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Is 3+1 spacetime as privileged as is claimed?

Regardless of your favorite theory of how many dimensions the universe has in total, the universe seems to have a deep preference for displaying three fully interchangeable large-scale spatial dimensions (plus time) within any given frame of reference.

But why? That is, has anyone ever come up with a persuasive argument for why the number three is or is not the required number of large-scale spatial dimensions in a universe?

This question from way back in November 2010 appears related, but after reading through it I'm pretty sure it is only pointing out that the known laws of electrostatics have three spatial dimensions built into them, which is most certainly true. But universes with fewer or more than three large-scale spatial dimensions would presumably have different force rules reflecting their different geometries, so this kind of analysis only shows self-consistency within a universe.

(I should also warn responders in advance that while I respect the right of some theorists to suggest that it is three "because our universe evolved that way out of a fractal multiverse," I also respect my own position that such statements are equivalent to saying "We haven't the foggiest idea why." An answer along those lines would at the very least need some powerful anthropic principle support, e.g. a proof or near-proof that universes with less or more than three large-scale spatial dimensions would have extreme difficulty supporting life.)

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Terry Bollinger
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    I wonder if its possible to answer this question, as it asks for not merely the law but a reason for the law. Asking why gravity one should terminate at a phrase like because we observed... Likewise the 3+1 dimension theory exists because quantum experiments were observed - in the same manner as it is increasingly apparent more dimensions might not exist due recent LHC runs. – Mikhail Nov 30 '12 at 06:51
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    There's a really good review article on this out there somewhere, but I'm damned if I can find it. Three spatial dimensions is obviously a minimum, and more than three allows too much freedom e.g. no stable planetary orbits. – John Rennie Nov 30 '12 at 06:58
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    Possible duplicates: https://physics.stackexchange.com/q/10651/2451 and links therein. – Qmechanic Nov 30 '12 at 08:11
  • Qmechanic, thanks. My question is indeed a duplicate of that one. I looked for matches, but unfortunately didn't find any due to emphasizing space ("3") over spacetime ("3+1") in my title. Should I just delete this one? – Terry Bollinger Nov 30 '12 at 08:50
  • Math Overflow: https://mathoverflow.net/q/286288/333546 "The specificity of dimension 1+3 for the real world". Arxiv: https://doi.org/10.48550/arXiv.gr-qc/9702052 "On the dimensionality of spacetime" by Max Tegmark. – Quillo Feb 15 '23 at 11:00

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A few quick references before you close the question:

There's a rather technical discussion on what's special about four dimensions on the Math Overflow (way over my head!).

The article I was thinking of is actually on Wikipedia. This picture from the article:

Dimensions

succinctly explains why our space is 3+1 dimensional.

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John Rennie
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  • Nice! (That's from Wikipedia??) I'm hurrying the award on this one a bit, since I had not realized I was asking a duplicate. This gives a nice update to the earlier question, one of the anthropic selection variety. Also, anyone else: If you know of a mathematical argument for "why 3+1", I'd love to hear it and (true confessions) might re-reward? I still think it's fascinating that Hamilton had high (but signature-dashed) hopes for his quaternions as just that, a hope he based I think solely on their similar breakout of 3+1 axes. So, is something similarly simple but workable still out there? – Terry Bollinger Nov 30 '12 at 11:16
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    Note the source of that image is http://space.mit.edu/home/tegmark/dimensions.html – SztupY Aug 26 '16 at 10:57
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    @Bollinger: 3 dimensions of space are special, because this is the lowest number of dimensions, where a random walk doesn't return to it's origin with certainty, see http://mathworld.wolfram.com/PolyasRandomWalkConstants.html . – asmaier Mar 04 '17 at 12:48