Is the dimensionality of space considered a universal constant?

Question

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

Answer 1

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.