a frequency gradient to emerge. Frequency difference triggers the so-called ‘spider-effect’ (fig.130b) [4], i.e. deformation of the general field of interference and deformation of internal relations. The latter implies a directed shift of the nodes of the wave crystal lattice relative to atoms. Atoms seek to stay in the nodes and therefore are forced to move constantly in the nodes’ wake. The system starts moving.


Gravitational drift and weight loss


The Black Hole (here we refer to any source of gravitation) imposes a vector deformation on the body which it seeks to avoid (get rid of deformation) by all means available, one of which is motion in the wake of its own interference field. Which results in drifting toward the black hole, viewed by us as a free fall.


If the cause of the free fall can be described as frequency discordance, i.e. through internal causes, there is no need to introduce the notion of space curvature. It would be more logical to talk about distribution in linear space of potential characteristics capable of creating energy discomfort in bodies.


As for curvature, here one should turn to comparison of the standards of length positioned in different places in space, the metrics of those standards being tied entirely to the frequency state of matter.


Absence of gravitation source guarantees equality of frequency states for the standards, and consequently equality of their lengths (fig.131a).  Appearance of a gravitating body breaks frequency equality, the standards become unequal, i.e. they cannot be used to construct linear figures which is associated with curvature (fig131b). Whereas rhythmodynamics speaks of curvature illusion.





If gravitational drift is caused by frequency discordance, the leveling of frequencies would inevitably lead to end of the fall, i.e. to anti-gravitation [12]. The body would lose weight (not mass) and hang up! But not ‘for free’, though.




Fig.132 Assuming levitation to be a potential human ability, one might say that those rare cases known in history of its manifestation, despite their exceptional nature, testify to a possibility of weight loss at the expense of a changed inner state of human body.


Frequency horizon


What happens if relative to the observer the frequency characteristics of the object under study were to move completely into infrared band? Such body is expected to become invisible for the observer.


Something similar might happen in the area near the black hole because in the course of the body’s approach to it the body’s frequency characteristics are shifted in the infrared band.


Suppose, the body were falling from A to D (fig.133 b).  For the observer A the spectral lines of the body would be moving to the infrared band. He watches the departing body first turning red, then disappearing. Visual detection would cease the moment the package of spectral lines moved completely in the infrared band. If another observer were to fall along with this body he’d find himself in a symmetrical situation: the package of spectral lines characterizing the state of A would move completely to the ultraviolet band. It must be pointed out that none of the observers would notice any frequency changes within his own system.




                               a                                                             b

Fig.133 To illustrate the event two types of the clocks are to be used: real and imaginary ones (a).  Picture (b) shows gravitational red shift of spectral lines (frequencies) in systems B, C and D relative to the scale of system A.


One might say that A and the falling observer ‘disappeared’ for each other, i.e. they are separated by Schwartzschild’s surface. Though it would be much more logical to explain this mutual ‘disappearance’ by significant difference in frequency characteristics of the objects. In this sense Schwartzschild’s surface could be viewed as frequency horizon: the disappeared observers actually stay where they were before, and even can observe each other for some time with the help of the infrared and ultraviolet vision devices.


Nor there is any justification in banning the electromagnetic signals from leaving the black hole, i.e. come out on surface. The other matter is what happens with the sources of these signals, if the black hole matter were considered as such?


If everything is centered on the red shift and its dependence on concentrated mass, then, with its appropriate accumulation, the frequency characteristics of the falling matter which hasn’t reached the surface of the black hole yet would be in radio frequency band. In this respect the body falling on the black hole would behave like a radio source. But the frequency state of the black hole increases (). 


Let’s summarize the results of this simulated experiment:


·        For outside observer A the objects situated between the Schwartzschild’s sphere and the black hole body are invisible because all their frequency characteristics are shifted toward the infrared part of the spectrum.

·        For observer D situated near the black hole surface the outside observer becomes invisible because all frequency characteristics of the outside objects for him are shifted into ultraviolet part of the spectrum.

