The uniqueness of D=4

In summary, "The uniqueness of D=4" refers to the distinctive characteristics of four-dimensional spacetime in the context of physics, particularly in general relativity and string theory. Unlike other dimensions, D=4 allows for a unique formulation of gravitational interactions and the behavior of fields, leading to significant implications for the structure of the universe. This uniqueness is highlighted by the interplay of geometry and topology, as well as the specific properties of massless particles and black holes, which are not replicated in other dimensions.
  • #1
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.
 
  • #3
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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