The Einstein field equations or Einstein equation are not a dynamical equations that describe how matter and energy change the geometry of space-time, this curved geometry being interpreted as the gravitational field of the matter source. Einstein tried to propound geometrical structures of space by mathematical equations. So, he used non-Euclidian geometry. There are three considerable notes on Einstein’s equations;

  A. Einstein Field Equations do not come from the equivalence principle directly. These equations are simply equations that are suitable for general relativity.

  B. There is a physical explanation for the path of light in a gravitational field. Although explaining the frames of reference is a physical concept, there is not any explanation of how gravitational field affects photons in general relativity. Then how can we explain this phenomenon by quantum mechanics?

  C. Space-time is a continuous quantity in general relativity. But the changing of photon frequency and production of energy are quantized. That gravitational blueshift (or redshift) is a special case of gravitational field that affects the photon. My question is therefore: how can we explain the gravitational blueshift according to the relationship between photon energy and its frequency?

https://www.researchgate.net/publication/280491440_Reconsidering_relativistic_Newton%27s_second_law_and_its_results

Article Reconsidering relativistic Newton's second law and its results

 Dear Prof. Mohamed

Hilbert's postulate was elegantly simple. It was only that

LG=λR

I.e. that the Lagrangian Density of Gravity was proportional to the Ricci Scalar. From then on, he applied the Hamilton's principle to this's equation and found that the field equations for gravity are

Gμν=κTμν

And then, he showed how this is a better theory of gravity etc. etc.

Einstein's postulate was not so elegant or simple, in my opinion. However, many hold that it was simpler. His postulate was the field equation itself! I.e that

Gμν=κTμν

The reason why people hold this to be very elegant is that ∇μGμν=0 and ∇μTμν=0.

DEAR HOSSEIN,

In my transformation

x=R^2(x'-vt')

t=R^2(t'-vx'/c^2)

y=Ry' and z=Rz'

R is the Lorentz factor. According to my transformation space is invariant and it is only time dilation. Now what you see in my transformation there is no symmetry in the universe, and observations from the background radiation illustrated there is no symmetry....right???

DEAR HOSSEIN,

Do you believe that macro world wold must move according to objectivity and thus continuity?

Dear Azzam

What you mean of space is invariant? In fact what you mean of space?

That means there is no length contraction in the direction of the velocity. length is invariant for both the two observers. Review the paper below

http://arxiv.org/abs/1405.5174

Hossein, thank you for the post summarizing the different derivational techniques of the field equation for Einstein and Hilbert.  I had encountered variations of these in textbooks, without knowledge of the history.

There are others who gave, in my opinion, better heuristic reasons for the "big postulate" of Einstein's approach.  But often in the "action principle" approach, the heuristic reasoning is glossed over.

You appear to answer your own question succinctly enough, so I'm not sure what you are looking for on this thread.  I agree that GR is not a dynamic theory, and have my own QA thread asking if quantum gravity theories are doing anything about this, and the answer seems to be maybe, but they are still a bit at the stage of figuring out what it would mean.

It appears Einstein used the Equivalence Principle (now days we would call it the Strong Equivalence Principle, I think) in two ways.  It was justification for the Geodesic Principle, and probably should be considered essentially identical to it.  But as far as the so-called Field Equation (FE), the EP could only be considered another heuristic which justifies the use of Riemann geometry, but not a specific contributing postulate for the FE.  As you point out, it is impossible to find a postulate from which the FE is derived in Einstein's own work, so it must be taken as the postulate itself.  Heuristic reasoning of others holds that it is based on the gravitational form of Poisson's equation, taking an analogous tensor.  

At the time this was reasonable, since the only prior known field was the electromagnetic field, which obeyed this law.  It builds in something analogous to an inverse square acceleration law.  Since then, two new fundamental forces were discovered that don't follow such a principle.  This over constraint results in singularities, wormholes, and other oddities.  I am probably the only person who objects to it.

Equivalence principle is not the origin of general relativity. The origin of GR is Einstein's law of gravitation which equates Ricci tensor to zero in the absence of matter (empty space). Derivation of Ricci tensor is purely mathematical based on Riemannian geometry with one exception involving physical assumption that the track of a particle is geodesic. Next the Newtonian approximation is independently derived which relates acceleration with the coefficient g(mu.nu) as though the coefficient were some kind of potential. At this point Einstein's law of gravitation is introduced to obtain a condition for the potential g(mu.nu). Then d'Alembert equation written in covariant form is introduced and satisfying Laplace equation, weak field approximation is introduced. This results in derivation of principle of equivalence. Therefore Einstein's law of gravitation goes over to Newton's when the field is weak and when it is static.

