The Theory of Infinite Hierarchical Nesting of Matter as the Source of New Ideas by Sergey G Fedosin

Armin Nikkhah Shirazi

Dear Sergey,

Here is some honest feedback on your essay.

You begin you work with: "Over the past 20 years, both in physics and in philosophy, new results were obtained related to the rapid development of the Theory of Infinite Hierarchical Nesting of Matter. At the present time this theory claims to be the dominant scientific paradigm, affecting the whole science."

I wonder whether you meant that this theory was the "dominant scientific paradigm" in the community of researchers advocating its ideas (it would then be a tautological statement), or whether you meant "most promising" instead of "dominant", but as stated in your paper it does not appear to be correct. For better or worse, the dominant scientific paradigm in fundamental physics at present appears to be string theory (I am only stating a matter of fact as I understand it, I am not a proponent of string theory).

Then you introduce an unfamiliar term (syncretic logic), giving a reference to a book you wrote in Russian. For those of us who don't know Russian the reference will not be very useful in understanding this concept which seems to play an important role in your theory. Then the next several paragraphs contain references and terms that are unfamiliar to me, and which are usually not explained, except for providing links to some long Wikiversity articles.

All of these factors have made it very difficult for me to understand your ideas. My suggestions would be as follows:

1) When introducing non-standard or unfamiliar terms, I believe it would be better to try to give a concise definition in your paper, perhaps even with an example. This could be done within the body of your paper, or a glossary at the end for easy reference.

2) You have evidently worked on this theory for a long time, and as a result, it seems very familiar to you. You may also be interacting within a community of like-minded individuals who basically agree on the major concepts, and as a result, you may think that the theory better known than it actually is. I had never heard of this theory previously, and the discussion in your paper did not help me understand how it works. It may well be the case that it has some very useful ideas in understanding nature more deeply, but I could not understand enough to be able to tell whether that is the case or not.

3) When making major radical claims, I believe it is absolutely, fundamentally, essentially, critically, vitally important to include new predictions that can be tested by experiment. The more unfamiliar the ideas you present, the more important it is to include new falsifiable predictions. If you don't do this, it becomes just too easy to dismiss your theory as just another crackpot scheme.

I could not tell whether your theory made any new predictions. Remember, explaining patterns that we already know doesn't count, it must be a new prediction of an experiment, the outcome of which is genuinely not yet known. Explaining what we already know is just the minimum for any framework whatsoever just to begin to considered.

Ok, I have attempted to give you frank criticism, not to put you or your theory down or to insult you, but because I have observed certain features which may make it more difficult for your ideas to be disseminated or considered more widely, and want to try to help you recognize these features, and if you are so inclined, to eliminate them. I hope you found my criticism useful.

All the best,

Armin

Sergey Fedosin

Dear Armin,

Thank you for feedback. I suppose that in beginning of the essay it should better to write that the Theory of Infinite Hierarchical Nesting of Matter try to develop into the dominant scientific paradigm. I agree with you that glossary at the end of essay is very useful. But when the essay was ready its size was more then 25,000 characters, so some part of the text was excluded. It is really impossible give all the predictions of the theory in such small essay. I hope additional information available in the references of the essay may be useful for better understanding of theory.

Sergey Fedosin

Dear Hoang,

Thanks for the nice thoughts.

Sergey Fedosin

[deleted]

Dear Sergey,

Thank you for your considered and thoughtful reaction to my reaction. It is because of your openness to my criticism (which I take as a sign of your integrity) that I have taken the liberty to give additional comments.

It is really too bad that the word limit did not permit a more comprehensive explanation of the building blocks of your ideas. I would like to mention that the 25k word limit applied only to the body of the essay. There are several essays in this contest above this limit which were allowed entry because the excess words were part of the 2 page additional information. Although I cannot speak for FQXi, of course, it is possible that having a glossary or something like that no longer than 2 pages in an appendix might have been acceptable for your essay even in its current form.

