The Tiny Donut That Proved We Still Don't Understand Magnetism

[00:00] and you fire off a stream of electrons. how those electrons behave is by applying an electric or magnetic or gravitational force to them.

[00:14] In the 1950s, You could have electrons travel through a region and yet by flipping a switch,

[00:28] - The magnetic field could be just zero, could actually lead to observable effects. - This experiment split the physics community in two.

[00:44] or whether something that was supposed to be was actually more core to reality.

[00:56] one of the hardest unsolved problems in physics, That is if you have three bodies under the influence of each other's gravity?

[01:13] which occupied literally generations, incredibly ambitious, talented mathematicians, - The fact that this problem is so difficult to solve

[01:28] because if you have just two bodies, In fact, the general case was already solved over 300 years ago by Newton himself.

[01:40] well, that's when everything fell apart. always pointing where the system's shared center of mass.

[01:52] When you try to calculate the forces, In addition to worrying about the magnitude of the forces, So you end up with this chaotic mess of vectors.

[02:08] everyone who tried to solve this problem failed. But what if there was some other way to approach it, and not have to worry about these three-dimensional vectors?

[02:21] In the 1770s, and he came up with a new approach. Say you've got a single mass like a star,

[02:36] to each point in space around the star. and the distance from the star. and if we then turn this into an altitude map,

[02:49] What Lagrange had developed was And what's important to note is that V is a scalar, So the genius in Lagrange's idea is this.

[03:06] where the size of the arrow corresponds We can repeat this process at every point, look, what we've got is the gravitational field of the star.

[03:22] is equal to the negative gradient of V. between one of vectors and one of scalars.

[03:34] adding scalars is a piece of cake. you just add up their individual potentials. to get back to forces if you want.

[03:49] like the Earth orbiting the sun, If you look closely, And so Lagrange realized the forces there are also zero,

[04:04] you could place a tiny third body That is if it isn't disturbed. And while they didn't help solve the three-body problem,

[04:19] In fact, But for that to work, he needed the potential energy and the kinetic energy too.

[04:33] they think potential energy. If you have the potential that's basically the field corresponding to a single body,

[04:47] which is described as V equals minus G M over r, But to get the potential energy,

[05:00] So let's say that's the Earth. is basically just the potential So they're very similar, but they're slightly different.

[05:14] That's of course 1/2 mv squared. In fact, we made a whole video on this over a year ago,

[05:26] we can write down the kinetic minus potential energy to the so-called Euler-Lagrange Equation, For example, predicting the motion of a double pendulum

[05:41] by using this standard forces approach is infamously hard. for the pendulum hanging below it. in this moving reference frame as it's swinging.

[05:54] into the Euler-Lagrange Equation, then you can quickly get to a solution at least numerically. - I remember thinking,

[06:06] You can do it if you're good, But with the Lagrangian approach, plug it into the Euler-Lagrange Equation,

[06:19] and you don't have to be a good physicist. the potential wasn't enough In 1887, mathematician Heinrich Bruns finally proved

[06:34] There are simply too many unknowns So the best we've got are computer simulations, and use that to predict how the system will evolve in time.

[06:51] that the three-body problem is beautiful Even though we now recognize as many folks had hoped to do.

[07:03] modern mathematical physics. - The potential helped simplify a wide array of problems. it even replaced forces as their primary tool.

[07:17] if other forces in nature might have starting with the electric force. you notice that it's remarkably similar to that for gravity,

[07:32] In the 1810s, Simeon Denis Poisson, one of Lagrange's students also noticed the similarity. an electric potential phi in a very similar way.

[07:46] And that is while two masses can only attract, So now, with the potential you don't only get pits,

[07:58] But one force was much trickier to find the potential for, a fundamentally different beast Take a bar magnet,

[08:13] It looks something like this. this looks very similar to the electric scenario but this picture doesn't look at what's going on

[08:26] and you see that these lines actually continue, So magnetic field lines are actually loops, And that fundamentally changes things.