Dear Azzam

Length contraction is a result of limit light speed principle that has calculated by mathematics.

There is "The length interval between the aircraft and its starting point is therefore the same in the frames S and S’ in relative motion -there is no ‘length contraction’ effect." in article that you have attached.

Consider that "Ehrenfest paradox" has discussed from 1909 with different views, this article is one of them.

DEAR HOSSEIN,

So what is observed during the motion is the length contraction according to the reciprocity principle. In fact according to SRT the moving train is not moving on the space on the ground according to the principle of relativity. And velocity is related to the proper time and length which is related to the invariance of energy momentum four vector. Now how the classical acceleration  which is depending on the coordinates of time and space is affected on the change of the velocity which is depended on the proper time and proper length which is related to the invariance of energy momentum four vector??? Hossein! Can you help to me understand that?

Dear Robert

I appreciate your interesting on this discuss.

"You appear to answer your own question succinctly enough, so I'm not sure what you are looking for on this thread." I would have two objectives:

1- I need know more about it and learn of other colleagues (such as you), really. So, thank you for your interesting mentions.

2- The study of history and philosophy of science is effective in better understanding. So, I think it is useful for younger friend.

"... if quantum gravity theories are doing anything about this, and the answer seems to be maybe,..."

Although I have worked a long years for finding a quantum gravity theory, I do not believe a quantum gravity theory is able to solve every physical problems, it is a step to develop our understanding, only.

Dear Vikram

Thank you for interesting comment, I learn of you.

Dear Hossein,

Now I'll prove to you the acceleration which is proposed in the equivalence principle of Einstein is nothing, and it is not even classical.

How Einstein proposed the equivalence principle?

Simply, Einstein proposed first the moving train on the ground, and thus according to his SRT for the observer on the ground the length of the moving  train must be contracted in the direction of the velocity. Now Einstein removed the reciprocity principle in SRT in this case, and because of that the paradoxes disappeared, and at the same time he kept on the objectivity and continuity according to spacetime continuum. Now Einstein imagined in this case if the moving train on the ground which his length is contracted for the observer on ground is accelerated in constant acceleration a. He found according to his imagination how the space-time continuum will be curved according to his proposed illusionary acceleration.  This proposed acceleration will not affect to the change of the velocity which is related to the invariance of energy momentum four vector. Because this proposed acceleration is an illusionary and it is related only to how the space-time will curve if the moving train on the ground which his length is contracted in the direction of the velocity for the observer on the ground. Because of that according to this illusionary acceleration there is no any change to the relativistic mass. This acceleration will not affect to the relativistic mass. Also since Einstein depended on his proposed illusionary acceleration on one side of the length contraction without the reciprocity principle. In this case it is resulted the speed of the light must be variable according to this illusionary acceleration, and in this case the constancy of the speed of light which is resulted by reciprocity principle is disappeared. So the acceleration which is proposed in the equivalence principle is not even classical, because the classical acceleration is related to change to the classical velocity with time, and the classical velocity is related to the change in the distance with time.

Dear Azzam

Why you have stopped at the old theory?

We need to new understanding of spacetime, energy, speed and acceleration.

Motion is an intrinsic property of physical existence. But there is a problem about concept of acceleration in theoretical physics. First of all, what we know about acceleration? And what is the definition of acceleration?

In physics, acceleration is the rate at which the velocity of an object changes over time that in classical mechanics is given by Newton's second law with a=F/m. In special relativity an accelerating particle has a world-line which is not straight. This is not difficult to handle. The 4-vector acceleration can be defined as the derivative with respect to proper time of the 4-velocity. It is possible to solve the equations of motion for a particle in electric and magnetic fields, for example. Accelerating reference frames is a different matter. In general relativity the physical equations take the same form in any co-ordinate system. In special relativity they do not but it is still possible to use co-ordinate systems corresponding to accelerating or rotating frames of reference just as it is possible to solve ordinary mechanics problems in curvilinear co-ordinate systems. This is done by introducing a metric tensor.

http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html

However, Newton and Einstein define the acceleration regardless of the structure of particles (in classical mechanics and relativity). This definition belongs to Newton era or macroscopic level era. It should be noted that the interaction between large objects (e.g. collision of two bodies) under the action of the quantum layer (in fact sub quantum level) has been done. Thus, according to quantum mechanics and mass–energy equivalence E=mc^2, we must redefine acceleration. It means we should review the relativistic Newton's second law.

There are a lot unanswered questions and complex concepts in theoretical physics that the standard model and relativity do not have answers for and the physicists believe that it is due to the inability of theories.

