Inverse Square Law + Special Relativity

[nassboy]

If one assumes that Newtons inverse square law does not act instantly at a distance, and instead obeys the rules of special relativity does it make similar predictions as general relativity?

Has anybody worked this out? Maybe the result is similar to maxwell's equations.

 

[Meir Achuz]

The EM potential acting at a retarded time already followed from Maxwell's equations, well before relativity. The effect is well understood and has nothing to do with GR.

 

[Count Iblis]

If one assumes that Newtons inverse square law does not act instantly at a distance, and instead obeys the rules of special relativity does it make similar predictions as general relativity?

Has anybody worked this out? Maybe the result is similar to maxwell's equations.

Yes, and the results are similar to GR, but there are differences. Wald writes in his book on GR that this would have been the more straightforward way to describe gravity. Had Einstein not invented GR, we would very likely have been stuck with a flawed theory for a very long time (because if observations show a small discepancy, you can always model that by introducing extra terms).

Kaku has claimed that GR would only have been formulated in the 1970s, had Einstein not discovered it.

 

[A.T.]

f one assumes that Newtons inverse square law does not act instantly at a distance, and instead obeys the rules of special relativity does it make similar predictions as general relativity?

Similar but not the same. It doesn't predict spatial curvature and gravitational time dilation. Discussed here:
https://www.physicsforums.com/showthread.php?t=324457&p=2270590

 

[nassboy]

Reversing the question then...can maxwell's equations be formulated more like GR?

 

[jtbell]

Electrodynamics in Curved Spacetime, from Misner, Thorne and Wheeler's "Gravitation."