Hopefully in future contests you will be able to maximize the possibilities with the given constraints to help the reader better understand your ideas.

As for the predictions, it seems to me that when faced with space limitations, one should prioritize the importance of the predictions to be given and focus just on the ones that have the greatest importance. The criteria for prioritization are of course yours to determine, but some I would consider are:

1) How unexpected would it be if the prediction was confirmed?

2) How likely would it be that the prediction could be explained using current theories (i.e. how well does the result fit in our current paradigm)?

3) How realistic is it that the experiment can be performed?

Again, I hope you find this helpful and wish you all the best,

Armin

Benjamin Dribus

Dear Sergey,

I enjoyed your essay. It seems that each new generation of physicists discovers finer structure than was previously believed to exist, from atoms to nuclei to nucleons to quarks and so on. There's no obvious reason to expect this process to terminate, although it also seems that each generation believes they are near the bottom! In any case, I agree that scale dependence and self-similarity are crucial concepts that have not received the level of attention they deserve. Take care,

Ben Dribus

Sergey Fedosin

Dear Benjamin,

In accordance with your essay the general relativity and the standard model of particle physics need to be more clarified and demand some refinement. I agree with you and think we must use now not the pure mathematical models but real physical models. It is the main goal of the Theory of Infinite Hierarchical Nesting of Matter. From the axiomatic point of view any new theory must have about 5 axioms. But in Standard Model there is about 20 unknown parameters! It seems such theory is more adaptive then physical theory.

Sergey Fedosin

Dear Hoang,

The reason for mass of a body in the Le Sage s theory of gravitation is interaction of graviton fluxes with the substance of the body. When the velocity of the body is constant in relation to the reference frame in which the graviton fluxes are isotropic the force of inertia is absent. But the force of inertia appears in acceleration of the body since the action of graviton fluxes changed. About connection of mass and energy see also the article: The Hamiltonian in covariant theory of gravitation. vixra.org, 22 May 2012.

The mass of Higgs boson is considered about 125 GeV from the proton-antiproton collisions at sqrt(s) = 1.96 TeV. See http://arxiv.org/abs/1207.0449 and http://www-d0.fnal.gov/Run2Physics/WWW/results/higgs.htm. In my opinion W-bosons and Higgs boson are quasiparticles. In the comment No 6 (February 11, 2010, http://serg.fedosin.ru/download/com.pdf) of Comments to the book: Fizicheskie teorii i beskonechnaia vlozhennost' materii. Perm, 2009, 844 p. ISBN 978-5-9901951-1-0. (in Russian), I found that appearance of W-bosons is a demonstration that substance of collided protons has speed about the value of escape velocity at the surface of proton in the field of strong gravitation. On the other hand it is supposed that the characteristic speed of substance of neutron star is 0.23 c (where c is the speed of light), and in nucleons the characteristic speed is c. Accordingly for praons the characteristic speed is 4.3 c. Praons relate to nucleon in the same way as nucleons relate to neutron star. So if we shall collide protons then it possible the case that their substance speed is equal to the speed 4.3 c of praons. According to calculation the energy of protons in such collision must be more then sqrt(s) = 1.4 TeV. The situation with Higgs boson may be similar to such collision of two neutron star when their substance fly with the speed of light after collision. About weight and force of gravitation see for example Model of Gravitational Interaction in the Concept of Gravitons. Journal of Vectorial Relativity, March 2009, Vol. 4, No. 1, P.1-24.

Sergey Fedosin

Janko Kokosar

Dear Sergey,

Thank you for your comment.

You describe that interactions of elementary particle do not give black holes (BHs). Thus you conclude that black holes do not exist. But I claim that elementary particles are already BHs without typical gravitational interactions. I also do not claim that elementary particles are the same type of BHs as large holes. (Quantum physics probably change a lot of properties.)

You also claim that enlarged gravitational constant at small distances exists. I claim that this is agains rules of general relativity, and against claims of Duff.

