Why is space-time 3+1 dimensional?

[bchui]

"Why is our space-time 3+1 dimensional?"
The question had been raised by Kant and Hegel for more than 100 years

Could there be any possibility of "simple explanation" within the framework of Relativity or Quantum Theory:shy:

 

[robphy]

It seems to me that both Relativity and Quantum Theory are dimensionally-independent theories of nature. So, I think the answer to your question is no.

[Pardon the following sentence... after finally writing it down, it sounds a little playful.] Dimensionality seems to appear in the relationship among the choice of underlying spaces (the "arena"), the choice of fields (the "players"), and the choice of equations, boundary conditions, and additional requirements [like stability, nontriviality, etc] (their "rules") imposed upon them.

One of the most popular examples is the role of dimensionality in Huygens' Principle. Another is the stability of orbits. These appear in:

P. Ehrenfest, “In what way does it become manifest in the fundamental laws of physics that space has three dimensions?” Kon. Akad. Wetens. Amsterdam. Proc. Sec. Sci. 20 (1918), 200–209; reprinted in Collected Scientific Papers, ed. Martin J. Klein (Amsterdam: North-Holland, 1959), pp. 400–409.

See also my posts in
https://www.physicsforums.com/showthread.php?t=89853&highlight=ehrenfest
https://www.physicsforums.com/showthread.php?t=97776&highlight=ehrenfest

There have been some interesting studies, like
http://adsabs.harvard.edu/abs/1985GReGr..17..545N