The modelling of space time through Riemann tensor calculus

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Discussion Overview

The discussion revolves around the modeling of space-time using Riemann tensor calculus, exploring the relationship between curvature and the mathematical structure of space-time as a manifold. The conversation touches on the theoretical underpinnings of space-time and its unification from the perspective of special relativity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how space-time can be explained through Riemann calculus.
  • Another participant argues that Riemann calculus is primarily necessary for describing curvature rather than space-time itself, suggesting that space-time is fundamentally a manifold.
  • A reference is made to a previous thread discussing the unification of space and time, indicating that this concept arises more from special relativity than from mathematical considerations.
  • One participant expresses frustration at the request for a comprehensive explanation of general relativity, suggesting that such a request is unreasonable and implies a need for individual effort in understanding the topic.
  • A later reply indicates that the thread is closed but encourages more specific questions in new threads.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity of Riemann calculus for explaining space-time, with differing views on its role and the nature of space-time itself. The discussion remains unresolved regarding the depth of explanation required and the appropriateness of the initial question.

Contextual Notes

The discussion highlights limitations in the depth of mathematical detail provided and the assumptions regarding the reader's prior knowledge of general relativity and manifold theory.

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How do we explains space-time through Riemann Calculus?
 
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Riemann calculus is really needed only to describe curvature, not space-time.

The mathematical structure of space-time, like the mathematical structure of just space, is that of a manifold. A manifold is built on top of some other math concepts, I'm not sure if I should go into that level of detail, for the moment I won't.

We had another thread recently on why we combine space and time into a unified "space-time". This basically comes not from mathematics, but rather from special relativity.
 
What Vanadium50 said. This thread is closed, but more specific and focused questions in new threads will be welcome.
 

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