·        With accumulation of its mass the black hole turns into a super-highfrequency object while frequency parameters of the falling matter will be shifting to the radio frequencies band.



Relativity of frequency horizon


The black hole matter forms appropriate medium inside and outside itself. Any material object which enters or leaves it must change its frequencies appropriately.


We matched frequency horizon with Schwartzschild’s sphere the radius of which is customarily determined by the formula , i.e. the greater is the mass, the greater is the sphere’s radius. In rhythmodynamics frequency horizon is a relative notion, because it has a different physical meaning. So the formula describing the horizon radius for a distant observer is different too: , where . Replacement of mass (M) in the regular formula by its frequency state () makes it possible to examine the phenomena and processes linked with the black hole in frequency aspect. Now we can say: the higher is the frequency of the black hole body, the bigger is the radius of its frequency horizon.  Unlike Schwartzschild’s sphere, frequency horizon is a relative notion which depends on relation of frequency states of the ‘observer – object’ systems.


If for observer A frequency horizon were defined by surface 1 (fig.133a), then object C would be invisible for him. For observer B the frequency horizon is different and defined by surface 2 that’s why object C is visible for him. The reason is different relativity of frequency characteristics.


It’s interesting that for observer C there may be two horizons: the inner one behind which system D is hidden, and outer one beyond which system A cannot be seen. System C and the observer happen to be isolated on both sides but if objects with similar frequency characteristics are to emerge in space, they will be visible for C.


Let’s examine a hypothetical example with two black holes of equal frequencies, on the surface of which there are observers D' and D. D' and D are in equal frequency conditions therefore communication between them is possible. But outside objects, say observer A, are invisible for them because of the large difference of frequency characteristics.


Understandably, A cannot see D' and D either. Here it would be proper to talk about frequency divided parts of a single space. For each type of observers the world seems real only in their accessible frequency band. Everything which stretches beyond this band seems to them beyond their comprehension, i.e. beyond their frequency horizon. In this respect every world limited by frequency band would be perceived by the other world as a kind of black hole!




Fig.134 In the environs of massive bodies illusion of frequency (pseudo-frequency) space emerges.



Objects’ materialization and dematerialization illusion


A material object moving from D' to D (or vice versa) and passing by A would behave quite weirdly: first, it would appear as if out of nothing, then, departing, would disappear as if dissolved. The cause of this are changing frequency characteristics of the moving object: when they fit into the range of visual perception of A the object becomes visible. Further shift of frequency characteristics leads to the object’s visual disappearance. But, as was said before, the object could be observed for some time in the infrared band with the help of special vision devices.




Fig.135 Illustration of frequency horizon issue.  The angle of reflection does not allow observer on the surface to see objects under water, nor can observer under water notice a falling diver before he hits the surface. The transfer through real and at the same time conditional border between air and water is accompanied not only by disappearance of the object in one world and its appearance in the other but by intensive wave disturbances on the dividing line. The observer under water might think that spontaneous birth (materialization) of the object took place, while the observer on the surface might imagine it disappeared (dematerialized). In this example the border between different frequency mediums is evident because our sense organs cover both frequency bands.  Interesting situation might emerge when different frequency worlds (mediums) are encapsulated in their volume one in the other. If frequency barrier is sufficiently big, i.e. cannot be bridged by our sense organs, the transfer from one frequency band to the other would be accompanied by effects of disappearance in one world and appearance in the other, and wave disturbances of the conditional division line. These effects are not only possible to calculate without the use of additional dimensions, they are also comprehensible within our three-dimensional logic.


The mechanism of materialization and dematerialization was described in my work “Frequency space” [3]. It was also suggested there to use frequency as a coordinate ().  


Introduction of a frequency coordinate seems a natural and logical step. With additional frequency coordinate we have a chance of a deeper penetration into the root-cause of things.


The motion along frequency coordinate in free space differs from similar motion in the field of the black hole.


On the outskirts of the black hole the change of objects’ frequency characteristics is not direct and is always linked with the transfer in metric coordinates. In this sense the black hole creates conditions similar to frequency space.


