Perihelion Precession of Mercury vs Modern Physics vs Pataphysics

Science of Imaginary Solutions: Pataphysics

Einstein's General Theory of Relativity GR (1915) is viewed to be a crown jewel of modern physics replacing classical concepts of space, time and motion under gravitational force expressed in Newtonian mechanics, by an entirely new geometric world of "curved space-time" without gravitational force. 

Newton's mechanics fostered the scientific revolution in the 18th century, while GR opened to the revolution of modern physics of the 20th century. 

At least, this is what (most) modern physicists tell us: Newton's world of mechanics has to be replaced by Einstein's GR world of geometry. More precisely, Newton's mechanics has to be replaced by GR only for extreme speeds or gravitational force/curvature, while GR and Newton agree in most cases. 

The acceptance of GR has grown only slowly over the 20th century, since evidence of superiority of GR over Newton has shown to be evasive, as expressed by fact that the first Nobel Prize directly connected to GR was given only in 2020 to Roger Penrose:

•  for the discovery that black hole formation is a robust prediction of the general theory of relativity. 

The Prize is thus given to the "discovery that GR predicts" the existence black holes, which however cannot be verified. Is that evidence that GR is correct? That GR gives a prediction, the correctness of which cannot be tested? So the Prize in Physics has been awarded to the discovery of an aspect of GR as mathematical fiction regardless of any actual real truth value of GR.  It is like discovering that a certain mythological tradition admits the existence of Unicorns, regardless of the existence of any real ones. This looks like a Nobel Prize in Pataphysics as a branch of philosophy or science that examines imaginary phenomena that exist in a world beyond metaphysics. 

The first evidence of GR was presented by Einstein in a computation using GR to correct a Newton prediction of the precession of the perihelion of Mercury (very slow rotation of the elliptic orbit around the Sun) to exactly fit with observation. But the Newton prediction was made without a computer and so could not account for the full complexity of the problem involving all other planets and unknown inner motion of the Sun and more. 

So it is not clear that Newton fails as concerns Mercury. An example of the correction brought by viewing Sun-Mercury as a true two-body problem still within Newtonian mechanics, with Mercury influencing the motion of the Sun, instead of a one-body problem with fixed Sun, is given in

• The secret of planets’ perihelion between Newton and Einstein by Christian Corda. 

This shows that the correction captured by GR can also be captured by Newton. This is not surprising since the orbit of Mercury is not extreme at all, and so Newton and GR should agree. 

If then Mercury can be taken off the list of evidence of superiority of GR, what remains are extreme cases, so extreme that not even GR can be expected to work, such as black holes, so extreme that they cannot be observed, or even predicted by GR to be honest?  

Why is it important to normalise modern physics back to Newton's mechanics? Because, Newton's mechanics works very well together with quantum mechanics, where speeds are low and gravitation weak. Hopefully this can take modern physics out of its permanent crisis since 100 years caused by an unresolvable conflict between Einstein's mechanics and quantum mechanics: From pataphysics to real physics! In particular, quantum mechanics can be relieved of relativistic mechanics since speeds are low. 

PS1 The Nobel Prize to Penrose/GR is more precisely motivated as follows:

• A black hole is a supermassive compact object with a gravitational force so large that nothing, not even light, can escape from it. 
• In 1964, Roger Penrose proposed critical mathematical tools to describe black holes. 
• He showed that Einstein’s general theory of relativity means the formation of black holes must be seen as a natural process in the development of the universe. 
• He was also able to describe black holes in detail: at their farthest depths is a singularity where all known laws of nature dissolve.

Every word here triggers questions: Supermassive? Nothing can escape? Proposed? Critical mathematical tools? Must be seen? Natural process? In detail? Farthest depths? Singularity? All known laws of nature dissolve? 

Compare with Ethan Siegel: 

• This Is Why Scientists Will Never Exactly Solve General Relativity

Returning to Newton could offer a great relief from a 100 year spell. 

It is illuminating to inspect the picture presented by the Nobel Committee in its description of the scientific work of Penrose as concerns the nature of the interior of a black hole: 

Sometimes a picture tells more than 1000 words...

PS2 GR was initially met with deepest skepticism and was counted down and out by the 1950s. Then miraculously GR was revived in the 1960s and on, until the great triumph of detection in 2015 of utterly faint gravitational waves emitted by the most violent event thinkable in the from of collision of two black holes 1.3 billion years ago. Credible?  How much of the present crisis of physics can be blamed on GR?