What is the value addition of GR?

[Dale]

There are three uses for any theory.

1. Reformulation : One use of a new theory could be an effective reformulation of an existing theory to help solve problems in an easier way which otherwise would have been cumbersome if done in the original manner like say some problems could be solved easily if we choose a different coordinate system (say polar coordinates instead of cartesian) or some problems get solved easily through the Lagrangian formulation. So in this case the idea is to take an existing theory and reformulate it for easier use but not modifying the "algorithmic complexity or algorithmic content" resident in the theory.
2. Revision: Another use of a new theory would be to explain phenomenon which otherwise cannot be explained by existing theories. It removes an inconsistency/gap between existing theories and observations by modifying existing theories, like what quantum mechanics did. This means that the existing theory has a certain "algorithimic content" to it but that doesn't match up with the "algorithimic content" of nature as observed through experiments. There is something more which is present in nature, which is not present in the existing theory. That gap or impedance mismatch is corrected by revising the theory. This is a more fundamental use than just reformulation.
3. Interpretation: Another use of a new theory is that it helps gain greater insight into why things are the way they are. It doesn't help problems to be solved in an easier way or remove inconsistencies between existing theory and observations. It helps in understanding nature in a more graspable manner for the human mind. It is a new way to articulate mathematical symbols so that it helps us gain greater insight into the "heart' of the theory.

So, I don't know if there is an authoritative classification, but personally I would not classify 1 and 3 as a new theory.

I would classify 1 as a reformulation of the existing theory. In other words, I would not describe Lagrangian mechanics as a different theory than Newtonian mechanics, but just a reformulation of it.

I would classify 3 as an interpretation of the existing theory. For example, I wouldn't call MWI and Copenhagen different theories, but just different interpretations of quantum mechanics.

Only 2 constitutes a genuinely new theory, and GR does that. Any reformulation or reinterpretation is incidental.

 

[controlfreak]

Only 2 constitutes a genuinely new theory, and GR does that.

Well that may be one way of looking at the word "theory" but then I see that you understand what I was saying. And we are in agreement that GR does all three functions, incidental or not.

Those two theories are not mathematically equivalent.

I am not sure what are you referring to here. I didnt say Maxwell's theory is mathematically equivalent to GR. And it is a big thread and not sure what specific point you are referring to as you haven't quoted any sentence of mine. I only pointed out the fact that LITG explains gravity with equations similar to Maxwell's equations and also incorporates SR. These links will help clarify - http://serg.fedosin.ru/muen.htm , http://serg.fedosin.ru/gmen.htm. In that manner I had said the phenomenon of Gravity can be explained/articulated using two mathematically different forms - one form as given by GR and another as given by LITG which looks similar to Maxwell's equations.

 

[ShayanJ]

I am not sure what are you referring to here. I didnt say Maxwell's theory is mathematically equivalent to GR. And it is a big thread and not sure what specific point you are referring to as you haven't quoted any sentence of mine. I only pointed out the fact that LITG explains gravity with equations similar to Maxwell's equations and also incorporates SR. These links will help clarify - http://serg.fedosin.ru/muen.htm , http://serg.fedosin.ru/gmen.htm. In that manner I had said the phenomenon of Gravity can be explained/articulated using two mathematically different forms - one form as given by GR and another as given by LITG which looks similar to Maxwell's equations.

GravitoElectroMagnetism is not equivalent to GR. GR is highly non-linear while GEM is linear. In fact you even can derive GEM from the non-relativistic limit of linearized GR for a stationary source(Gravitation by Padmanabhan,section 6.4.1).
So what you say is wrong and I'm really wondering where you got it from. Even the links you yourself presented explain that those equations are valid under some conditions and approximations.

 

[controlfreak]

GravitoElectroMagnetism is not equivalent to GR. GR is highly non-linear while GEM is linear. In fact you even can derive GEM from the non-relativistic limit of GR for a stationary source(Gravitation by Padmanabhan,section 6.4.1).
So what you say is wrong and I'm really wondering where did you get it.

Thank you for your response. You are right.

Infact I was just contemplating about the similarities in the force/field laws in the static world between Electrostatics and Newton's Law of Gravity (Gravitostatics) and was wondering if instead of going the GR way is it possible to come up with a theory of gravitation similar to the form Maxwell did for EM which explained the change in Electrostatic force laws when the source (charge) started moving. When charge started moving magnetism arose and I felt that when mass moved something similar has to occur and its just that the Gravito Magnetic force would be so weak it wouldn't be observed easily like how magnetism gets observed easily. Maxwell was able to capture that in his EM equations and which also satisfied Lorentz Invariance. I felt if he could do it for charge, we can come up with a similar approach for mass sources as well. Then I googled and got to these links like GEM and LITG. But then it has also been mentioned GEM/LITG are alternatives to GR in weak field approximation like you have pointed out and hence not fully equivalent to GR. But if we generalize Maxwell's equations for strong fields and make it Non Linear and apply the same approach to GEM or LITG will we get an equivalent theory?