Motion in classical frequency space is different: the object, moving along frequency axis, materializes and dematerializes without changing its position. Does it mean that it’s physically absent in space? From rhythmodynamics positions, the object is present but not visible.


We’ve come close to the dividing line by crossing which we inevitably get into the other equally real world. Such worlds can coexist with each other side by side being separated by frequency horizon, and therefore visually, they regard each other as ‘black holes’. They barely interrelate [11], that’s why such interrelation is called sensual, informational [9] perceived at the level of intuition [10].




·        Rhythmodynamics space has non-linear distribution of frequency-amplitude characteristics (potentials, conditions) which creates curvature illusion.

·        Frequency pulling is the cause of gravitational red shift, slow down of the pace of atomic clocks, and frequency discordance.

·        Frequency discordance of the body leads to directional (vector) deformation of interference field. The action of deformation is countered by reaction of motion (free fall).

·        Massive body becomes invisible due to the shift of its frequency characteristics toward ultraviolet part of the spectrum. In such interpretation ‘collapse’ is viewed as a fast shift of the body’s frequency characteristics.

·        The notion of ‘Schwartzschild sphere’ is replaced by frequency horizon, once beyond it the object becomes invisible.

·        Electromagnetic waves freely pass through Schwartzschild sphere in both directions.


Although until now on the issue of black holes there were two antagonistic hypotheses: classical (diffuse) one and Burakan one, with the publication of this paper a new point of view has emerged, that of rhythmodynamics, which asserts that:


·        There are no curvature of space and black holes in their usual sense but there is illusion: the  bodies become invisible due to the frequency characteristics shift toward infrared or ultraviolet area.

·        Our universe is surrounded on both sides by frequency horizon, and therefore is invisible for the outside worlds, i.e. being a ‘black hole’ for them!

·        In the course of the black hole’s mass accumulation its overall frequency increases until a moment comes when any further frequency increase would lead to, first, weakening of gravitational properties (because of weakening effect of frequency pulling) until their complete annulment , then to the black hole transfer into other frequency band of space. For residents of a different frequency dimension this process may look like a birth of a new star, or an elementary particle.





1.        Jay Orear. Physics. Translated from English. Mir, 1981.

2.        Blekhman I.I. Vibrational mechanics. Fizmatlit, 1994.

3.        Ivanov Yu.N. Frequency space. Novy Tsentr, 1998.

4.        Ivanov Yu.N. Rhythmodynamics. Novy Tsentr, 1997.

5.        Yarkovskiy I. O. Universal gravitation as a consequence of formation of weight in matter of stellar bodies. Kinematic hypothesis. Kushnerov publishers, 1912.

6.        Atsukovsky V.A. Hypotheses of Etherdynamics. Petit publisher, 1997.

7.        Detlef Kamke, Klaus Kramer. Physical foundations of measurement units. Translated from German. Mir, 1980.

8.        Strutt, John (Lord Rayleigh). Theory of sound. Gostehizdat. 1944.

9.        Yuzvishin I.I. Informationology. Radio i svyaz. 1996.

10.     Ivanova N.M., Ivanov Yu.N. Life by intuition. Komplekt, 1994.

11.     Stavitskiy A.I., Nikitin A.N. Speaking the language of nature. Intan, 1997.

12.     Ivanov Yu. N. Compression of standing waves, rhythmodynamics and third state of quiescence. RIA, 1996.

13.     Logunov A.A. Relativist theory of gravitation and Mach principle. Institute of high energy physics, vol.29, edition 1, 1998.


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10. About Louis de Broglie’s law of phase harmony


By N. Nevesskiy


I’d like to tell about the law of phase harmony formulated by Louis de Broglie in 1924. This law is seldom mentioned in the papers on quantum theory, although it actually kick started this theory, and despite the fact that de Broglie himself thought this discovery of his was pivotal in his life.


Louis de Broglie was born in 1892, into one of the most aristocratic families of France. He had the blue blood of French royal family, he was a duke, but despite his noble standing he lead the life of ordinary people. Having graduated from a college he entered Paris University and studied humanities: history, literature, paleontology.