[08:41] to describe the magnetic potential. from an undergraduate student named William Thomson. as much fancy calculus as possible.

[08:54] - Thomson found that the mathematics of his day between a magnetic field and its associated potential. So he came up with an entirely new function, the curl.

[09:07] imagine the arrows of this vector field are like it would start to rotate rapidly counterclockwise. At this spot,

[09:21] so it has lower negative curl. the current pushes on it equally in both directions, This spot has zero curl.

[09:34] could be defined as the curl of some other vector field, Now even though they're both vector fields, than the magnetic field itself,

[09:49] - Thomson was showing there was a kind of that would streamline the calculations. a helpful device,

[10:03] and not a substitute for like the real physics. for his contributions to science With Kelvin's latest edition,

[10:16] relating the potentials to their respective fields. you could now solve problems much easier. instead of forces or fields

[10:32] Potentials even show up But that raises an important question. then do they actually represent anything physical,

[10:47] Well, to most physicists, the answer was a resounding no. for example, and this would shift the overall landscape.

[11:04] remains the exact same. and the force an object would experience at any point In fact, we can add any constant,

[11:19] 10, a hundred, a million, and the field doesn't change. And so the forces an object would experience going around it we could write the gravitational potential

[11:33] and get the system to evolve in the same way. The value of the field and thus the force is fixed,

[11:45] So from this, most physicists concluded that It must just be a trick that makes the math easier. - [Derek] In 1942, 23-year-old David Bohm was hard at work

[12:03] when one day he received an unexpected visit. who was David Bohm's PhD advisor, - [Derek] This was a life-changing opportunity.

[12:16] with some of the top minds in physics. The project's military director General Leslie Groves And when he ran a background check on Bohm,

[12:29] the American branch of the Communist Party he quit pretty quickly 'cause he got bored. - [Derek] Even so, Groves deemed Bohm a security risk

[12:44] But things got even worse. the topic was then classified. so he couldn't even work on or even write up

[12:57] So Oppenheimer had to certify that Bohm had done good work. that was sufficient for Bohm to actually get a PhD. Bohm became an assistant professor at Princeton University.

[13:11] followed him wherever he went. the House Un-American Activities Committee for questioning. Princeton let his professorship lapse.

[13:24] the university refused to reinstate him. It seemed that Bohm was destined for obscurity. leave the country and start fresh somewhere else.

[13:38] and he didn't want Bohm to suffer the same fate. His journeys brought him to Brazil and then Israel. he still found himself an outcast.

[13:54] were put off by his more unorthodox ideas, and his new theory of human consciousness. and that was Yakir Aharonov.

[14:11] and also had a very nice personality. So it was beautiful to interact with him.

[14:23] this time moving to the University of Bristol in England, And it was there in Bristol in the 1950s that Aharonov and Bohm stumbled upon something huge.

[14:37] deeply about the interpretation of quantum mechanics. It wasn't to solve any problem, it was just curiosity. at the smallest scale, particles behave like waves.

[14:53] And this behavior is governed by the Schrodinger equation. the wave function psi. you get the probability density of finding a particle

[15:06] The left side of this equation tells you how the wave function changes over time and space. that this change depends on H,

[15:18] It's basically just the total energy of the system. the solution to the Schrodinger equation Where this is just a constant.

[15:31] It looks complicated, So let's plot it in two dimensions The different colors here represent the different phases.

[15:45] And you can see how the phase evolves over time and space. Now, if you look closely at the original phase term, the magnetic and electric potentials.

[16:00] that points in the same direction You can see that the wave stretches out. than it did before.

[16:13] then now the wave gets more compressed And a similar thing would happen Now, this by itself,

[16:26] Just as you would always use the potentials But really what's responsible for these, But you spoke to Aharonov. - Yeah.

[16:41] If you look at the Schrodinger equation, with the electric field E. - Okay. - Because remember,

[16:54] for a specific electric field but that information is lost There's another way

[17:07] - So if you have an expression like 5x squared plus 5, the integral of 10x dx, right? Because the integral is 5x squared plus.

