Combining Special Relativity & Newtonian Gravity: Can We? Why?

[TimeRip496]

Can we just combine special relativity and Newtonian gravity? If cannot, why is it intuitively not possible? If can, why is the intuition behind it? Because if can, there seems to be a need for a mediator of force for gravity which can only travel at light speed.

 

[Vanadium 50]

Can we just combine special relativity and Newtonian gravity?

Sure. But such a theory disagrees with observation.

 

[wabbit]

While GR is the standard approach and is firmly supported by observations, there have been alternative proposals such as teleparallel gravity and others.
I don't think any of them could be described as "just combine" though.
As you mention, there is an implied infinite speed of signal transmission in NG so this must be changed at least.

Edit : also, in case that's what you had in mind, those I know of all somewhat "look like" GR in the sense that they involve a manifold, metric tensor, geodesics, curvature, a field equation, etc. None of these seem "simpler" than GR.

 

[russ_watters]

Sure. But such a theory disagrees with observation.

Can we, even? Newtonian gravity is based on an instantaneous speed of propagation. It would seem to me that it and SR directly contradict each other.

 

[wabbit]

Can we, even? Newtonian gravity is based on an instantaneous speed of propagation. It would seem to me that it and SR directly contradict each other.

According to https://en.m.wikipedia.org/wiki/Brans–Dicke_theory, Brans-Dicke manages to combine the two as much as GR does. Not familiar with it at all though.
Of course any such combination must involve finite-speed transmission

 

[PeterDonis]

Newtonian gravity is based on an instantaneous speed of propagation. It would seem to me that it and SR directly contradict each other.

Yes, they do. In order to "combine" them, something has to give. I suspect that what V50 was referring to was letting the instantaneous propagation speed give, so that you have SR + quasi-Newtonian gravity, with the same form of the force law but replacing the instantaneous propagation with light-speed propagation--basically you need to replace the $r$ in the force law, which is "radius at the same instant of time", with an appropriately propagation-delayed distance that is relativistically invariant. You can make a consistent theory this way (IIRC Einstein tried something along these lines as one of his early attempts at expanding SR to include gravity), but it does indeed disagree with observation.

 

[Vanadium 50]

My thinking was that a "combination" would be a theory that is consistent with SR and the limit v -> 0 recovers Newtonian gravity. This is done with retarded potentials like you do in electromagnetism, replacing the charge in Coulomb's Law with mass. Since m needs to be a Lorentz scalar, the only possible choice of mass is "invariant mass".

As I said before, this theory disagrees with the data.

 

[PeterDonis]

This is done with retarded potentials like you do in electromagnetism, replacing the charge in Coulomb's Law with mass. Since m needs to be a Lorentz scalar, the only possible choice of mass is "invariant mass".

This is more or less what I thought. And I agree that this theory disagrees with observation.