Later in his life his knowledge of humanities benefited him greatly: he was excellent writer, and his books on the most difficult issues of wave mechanics testify to this. He was also an avid reader of the history of science works (he confessed he had read more books on history than on physics), whereas his study of paleontology had probably lead him to conclusion that all things were alive because even seemingly lifeless stones kept the traces of life which had flourished millions of years before…


When young, de Broglie felt that his liking for science prevailed over humanities, he put aside his recently acquired diploma and reentered the university to study for science degree. After graduation he takes up research of the most crucial at the time issue of quantum-wave dualism, an odd phenomenon but strikingly manifest during experimental studies of light, as well as x-ray and g-radiation.


His closest teachers were Paul Langevin and his elder brother Maurice de Broglie.  Maurice who was 17 years Louis’ senior was at the time an acknowledged physicist who took part in the first Solvay conference and who had a well-equipped laboratory specializing in roentgen spectroscopy research. There the young Louis learned the secrets of experimental science, grasped firmly the range of problems which required solution and began tackling them. There his work as a theorist started, and the results of it lay foundation for his doctorate thesis.


The law of phase harmony became the central point of his paper. The essence of de Broglie’s idea was brilliantly expressed by G. Lochak [1], his closest pupil and aide.


On the one hand, the idea seems simple, on the other, it’s a mystery how one could come to it. The very train of thought was extraordinary. May be it was the result of some sort of enlightenment, or it could be the result of a special way of De Broglie’s thinking.


De Broglie, it must be emphasized, had a very imaginative thinking. He stressed that for him understanding implied very clear, as if real, vision [2]. There was no understanding without image. The abstract mathematical method which physicists used was strange to him.


De Broglie was also a rabid supporter of relativism. Relativity theory had just emerged but was already acknowledged, and De Broglie, too, was fascinated by its unusual beauty. In a number of basic reasonings of relativity theory ‘observers with clocks’ were used which was, in De Broglie’s opinion, a very apt revealing image. ‘Observers’, according to the theory, were not theorists striving to comprehend the developments in micro-world, but the residents of this world: electrons, protons, etc.


Elementary particles are those observers; which is important. All of them have their own clocks and interrelate with each other through wave signals exchange. A very powerful analogy which De Broglie, with his image thinking, accepted literally.


Elementary particles, he reasoned, are complex systems (because only complex systems can interrelate in such way). Each particle has its own inner periodic process, which, on the one hand, serves as a measure of internal time (i.e. ‘tells time’), on the other, provides for creation of those wave signals used in communication.


For propagation of those wave signals a medium was needed, and ether (in its classic sense) was no good for this role as its use could lead to conflict with relativity theory. Which De Broglie avoided by all means being a devout believer in relativity. Later on he, nonetheless, introduced this medium in such a way as not to harm relativity. But initially, in 1924, when he wrote his doctorate thesis, all his attention was focused on ‘internal clocks’.


So, every elementary particle had its own internal oscillatory process. It sets the scale of time and functions as internal clock with the help of which the particle can navigate in time. De Broglie doesn’t dwell on the process itself. What interests him is process frequency, which he describes in his famous formula:




Both parts of this equation were known before, but De Broglie was the first who brought them together. “That’s how it should be, he wrote, due to the great law of Nature”.


This is the first formula in his thesis. It was very beautiful, and could be the most beautiful, but for one thing. This equation determines the frequency of inner process only in one’s own frame of reference. After transfer to the other system it stops to work, being not Lorentz-invariant. Indeed, in the case of a moving electron (he usually referred to electron when speaking of elementary particle) mass increases like:  while the frequency of clock pace decreases like: (here). Thus, equation (1) loses its validity.


De Broglie noticed this at once, and this situation puzzled him greatly. He was bubbling with relativist ideas, which he never doubted. He sought to defend the equation (1), but at the same time he knew he wouldn’t succeed unless he made this equation relativist.  De Broglie solves this task, making a second, resolute and radical step by introducing the notion of stationary wave.


