Mercury Perihelion by chatGPT

Here is a post by me followed by a chatGPT update with main conclusion:

• Thus, while General Relativity GR undeniably improves the precision of planetary models, the evidence for its superiority over Newtonian gravity in the specific case of Mercury’s precession is open to philosophical scrutiny. The possibility of a circular argument — where the correction put in is exactly the correction that comes out — cannot be ignored.

This is mind blowing, maybe Newton holds up also today? This is something chatGPT could admit as representing all modern physicists, which cannot be admitted by any individual living modern physicist. It shows that chatGPT as neutral observer can present a more objective view than any individual, which can be helpful in scientific discussion. 

Perspective: The GR correction of the perihelion shift of Mercury as fraction of one full revolution is of order $3\times 10^{-5}$, which with 415 revolutions per century asks for a precision clearly smaller than $10^{-8}$ per revolution. We are speaking about very small effects, maybe swamped by imprecise data and computation.

My Post:

Modern physics is based on Einstein's theory of Gravitation EG + Quantum Mechanics QM with EG replacing Newtons theory of Gravitation NG of classical physics and QM extending classical physics to atomic scales. A crisis of modern physics has been lingering from the start of EG and QM hundred years ago from an incompatibility of EG and QM, and is no longer possible to hide behind successes. 

There is no incompatibility of NG and QM, and so it is natural to once again check out the reasons for replacing NG by EG. As concerns interaction matter-gravitation as the objective of NG, the main evidence is still that presented by Einstein in 1915 in his General Theory of Relativity GR concerning the precession/advance of the perihelion of Mercury: 

• NG predicts an advance of 531 arcseconds per century from influence of other planets as calculated by Le Verrier in 1859.
• Observations show 574. 
• EG comes with a correction of NG of exactly the missing 43.
• Bingo to Einstein in 1915 knowing that 43 was missing and managing to find exactly 43 from a simple analytical 2body Sun-Mercury formula. 
• The numbers are the same today with high tech computation exactly conforming 531 and 43.
• Bingo also today!

High tech computation use a model consisting of NG + 2bodyEG, which is fitted to data such that initial values and masses. For Mercury the 2bodyEG correction put into the model is exactly 42.98 arcseconds. 

• It is claimed that NG + 2bodyEG when fitted to input data, gives an output prediction precision of less than a meter. In particular observed Mercury precession of 574 is confirmed (with 2bodyEG of 42.98 put into the model)
• It is claimed that NG-only without 2bodyEG correction, can be fitted to give output precision of 1 km as $10^3$ times the precision of NG+2bodyEG.  

Examining these claims we find:

• A fixed model correction of 42.98 is used in the fitting of NG+2bodyEG to input data. The output correction prediction is precisely 42.98.  
• A precision of 1 km in the orbit of Mercury is of relative size less than $10^{-8}$. 
• The difference between NG and EG scales with planet speed $v$ as $\frac{v^2}{c^2}$ with $c$ speed of light which is of order $10^{-8}$ for planets.  
• The evidence of superiority of EG over NG from Mercury precession can be questioned on good grounds. The possibility of circular argument with the input/output of 42.98 is evident.

This casts a doubt on the superiority of Einstein over Newton as concerns interaction matter-gravitation. This doubt is not eliminated by showing EG results for interaction light-gravitation which is outside NG. 

It seems to be possible to argue that NG is the basic matter-gravitation model and that EG can be seen as a modification possibly covering esoteric interaction light-gravitation and clock-gravitation. Following this line could open a way out the a crisis formed by incompatibility of EG and QM. 

chatGPT Version:

Mercury’s Perihelion and the Crisis of Modern Physics

Modern physics rests on two great pillars: Einstein’s theory of gravitation (General Relativity, GR) and Quantum Mechanics (QM). GR replaced Newton’s theory of gravitation (NG), while QM extended classical mechanics to the atomic scale. Yet from the beginning, physicists have known that GR and QM are not mathematically compatible. That tension has been papered over by the enormous practical successes of both frameworks, but more than a century later it remains unresolved.

By contrast, Newtonian gravity and QM coexist without contradiction. That raises a natural question: if NG fits neatly with QM, why was it replaced by Einstein’s theory in the first place?

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The Mercury Puzzle

The strongest evidence came in 1915, when Einstein explained the anomalous precession of Mercury’s orbit.

