Insights Answering Mermin’s Challenge with the Relativity Principle

[RUTA]

There is no "where M is" in the Schwarzschild solution; it's a vacuum solution with zero stress-energy everywhere. Also $r = 0$ is not even part of the manifold; it's a limit point that is approached but never reached, so it can't be "where" anything is.

M in the Schwarzschild solution is a global property of the spacetime; there is no place "where it is".

You can model Schwarzschild surrounding matter solutions and the Schwarzschild solution holds all the way inside the horizon to that matter. So, as you go smaller and smaller you approach $\rho = \infty$.

 

[PeterDonis]

You can model Schwarzschild surrounding matter solutions and the Schwarzschild solution holds all the way inside the horizon to that matter. So, as you go smaller and smaller you approach $\rho = \infty$.

You can do this in a model such as the 1939 Oppenheimer-Snyder model, sure. That's not what I was using "the Schwarzschild solution" to refer to, but yes, it's a valid model, and is subject to the same limitation that Wald describes, assuming Wald's viewpoint that classical GR will break down at Planck scale curvatures is correct.

 

[RUTA]

For those interested here is Mermin's original paper:
https://pdfs.semanticscholar.org/76f3/9c8a412b47b839ba764d379f88adde5bccfd.pdf
Feynman in a letter to Mermin said 'One of the most beautiful papers in physics that I know of is yours in the American Journal of Physics.'

I personally am finding my view of QM evolving a bit. Feynman said the essential mystery of QM was in the double slit experiment. I never actually thought so myself, but was impressed with it as an introduction to the mysteries of QM at the beginning level. I am now starting to think entanglement may be the essential mystery.

Thanks
Bill

I ordered the book ILL and copied the letter from Feynman to Mermin and Mermin's response. I'll attach those copies here.

 

[RUTA]

The paper that this Insight is based on has now been published: Answering Mermin's challenge with conservation per no preferred reference frame, Scientific Reports 10, 15771 (2020).