Which meant the following: Suppose, he said, the oscillatory process going on somewhere inside the particle at frequency  is reflected (or somehow permeates) outside so that in every point of space around the particle an oscillation is initiated of exactly the same frequency. Or, in other words, in every point of the Universe a clock emerges running in pace with the clock of the elementary particle.


Mathematically, this supposition could be described by formula:



(In every point oscillatory process with frequency  takes place. All processes are in phase irrespective of coordinates).


The same is true for its own system where electron is motionless. If it moves time is transformed according to Lorentz: . As a result of which all clocks become asynchronized and equation (2) turns into:




Which is the stationary wave.


It can be seen from definition. Its frequency is , i.e. it changes the same way mass does. So equation (1) can be made relativist if its frequency were referred not to the frequency of internal process, but to external one, the frequency of Universe tuned to the rhythm of the particle. So ‘zeros’ of (1) can be erased and one can write:



This formula is already relativist!


Stationary wave propagates with phase frequency  and its wave length is , where- frequency impulse.  


This is the De Broglie’s wave length.


So, De Broglie managed to make the relation between energy and frequency Lorentz-invariant. But at what a price! The general picture, compared with classic one, became much more complex. In classics, when you examine a moving particle you deal with only one object, this very particle. De Broglie has two objects to deal with: particle and stationary wave linked to it. Both objects are independent, though related.


Incidentally, De Broglie has no quantum-wave dualism at all, he has no notion of some ‘particle-wave’. This physical centaur was born later, and it was introduced in physics not by De Broglie but by other later interpreters. De Broglie regarded both the particle and wave as independent entities, and he thought the wave to be physically real wave.


Studying these two objects as independent ones, he came to his famous law of phase correspondence or phase harmony which says that “The moving electron is always in phase with its stationary wave, or - the phase of stationary wave in the point of electron position always  coincides with the phase (inner clock) of the electron itself”.


This assertion is easy to prove. The phase which electron has in time t is , while the phase of stationary wave in the point of electron’s position (with ) is:


, i.e. the same value.


So, . But what’s next? De Broglie thought the stationary wave linked with electron, being physically real, can somehow influence the behavior of the electron itself, once they are always in phase. Following this view, he studied hydrogen atom so as to apply his assumptions in concrete problem solution and with their help obtain the rules of orbits quantization. (Such rules had already been set by Niels Bohr. They looked beautiful but were completely incomprehensible).




His reasoning was the following: Suppose, says De Broglie, electron were moving in circular orbit with speed v. The stationary wave linked with it moved in the same orbit and the same direction, but with speed  (i.e. much faster). After some time  the stationary wave catches up with the electron (fig.136). Time  is determined from relation  (where  – length of orbit), from which: .


By this moment the electron accumulates the phase:

. And the same phase is accumulated by the stationary wave.


“It’s almost self-evident (in De Broglie’s own words) that this phase should correspond to interger of electron’s oscillations”, i.e.:




So, a whole number of De Broglie’s waves (stationary wave lengths) must fit in the orbit. Hence is the outline of the physical meaning of statement about a whole number of oscillations because only in this case the stationary wave covering several times the circumference of the orbit won’t suppress itself.


As , where  is orbit’s radius, the latter equation can be transformed to:



which is the second postulate of Bohr. So, the notions introduced by De Broglie about internal process and stationary wave proved quite effective if they allowed to obtain so easily the rule of quantization of the impulse’s moment for Bohr’s orbits.


This was a certain feat appreciated by everyone. De Broglie received unanimous acclaim from scientific elite; his works were studied, and efforts were made to their advancement [3]. De Broglie’s concept had definitely clarified something, but at the same time raised lots of new questions. For example:

·        how (why) does stationary wave move in circles? (Radial heterogeneity was apparently necessary for this which could have the wave locked on itself due to internal reflection. This issue was studied by Ervin Schrodinger);

·        what was exactly meant by “internal periodical process?”

·        what’s ‘stationary wave’? Is some sort of medium necessary for its propagation, if so, how is it to be introduced without contradicting the special theory of relativity? How does it relate to electron: is it born by (only) it, or is the whole Universe participating somehow in its conception?

