Dear Harihar Beherera,

 “the law(s) of gravity” will take in an inertial frame of reference whose existence is not denied in General Relativity by its so-called strong Equivalence Principle, which states that for every point-like event of space-time, there exists a sufficiently small neighborhood such that in every local, freely falling frame in that neighborhood, all laws of physics obey the laws of special relativity."

The intertial systems are differently defined in classical mechanics and General Relativity and in conflict.  First thing I would stress what is generally recognised I recently read in Penrose's book about not agreeing viewpoints :

A free falling reference system for Newton and classical mechanics is not  inertial (it is not still and laws gets complicated).

A reference system on massive object for GRT is not inertial (there is an apparent force pushing on the ground).

Classical Mechanics is not necessarily  "Newtonian" but starts from galileo passes through Newton and is accomplished with the Euler-Lagrange equations and Hamilton-Jacobi's,  still widely used in all mechanics.

Lorentz transformations extend them in quantum electrodynamics, due basically to the constancy of c in every reference frame.

There is general agreement though, that a "Galielan system", or unaccelerated system far from massess  is a very good approximation of an inertial system.

Then everything else like the SEP has to be carefully analysed under the light of Noether's theorem, with possible issues emerging.

Dear Aleksei Bykov, Your point,"Newtonian graivty can not be made relativistic theory" is not convincing to me. Because as you can see in our paper (Behera-Naik , Int.J.Mod.Phys. A,19 (2004),4207-4229; arXiv:gr-qc/0304084) we have formulated a self-consistent spin-1 relativistic vector theory of gravity in flat-space time in a natural way without any new postulation/assumption. The theory of gravity we have developed relativistically (which we call Maxwellian Gravity) happens to coincide with Heaviside's gravity. Maxwellian gravity is analogous to Maxwell's Electromagnetic theory, with certain unique properties due to the fact that like-masses (i.e., like gravitational charges)  attract each other gravitostatically. However, for a full description I would request you to have a reading of the above paper. I believe, if you read that paper you would be fully convinced that it is possible to make "Newtonian gravity" compatible with special relativity. Please do not misunderstand us that we rule out the possibility of space-time being curved near massive objects. How to extend Maxellian gravity to non-inertial and curved space-time is another issue we have not worked yet. Now I contemplate what would have been Einstein's approach to relativistic gravity had he seen Heaviside's gravitational field equations. I believe Einstein had not seen Heaviside's gravitational field equations, otherwise his remark on Newton’s theory of gravity would have been different than what he made before the 1913 congress of natural scientists in Vienna, viz., 

"“After the untenability of the theory of action at distance had thus been proved in the domain of electrodynamics,confidence in the correctness of Newton’s action-at-a-distance theory of gravitation was shaken. One had to believe that Newton’s law of gravity could not embrace the phenomena of gravity in their entirety, any more than Coulomb’s law of electrostatics embraced the theory of electromagnetic processes.”

I am anxious to read your comments on our above cited paper.

Dear  Harihar Behera ·, I read in your paper.

"Inasmuch as the theories of other physical fields, a unified conservation law of energy-momentum exists for different forms of matter, and since there is at present no experimental evidence of its violation (moreover, the history of physics has always illustrated its tenacity and truth ), there is no reason to reject this law."

It is not that there is no reason to reject this law , I consider your requirement too loose, but it has to be strictly complied that law. How could Gravitation and  the other interactions merge without this fundamental law which is derived directly from the structure/behaviour  of the space-time encoded in the NOETHER's theorem.

This is also a remark made by Yurij Barishev who is dealing with Field gravitaiton FG of THIRRING, KALMAN, FEYNMAN who complained about the absence in GRT of the tensors of the Gravitaitonal energy and wrote FG also in order to account for it.

Dear Stefano Quattrini, Thank you very much for reading our paper, your comments on it and providing some valuable reference to Field Gravitation. If I have not misunderstood your comments, viz.,

"It is not that there is no reason to reject this law , I consider your requirement too loose, but it has to be strictly complied that law. How could Gravitation and the other interactions merge without this fundamental law which is derived directly from the structure/behaviour of the space-time encoded in the NOETHER's theorem." 