By using review of relativistic Newton's second law we can explain zero point energy and vacuum energy directly (without using the uncertainty principle). Also, it is a powerful tool to answer the unanswered questions and complex concepts in theoretical physics. According to the special relativity theory, nothing moves faster than light speed. Also, boundary between visible particle and invisible particles is light speed, where real space-time and virtual spacetime intertwine and interact with other.

https://www.researchgate.net/publication/279185909_Graviton_and_Newton%27s_second_law?ev=prf_pub

https://www.researchgate.net/publication/270276224_Interactions_Between_Real_and_Virtual_Spacetimes?ev=prf_pub

Article Graviton and Newton's second law

Article Interactions Between Real and Virtual Spacetimes

Dear Hossein,

You may learn more about the history from my article: "Einstein's Zürich Notebook and his Journey to General Relativity,  arXiv:1106.0900v2.

DEAR HOSSEIN,

At first SRT says nothing about acceleration, it is related only to the inertial frames of reference, and the proposed acceleration in the equivalence principle is not related to velocity in SRT which is related to the invariance of energy momentum four vector, because of that if we consider this acceleration which proposed in the equivalence principle, it does not cause any change in the velocity or  in the relativistic mass, which means it does not affect or related even  to the invariance of energy momentum four vector. Also as I illustrated before this acceleration is not classical.

Now basis on what, we say relativity is classical theory?

We say that because we see in SRT according to the reciprocity principle, we keep on continuity and objectivity as in classical physics, and basis on this continuity and objectivity which is resulted in SRT, we say it is exist in GR too. How? continuity in SRT resulted from the reciprocity principle and in GR there is no reciprocity principle, Furthermore the proposed acceleration in the equivalence principle is not classical too. I agree with you Newton's second law must be defined as relativistic, but that is impossible according to the continuity of SRT. In fact we need Newton's second law to be defined as relativistic quantized.  

Dear Azzam

"SRT says nothing about acceleration" GR is based on acceleration, what a frame is?

A frame is based on a physical being.

"In fact we need Newton's second law to be defined as relativistic quantized. " Exactly true, and I did it.

Dear Norbert

Thank you for link, seems it is very interesting. I appreciate your work.

I will read carefully it.

Best Regards

Hossein

Dear Hossein,

Heisenberg  said in his book "Heisenberg, W., "Physics and Phylosophy", (1958), Allien and Unwin" "It is impossible to reach to the unified theory without defining the force in terms of frequency. Also, Einstein said " there is no way to reach to unified theory without reinterpretation of relativity according to Copenhagen school". You said that you reached to a relativistic quantized force, but the relativistic quantized force is impossible to be right according to the continuity that resulted from relativity theory. And I explained that too much and you refuse to discuss in that. In fact the relativistic quantized force must depend on the wave-particle duality and Heisenberg uncertainty principle. Einstein hide the wave-particle duality and Heisenberg uncertainty principle in macro world behind the reciprocity principle and from the reciprocity principle it is resulted the space-time continuum and thus the continuity same as in classical physics. To understand if the reciprocity principle is real in physics, review the experimental results of the background radiation and from these results, is the universe moving according to symmetry? Please answer me!!! Also, 

two separate research groups, one of which is from MIT, have  presented evidence that wormholes — tunnels that may allow us to travel through time and space — are “powered” by quantum entanglement. Furthermore, one of the research groups also postulates the reverse — that quantum entangled particles are connected by miniature wormholes.

Phys. Rev. Lett. 111, 211603 (2013).

Phys. Rev. Lett. 111, 211602 (2013).

So how can we explain that according to continuity of SRT and GRT?

Hossein, How many questions did ask within the framework of relativity in researchgate and in Linkedin, and how many questions have been?answered?

Dear Azzam

You have written: "... quantized force is impossible to be right according to the continuity that resulted from relativity theory." I have worked beyond the relativity. Then I found relativistic principles is result able by my theory.

You have written: " ...the relativistic quantized force must depend on the wave-particle duality and Heisenberg uncertainty principle." I have described physical phenomena without useing uncertainty principle.

"Hossein, How many questions did ask within the framework of relativity in researchgate and in Linkedin, and how many questions have been?answered?"

Sorry my dear friend, your questions is over my head.

Sorry my dear friend, your questions is over my head"

Ok! if quitting continuity objectivity will answer all of your questions successfully, So why you refusing to understand the macro world according to the wave-particle duality and Heisenberg uncertainty.

Now I understand why Einstein was hating quantum theory and Heisenberg uncertainty principle.

Basically he started with something that was equivalent of a four dimensional version of Newton. This was  expressed in terms of curvature produced in flat space-time using 4D-pythagoras.