·        how does the stationary wave influence electron’s behavior, and what is after all behind the law of phase harmony?


And so on and so forth, including the question as to ‘what’ or ‘who’ is the electron? The idea of the electron’s free will was quite seriously debated, in which N. Bohr himself took part.


In short, passions were running high, and physics was rapidly developing. Schrodinger produced his famous equation. Bohr suggested its probable interpretation. Calculus was rapidly developing, and theory was acquiring quite definite outline.


De Broglie himself was working incessantly. He was developing the so-called ‘double solution theory’ according to which particles, remaining localized entities, were sort of inserted in the wave in the form of singularities of a uniform solution. According to this concept, the particles acquired sort of wave-like wings.  The work progressed slowly due to serious mathematical problems. One had to study non-linear equations producing soliton-like solutions, which was not easy and required time and strength.


Meanwhile, physics was pushing onward. Though it moved in not quite the same way de Broglie chose, and with the help of other, abstract mathematic means which were alien to de Broglie. “He was witnessing the emergence of an entirely different approach to theoretical physics. Which was based not on description of the laws of nature with the help of space-time images, but on algebraic and geometric constructs in abstract, usually complex and multi-dimensional spaces”[4].


Physics was replaced by math. Surprisingly enough, this approach brought fruit. Theorists dived boldly into mathematic abyss and brought up the treasure-troves in the form of elegant formulas proved by experiment.


Such abstract method was alien to de Broglie. He had an image thinking, which for him was a matter of principle. He went his path, though he felt he was lagging behind, and could become a straggler for good. In 1927, at the 4th Solvay conference he nonetheless chose to fight and delivered a report about his double solution theory, not yet completed at the time. The report went unnoticed.  De Broglie was not understood, nor supported, and he finds himself alone. The victory was won by the indeterminist interpretation of quantum mechanics developed by the Copenhagen school (which is still generally accepted). After which the defeated de Broglie leaves the scene.


Discouraged he returns to Paris where he teaches theoretical physics at the Institute of Henri Poincaré. He suspends his research being in a way convinced that the path he had chosen was wrong and the right one was the main road chosen by the rest of the world physics. Amongst others, he teaches quantum mechanics which he persists to call wave mechanics sticking to its orthodox interpretation.


Time passed leaving youth to recollections. De Broglie seemed to reconcile himself with his defeat and didn’t grieve much that his idea about phase harmony passed into oblivion.


25 years later, when de Broglie was slightly over sixty, the scales fell off his eyes. He understood that ideas of his youth were significantly richer in content than the present ideas of quantum mechanics, and the path he had gone before and which he left was in fact the true and the most promising one. Since that moment a second rise in de Broglie’s creative life began. He writes numerous papers and publishes a whole range of books devoted to refutation, criticism and re-interpretation of the foundations of quantum mechanics (on the whole over 50 papers and 12 books!). He returns to the ideas of his youth, and begins to examine steadily the numerous difficult issues which he left out before.


First of all, those devoted to the composition, structure and internal dynamics of elementary particles as well as the medium which fills in the inter-particle space and which is necessary for the existance of stationary waves as their support and propagator. He brings in the notion of such medium which he calls subquntum medium and models it as a tachyon gas. Tachyons are the particles with pseudo-mass and super-light velocity. De Broglie borrowed this idea from the Russian physicist Terletskiy and used it because he thought it didn’t contradict relatiist postulates.

According to de Broglie, particle is the most complex system engaged in a constant mass and energy exchange with environment.  It’s a sort of a drop of mist suspended in steam. To describe the life of such system, particle plus environment, he used thermodynamics methods, generalizing them and applying at the next hierarchic level of matter organization. One of his books has this name: ‘Thermadynamics of isolated particle’ [5]. He thought subquantum medium to be energy containing substance which he called the ‘hidden thermostat’. In particular, physical and thermodynamic characteristics of this medium as well as internal characteristics of elementary particles themselves - they represent the ‘hidden parameters’ of which there’s so much talk nowadays.