Are you under the impression that Maxwellian Gravity is not in compliance with the law of energy-momentum conservation for field and matter? If this is your impressing about  Maxwellian Gravity, then you have misunderstood our paper. In the subsequent  lines that you quoted from our paper, you will find that Maxwellian gravity does strictly comply with that sacrosanct law if one examines it.  

Please let me know if I misunderstood your comments.

By the way I would like to know what is sign (positive or negative) of gravitational field energy in the Field Gravitation of Thirring, Kalman and Feynman?

Dear Mohamed El Naschie,

I fully agree with you that generally neither special nor general relativity are perfect. Neither may be totally wrong. In any case, as Einstein said any scientific thought is a development of some per-scientific thought. We study all imperfect laws to make them more perfect.

Dear Harihar Behera,

you paper is quite interesting. The Field Gravitation of Thirring Kalman and Feynman based on the least ACTION principle is a  good theory from which the Schwartzshild solution is derivable too. Yurij Barishev tested it in Astronomy with good results.

I share the view point of angular momenta, being it the ACTION , it is the responsible of the curvature of spacetime as Eddington brightly said in his book SPACE-TIME-GRAVITATION.

I just want to say that GRT won't ever merge into QM if it is not transformed in something which by itself complies the NOETHER's theorem.

I'm collecting some physical examples where  the application of the equivalence principle and inertial systems as Einstein formulated, in their predictions violate the energy conservation laws.

Dear Aleksei Bykov,

                          Thank you very much for your reply, comments, suggestions. As recommended by you, I will study chapter 7 of the first volume of Misner, Torn, Wheller's "Gravitation" for further reasoning of the incompatibility of the SR with the gravity and of the equivalence principle.

Dear Stefano Quattrini,

                          Thank you very much for your interest in our paper on Maxwellian Gravity and for liking it. As you are aware Newtonian Gravity plus the concept of space-time curvature gives us Schwartzshild metric, which explains a number of observed gravitational effects.  Now the question is, "Can Schwartzshild metric be derived from Maxwellian Gravity? I believe since Maxwellian Gravity reduces to Newtonian Gravity under slow motion approximation, just by introducing the concept of space-time curvature into the theory, one can derive Schwartzshild metric from Maxwellian Gravity. I contemplate this way Maxwellian Gravity may be made to agree with certain experimental facts. However, I have not yet tried this line of approach to relativistic gravity. I would be happy if someone tries this. In the hindsight, I contemplate what would have been Einstein's approach to relativistic gravity, had he seen a relativistic formulation like Maxwellian Gravity developed in our paper.  I believe he would have tried a curved space-time version of Maxwellian Gravity in such a way that theory should reduce to Maxwellian Gravity when space-time curvature is switched off and Maxwellian Gravity then can be reduced to Newtonian Gravity in low motion approximation. This is the idea behind my original question posted here. The correspondence principle in this case would have been:

Some Curved Space-time Theory (Not exactly GR) =>Maxwellian Gravity =>Newtonian Gravity.

Dear Harihar,

an intriguing and powerful Einstein's thougth was the use of the Tensors making of the space time an Hypermedium .

He implemented in his theory the very daring thing:

"an infinitesimal region of the space-time continuum can always be considered galielan" or rather, "there will be Always a region though small where the space-time can be considered fully Minkowskian".

This is peculiar, since it is implicitly declared there, that the gravitational interaction has a breakdown before other interactions, goes to zero faster. 

Credible since the  gravitational interaction between particles is nothing compared to EM or other interactions.

Dear Stefano,

                 Yes, I agree with your point of view on GR.

This is a deep question...

To measure any field, the only procedure is to measure the change in the motion of a particle or material body when it is subjected to the field. This measure is always done by comparing the motion with or without the field. And it is always done with respect to an observer : in GR motion is absolute, but its measure is relative.

The fact that all material bodies have the same behavior when no field other than gravity is involved show that actually the inertial forces, which appear when one tries to change the motion of the body, are the same as the gravitational forces. This is the meaning of the law of equivalence. Inertia = gravitation.

