Dimension of Space

[dioib]

How do we know that the (effective) dimensionality of "space" is three in a typical physical theory?

[tom.stoer]

a) because we see it
b) because we can measure it, e.g. via the Coulomb law which shows a behaviour like U(r) ~ r-(D-2)
c) because there are a huge number of physical predictions depending on the dimensionality (besides the Coulomb law there are the gravitational potential, diffusion processes, ...)

[dioib]

a) because we see it
b) because we can measure it, e.g. via the Coulomb law which shows a behaviour like U(r) ~ r-(D-2)
c) because there are a huge number of physical predictions depending on the dimensionality (besides the Coulomb law there are the gravitational potential, diffusion processes, ...)

Thank you for breaking it down into parts:
a') Because we can't see/perceive "further/higher".
b',c') Taking (a'), how can I make sure it will not affect (b,c)?

[tom.stoer]

I think you can't.

a) is certainly reasonable in the macroscopic domain
b) is valid in the microscopic domain at least at scales currently measured at the LHC (there is a minor chance to find indications for large extra dimensions at the LHC which would mean that the effective dimension D becomes energy dependent D(E) and will deviate from 3 at high energies E)
c) just means that there are other processes from which such deviations could be determined, e.g. gravitational interactions

[Oxieee]

Thank you for breaking it down into parts:
a') Because we can't see/perceive "further/higher".
b',c') Taking (a'), how can I make sure it will not affect (b,c)?
yes i have the same confusion