But that gave him the same answer as Newton

So he added an extra term for the extra curvature of space time in the vicinity of gravity.

So he was able to calculate the advance in the perihelion of Mercury (using a similar equation to Paul Gerber)

But actually the problem with that tensor format gives you recurrent terms, which gives you the infinities you see with the black hole singularity.

Fortunately this can be re-expressed without the infinities by deconstructing the equation and translating back from 4-D to 2-D Newton, and your infinities disappear and you can also begin to explain dark matter using the same principles.

Article An advanced dynamic adaptation of Newtonian equations of gravity

Well, Einstein had a number of goals that he needed to reach  to satisfy his sense of a complete theory"

(1) The Principle of Equivalence, which he actually conceived us as early as 1905 on Zurish, although serious work on GR began in Prague in 1912

(2) The essential conservation laws , those of momentum, mass and energy, the latter two being modified by the equivalence E=mc^2

(3) The correspondence principle by which GR would turn into Newton''s theory of gravitation in the case of very weak gravitational fields

To achieve these goals he adopted both a "physical" and an "mathematical strategy". The physical came from the need to find experimental verification of the precession of the perihelion of Mercury, and evidence for the bending of light rays under the sun's gravitational field.

For the mathematical strategy he needed the help of Marcel Grossman, who taught Einstein every thing he needed to know about Differential Geometry. GR should mbe called the Einstein-Grossman theory of gravity! It was from their collaboration that Einstein introduced a final principle, namely general covariance, namely that the laws of nature should be the same for massive systems in the presence of all gravitational fields. It was this that led to the competition of Einstein and Hilbert, because Hilbert, being a mathematician, saw right away how to cast the field equations into a covariant form, while Einstein had to struggle with it in many pages of calculations before he reached the result.

Dear Azzam

I am a scientist, not a philosopher. I am trying to reconsider some physical phenomena, only. I hope my finding be considerable.

Dear Andrew

I read your interesting article. I suggest see my work about singularity.

https://www.researchgate.net/publication/279446746_Graviton_and_cosmology_equations_before_the_Big_Bang?ev=prf_pub

Article Graviton and cosmology equations, before the Big Bang

Dear Roy

Thank you for your interesting historical mentions, I have enjoyed and learned of it.

Dear Hans

Thank you for interesting and useful details.

Dear Hossein,

The main postulate which is built in GR is the equivalence between a free falling RF and a Galilean RF or IRF, such that a free falling RF is an IRF (inertial reference frame). This Equivalence  sometimes I've seen classified as the SEP.

The only equivalence principle experimentally proven to a very high precision in the EOTVOS experiment is the equivalence of inertial and gravitational mass and let's say it is the original EP or the NEP Newton's equivalence principle. The eotvos  is  virtually a static experiment, it is arbitrary to extrapolate its result to  generic moving objects.

The WEP is something in between the SEP and the NEP/EP, it regards free falling objects but regards also the compliance of the gravitational and intertial masses equivalence.

It emerges something which should not be given for granted:

1) the extension of EP or NEP in order to make it work in dynamic cases

2) the extension of the concept of inertiality to free falling objects in a grav field from the Galilean one.

The first is related to non accounted variations  to the rules of SR.

 The second is related to have postulated that the outcomes of gravitation are irrespective of the masses at stake, or are independent.

Once in the geodesic equation d2x/dt2 = tensor(space-time) we get rid of the masses hence of the forces,  no work is performed by the gravitational interaction, or rather there is not an interaction at all. Such point of view brings naturally to infringement of energy conservation and is at the base of what also Penrose and Feyman, Thirring, Kalman, Baryshev and others stressed while developing the Poincarè gravitation FGT through variational principles .

It seems that Hilbert got the same answers before Einstein:

On “Belated Decision in the Hilbert-Einstein Priority Dispute”,

published by L. Corry, J. Renn, and J. Stachel

Not very surprised to see Einstein as a plagiarist for the second time...first time was with Poincarè..

http://www.znaturforsch.com/aa/v59a/s59a0715.pdf

Dear Stefano

I appreciate your interesting comment. I learned and enjoyed of it, thank you very much.

Yes.. But Missing QM in the picture it is impossible any motion...The static strutture of the hyper medium is well represented..Pity that in principle nothing can move...

DEAR Hans van Leunen,

Have you thought in Zeno's paradoxes and how he described the motion? I think the motion according to the wave-particle duality is very near to what described in zeno's paradoxes.

No, I don't think so.

