I The uniqueness of D=4

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The discussion explores the uniqueness of four-dimensional spacetime, highlighting early contributions from Weyl, Ehrenfest, and Whitrow, and noting the significance of Tangherlini's work on Schwarzschild metrics. It raises questions about relevant literature and how modern theories address Ehrenfest's arguments regarding dimensionality. The concept of "extra dimensions" being microscopic is proposed as a possible explanation for higher dimensionality. The mathematical implications of compactifications and their stability are also considered. Overall, the conversation emphasizes the complexity and ongoing exploration of dimensionality in theoretical 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...
 

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