I did not read your articles precisely, are my arguments enough?

Best regards,

Janko Kokosar

p.s. Some time ago I searched theory of strong gravitation as a reference. I do not rememember precisely, do you the only author of this idea?

Sergey Fedosin

Dear Janko,

According to your essay: < But this confirms that the elementary particles are BHs or something very similar to BHs or at least that they are gravitationally built up objects.> I supposed that you understand black holes (BH) in usual way. The idea of strong gravitation is very old. A lot of people try to calculate Strong gravitational constant. With this constant the radius of a particle with the mass of proton is close to radius in the formula for the black hole: [math]R = \frac {2\Gamma M_p}{c^2} = 5.63\cdot 10^{-15} m[/math], where [math]\Gamma = 1.514 \cdot 10^{29} m^3 /(kg s) [/math] is strong gravitational constant, Mp is proton mass, c is speed of light. But in reality radius of proton Rp is equal to [math]8.73 \cdot 10^{-16} m[/math], and so Rp < R. On the other hand instead of c we must use speed 4.3 c in the formula for the radius of black hole. It is so the speed of light for the proton is the characteristic speed of its matter, as for the neutron star the characteristic speed of its matter is equal to [math]C_s = 6.7 \cdot 10^7 m/s[/math]. See Stellar_constants. Then for the black hole at particle level of matter must be: [math]R_b = \frac {2\Gamma M_p}{(4.3 c)^2} = 3 \cdot 10^{-16} m[/math]. We se that Rp > Rb, and proton is not a black hole, as a neutron star.

Sergey Fedosin

Janko Kokosar

Dear Sergey

My theory,, (and this) give that electrons are black holes. They are superpositions of Planck's masses and mass zero and they can be calculated. Thus they are not against uncertainty principle. I admit, if Higgs mechanism will be confirmed in CERN, this model will be probably rejected. But in my essay I have also other parts of this theory, which will survive Higgs mechanism.

I do not yet see hope for your theory:

1. You included strong gravitational constant which rejects some benefits given by general relativity. They are, the principle of equivalence, background free spacetime etc.

2. You do not enough include quantum field theory and quantum mechanics, which are base of our world.

3. Where do you obtain 4.3c?

4. I think that idea of strong gravitational constant is to reject contradictions against QM, which arise when black holes are smaller than Plank's mass. Am I correct?

Otherwise, you were very sucessful to read 250 essays. I do not succeded in this. Which essay do you recomend?

Regards Janko Kokosar

Sergey Fedosin

Dear Janko,

Here are answers to your questions:

1.< You included strong gravitational constant which rejects some benefits given by general relativity. They are, the principle of equivalence, background free spacetime etc.> The general relativity may be changed by Covariant theory of gravitation . In view of it the principle of equivalence, background free spacetime etc. are not more benefits given by general relativity.

2. < You do not enough include quantum field theory and quantum mechanics, which are base of our world.> The approach of quantum field theory and quantum mechanics is very limited to waves form of calculation in physics and is probabilistic. It is not a common physical approach.

3. < Where do you obtain 4.3c?> From the similarity relation for speeds, see my essay. The characteristic speed of the proton substance is c and its rest (absolute value of total) energy is [math] M_p c^2 [/math] where Mp is mass of the proton. For the neutron star we have characteristic speed of substance [math]C_s = 6.7 \cdot 10^7 m/s[/math] and absolute value of its total energy is [math] M_s C_s^2 [/math] where Ms is mass of the star. From here the ratio is c = 4.3 Cs. Accordingly, the speed 4.3c is the characteristic speed for the substance inside of the particles which are inside of proton.

4. < I think that idea of strong gravitational constant is to reject contradictions against QM, which arise when black holes are smaller than Plank's mass. Am I correct?> From the theory it follows that Planck mass is equal to product of proton mass and similarity coefficient in size between star and atomic levels of matter. So the Planck mass is not a mass of a real particle, since there is should be similarity coefficient in mass, not similarity coefficient in size. In view of it strong gravitation do not depend on quantum mechanics and its Planck mass.

