ChatGPT-4: Newton's Inverse Square Law

After a bit of discussion ChatGPT-4 delivers the following conclusion concerning Newton's inverse square gravitational law for pointlike bodies with mass/point masses: 

• Newton's law for pointlike bodies is accurate and applicable when dealing with objects that can be reasonably approximated as point masses. In such cases, where the assumption of pointlike bodies is valid, Newton's law provides accurate predictions of the gravitational interactions between those bodies.
• For example, when considering the motion of planets in our solar system or the behavior of objects in everyday scenarios, treating them as point masses yields highly accurate results using Newtonian gravity.
• So, if the objects under consideration can be effectively modeled as pointlike bodies, Newton's law is a reliable and precise description of their gravitational interactions. The law has been extensively tested and validated in numerous practical applications.
• However, it is important to note that there are situations where the assumption of pointlike bodies breaks down, such as when dealing with objects of finite size, strong gravitational fields, or high speeds. In these cases, more advanced theories, such as general relativity, are necessary to accurately describe the gravitational interactions.

GPT-4 is educated by the physics community and so can tell truths carried by the community, truths which typically may be covered up in a discussion with any member of the community. GPT-4 has not yet been educated to hide possibly inconvenient facts, so if you persist a bit with questions you can learn something.

The truth told by GPT-4 is that Newton's law for point masses is correct, and so necessarily for all bodies composed of point masses = all bodies,  and so there is no need for Einstein's General Theory of Relativity GR. 

GPT-4 seeks to cover up suggesting that bodies composed of point masses would not be covered by Newton's law, which lacks rationality, and so give room for something more advanced than Newton's law = GR as the holy grail of modern physics. The key argument used by Einstein to replace Newton's mechanics by GR, was that Newton's mechanics does not correctly predict the precession of Mercury as a slow turn of its elliptical orbit around the Sun of about 2 degrees per century since there was a 1% difference to observation, which Einstein could fix with GR to an exact fit. 

But Einstein's argument, today accepted by the physics community as the key reason to switch from Newton's mechanics to GR with all the complications coming from throwing out the best of classical physics, is weak because the precision of a Newtonian computation with all its uncertainties concerning planetary masses and the value of the gravitational is not small enough to allow a verdict that it does not match observation. This fact is acknowledged by asking GPT-4 if a Newtonian computation within its precision may fit with observation, which gives the following answer:  

• Yes, that is a possibility. If a Newtonian computation of the precession of Mercury's orbit is performed with sufficiently accurate initial conditions, precise numerical methods, and inclusion of relevant gravitational influences, it is conceivable that the computed precession could agree with the observed value up to the computational precision.
• By employing more advanced computational techniques and including additional factors such as the gravitational influences of other celestial bodies, it is possible to improve the accuracy of the Newtonian prediction. However, it is important to note that this would still be a purely Newtonian approach without considering relativistic effects.
• In practice, the precision achieved in a Newtonian computation would depend on the specific details of the calculation and the accuracy requirements of the problem. While a sufficiently precise computation could potentially yield a result that matches the observed precession, it is worth noting that the discrepancy between the observed precession and the Newtonian prediction was one of the factors that motivated the development of general relativity.
• General relativity provides a more accurate description of the precession of Mercury's orbit, including the contributions from spacetime curvature and relativistic effects. Therefore, to achieve a high level of precision that matches the observed value, it is typically necessary to consider the effects of general relativity in addition to the Newtonian computation.

GPT-4 thus states that the Mercury reason to replace Newton by GR is very weak, and that is the main reason as concerns Newton's mechanics for bodies with mass, which does not say anything about light without mass. Newton does not have to be dethroned by Einstein.  

Warning: If a theoretical/computational prediction exactly agrees with observation, such as Einstein's GR prediction of the precession of Mercury,  then an alarm signal is motivated: It requires both theory and observation to be exact, which is impossible to achieve. There is good reason to believe that Einstein knowing what observation to fit, simply adjusted his computation until exact fit, exact! Mercury is still the best argument put forward to promote GR before Newton, after more than 100 years...

PS Suppose the time step in a Newtonian computational simulation of the planetary system with objective of predicting the precession of Mercury over a century, is one second. The total number of time steps would then be about $3\times 10^9$ and to reach 1% accuracy would require a precision of size $3\times 10^{-12}$ in each time step, which seems pretty formidable...To rule out Newton's theory of gravitation by not reaching agreement with a certain observation better than 1% in a certain computation with finite time step, thus may not be called for...