But then we have two issues. The first is that to measure the kinematic characteristics of material body we proceed by measuring the change in the motion of bodies under some applied force (whatever it is).  This is possible because one can shut down the forces which are applied and check the difference. We do not knw how to shut down gravity, only to be in situations where it has a different value. So to have a consistent measure of both the kinematic characteristics of material body and of gravitational field, one needs to precise some protocol about the observers themselves, whence the concept of inertial observer. In an ideal situation, these would be observers which are not subjected to any gravity. In a more realistic view they are observers who do not measure a change in gravity, which can then be measured by the fact that they do not feel a change in the inertial forces. In the Newtonian case they travel at constant speed on straight line. In GR they travel on geodesics.

The second issue is general to all fields : because charged bodies are the source of field, and we cannot suppress this field, it is difficult to measure the true field, without the source. And this is more acute for gravity because all material bodies are sources. However it can be neglected, in usual case.

Dear Prof. Dutailly, Thank you very much for your answer which I like. As a follow up question to your statement in the last paragraph, viz,. " And this is more acute for gravity because all material bodies are sources.", I wish to know, "do all forms of energy (or matter create and yield to gravity?" Can we treat a photon a material particle which not only yields to gravity but also yields to gravity? As per an analysis of a thought  experiment (please see: Behera-Naik ,Int.J.Mod.Phys. A,19 (2004),4207-4229; arXiv:gr-qc/0304084), we found that it is the proper mass (or energy) of a body that is the source of gravitational gravitational field. If is the case, a photon having zero proper mass should not be a source of gravity. I wish to know what you think of it. I request you to read the cited paper, and let me know what you think of this paper also.

Dear Harihar,

"a photon having zero proper mass should not be a source of gravity."

yes such photon should not be able to curve the space it is crossing, or rather to contribuite to the bending of the hypermedium. Eddington said that we don't have elements to affirm that radiant energy behaves like tied energy. But since radiant energy does not have a mass and its momentum is strictly connected to a quantum absorption, radiant energy  should not have any possible to build a gravitational field.

Dear Stefano,

                  It is nice to see your thoughts resonating with my thoughts on the question of gravitational property of photons. Thanks for your answer.

Dear Harihar,

it is experimentally verified that in an orbiting condition only tidal effects are present, which are orders of magnitude smaller than the gravitational potential of the still position.

Orbiting space-station at 500 km over the Earth's surface, repeting the Pound and Rebka experiment in the orbiting laboratory in radial direction it is very likely that the Redshift comes out to be negligible. The time dilation should negligible between the two orbiting points, if not, there would be a way to infringe the conservation law.

But what is the law which makes go to 0 such Redshift from the condition of maximum Redshift in the Pound and Rebka experiment setup??

Take a look at the paper below. We develop the gravitational potential for relatively moving bodies in Newtonian space. From this we derive the correct equations for the shift in Mercury's perihelion, the deflection of a solar grazing photon, and the time delay of a solar grazing photon.

Article The time delay of a solar grazing photon

Article The gravitational potential for a moving observer, the perih...

Dear Hariar,

GR cannot be reduced to a concept of SR gravitation. Both of the theory have to be changed in some aspects.

a) GRT is successful in geometry, describiing the confirguration of the potentials, the Schwarzschild solution is experimentally validated.

b) SR is perfect in describing dynamics of pointlike masses as in accelerators, but then realtiy is never a point like mass.

c) Newtonian gravitation is still valid to a very good degree

GRT fails in describing the dynamics because with its inertiality assumptions, it cannot describe anything moving,  unless infringing the conservations laws. The gravitational potential energy is missing.

SR cannot be used to describe dynamics of large objects.

The problem of the free falling objects in a gravitational field has been faced with superficiality from the time of Einstein. The assumption according to which the gravitational interaction disappears totally, making the free falling system  a Galilean inertial system locally, is an arbitrary postulate which has severe consequences on the theory. Such assumption which is certainly verified for absence of local internal forces is against the energy conservation in general and has implications on the expected behaviour of atomic clocks free falling in a gravitational field.