Sergey Fedosin

[deleted]

Dear Sergey,

I posted the following under Goerge Ellis' essay giving reference to your essay.

Also this addresses your question to me on Sep.14. You wrote: "Also I can not understand why you brake up the energy Mvc with the help of speed u ? The particle speed v is relative to the centre of inertia of system of particles, and the speed u is the speed of system of particles as a whole. These speeds are not correlated with each other. So can you prove that Mvc( 1-u/c) is a physical quantity and has physical meanings?" (Note: v is the velocity of one particle relative to earth and u the velocity of the earth i.e. velocity of the centre of mass, relative to the next hierachic level).

------------------------------------

SECOND LAW OF THERMODYNAMICS - A TOP DOWN CUASATION

Dear Fred and George,

"I am wondering if top-down / bottom-up causation is a duality? Could one exist without the other? I think that is what you are saying or the point you are trying to make".

'Top Down' concept is not something trivial and marginal as the author of the essay thinks. (For instance he thinks the top down causation of the Sun on earth manifests in marginal effects like the tides. Well then lunar tides will have to be considered as 'Bottom Up!!!'). 'Top down' concept is far, far deeper. It is one of the basic principles in Nature.

Nature's processes are a hierarchy of self-similar structures. (Sergey Fedosin brings this out in his essay). If they are a 'hierarchy' how is the hierarchic dominance and organic links established between two adjacent levels?.

Here is Newton for you: "And thus Nature will be very conformable to herself and vey simple, performing all the great Motions of heavenly Bodies, by the Attraction of Gravity, which intercedes those Bodies, and almost all the small one of their Particles by some other attractive and repelling Powers which intercede the Particles. ...... To tell us that every Species of Things is endow'd with an occult specifick Quality (of Gravity and of magnetick and electrick Attractions and of fermentations) by which it acts and produces Effects, is to TELL US NOTHING: But to derive two or three general Principles of Motion from Phaenomena, and afterwards to tell us how Properties and Actions of all corporeal Things follow from those manifest Principles, would be a VERY GREAT STEP in Philosophy...." (Query 31)

One of those GENERAL PRINCIPLES: The process below forms an organic links with the next higher level in the hierarchy. Or looked at it the other way, the two processes form an interface between the two levels by usurping a fraction of energy from the lower level.

The second law of thermodynamics comes into effect by way of this process of interfacing of the two levels of energy.

Let us look at Carnot's ideal engine, where not all the heat energy (Q = S1T1) generated gets converted into work. It is found that a fraction Q = S1T2 gets 'lost', and what is available for conversion to work is S1(T1 -T2) where T2 is the temperature of the background field. This is why the perpetuum mobile of the second kind is impossible.

Einstein understood that there is a analogical connection between the perpetuum mobile and the Lorentz transformation. (See my essay: http://fqxi.org/community/forum/topic/1549 )

"The universal principle of the special theory of relativity is contained in the postulate: The laws of physics are invariant with respect to Lorentz transformations, ..... This is a restricting principle for natural laws, comparable to the restricting principle of the non-existence of the perpetuum mobile which underlie thermodynamics" (1, p.57).

Well if there is "an analogical connection", there has to be a GENERAL PRINCIPLE underlying both processes. Hence Einstein wrote: . "By and by I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more despairingly I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead to assured results. The example I saw before me was thermodynamics. The general principle was there given in the theorem: laws of nature are such that it is impossible to construct a perpetuum mobile" (1, p.53).

So what is this GENERAL PRINCIPLE: In general terms, the fraction of energy Q usurped to form the organic link with the background is given by the product of the extensive component Ea of the energy in action and the intensive component Ib of the energy of the background. Thus the fraction of energy forming the organic link with the background

Q = Ea x Ib.