[17:20] So it includes 5, but it also includes any other number. But importantly, C is not 5, when you grow from a potential to an electric field.

[17:36] So he thought, what if every quantum system - So it's the potential that shows up He had to find a way to prove that what we're observing is

[17:54] - How do you do that? See, Aharonov had to design an experiment where there's no electric or magnetic field,

[18:08] if the phase of the particle's wave function that had to be the direct result of the potential itself - But that's where you run into a problem

[18:24] the phase of a particle's wave function. that can yield a measurable result? and together they came up

[18:38] It starts with a beam of electrons, which is split into two. is a tightly coiled wire known as a solenoid. When you run a current through one,

[18:52] and a very weak field outside the coil. For simplicity, with an ideal, infinitely long solenoid,

[19:06] is exactly zero. the electron beams are redirected back towards each other And here at this point, they intersect.

[19:19] the waves from the intersecting beams overlap bright fringes with gaps in between them. When the solenoid is off,

[19:33] and there is no magnetic potential. in the same way across both beams, And so you get an interference pattern that looks like this.

[19:49] well, there is still no magnetic field but there is a magnetic potential. the magnetic field is the curl of the magnetic potential.

[20:04] even when the potential itself is not. Now take a closer look at the vector potential.

[20:16] the potential points in the opposite direction as the beam. But below the solenoid, So the phase changes slower.

[20:29] and not the field, So as a result, the interference pattern should shift - The magnetic field could be just zero,

[20:45] and yet the presence of some vector potential That wasn't supposed to happen, right? individual people can challenge entire paradigms.

[21:00] many of the smartest minds in history were nothing more than mathematical tools. and defied that interpretation.

[21:13] they took on the entire scientific establishment. what motivated me to partner with Planet Wild. when we look at the huge problems facing the Earth today.

[21:29] and the extinction of entire species. and hope someone else will do something about it. and they make it easy for anyone to join the cause,

[21:46] Another reason is that every month to clean up oceans, rewild forests, You can think of Planet Wild as crowdfunding for nature.

[22:03] through outstanding monthly videos, Take this for instance. It's a scalable technology that stops plastic at the source,

[22:17] preventing 10 tons from reaching the ocean every month. and that money didn't come from governments or corporations, it came from ordinary people like you and me.

[22:31] and cancel any time. The first 150 people to sign up using my code VERITASIUM1 Just scan this QR code or click the link in the description.

[22:47] then go check out their YouTube channel. in the description. And now back to the mystery of the potential.

[23:00] and the reception was mixed. many people thought that it can't be true. that tried to write articles against it.

[23:16] found it impossible to accept in the absence of any force. Richard Feynman wrote,

[23:28] in the wave equation of quantum mechanics no one thought of discussing this experiment until 1959, and made the whole question crystal clear."

[23:43] He later wondered why he had never noticed the effect. "The first reaction to this work is that it's wrong. Ultimately, there was only one way to settle the debate.

[24:00] The first to try was a colleague of Aharonov and Bohm's Chambers experiment largely followed

[24:12] with one notable exception. which is physically impossible. So instead, Chambers used a tiny needle-like piece of iron,

[24:24] about a millionth of a meter thick and 500 times as long. it produced a magnetic field as well as a magnetic potential

[24:37] To get a baseline interference pattern, around an empty region of space. When he fired the beams again,

[24:50] It seemed that Aharonov and Bohm were right. - People objected to it because there is always some magnetic field that will go out.

[25:08] not the potential. who did these cool experiments. - And so it went for several decades.

[25:21] Experimentalists repeatedly tested the Aharonov-Bohm effect, that left the result open to debate. a team of Japanese researchers led by Akira Tonomura

[25:35] See, they used a tiny donut-shaped magnet all the magnetic field is contained within the loop. And as an added layer of protection,

[25:51] in a layer of superconducting niobium, Now, previous experiments relied on but Tonomura's team took on a different approach.

