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joelr315

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- TL;DR Summary
- Looking for explanation of Einstein's remarks on geometry/GR

I have seen people using Einstein's comments on the geometrical description of spacetime to mean that he didn't believe in the curvature of spacetime. While I do not think this is true I cannot fully understand what his remarks mean.When reviewing a book on relativity by Emile Meyerson: La deduction relativiste in 1928 Einstein said:

"I would like to deal more closely with this last point because I have an entirely different opinion on the matter. I cannot, namely, admit that the assertion that the theory of relativity traces physics back to geometry has a clear meaning."

According to the general theory of relativity, the metric tensor determines the behavior of the measuring rods and clocks as well as the motion of free bodies in the absence of electrical effects. The fact that the metric tensor is denoted as "geometrical" is simply connected to the fact that this formal structure first appeared in the area of study denoted as geometry.

"However, this is by no means a justification for denoting as "geometry" every area of study in which this formal structure plays a role, not even if for the sake of illustration one makes use of notions which one knows from geometry. Using a similar reasoning Maxwell and Hertz could have denoted the electromagnetic equations of the vacuum as "geometrical" because the geometrical concept of a vector occurs in these equations."So he objected to Meyerson's view of GR as geometrical but he does consider curved spacetime as a reality I assume. But I can't explain how he did believe in spacetime but seems to reject the geometrical interpretation? I'm confused?

This paper also explores this issue:

https://www.sciencedirect.com/science/article/pii/S1355219813000695

But again I can't get at what exactly it's saying about what Einstein did and did not consider true?

"I would like to deal more closely with this last point because I have an entirely different opinion on the matter. I cannot, namely, admit that the assertion that the theory of relativity traces physics back to geometry has a clear meaning."

According to the general theory of relativity, the metric tensor determines the behavior of the measuring rods and clocks as well as the motion of free bodies in the absence of electrical effects. The fact that the metric tensor is denoted as "geometrical" is simply connected to the fact that this formal structure first appeared in the area of study denoted as geometry.

"However, this is by no means a justification for denoting as "geometry" every area of study in which this formal structure plays a role, not even if for the sake of illustration one makes use of notions which one knows from geometry. Using a similar reasoning Maxwell and Hertz could have denoted the electromagnetic equations of the vacuum as "geometrical" because the geometrical concept of a vector occurs in these equations."So he objected to Meyerson's view of GR as geometrical but he does consider curved spacetime as a reality I assume. But I can't explain how he did believe in spacetime but seems to reject the geometrical interpretation? I'm confused?

This paper also explores this issue:

https://www.sciencedirect.com/science/article/pii/S1355219813000695

But again I can't get at what exactly it's saying about what Einstein did and did not consider true?