When this general principle is applied to the motion of a particle relative to the background velocity field of the earth's orbital motion, a similar fraction of energy will be required to form the interface. Lorentz opens his 1904 paper (which is on the 'Lorentz transformation') recognises such a process. But the problem was how to account for the gamma-factor. See my paper to find out how the gamma-factors comes into being in equations -.http://fqxi.org/community/forum/topic/1549

Best regards,

Viraj

Sergey Fedosin

Dear Viraj,

From the Carnots ideal engine follows the possible work in the form: [math] dQ = (S_2 -S_1) (T_1 -T_2) =dA[/math] Where dQ is the heat converted to the work dA, S2-S1 is difference of entropy in states 2 and 1, T1 is the temperature of the high temperature reservoir, T2 is the temperature of the low temperature reservoir (background). Here S is extensive (additive) quantity, T is intensive quantity. I think the formula for dQ in the Carnots ideal engine is inapplicable as analogy for deducing of quantity Mvc( 1-u/c) since speed v is measured in the Earth reference frame and speed of the Earth u - in the Sun reference frame, i.e by different observers.

Sergey Fedosin

Jose Koshy

Dear Sergey,

I read your essay, but sorry to say, I could not follow much.Is it a new theory or a new approach entirely developed by you? Are you suggesting that there can be an infinite number of layers if we consider mass of the body as the only criterion? I have developed a new theory 'The finiteness theory'. However in the essay "Incredible foundations", I have not mentioned the details, but only referred to the approach that I used.

One thing that I got interested is the way you calculated the strong gravity.Are you saying that the strong nuclear force is actually gravity at the level of particles? My opinion is that. However, I calculated the strong force constant in a similar war using the force between two electrons when they just touch. This worked out to be 2.78x10^32. The gravitational constant of hydrogen atom that I got is close to the strong gravitational constant you obtained.

Sergey Fedosin

Dear Jose,

In the Theory of Infinite Hierarchical Nesting of Matter not only mass, but also size of objects are important as the rate of similar processes and other quantities. If you have papers about Strong gravitational constant please give me the references.

Sergey Fedosin

Jose Koshy

Dear Fedosin,

I am an independent researcher and have not published any papers..My theory being purely classical (denying both the QM and the relativity theories of Einstein) and with no institutional back up, it is difficult to find any journal willing to publish my work. However, my findings have been self-published in the book form titled "The reality of the physical world" now available at amazon.com. I am also planning to hoist a web site for providing information to anybody interested.

In my theory, the nucleus is made up of electron-positron pairs (held together by alternate gravitational and electrostatic bonds) with lone positrons distributed symmetrically (similar to electron distribution outside) among them. The force available to an electron/positron is finite and the whole force is used to form electron-positron chains. So only the force available to to the lone positrons is available to the nucleus for outside interactions.The electrostatic and gravitational forces of electron are taken to be equal, and the strong constant can be got from this. In a hydrogen atom, the gravitational force between the nucleus and the electron is calculated using the same constant, and it is proposed that the spin energy of electron (actual spinning motion) is balanced by gravity and its kinetic energy is balanced by electrostatic force. As there are three independent forces (including the inertial force due to the motion of electron), the atom is spatially stable.

jose p koshy

[deleted]

Sergey,

You wrote: "analogy (is inapplicable) for deducing of quantity Mvc( 1-u/c) since speed v is measured in the Earth reference frame and speed of the Earth u - in the Sun reference frame, i.e by different observers".

The reference frame interpretation is incorrect. It is in fact a gross misinterpretation of the experimental data (see below) which Lorentz used in discerning the Lorentz transformation. The reference frame interpretation is a fantasy and introduces a fantastic illusion into science to create a makeshift working hypothesis to overcome the problem Lorentz faced as stated below.

