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Detecting the Aharonov-Bohm effect for gravity is a super impressive experimental achievement, though it's not as "weird" as the effect for magnetic fields. On
by antognini 4y ago
Detecting the Aharonov-Bohm effect for gravity is a super impressive experimental achievement, though it's not as "weird" as the effect for magnetic fields.
One way of interpreting the normal Aharonov-Bohm effect is that it implies that the electromagnetic potential is more "real" than the electromagnetic field. We tend to think of the electromagnetic field as what's "really" out there because if you stick a charge in an electric field you can measure the field strength by measuring the force the charge feels or you can measure the force on a moving charge and calculate the magnetic field. By contrast the electromagnetic potential is not uniquely defined which makes it feel like a mathematical construct. You can add any function with zero divergence to the electric potential and any function with zero curl to the magnetic potential and have a potential that behaves identically for any experiment you could do (these are different gauge choices in the parlance).
The classic Aharonov-Bohm effect is that you take a particle and pass it around a magnetic solenoid in a superposition of two states --- say one state goes to the left of the solenoid, the other goes to the right. In a sense the particle takes both paths simultaneously. The magnetic field is zero along both paths the particle takes. If you turn the solenoid on and off you would think it would make no difference because no matter what you do, the magnetic field the particle encounters is zero. The key, though, is that the magnetic potential is not zero along the particle's path, and the magnetic potential affects the particle's phase in measurable way when the two states recombine.
Sometimes I see interpretations that this means that there is a small but non-zero chance that the particle is found inside the solenoid where the magnetic field is non-zero, but I don't think that's right. You can construct the experiment in a way that the chance of this happening is negligible. The real implication seems to be that the electromagnetic potential is the more physically fundamental quantity even though it is not generally directly observable.
All the math for the Aharonov-Bohm effect applies for gravitational fields as well. But here it's not quite as "weird" a result because gravitational fields can't be shielded the same way magnetic fields can be. The particle always encounters the gravitational field along both paths, so it's not so spooky that the field has a measurable effect.
- hammock 4y agoIs magnetic fields not being real kind of like centrifugal force not being real?
- antognini 4y agoI think it's a little bit different in this case. As physics has progressed, one of the things we've found is that the things that seem to actually exist in the physical universe aren't necessarily directly observable. So the wavefunction of quantum mechanics is one of these "real" objects, but we can't see a wavefunction directly. It and collapses any time we measure it, and, to make matters even worse, it's a complex number --- how do you measure a complex number? We can infer the existence of the wavefunction based on various experiments, but we're never looking at it directly. The centrifugal force, by contrast, is more a consequence of a particular choice of reference frame. Whether it exists or not picks out certain reference frames as being special. But something like the wavefunction or magnetic potential is not directly observable in any reference frame. That said, one way in which the magnetic field is similar to the centrifugal force is that it is a direct consequence of special relativity. If you look at a stationary electron, you'll just see an electric field. But you can show that if you're looking at that electron in a moving reference frame, you'll see an extra force. We call that extra force the magnetic force.
- lalaithion 4y agoHow does the Aharonov-Bohm effect avoid fixing the gauge? e.g. if I can find a potential at which the particles act like there’s no cylinder there at all, isn’t that equivalent to fixing the gauge of the potential, by finding a privileged 0?
- antognini 4y agoYou never measure the potential directly. The potential causes a phase shift between the two paths that the particles can take. Different gauges will produce the same phase shift. So if you turn the solenoid off, you could fix the gauge by setting the magnetic potential to zero, but you don't have to. You could still add any function whose curl is zero and have a valid magnetic potential. This would not change the observed phase difference. So there's still no preferred gauge. (Some choices of gauge may make the math easier in the same way that some choices of coordinate systems are more natural to the experiment, but any choice of gauge is valid, just as any choice of coordinate system is.)
- lalaithion 4y agoBut doesn’t > If you turn the solenoid on and off you would think it would make no difference because no matter what you do, the magnetic field the particle encounters is zero. The key, though, is that the magnetic potential is not zero along the particle's path, and the magnetic potential affects the particle's phase in measurable way when the two states recombine. Imply that you can measure the potential somehow? That the particles phase is affected by the potential being non-zero, and therefore the gauge is at least somewhat fixed?
- antognini 4y agoThe issue is that the choice of gauge changes the equation between the value of the potential and all the observable quantities. So you can go ahead and measure the phase difference, the charge of the particle, and the value of the magnetic flux within the solenoid, but in order to turn that into a value of the magnetic potential, you need an equation relating them all. And different choices of gauges give you different equations. So there's no unique way to go from the quantities you've observed to a value of the magnetic potential.
- Agamus 4y ago"...so it's not so spooky that the field has a measurable effect." I'm sorry, but everything about forces is wondrously spooky to me. When we arrive at the time when we find fields to be non-spooky, and the idea of material reality existing exclusively as field excitations to be ontologically comfortable, well - then I will finally get to meet my brothers and sisters! Thank you so much for your excellent and informative comment, btw!