The modelling of space time through Riemann tensor calculus

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Riemann tensor calculus is essential for describing the curvature of space-time, which is mathematically structured as a manifold. The unification of space and time into "space-time" originates from principles of special relativity rather than purely mathematical reasoning. The discussion emphasizes the need for individuals to engage more deeply with the subject rather than expecting comprehensive explanations in a forum format. It suggests that more focused and specific questions are encouraged in new threads. Overall, the conversation highlights the complexity of general relativity and the importance of individual study.
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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.
 

Thread 'EPR revisited'

In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
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