What is the value addition of GR?

[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.