I refer you to Lorentz 1904 paper, in which he iterated the data of Kaufman's experiments on fast moving electrons (on Earth!!), and by trial and error he discerned the EMPIRICAL EQUATION which we now know as the "Lorentz transformation". If you read the opening lines of Lorentz' paper, you will find that the "observer on earth" that is data obtained for the motion of a particle (which was expected to move at velocity v) with respect to the lab frame contains a term involving Earth's motion of velocity u.

Lorentz wrote in the burning problem he faced in the opening paragraph: "The problem of determining the influence exerted on electric and optical phenomena ..... IN VIRTUE OF THE EARTH'S ANNUAL MOTION ...." (p. 11)

Then in art 2. The experiments (Rayleigh and Brace, Trounton and Noble) of which I have spoken are not the only reason for which a new examination of the PROBLEMS CONNECTED WITH THE MOTION OF THE EARTH is desirable.(p.12)

The problem was just like the background temperature field (of temp T2) in the hierarchy influence the heat (S1T1) generated within it, by usurping a fraction of it, the background "velocity field" of velocity u, was found to influence the energy Mvc by usurping the fraction.

But Lorentz problem was: It "admits a simple solution, so long as only ....the first power of of the ratio between the velocity of translation (of Earth) u and the velocity of light" is taken into account.

So he means that if the term is Mv( 1-u/c) the solution to the problem is simple. But it is Mv(1-u/c)/(1 - u2/c2) the solution becomes difficult.

"Cases in which quantities of the second order, i.e. of the order u2/c2 may be perceptible, present more difficulties".

This difficulty was overcome in SRT by merely postulating that time t changes to t' = t(1- xu/c2)/(1-u2/c2)1/2. If this contention has any validity, then this equation should have been verified by experiment. Can you tell me at least one experiment which has verified the above equation? If this is not verified, then the two reference frame hypothesis falls.

Best regards,

Viraj

Sergey Fedosin

Dear Viraj,

See the Ives-Stilwell experiment .

Sergey Fedosin

[deleted]

Dear Sergey,

The question I asked you is that has there been even a single experiment which has confirmed, that when x' = gamma(x -ut) the corresponding time is

t' = gamma(1- ux/c2)t?

And your answer: See the Ives-Stilwell experiment . This concerns time dilation equation (1) (below).

YOU ARE MAKING THE SAME GRAVE ERROR THAT GEORGE ELLIS DID JUST TWO DAYS BACK. YOU ARE CONFUSING BETWEEN THE SO-CALLED TIME DILATION EQUATION (1) AND LORENTZ TIME TRANSFORMATION EQUATION (2)

t' = t/(1 - v2/c2)1/2 --------------------(1)

t' = gamma(1- ux/c2)t ----------(2)

Just like you referring me to Ives-Stilwell Experiment by confusing equation (1) for equation (2), George Ellis also made the same error by referring to another group of experiments. He wrote: "all those collider experiments at places like SLAC and CERN verify it millions of times over each time they do a run".

My reply was: In those "millions of times" of verifications, what was verified was

a) that displacement is given by x' = gamma(x -ut) where U IS THE VELOCITY OF ORBIT OF THE EARTH and gamma determined by u. Hence the gamma-factor (for all experiments conducted on earth) is a constant. Gamma = 1.000000005.

b) And in the experiments to verify the decay time of a muon at CERN it confirmed the 'time dilation equation' t' = t/(1 - v2/c2)1/2. In this v is the velocity of the particle in the gamma-factor. In this equation gamma is a variable. In the CERN experiment gamma v = 0.99c and gamma = 7.088, and when moving in a cosmic ray (as in Feynman example below, v = 0.9c and gamma = 2,294.

To quote from Feynman: . For example, before we have any idea at all about what makes the meson disintegrate, we can still predict that when it is moving at nine-tenths of the speed of light the apparent time that it lasts is (2.2x10-6)/ sq rt [ 1- (9/10) squared] sec; and that our prediction works ..." (Vol I Ch 15 - 7).

