What if the dimensionality was something like 3.0001 or 2.999? Would we be able to tell the difference? I heard about fractional dimensionality in 3b1b and was wondering about its implications for physics
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could you point to the source? – Umaxo Feb 13 '20 at 11:35
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Possible duplicates: https://physics.stackexchange.com/q/19802/2451 and links therein. – Qmechanic Feb 13 '20 at 12:28
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Could you define what you mean by a fractional dimension here? Space is usually considered as a manifold, for which only integer dimensions are defined. – Slereah Feb 13 '20 at 12:28
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The dimensionality of spacetime affects how forces spread out. Gravity and EM radiation decline as $1/r^{D-1}$. This has observable effects, for example that only in $D=3$ will orbits close (Bertrand's theorem) and how the wave equation allows information to spread. I have not seen estimates, but given that light from remote quasars still remain undispersed $D$ must be close to 3.
Anders Sandberg
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