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Subject: Re: Is Curved Space An Improvement Over The Use of the Concept of
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Date: Sun, 17 Nov 2024 07:50:42 +0000
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On Sat, 16 Nov 2024 23:48:09 +0000, LaurenceClarkCrossen wrote:

> Is Curved Space An Improvement Over The Use of the Concept of Forces?

[SNIP]

The following text has been edited very little from the version that
I added to Wikipedia in April 2018.
https://en.wikipedia.org/wiki/Spacetime#Is_spacetime_really_curved?

Is spacetime really curved?

In Poincaré's conventionalist views, the essential criteria according
to which one should select a Euclidean versus non-Euclidean geometry
would be economy and simplicity. A realist would say that Einstein
discovered spacetime to be non-Euclidean. A conventionalist would say
that Einstein merely found it more convenient to use non-Euclidean
geometry. The conventionalist would maintain that Einstein's analysis
said nothing about what the geometry of spacetime really is.

Such being said,
  1) Is it possible to represent general relativity in terms of flat
     spacetime?
  2) Are there any situations where a flat spacetime interpretation
     of general relativity may be more convenient than the usual
     curved spacetime interpretation?

In response to the first question, a number of authors including
Deser, Grishchuk, Rosen, Weinberg, etc. have provided various
formulations of gravitation as a field in a flat manifold. Those
theories are variously called "bimetric gravity", the "field-
theoretical approach to general relativity", and so forth. Kip
Thorne has provided a popular review of these theories.

The flat spacetime paradigm posits that matter creates a gravitational
field that causes rulers to shrink when they are turned from
circumferential orientation to radial, and that causes the ticking
rates of clocks to dilate. The flat spacetime paradigm is fully
equivalent to the curved spacetime paradigm in that they both
represent the same physical phenomena. However, their mathematical
formulations are entirely different. Working physicists routinely
switch between using curved and flat spacetime techniques depending on
the requirements of the problem. The flat spacetime paradigm is
convenient when performing approximate calculations in weak fields.
Hence, flat spacetime techniques tend be used when solving
gravitational wave problems, while curved spacetime techniques tend be
used in the analysis of black holes.