 

[Dale]

was wondering if instead of going the GR way is it possible to come up with a theory of gravitation similar to the form Maxwell did for EM

As has already been mentioned to you several times, many people have tried, but none has succeeded in obtaining such a theory which is consistent with observation.

Since you have essentially already exhausted this route, perhaps you might consider an alternative approach to your question. Perhaps consider what it would take to geometrize Newtonian gravity. See Newton Cartan gravity.

 

[harrylin]

I am not asking to avoid geometry altogether as that doesn't make any sense but the idea of geometerization of a force/field or specifically the curving of the Minkowski space time by a field. This link will be useful to clarify - https://www.physicsforums.com/threads/gravity-on-the-minkowski-spacetime.383877

Ok, a mathematical reformulation may be possible of course; as I mentioned earlier GR was developed as a field theory and Einstein found a geometrical formulation that (almost) achieved what he wanted. I already gave you a link to Einstein's description of how in the weak field approximation clocks ("time") and rulers ("space") are affected by the gravitational field. Not surprisingly, Einstein rejected the geometry based interior solutions of black holes.

" A body at rest gives way before the action of an external force, moving and attaining a certain velocity. It yields more or less easily, according to its inertial mass, resisting the motion more strongly if the mass is large than if it is small. We may say, without pretending to be rigorous: the readiness with which a body responds to the call of an external force depends on its inertial mass. If it were true that the Earth attracts all bodies with the same force, that of greatest inertial mass would move more slowly in falling than any other. But this is not the case: all bodies fall in the same way. This means that the force by which the Earth attracts different masses must be different. Now the Earth attracts a stone with the force of gravity and knows nothing about its inertial mass. The "calling" force of the Earth depends on the gravitational mass. The " answering" motion of the stone depends on the inertial mass. Since the " answering " motion is always the same all bodies dropped from the same height fall in the same way it must be deduced that gravitational mass and inertial mass are equal."

- A. EINSTEIN, The Evolution of Physics.

Exactly. The claim that "the Earth attracts a stone with the force of gravity and knows nothing about its inertial mass" is wrong if one adheres to the meaning that mass corresponds to the amount of matter that makes up the stone, and that this amount of stone can be determined by different means. Once more: a rabbit indoors is equal to the same rabbit outdoors.
Likely it's just a matter of words and definitions, so I won't elaborate further.

 

[controlfreak]

Since you have essentially already exhausted this route, perhaps you might consider an alternative approach to your question. Perhaps consider what it would take to geometrize Newtonian gravity. See Newton Cartan gravity.

Thank you for that idea but the approach of geometerizing Gravity has already been the approach provided by Einstein and has worked extremely well. I want to see if there is a possibility to articulate gravity like how Maxwell did for EM without bringing geometerization into picture. And people have done it using GEM/LITG but the problem here is that Maxwell's equations for classical electrodynamics itself only handles weak fields and hence its direct counterpart GEM/LITG also can handle only weak fields in Gravity. So we need to see if someone has handled strong fields in EM and has created an upgraded version of Maxwell's equations for the non linear case so that we can use that theory and pivot it for Gravity. With some searching I found that that has definitely been attempted in 1933 itself by Born and Infeld as cited by Dirac here - http://www.jstor.org/stable/2413797?seq=1#page_scan_tab_contents. But need to look into that theory further to understand if it would lead to what I am looking for or if already someone had thought of it and done it.

 

[Dale]

I want to see if there is a possibility to articulate gravity like how Maxwell did for EM without bringing geometerization into picture.

OK, this thread is clearly going nowhere. Thread closed.

I don't know why you bother to ask a question if you are simply going to ignore the answers:

there is really no such thing as SR + Newtonian gravity. Its action at a distance in incompatible with SR, and this was immediately seen by physicists after 1905. Thus many were working on a resolution, some of which worked well enough (e.g. Nordstrom's second theory), but conflicted with experiment.

Newtonian gravity, with instantaneous action at a distance, isn't really compatible with special relativity.

Possibly useful
https://en.wikipedia.org/wiki/Alternatives_to_general_relativity#Early_theories.2C_1686_to_1916
"Early Theories..."

As I mentioned earlier, Nortdstrom's second theory was the best attempt of this type. However, it gave no deflection of light and a much too small perihelion shift for Mercury. (Note, there are formulations of Nordstrom's second theory that use a non-flat metric, but it was originally formulated with Minkowski metric, and that is the formulation most closely meeting your desire).

See
Field Theory of Gravitation: Desire and Reality
Yurij V. Baryshev

here http://arxiv.org/abs/gr-qc/9912003

GravitoElectroMagnetism is not equivalent to GR. GR is highly non-linear while GEM is linear.

, many people have tried, but none has succeeded in obtaining such a theory which is consistent with observation.