Attached please find my research work on the interpretation of the nature of inertial forces and the corresponding modification of the fundamental physical picture for spacetime. (File1: the physical picture of my work on the nature of inertial force ;Fiel2: Relativistic spacetime based on absolute background )

According to the fundamental particle physics theories and energy issues in the production and decay of pairs of matter–antimatter are included in finding the common features between matter and energy which can be considered the constant velocity of photon as a property that can be transmitted from matter into energy and vice versa and also differences in the mass, structure of matter and its relation fields are explained by the relationship between length contraction (reduce in volume) and relativistic mass and relativistic Newton second law which show the mass variations (i.e., the infinite speed in classical mechanics is replaced by the infinite mass). Infinite mass is not observable (such as infinite velocity), how can we explain the limit of speed without infinite mass?

The important concept in relationship between 'mass' and energy is c, regarding the phenomena of creation and decay of electron-positron pair, why do the related photons move at constant speed, but we could change the speed of matter and antimatter? What is the unique characteristic of matter which is convertible to photons that move with constant speed c (speed of light)? The idea that object/particle could not travel at superluminal speeds, originates from the structure of matter and the mechanism of interaction between field and mass; that with presenting a postulate we could generalize the constancy of speed from energy to mass. By gravitational blueshift, the energy of photon and consequently its frequency will increase. What is the mechanism of increasing in the photon energy that causes increase in its frequency? Are there more results than before in the energy-mass equivalence equation?

https://www.researchgate.net/publication/280491440_Reconsidering_relativistic_Newton%27s_second_law_and_its_results?ev=prf_pub

Article Reconsidering relativistic Newton's second law and its results

Luiz C. L. Botelho,

YOU SAID: But will it works ?(on the modern scientific standards..,,,)

BUT who determines these standards?

Revelation 13:17

And that no one would be able to buy or to sell, unless he has that mark, the name of the beast or the number of his name.

I think I see many ideas in GR which have nothing to do with the equivalence

principle.

Luiz,

The matter energy stress tensors is Einstein,  the curved space is already not. It be longs to Clifford who invented geometrodynamics for the first time for any interaction...

The origins of space and time

Many researchers believe that physics will not be complete until it can explain not just the behaviour of space and time, but where these entities come from.

http://www.nature.com/news/theoretical-physics-the-origins-of-space-and-time-1.13613

In generally, of the first we need to ensure that our theory is exactly compatible with the laws of nature or not? For example, is exactly relativistic Newton's second law compatible with the laws of nature?

Reconsidering relativistic Newton's second law and its results

https://www.researchgate.net/publication/280491440_Reconsidering_relativistic_Newton%27s_second_law_and_its_results?ev=prf_pub

Article Reconsidering relativistic Newton's second law and its results

Dear Hossein,

I agree with you that Newton's second law must be defined as relativistic and quantized also. But the problem is within the objectivity and then continuity of classical physics, and because of that, it is impossible to define Newton's second law as quantized or relativistic. That is because  to define the motion of the massive object in space and time, you find time and space are joined (weaved) to each other. That will make a constraint to define the change of the velocity with respect to time to be only within the range of classical acceleration. The particle according to the space-time continuum is restrained to change his velocity with respect to time out of the classical acceleration. In quantum theory, space and time are separated, and in this case the particle is free to change his velocity according to quantized energy. So if we consider the change of velocity is depended on the quantization of energy, here we must understand from where the concept of quantization comes from. As we understand light or photons are moving according to the wave-particle duality, and its energy is quantized. From the equivalence of mass and energy E=mc^2, mass and energy are two faces for one currency. According to that massive objects, micro and macro and their motion must follow the behavior of photons according to the wave-particle duality and the quantization of energy, and since in quantum theory there is no objectivity and continuity, in this case in macro world same as in micro world, there is no objectivity and continuity. From here we can understand why GR is not consistent with quantum theory, that is because at first SRT is built basis on objectivity and continuity, and from that it is resuted the space-time continuum, and then this principle was applied in GR by what is named curved space-time

Botehlo:  Einstein chose the second rank tensor formulation rather than the scalar formulation because the energy-stress tensor is a symmetric second rank tensor.  Einstein understood that this tensor gives a complete description of matter - leaving quantum mechanics aside.  He had two guides to the field equations: 1- the energy-stress tensor has a vanishing covariant derivative, so the field side of the equation must have a vanishing covariant derivative, 2- the field side of the equation has to contain the second derivatives of the metric tensor which is the 'potential' of the gravitational field..  There are two possible tensors for the field side: 1- the Einstein tensor, 2- the metric tensor.  Einstein first included then excluded the metric tensor in his equations and called its inclusion the greatest mistake of his life.  I think that its exclusion was his greatest mistake.  There is no reason to exclude it and it has now been included again.  With both the Einstein tensor and the metric tensor included in the field side of the equations we have the most general mathematically acceptable equations.  The analogy with the (relativistic) Maxwell's equations is useful.  The difference is that the gravitational field produces energy which then becomes an additional source of the field; this explains the terms quadratic in the Christoffel symbols in the field equations.  The electromagnetic field is electrically neutral, so there is no corresponding term in the Maxwell equations.

