Krishna explains the Aharonov-Bohm effect, in which electrons split around a solenoid show a shifted interference pattern even though the magnetic field outside the solenoid is zero. The result suggests the electromagnetic vector potential, long treated as a mathematical bookkeeping device, may have real physical effects, since the whole path geometry matters rather than just the local field strength along each path.
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The effect was described by Yakir Aharonov and David Bohm in 1959, and because Bohm died in 1992, Aharonov alone would be eligible for a Nobel Prize if it were awarded now.
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Michael Berry is named as a possible co-recipient for his 1984 work on geometric phase, where a quantum state picks up an extra phase when its parameters trace a closed loop, a related but distinct topological effect.
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18:39Uh, the physics Nobel Prize. And so we have, I believe, two predictions. >> Yes, we've got two predictions. The first one I think is really a no-brainer. And I cannot believe that the Nobel committee still hasn't given him a Nobel Prize. This is also a recycle from last year because I am fully convinced that this guy deserves it. This is Yakir Aranov and the Arnov bomb effect which he and David Bomb described in 1959. David Bomb is the very famous physicist behind the pilot wave theory or the pilot wave interpretation of quantum mechanics. This was the first non-Copenhagen interpretation of quantum mechanics.
19:20Neils Boore ran him out of um Copenhagen when bomb went over to like try to pitch um and then he was run out very sadly of the country because this was the McCarthy era and he was ideologically a communist. So he had to he had to go to Brazil for the rest of his career. um which you know given his stature he could have done a lot more in some of the bigger universities but um he he went to Brazil he had a nice time there the Arnoff bomb effect people have said that this is the biggest development in quantum mechanics since
20:02Drock's um prediction of antimatter okay >> pretty good >> that's pretty good the Arnoff bomb effect is so fundamental. It doesn't make sense why it hasn't gotten a Nobel Prize. Seriously. So, here's the idea. The Arnov bomb effect. And, you know, hopefully I really hope they do give him the Nobel Prize because then I get to do a deep dive on it for 45 minutes. But, I'm going to give you a real quick um >> justification of the whole thing. So, remember the double slit experiment? The idea was that you know you have two paths that the photon can go through or the electron can go through and then it interferes in the back and you get an interference pattern and this is key to
20:43quantum mechanics. So now imagine actually if we can bring that >> yes um photo 11. So now imagine we've got a beam splitter of electrons. This time the electron follows one path to the left, one path to the right, and it meets back up recombined at a detector in the back, right? And in the middle in between these two paths is a solenoid that has a current going through it. And because it has a current going through it, inside the solenoid, there's going to be a magnetic field. But if you remember from your undergraduate physics, outside the solenoid, the
21:23magnetic field is zero because you can run ampier's law outside the solenoid. There's no current that's involved because there's net current going in, net current coming out in in those directions. And so there's no actual current, which means there's no magnetic field outside the solenoid. The magnetic field is localized inside of the solenoid. Okay? Now for all intents and purposes in physics the field is the real thing. >> But you can construct fields out of potentials. For example, the gravitational field is the real thing. But in order to sort of do mathematics with the gravitational field, we can invent something like a gravitational potential and say that you know the
22:04potential here is something the potential here is a little bit more. And so the amount of energy it takes for me to go against the field is just the difference in the potential. And it's always the difference in the potential. >> The the I think the example you talked to me about one time is like imagine a hill >> and you have someone you're at the top of the hill or the bottom of the hill and your gravitational potential at the top of the hill is greater and then it could do the so >> and then and then you can figure out how fast a ball would roll down the hill based on the difference. Now, the key thing is if I had the hill down at sea level, but then I took the same like cardboard landscape, let's say, of the balls rolling and I've got a cardboard landscape and I took it up to Mount Whitney, as long as the gravitational field is exactly the same, >> it doesn't matter if I'm at Mount
22:46Whitney or at sea level, >> the dynamics on my cardboard mesh thing is going to be exactly the same. Yeah. >> Right. Because the only thing that matters is the difference in the potential. >> Okay, that's fine. Um for magnetic fields we can also construct a potential that describes a magnetic field but instead of a scalar potential which in this case is just height so there's no vector right it's just a number for a magnetic field it requires a scalar potential I mean sorry for the magnetic field it requires a vector potential not a scalar potential >> now that introduces some interesting things because if you've got a vector potential then all of a sudden direction matters in terms of like which way you're traversing this potential But the
23:29potential is just a trick, right? It's supposed to be a mathematical trick. >> The field is the real thing. And in the Arnoff bomb effect, my electron is moving one way and the other way. The field is in the middle. The solenoid is in the middle. And the field is localized inside the solenoid. So it shouldn't affect the two paths. That ends up not being true. If I turn on the magnetic field on and off, that changes my interference pattern. >> Right. >> So this is very strange. >> Yeah. Right. Right. Because the the the the institutional understanding was there should not be an effect on your beam. >> Yeah. >> Outside of the solenoid. >> Outside of the solenoid because the field is the real thing. Here we're saying perhaps the potential could be a real thing. It's not just a bookkeeping
24:10thing. Right. There are multiple interpretations of how this thing works. But the fact that it works and that I can experimentally do it introduces a lot of nuance into how we understand quantum mechanics, right? And that's why it's one of the biggest developments since Drock's equation and his prediction of antimatter. So this was in 1959. It's quite late in terms of fundamental quantum theory. And here yet you have something that is so fundamental and so in your face and something that we don't really quite understand from a philosophical and metaphysical level. Okay, we can we can we can do the calculations, right? It turns out that you know what you have to do is the quantum interference depends
24:51on the complete path geometry not just on these two paths but like you you do a sum over paths on every single one and perhaps maybe there's some that go through it's still like you know is that is that really what's happening right and wavy >> yeah um like but the the the local force along the path is not the only thing that matters that's the key right >> there's there's like >> it's it's it's a global thing it's a global phenomenon >> I I and One of the things that always trip not trips me up but um is so interesting when we talk about these quantum mechanical stories is this idea that >> you have it's not just everything
25:31matters >> even the things that are not what you end up seeing experimentally. >> Exactly. >> Um and that uh is a brain teaser. >> Yeah. in terms of how your frame your mental framework about what it is all this stuff around us and reality and the physicality of it um the physicality is not that we can engage in at the human scale is not the only thing >> not the only thing yeah it's an it's I mean it's a trip every time you dive too deep into it you know um so David Bomb died in 1992 and so Yakir Arnov would be the only recipient he's actually a professor of theoretical physics at Chapman university in Southern California. Ah, look at that. Right. So
26:13th this would be a long time coming I think. Um he he published that paper in the 19 late 1950s when he was a doctoral student. So this this would be one of the record holders for like the the amount of time it took >> right from like 1959 till now. Um that would be a big one. Um, Michael Barry. We were just on the Instagram live before taping this and someone >> said Barry. This is who they're referring to. >> Michael Barry is a natural possible co-reient. In 1984, he showed that a quantum state can acquire an additional phase when the parameters slowly trace some type of closed loop. It's a topological argument. It's related to
26:55the Arnoff bomb effect, but not exactly the same. Um again topological physics is something that is incredibly deep, complex and yet simple. Um so you know if if the Nobel Prize committee decides to award topological physics another Nobel Prize um I'll have a field day explaining it. That'll be that'll be really fun. >> Does this relate to when we had these conversations about gradient descent >> and and related and the >> related concepts? I can't remember what episode it was. Um, we had one where we went really deep on it. Um, but it's it's escaping me right now. However, if there's a win, we will cover it.
27:36>> Yeah, we will cover it for sure. Uh,