Post-Modern Newton vs Modern Einstein

The shift to modernity took place in the beginning of the 20th century in a revolt against classical ideals in politics, arts and music in parallel to Einstein's General Theory of Relativity GR, degrading Newton's theory of Gravitation NG to a simple special case, and then taking the role of fundamental pillar of modern physics together with Quantum Mechanics QM.  

GR and QM were from the beginning understood to to be incompatible, but could nevertheless be allowed to coexist for some time, but at the end of the 20th century this was no longer credible, which triggered a crisis of modern physics today witnessed by all leading physicists. Something is evidently fundamentally wrong, but what?

To seek an answer we are led to seek to understand the difference between GR and NG. We recall that in NG gravitational acceleration (of a test particle) only depends on position and not on velocity, while in GR it depends on both position and velocity. This fact can alternatively be espressed as follows:

• NG takes place in a Euclidean space-time coordinate system which does not interact with gravitation.
• GR takes place in a curved space-time coordinate system, which interacts with gravitation and makes gravitational acceleration depend on both position and velocity.   

From mathematical point of view it is natural to view a coordinate system as a form of passive recording device which does not interact with what is recorded. Like a passive microphone without interaction with the source. This corresponds to gravitational acceleration only depending on position and not velocity as in NG. It means that the coordinate system does not carry any physics which can interact with the physics being recorded.

In GR gravitational acceleration depends on both position and velocity, which means that the coordinate system is no longer passive, but interacts with the test particle. In this case the coordinate system carries physics which has to be identified. But this has not been possible. Physicists speak about "fabric" of space-time but cannot explain its physics. 

The pertinent question is now: What would happen if we gave up GR and returned to NG as the most successful theory of all of classical physics? What would be lost? What would be gained is that the crisis would evaporate since NG and QM are compatible. 

The basic evidence that NG has to be replaced by GR as concerns interaction matter-gravitation, is the anomalous advance-of-the-perihelion/precession of Mercury of 43 arcseconds per century (0.004%), as the difference between observed advance (574) and predicted advance by NG (531), claimed to be exactly captured by a 2body Sun-Mercury GR correction by analytical formula (42.98). In all other cases NG works:

We thus have that (i) NG predicts 531, (ii) 574 is observed and (iii) GR 2body analytical formula gives missing 42.98. 

To give these numbers perspective recall:

1. The model NG + 2body GR (42.98) gives observed 574 after fitting with data
2. It is claimed that NG alone after fitting with data gives 531. 

We understand that superiority of a GR model as NG + 2body correction over NG-alone is that (i) NG-alone gives 531 after fitting and (ii) 2body GR correction gives 43. Here (ii) is guaranteed by simply putting in a correction o 42.98, but (i) can be questioned. What says that NG after fitting must give 531? What would happen if NG gave 550 instead after fitting? Then the 2body GR correction of 42.98 would not show superiority of GR over NG.

Altogether, it is possible that NG can come back in post-modern physics of the 21st century. That would put GR into a bin of miscalculated modern reform projects, like the 12-tone music by Schoenberg, or 68-revolution.

It may be time for a post-modern Newton to replace a modern Einstein. 

To get a view how a modern physicist views the world listen when theoretical physicist Sean Carroll explains why (modern) physics is both simple and impossible in terms of all the buzz words, and ask if anything makes sense to you.