The uniqueness of D=4

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    Dimension Uniqueness
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SUMMARY

The discussion centers on the uniqueness of the four-dimensional spacetime (D=4) and its implications in theoretical physics. Key figures such as Hermann Weyl, Paul Ehrenfest, and John Whitrow are noted for their early contributions to the topic, while Tangherlini's work on Schwarzschild metrics is highlighted as a significant modern reference. The conversation also touches on the concept of microscopic extra dimensions and the stability of compactifications in higher-dimensional theories, indicating a complex interplay between empirical observations and mathematical frameworks.

PREREQUISITES
  • Understanding of Schwarzschild metrics in general relativity
  • Familiarity with the concepts of extra dimensions in theoretical physics
  • Knowledge of compactification in string theory
  • Awareness of historical contributions to physics by Weyl, Ehrenfest, and Whitrow
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  • Research the implications of compactification in string theory
  • Study the historical context of Weyl and Ehrenfest's contributions to spacetime theories
  • Explore modern interpretations of higher-dimensional theories in physics
  • Investigate the mathematical frameworks supporting microscopic extra dimensions
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The discussion is beneficial for theoretical physicists, cosmologists, and students interested in the foundations of spacetime theories and the implications of higher dimensions in modern physics.

arivero
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Discussions about having 3 spacial dimensions
I have found an interesting rabbit hole, because I thought the question of why we live in 3+1 was mainly a matter of footnotes and off-press debates. But it seems if was touched early by Weyl, Ehrenfest and Whitrow

https://einsteinpapers.press.princeton.edu/vol13-doc/764
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And then elaborated for Schwarzchild metrics by Tangherlini, who seems to be the root citation nowadays.

Is there any other relevant literature? What have you read on the topic? How does modern theory evade Eherenfest's arguments?
 

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For higher dimensionality, it seems to me that one way is to have “extra dimensions” be microscopic.
 
robphy said:
For higher dimensionality, it seems to me that one way is to have “extra dimensions” be microscopic.
That is empirically, of course. But point is, mathematically? with extra dimensions the argument does not disappear; it has some extra discussion about what compactifcations are stable. The point of D=7+4...