[cowboysauce]

The article's description of the Aharonov–Bohm effect seems kinda misleading to me. It's not that particles are being affected by a field that's not there, it's that the particles are affected by the electromagnetic potential, which can be non-zero even though the field is zero (the two are related through some simple equations).

[rnhmjoj]

Some argue that it's neither a non-local interaction (the test particle being affected despite no field in its region) nor that the interaction is caused by the four-potential, which would then be physical and more fundamental than the field tensor. On the contrary, it may just be an artefact of the semi-classical treatment that is normally done: classical theory for the fields, quantum one for the test particle. See this, for example: https://arxiv.org/abs/1110.6169

[kurthr]

So to be simple you're saying the field is the slope (or actually gradient) of the potential. So if it's constant (but high) there is no slope, but significant potential, like being on a mesa. And that difference in potential rather than slope affects the paired quantum particles?

[bobbylarrybobby]

Kinda. The magnetic field is the curl of the vector potential. If the vector potential is nonzero but curl-less then you get zero magnetic field, but the particles’ wavefunctions still feel the vector potential.

(Specifically, the phase of the wavefunction is affected; obviously nothing observable about a single wavefunction could be affected in the absence of a field, via the correspondence principle. But when you have two electrons, that phase difference does show up in their interference pattern.)

[eternauta3k]

I think I understand the Aharonov–Bohm effect for magnetism, but I don't understand how you can have the branches at different gravitational potentials without the packets experiencing a field somewhere when they branch/join.

[kurthr]

I'm trying to figure out how gravity has curl?

[AnimalMuppet]

It's not the electric field; it's the magnetic field. There is still a potential, but the potential is a vector.

My ability to picture what is going on has never extended to the magnetic vector potential, so I have no intuition about how that plays in here...

[cowboysauce]

There is an electrical variant of the effect, it just hasn't been well tested experimentally.

[cowboysauce]

Right, but pairs of particles aren't relevant. The effect occurs for any particle that interacts electromagnetically. And the magnetic field is the curl of its potential.