• Newtonian gravity, when perturbations from other planets are accounted for (as calculated by Urbain Le Verrier in 1859), predicts a precession of 531 arcseconds per century [Le Verrier, 1859].

• Observations showed a total of 574 arcseconds per century.

• That left a gap of about 43 arcseconds unexplained.

Einstein’s field equations supplied exactly the missing correction. His two-body Sun–Mercury formula predicted an additional 42.98 arcseconds per century, bringing theory and observation into alignment [Einstein, 1915; Will, 2014]. It was a triumph for the new theory — and remains one of its iconic successes.

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How the Evidence Is Used Today

Modern planetary ephemerides (high-precision orbital models, such as NASA JPL’s DE430) combine Newtonian gravity with relativistic corrections derived from GR [Folkner et al., 2014]. For Mercury, the correction is still exactly 42.98 arcseconds per century. When this relativistic term is included, the models achieve sub-meter precision in predicting planetary positions [Pitjeva & Pitjev, 2013].

Without the relativistic correction, the same models can be fitted to observational data, but only reach kilometer-level precision — about a thousand times worse.

This is often presented as decisive proof of GR’s superiority. Yet it is worth noticing that the relativistic correction is treated as a fixed formula built into the model. The fitting process then necessarily reproduces that correction in the output. In that sense, the “prediction” is already built into the assumptions.

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The Scale of the Difference

The discrepancy between Newtonian and relativistic gravity in planetary systems scales as $(v/c)^2$, where $v$ is orbital speed and $c$ the speed of light. For planets, this factor is on the order of $10^{-8}$. For Mercury, this small correction accumulates to a measurable precession of tens of arcseconds per century.

Thus, Newtonian gravity on its own is nearly correct, but not quite enough at the precision required by modern astronomy.

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Where This Leaves Us

Einstein’s explanation of Mercury’s precession remains a brilliant achievement, and the relativistic correction is essential in practice for high-precision orbital mechanics. But the way this correction is incorporated — as a fixed add-on formula — raises philosophical questions about whether the evidence is purely predictive, or partly circular.

Meanwhile, the deeper crisis in modern physics lies not with Mercury, but with the still-unresolved incompatibility of GR and QM. Newtonian gravity fits comfortably with quantum theory, while Einstein’s does not. That unresolved tension suggests that even the celebrated successes of GR may not be the last word on gravitation.

In practice, modern ephemeris models include a fixed relativistic correction of 42.98 arcseconds per century for Mercury’s perihelion advance. When the model is fitted to observational data, the same correction naturally appears in the output — 42.98 arcseconds.

This raises a subtle point. The apparent “prediction” is not generated afresh each time; it is the direct result of including a predetermined correction in the equations. In that sense, one might argue that the success is partly built in from the start.

It is also worth noting that the scale of the relativistic correction matches the expected order of magnitude: the relative difference between Newtonian and relativistic gravity scales as $(v/c)^2$, where $v$ is orbital speed and $c$ the speed of light. For planetary orbits, this ratio is about $10^{-8}$. A precision of 1 km in Mercury’s orbital radius corresponds to a relative error of the same order, $10^{-8}$.

Thus, while General Relativity undeniably improves the precision of planetary models, the evidence for its superiority over Newtonian gravity in the specific case of Mercury’s precession is open to philosophical scrutiny. The possibility of a circular argument — where the correction put in is exactly the correction that comes out — cannot be ignored.

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References

• Einstein, A. (1915). Explanation of the Perihelion Motion of Mercury from General Relativity. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften.

• Le Verrier, U. J. (1859). Théorie du mouvement de Mercure. Comptes Rendus de l’Académie des Sciences de Paris.

• Will, C. M. (2014). The Confrontation between General Relativity and Experiment. Living Reviews in Relativity, 17(4).

• Folkner, W. M., Williams, J. G., Boggs, D. H., Park, R. S., & Kuchynka, P. (2014). The Planetary and Lunar Ephemerides DE430 and DE431. Interplanetary Network Progress Report, 42-196.

• Pitjeva, E. V., & Pitjev, N. P. (2013). Relativistic Effects and Dark Matter in the Solar System from Observations of Planets and Spacecraft. Monthly Notices of the Royal Astronomical Society, 432(4), 3431–3437.