De Broglie began and waged his great battle alone. He was only helped by youth. He was in the same situation he had been at the time of his youth, even in more complex one becausae quantum mechanics theory had long become fully developed, and he himself was not young and occupied a solid position in scientific world. His colleagues were puzzled. Opinions became split. Some were welcoming and interested, some neutral, others openly negative. But it didn’t discourage de Broglie. He worked with enthusiasm and delight. His new rise was confident and long. The peak of his creative acivity was during his 70s and 80s. ‘I often ask myself, he told his student G. Lochak on the eve of his 80th birthday, if the period after seventy was, from the point of intellectual work, the best period of my life?’


And de Broglie did manage to breach a gap in the quantum theory bastion which had already became classical, and thus violate the physicists quiet, stir their minds, instill in them doubt and hope and thereby spur them into new scientific research. He did succeed in this! He had no time to complete his theory, though much was done for its development and substantiation. The concepts of ‘pilot-wave’ and ‘phase harmony’ actually experienced their revival.


De Broglie pinned much hope on those who would follow him, urging them to think independently and not to be diverted by superficial results which produced elegant formulas but revealed little; he urged them to go ahead relentlessly, penetrating farther and deeper into the innermost essense of things. He urged all who had a passion for investigation of the foundations of nature to take a closer look at the law of phase harmony and discover the deep and crucial mystery hidden in it. He believed this mystery would soon be discovered and would bring fruit, and he was keen to pass on his belief and hope to those who walked in his footsteps.


* * *     


1.        G. Lochak. “De Broglie’s initial conception of de Broglie waves”. From book: “The wave-particle dualism”, Dordreht, Holland, 1984.

2.        Louis de Broglie. “Revolution in physics”. Atomizdat, 1965.

3.        Max Jemmer “Evolution of quqantum mechanic notions”. Nauka, 1985.

4.        L. de Broglie “Correlation of Heisenberg’s indefinites”. Mir, 1986.

5.        Broglie, Louis de. “La thermodinamique de la particule isolée”. Paris, Gauthier-Villars, 1964. 


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11. Rhythmodynamics’ place in physics


Science, a special kind of cognitive activity aimed at development of objective, systemically classified and substantiated knowledge about the world.


Physics, Gk physika. The major branch of natural science which deals with the forms of motion of matter, its properties, and with phenomena of non-organic nature.


Classical mechanics is a branch in physics which determines the laws of motion of macroscopic bodies whose velocity is much less then the velocity of light in vacuum.


Quantum mechanics is a theory in wave mechanics which determines the method of description as well as the laws of motion of micro-particles (elementary particles, atoms, molecules, atomic nuclei) and their systems (crystals, for example) as well as relation of quantities which characterize particles and their systems with physical quantities measured directly in macroscopic experiments.


Classical and quantum mechanics methods of research are ideologically incompatible, therefore these branches of physics are regarded independent.


Rhythmodynamics is a theory in wave physics determining: 1) the role of periodical processes in formation of natural phenomena and their properties; 2) processes forming all kinds of motion and properties of macroscopic bodies as well as micro-particles (atoms, molecules) in any speed regimes.


In the author’s opinion, rhythmodynamics occupies a place between classical and quantum mechanics (classical mechanics ↔ rhythmodynamics ↔ quantum mechanics).


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Conclusion: results and perspectives


No nonsense in science, please…


No scientific school can claim to possess the absolute truth because there is always a possibility to find fault with any of the system of ideas. In this respect competition between schools looks strange, to put it mildly, and has nothing to do with the actual science. There can be no winners in such type of competition – it ‘breeds’ only pseudo-truth which the winning school introduces into curriculum, thereby strengthening its supremacy over the defeated opponents.


Another matter are model interpretations which can coexist peacefully side by side. Because no one knows for sure what the World actually is, and why It is. Model interpretations allow us to take an unbiased look and say which of those models reflect most adequately the natural phenomena under study and therefore would be useful to society in the foreseeable future. Rhyt