FOR SRT TO BE CORRECT ON ITS FUNDAMENTAL CONTENTION OF THE LORENTZ TRANSFORMATIONS, (see Einstein's statement below) WHEN THE MUON DECAYS AFTER MOVING THROUGH A DISPLACEMENT GIVEN BY x' = gamma(x -ut) THE CORRESPONDING TIME HAS TO BE GIVEN BY (2)

t' = gamma(1- ux/c2)t. -------(2)

But this time is given by (1).

When I framed the question that way:

George Ellis HONESTLY CONCEDED. "YES I AGREE THAT THAT SPECIFIC EQUATION (2) PER SE HAS NOT BEEN VERIFIED BUT TIME DILATION (i.e equation 1) HAS, WHICH IS ITS CORE ELEMENT".

So Sergey, here is the fundamental contention of SRT in Einstein's own words: :.. "The insight which is fundamental for special theory of relativity is this: The assumptions 1)[constancy of the velocity of light] and 2) [principle of relativity] are compatible if relations of a new type ('Lorentz transformation') are postulated for the conversion of co-ordinates and the time."(Autobiography, p. 55).

I WILL ASK THE SAME QUESTION AGAIN FROM YOU AS WELL. CAN YOU GIVE EVEN ONE EXPERIMENT THAT HAS CONFIRMED THE EQUATION

t' = gamma(1- ux/c2)t?

Best regards,

Viraj

[deleted]

Dear Sergey,

1. You have not answered my question about Einstein's equation for the time in a moving frame whether it has been it has been proved even by a single experiment.

2. Thanks for showing the typo. In SRT's equation t on the right hand side is inside the bracket so the correct equation is t' = gamma(t - xu/c2)

3. I would appreciate if you would answer that question in regard to this correct equation.

Best regards,

Viraj

[deleted]

Dear Viraj,

Eq. (1): [math]x`=\frac {x-ut}{\sqrt {1-u^2/c^2}} [/math]

Eq. (2): [math]t`=\frac {t-xu/c^2}{\sqrt {1-u^2/c^2}} [/math]

Eq. (1) and (2) are Lorentz transformations from base inertial reference frame K to moving inertial reference frame K`. It is a correspondence of coordinate x and time t when K` moving in K along of axis OX with the speed u. How we can understand that speed of light c is constant in all inertial systems? This question is well seen in Extended special theory of relativity . It is shown that constancy of speed of light in all inertial systems may be a consequence of constancy of speed of light in isotropic reference frame where the speed is the same in all direction and may be connected with isotropy of fluxes of gravitons. Another reason is procedure of space-time measurement in special relativity which uses two-way propagation of waves. With such procedure averaging of speed of light take place giving the value of c. But real speed in a direction may be not c. If we begin from the electrodynamics and from the Lienard-Wiechert potential then we arrive to Eq. (1) and (2) if we want connect reference frame K and K`. Then with Lorentz transformations Maxwell equations will have the same form in all inertial systems. Also constancy of speed of light is necessary for the same form of electromagnetic wave equation in all inertial systems. So Lorentz transformations are in full agreement with the constancy of equations of electrodynamics for inertial systems. Also I want say that Eq. (1) and (2) is connected with each other by symmetry. If we take t in Eq. (2) and use it in Eq. (1) we find reverse Lorentz transformation for x: [math]x=\frac {x`+ut`}{\sqrt {1-u^2/c^2}} [/math] If we take x in Eq. (1) and use it in Eq. (2) we find reverse Lorentz transformation for t: [math]t=\frac {t`+x`u/c^2}{\sqrt {1-u^2/c^2}} [/math] In practice it is possible to find only increments of coordinate dx and time dt in experiments so we have for u = constant:

[math]dt`=\frac {dt-dx \cdot u/c^2}{\sqrt {1-u^2/c^2}} [/math] Part of this equation is checked in experiments (see the Ives-Stilwell experiment): [math]dt`=\frac {dt}{\sqrt {1-u^2/c^2}} [/math]

I do not know about proving another part: [math]dt`=-\frac {dx \cdot u }{ c^2 \sqrt {1-u^2/c^2}} [/math] it seems here problem with the smallness of the effect.

