[posix_me_less]

> If you consider the compactification of R^3 by a single point “at infinity”, an electric charge inside the surface is the same as the opposite charge at infinity (this is just Gauss’ result)

This is a mental operation, not physically possible. The difference is real: for example, charge inside a perfect conductor cavity generates electrostatic field outside. A charge outside perfect conductor cavity does not generate any static field inside.

[tgb]

This is what I wondered about back in physics class. Does that prove the universe is not compact? If it were, then inside-outside is the same. But surely that's not enough to know the shape of the universe. My 'resolution' of this was to say that the universe is surely very large and so the time to reach equilibrium will be very very long. So the experiment cannot really be run to completion.

But would a point charge outside a conductor cavity ever come to equilibrium where it does generate an electric field inside the conductor cavity? Assuming compact but very large universe. It seems strange but I guess it would.

[pfortuny]

Aaaahhhhh!!!!

Thank you for this comment, truly enlightening (I am a mathematician and know 0 physics). Shall have to think about it.