Dear Azzam

Newton's second law refers to acceleration by force (or in field). In both theories classical mechanic and quantum mechanics, particles accelerate. I agree that the original form of Newton's second is not suitable for quantum mechanics. But there is very efforts to find a suitable form of Newton's second law for quantum mechanics.

For examples see:

http://www.physics.drexel.edu/~bob/Manuscripts/Ehrenfest.pdf

http://www.eftaylor.com/pub/QMtoNewtonsLaws.pdf

These efforts show that acceleration is a fundamental concept to describe the nature, but old theories is not able analyze it in a general form. So, first of all, what we know about acceleration? And what is the definition of acceleration?

In physics, acceleration is the rate at which the velocity of an object changes over time that in classical mechanics is given by Newton's second law with a=F/m. In special relativity an accelerating particle has a world-line which is not straight. This is not difficult to handle.

Newton and Einstein define the acceleration regardless of the structure of particles (in classical mechanics and relativity). This definition belongs to Newton era or macroscopic level era. It should be noted that the interaction between large objects (e.g. collision of two bodies) under the action of the quantum layer (in fact sub quantum level) has been done. Thus, according to quantum mechanics and mass–energy equivalence E=mc^2 , we must redefine acceleration. It means we should review the relativistic Newton's second law. For more details please see:

https://www.researchgate.net/publication/279185909_Graviton_and_Newton%27s_second_law?ev=prf_pub

https://www.researchgate.net/publication/270339919_Interactions_Between_Real_and_Virtual_Spacetimes?ev=prf_pub

https://www.researchgate.net/publication/228332513_New_Discoveries_and_the_Necessity_of_Reconsidering_the_Perspectives_on_Newton%27s_Second_Law?ev=prf_pub

Article Graviton and Newton's second law

Article Interactions Between Real and Virtual Spacetimes

Article New Discoveries and the Necessity of Reconsidering the Persp...

Dear Hossein,

You said; In special relativity an accelerating particle has a world-line which is not straight.

"which is not straight" That is not SRT, it is GR!!

There is a difference between SRT which is dependent on the reciprocity principle and the GR, where there is no reciprocity principle. SRT did not say any thing how the particles accelerate or decelerate.  In GR we jump directly From  inertial frames to non-inertial frames without saying anything about acceleration in SRT or how the reciprocity principle disappeared in this case. According to SRT and the reciprocity principle we keep on continuity..right, and because of that entanglement is hidden behind the reciprocity principle. The entanglement will appear in case of acceleration which equivalent in quantum to the vacuum fluctuations and the uncertainty principle. So we propose continuity in GR basis on the reciprocity principle in SRT, and the reciprocity principle disappeared in GR without saying how????, and also, there is no any experiment proved the reciprocity principle in SRT. While all the experiments proved the entanglement and quantum theory.

Dear Ramzi

Thank you for interesting mentions.

There is a problem on the stress–energy tensor relative to gravity (in fact graviton).

In standard model, the graviton mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton is expected to be massless (because the gravitational force appears to have unlimited range) and must be a spin-2 boson. The spin follows from the fact that the source of gravitation is the stress–energy tensor, a second-rank tensor.

This old view on graviton is not able to solve the gravity problem in standard model, so seems we need a new definition of graviton.

https://www.researchgate.net/publication/260982893_A_new_Definition_of_Graviton

Data A new Definition of Graviton

Dear Azzam

"According to SRT and the reciprocity principle we keep on continuity..."

You are right, but it is not nature problem, its old theories problem.

Yes, you are right! its old theories problem. And SRT believed with the continuity and objectivity which exist in the old theories, and it adopted the same principle by proposing the reciprocity principle. So if objectivity and continuity are real in nature, why there is no any prove to the reciprocity principle? That's because objectivity, continuity and thus the reciprocity principle are only fake.

It is old conflict since the beginning of creation. It started on the ground since Cain and Abel!

It is the conflict of materialism and idealism. Who let the car  and everything to move, and who let the plane to fly, are they Newton's laws really? or another power?