Sergey Fedosin

[deleted]

Dear Dr. Fedosin,

You raises various interesting points in your Essay, hence I am going to give you an high score, although I disagree with you on a fundamental issue.

Not only general relativity, but also ALL the metric theory of gravity lack the stress-energy tensor of the gravitational field. In any case, this is NOT a fundamental drawback, indeed it is a fundamental beauty geometric characteristic of this kind of theories. In fact, the stress-energy tensor of the gravitational field CANNOT exist for Einstein Equivalence Principle. As we can ALWAYS choice a reference frame, the free falling one, in which all the gravitational fields, and hence their energies, are null. In other words, the gravitational energy CANNOT be localized. I suggest you to carefully read paragraph 20.4 at page 466 of the book "Gravitation" by Misner, Thorne and Wheeler, where this issue is carefully examined and explained. I recall that, today, Einstein Equivalence Principle is tested at a level 10^-13.

Best wishes,

Ch.

Sergey Fedosin

Dear Christian,

I agree with you that general relativity (GR) is perfect theory which give us exact results. But the problem with GR is connected with the methodology of physics itself and with the fundamentals of the theory. To make the situation more clear let take the next example. Suppose we have a steady flow of an incompressible liquid with a constant flow rate through the tube which has a variable cross-section S, in the absence of gravitational forces. If [math]\rho[/math] is the density of the liquid, V is the average speed of the flow, then the formula for the mass flux is: [math]\rho V S=const =C[/math] When the section S is changing the speed V of the liquid and the density of the kinetic energy Ek in this section is changed: [math]E_k=\frac {\rho V^2} {2}= \frac {C^2} {2 \rho S^2}[/math] In this case the density of the kinetic energy is inextricably linked with the geometry, and we can write the law of conservation of energy density [math]E_k + f(S)= const [/math] where [math]f(S)[/math] is a geometric function of the cross section S, which in general can arbitrarily depend on external conditions affecting S. On the other hand, we can do not use the geometry, and consider the potential energy of the liquid in the form of pressure P, then the sum of the kinetic and the potential energy will be saved regardless of S: [math]E_k +P= const [/math] This shows that the problem with pseudotensor energy field arises in general relativity because of the fact that there the role of energy is performed by geometric quantities, and the gravitational field itself is reduced to the metric field and the curvature of spacetime. Of course, gravity changes the movement and energy of photons, which are used for the spacetime measurements. Hence the conclusion that the metric tensor in the presence of gravity changes its form relative to the metric of Minkowski space in the special theory of relativity. Therefore, such a change in GR metrics associated with gravity so as to satisfy the principle of equivalence. But then in GR energy-momentum tensor of the gravitational field disappear, and the field itself is not a real physical field but the geometrical object. Hence, there are paradoxes. For example in GR contribution to the gravitational field can make any other field, but the gravitational field itself do not make similar in the form of contributions in other fields. Then, why the gravitational field has such unique status? Because of the geometrization of the field in general relativity, we may never know exactly what causes spacetime to curve near the masses? And what is the maximum extent of this spacetime distortion? And where is the evidence that the degree of curvature is able to achieve the status of a black hole? Some of these problems are solved in the Covariant theory of gravitation. In this theory, gravitation exists as a fundamental physical field and has its own energy-momentum tensor like the electromagnetic field. That's gravitational field affects the movement and energy of photons or other test particles, and thus changes the spacetime metric, found by these photons and particles. The role of geometry is reduced only to a change in the metric by gravitation. At the same time as the physical mechanism of gravitation provides a mechanism in the Le Sage theory of gravitation, i.e. gravitation is a consequence of the fluxes of gravitons. And we can find density of energy of gravitons fluxes (http://vixra.org/abs/1209.0076).

Sergey Fedosin

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