Accurate Results of General Theory of Relativity

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Discussion Overview

The discussion centers on the possibility of obtaining accurate results from the general theory of relativity while maintaining the concept of three-dimensional flat space. It explores theoretical implications and geometrical interpretations of gravity within the framework of general relativity and special relativity.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions whether accurate results from general relativity can be achieved without discarding the concept of three-dimensional flat space.
  • Another participant suggests that a flat embedding of four-dimensional spacetime might be necessary to describe gravity geometrically while maintaining a flat spacetime.
  • A different viewpoint notes that in the weak field limit, spacetime is generally approximated as flat, though the relevance to the original question is uncertain.
  • One participant explains that general relativity connects energy-momentum with the curvature of spacetime, allowing for the computation of time dilation and geodesics, and mentions that even special relativity requires embedding flat 3-space into a four-dimensional Minkowski spacetime.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between flat spacetime and the accurate application of general relativity, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

The discussion involves assumptions about the nature of spacetime and the conditions under which general relativity applies, particularly in relation to weak gravitational fields and the embedding of dimensions.

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is it possible to get accurate results of general theory of relativity without discarding concept of three dimensional flat space
 
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I believe that the only way in keeping a flat spacetime and describing gravity geometrically is to use a flat embedding for our 4-dimensional spacetime. But I'm not an expert in this :)
 
In the weak field limit (e.g. no strong gravitational fields) we generally approximate space-time as flat, but I'm not sure if that's what you're asking.
 
This is how I see it.

General relativity relates the presence of energy-momentum to the curvature of space-time. From the curvature or space-time, we can compute time dilation and geodesics, which are phenomenon of study in GR.

You don't even need GR. Even in SR the flat 3-space must be embedded into a 4-dimensional Minowski space-time when we relate time with proper time and length with proper length.
 

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