Dear Hossein,

I mentioned in my remark 'leaving quantum mechanics aside'.  The problem of reconciling general relativity and quantum field theory has not been resolved in a final manner.  Your remark is based on this problem which I had avoided.  The Einstein-Hilbert general theory of relativity is mathematically self-consistent and, in a sense, complete.  But it does not extend to the realm of quantum field theory.

 Ramzi Rihan,

How  can it extend on the realm of quantum field theory, while GR is classical? GR is even not relativistic, if it is relativistic,  then it could describe the escape velocity as relativistic. Read this paper https://www.researchgate.net/publication/275653449_Non-linear_energy_conservation_theorem_in_the_framework_of_Special_Relativity

Article Non-linear energy conservation theorem in the framework of S...

 Dear Azzam

I agree with you on old theories, but other items are outside of my field.

Dear Ramzi

"The problem of reconciling general relativity and quantum field theory has not been resolved in a final manner." Sure, you are right.

"But it does not extend to the realm of quantum field theory." I agree with you.

For an interesting step in this way please see following article:

https://www.researchgate.net/publication/280626794_Unified_Force_Energy_and_Mass?ev=prf_pub

https://www.researchgate.net/publication/260982893_A_new_Definition_of_Graviton?ev=prf_pub

Article Unified Force, Energy and Mass

Data A new Definition of Graviton

Dear Hans

Seems we need a new definition of graviton.

Hi

Thanks for mentioning my paper. Regarding the scape velocity, I would like to comment that, according to my work, the scape velocity at the Schwarzschild radius of a gravitational source turns out to be lower than the speed of light by a 20%. See eqs. (20-21) of my paper:

https://www.academia.edu/8962572/On_the_movement_of_a_particle_in_a_gravitational_field_in_the_context_of_the_Special_Theory_of_Relativity

In this sense, I think that the event horizon is a very problematic concept and I am not the only one, many theoretical physicist are starting to be skeptical about it (Hawking among others). In particular, there are serious concerns that such a concept could be incompatible with quantum mechanics. I think that some current modifications of Einstein´s theory are promising, specially the Palatini theories of gravity, where the connection is independent of the metric (unlike General Relativity, where the Levi-Civita connection derives from it). In these theories the geometry is essentially non-Riemannian,however, at low energies we recover the full Einstein´s equations (with a cosmological constant). Essential singularities like those of black holes are replaced by finite geometrical structures that have particle properties like geons. I recommend the articles of Gonzalo Olmo for example, which are very interesting.

Our physical observations and experiences are limiting of the visible universe or spacetime laws. Because human being and their tools are formed up of spacetime being and obey of spacetime laws. Seems we need review the Minkowski spacetime and cosmological equations.

https://www.researchgate.net/publication/270339919_Interactions_Between_Real_and_Virtual_Spacetimes?ev=prf_pub

https://www.researchgate.net/publication/264810425_Beyond_the_Modern_Physics_and_Cosmological_Equations?ev=prf_pub

Article Interactions Between Real and Virtual Spacetimes

Article Beyond the Modern Physics and Cosmological Equations

Dear Luiz

The scalar version was chosen by Einstein in the so called Einstein-Fokker theory of 1914, when Einstein was still at ETH in Zurich. (This proposal can be seen as a  general relativistic version of Nordström's scalar theory in the framework of special relativity.) The EF-theory implies no light deflection (because it is conformally flat), a fact that was not known in 1914. This was one of the reasons why Einstein urged astronomers in Berlin to measure the light deflection during the expected solar eclipse in the Crimea in 1914.-- It is a nice student exercise to show that the EF-theory predicts the wrong perihelion motion for Mercury (even the sign turns out to be wrong).

Dear Luiz and Norbert

Thank you for interesting notes. And spin of graviton refers to rank of the energy-stress tensor.

Botehlo, but the trace of the energy-stress tensor does not contain complete information about matter.  From the mass-energy equivalence of special relativity, all forms of matter must gravitate, and so you need the complete description provided by the energy-stress tensor.  This forces you to use the second-rank symmetric tensor formulation.  On the other hand, the Lagrangian must be a scalar, so there the contracted form (the scalar curvature) is used.

Luiz, in two dimensions you can use the scalar because the Riemann curvature tensor is expressible in terms of the scalar curvature and the metric tensor.  So this proves nothing.  It is only in four or more dimensions that the elements of the Riemann tensor are algebraically independent.  This is where the true theory shows itself.

Hi all friends

Thank you for interesting mentions, I enjoy and learn of them.

