About the nature of the Newtonian gravitational formula

[south]

TL;DR

Newton decided to leave the investigation of the innermost nature of gravitation to future generations. Einstein proposed one interpretation, and physicists are currently investigating another, one that includes quantization. My question focuses on quantum wavelength.

Could Newtonian formula be 100% quantum in nature, with the wavelength very approximately equal to the distance between the centers of mass of the two mutually gravitating bodies?

 

[Nugatory]

Could Newtonian formula be 100% quantum in nature, with the wavelength very approximately equal to the distance between the centers of mass of the two mutually gravitating bodies?

No. There’s a lot more to quantum mechanics than just things having a wavelength, and the Newtonian formula is incompatible with any quantum mechanical description of nature.

Another difficulty is that the Newtonian formula isn’t quite right. It’s nearly always a really good approximation, but it is incompatible with relativity (the problem that General Relativity solves, by providing an alternative theory of gravity that is), it doesn’t correctly predict the deflection of light by gravity, planetary orbits don’t quite follow Newton’s formula. Even if we could reframe Newtonian gravitation as a quantum theory, we’d just end up with a wrong theory.

 

[south]

Is it true that the Newtonian formula appears as a limiting case of GR?

 

[Ibix]

Is it true that the Newtonian formula appears as a limiting case of GR?

This is always true of older and newer models. The older model has to be consistent with experiment under a fairly wide range of circumstances and to fairly high precision or we'd never have used it. The newer model also has to be consistent with experiment under those same circumstances and precisions (and more) or we'd never adopt it. So the two models must make similar predictions under many circumstances, and thus it must be possible to extract the old model's maths from the new one with appropriate approximations.

In the case of GR, assuming that everything moves very slowly and all gravitational fields are weak lets you approximate the Einstein field equations until you get to Poisson's equation, which is a differential equation form of Newton's gravitational formula. Thus the two theories make pretty much the same predictions as long as fields are weak and velocities are low. The first evidence of issues with Newtonian gravity was the orbit of Mercury which, of all the planets, experiences the strongest gravitational field from the Sun and has the highest orbital velocity.

 

[south]

Thank you very much.

 

[FactChecker]

Is it true that the Newtonian formula appears as a limiting case of GR?

"Limiting" as which quantity goes to what value?
It is more accurate to say that it is an approximation rather than a limiting case. You can calculate the orbit of Mercury to any accuracy you want and the two theories will give noticeably different results.

 

[south]

My basic question has been answered. Thank you all very much. Kind regards.

 

[berkeman]

I'll tie off this thread for now. If anybody has more to add please send me a DM.