Dear Luiz,

There must be some misunderstanding of what I wrote. I know, of course, the Gauss-Bonnet theorem and related higher dimensional facts in differential topology. I just made a historical remark which is slowly forgotten by younger generations. On February 19, 1914, Einstein and Fokker submitted a paper (published in the Annalen der Physik 44, 321) with the translated title "Nordström,s Theory of Gravitation from the Point of View of the Absolute Differential Calculus". The field equation in this theory is: Ricci scalar = const T (T=trace of the energy-momentum tensor). [After the Einstein-Grossmann theory this alternative played some role in Einstein's thinking. At the time a decision in favor of one or the other theory on empirical grounds was impossible.] 

Excuse me in case you know all this. I did not say anything about lower dimensional gravity.

Luiz, 2-D models are indeed useful for understanding, but reality is four-dimensional.

Dear Luiz,

the FGT (Poincarè group) and GR (Riemann geometry) seem to have something which eventually is not acceptable.

FGT reconsiders the gravitational energy in order to make the interactions be consistent with the energy conservation (background should not leak or let in).

GR takes good pictures of the geometrical structure of the space time and the influence of the masses, but eventually in order to make body move has to "go back to work"...in other words it has to use the Newtonian gravitational potentials (work) to put bodies in motion, not very clear from where the energy comes from if it is not previously postulated.

Aren't we missing a dimension in all this??? Kaluza and Klein made an attempt and failed in order to insert a new dimension for the electromagnetism. Probably it was a right way but they did not have sufficient element to choose the proper set of dimensions. The CMBR and the absolute rest frame and the possiblity of an absolute time bring us back to Newton, quantum physics let a background (quantuum vacuum) emerge is not time to put them together without disturbing the strings??

Dear Stefano,

Now Everything becomes clear and very simple. The objectivity which leading to continuity in classical physics is the biggest problem in physics. Reinterpretation of the Lorentz transformation according to the Copenhagen school solves the problem and the gravity becomes gauge theory. Everything is very simple. My theory is tested by a well known physicists and accepted. 

Although the Einstein-Hilbert action is the simplest choice producing the observational successes of general relativity, no other a priori reason prevents from contemplating more general gravitational actions.

http://arxiv.org/pdf/gr-qc/0505128.pdf

Dear Hossein,

Two remarks: 1. The famous Lovelock theorem implies that there is no other choice, if the field equations contain, beside the metric, only its first and second derivatives. (In the early years this was known to people like Hermann Weyl under the additional assumptions that the second derivatives enter only linearly. Lovelock showed that this assumption is not necessary in four dimensions. Unfortunately, his proof is quite involved. For more details see, for instance, my book "General Relativity, Graduate Texts in Physics, Springer (2013), especially section 3.2: "The Gravitational Field Equations".)

2. Especially during recent years people have  studied Lagrangians that lead to higher order field equations. In the simplest version functions of the Ricci scalar have been chosen (and there is a whole industry on this), but also Lagrangians of the Yang-Mills type and others were analyst. The main motivation came from the profound dark energy problem.

Dear Hossein Javadi,

observation globally resulted as observation in the dispersion which related to vacuum energy, and in gravity which is related to the gravitational potential and the difference in the gravitational potential and it is working same the refractive index in optics. In this case there is no reciprocity principle..no objectivity and continuity, and everything is working as gauge theory. Here you get exact solutions for everything from Higgs to Galaxies.

Dear Norbert

Thank you for remarks, I will study Lovelock's theory of gravity.

Abstract of your book "General Relativity" shows it contains useful concepts and detail about foundations of general relativity. Thank you again.

Regards

Hossein

Dear Azzam

"... it is working same the refractive index in optics." I agree with you.

In my view the solution is description the relation between gravity and electromagnetic (in fact, relation between graviton and photon).

Well, yes General Relativity does follow "directly" from the Principle of Equivalence. The word "directly" is a long, long road indeed. Howeve, once one combines equ,ivalence with (a) The identify of gravitational and inertial mass (b)The reduction to Newton's world in the case of very weak gravitational fields (c) The possibiliies of living in  a non-Euclidean geometry for the geodesic structures of fields (still many difficulties!) , the Light Principle, etc....yes, indeed GR comes directly from "Free Fall" , that is to say, the equivalence principle

Einstein tries to consider directly the connection as the fundamental object of gravity, but he never completes the process of "dethronizing" g.

https://agenda.infn.it/getFile.py/access?contribId=9&sessionId=3&resId=0&materialId=slides&confId=7266

Dear all

I have thought of a new equivalence principle which makes one thinks whether the basis of GR is soilid enough.

Preprint A New Equivalence Principle with a Different Curvature of Light

I have also initiated a new discussion related to this new finding.

https://www.researchgate.net/post/What_is_the_real_shape_of_the_gravitational_bending_of_light