[26:05] but because of its unique shape, from the one in the center. and away from us on the inside.

[26:18] They started by firing off an electron beam, as two separate beams. and functioned as the control,

[26:31] whereas the other part washed over the entire torus. so that part of it passes around the torus a biprism deflects the electron beams toward each other,

[26:46] and this is where they create an interference pattern. what this interference pattern should look like. so we can fill that in.

[26:58] the Aharonov-Bohm effect is real or not. that looks something like this, But if it is real,

[27:13] would've experienced a different potential, So that should look something like this. You see these are the interference fringes

[27:29] And then if you follow what is a peak outside the torus - outside again. - It's real

[27:42] really the final proof, experimentally. The effect is real, sure, but how should we interpret it?

[27:56] about the nature of the universe? The first camp claims that they can influence physical reality.

[28:10] As they wrote in the abstract of their paper, there exist effects of potentials on charged particles, even in the region where all fields vanish."

[28:24] since the potentials show up in the Schrodinger equation more fundamental to physics than fields are. "A is as real as B,

[28:40] - I mean, I kind of like that interpretation, And that's the fact that It can be plus infinity.

[28:53] So wouldn't that change, you know, So much so that I actually ended up but it turns out it can't.

[29:06] it's the line integral. B vanishes, it's only A, but it's not A alone.

[29:18] if I pull up, you know. Now we can actually run this. So if you look at how the potential shows up,

[29:33] but it's the phase shift. Then the phase shift is line integral of A over the path Now you can imagine, okay, let's add a constant to this.

[29:48] And if our setup is roughly, you know, we start here, and the other one goes like this, then the potential here will point

[30:01] But here, it will point in that direction. Let's say instead of A, we do A plus C, some constant. we'll be adding that C and we'll be dotting it with dx.

[30:16] when we go this way, which is subtracted. So the potential, yeah, it does show up, all the arbitrariness of the potential,

[30:30] - It's a geometrical quantity solving A for which all that residual ambiguity - The potentials being physical might sound strange,

[30:44] but the second interpretation is even stranger. really are just mathematical objects But in Tonomura's experiment,

[30:57] For this interpretation to be true, That is a field can influence things outside the region of space where the field itself exists.

[31:11] - I think the idea of saying that undoes the reason why we have field theory, right? which has served us so well for more than 100 years,

[31:24] stubborn notion that local causes yield only local effects. from camp one to camp two. we called it the effects of potentials.

[31:38] and use the Schrodinger representation, But it's misleading because is really not physical.

[31:52] a non-local effects of the The electron can feel the effect of a field

[32:04] - While non-locality remains a controversial idea, a sizable portion of physicists do side with Aharonov. - I maybe have a third interpretation.

[32:20] And if it's bad, please tell me honestly. - So we did this other video about particles essentially exploring all possible paths all at once.

[32:32] or fields are acting non-locally. where the fields are still local but rather it's the particles

[32:46] You could potentially even have where there are fields, explores all possible paths,

[32:59] where the wave function is inside the field. That's for a strong ringing endorsement. - If we could think about these things as

[33:12] that's being affected, - Yeah. I think that's a perfectly reasonable way to to frame it. I'm pretty sure this isn't the complete answer,

[33:29] if someone else takes this idea, you know, but here is how it does work and now we're closer. Well, the best possible outcome is you're just right.

[33:43] that nudges the community more broadly That's right. is there also a gravitational version?

[33:56] In 2022, researchers at Stanford tested this. works something like this. into a tube-shaped vacuum chamber,

[34:08] Now atoms like electrons are So they split each rubidium atoms wave function and they launched them to different heights.

[34:22] whereas the other didn't. this created an interference pattern. and accounted for all other effects,

[34:34] as predicted by Aharonov and Bohm. the gravitational Aharonov and Bohm effect is real. this is a huge finding.

[34:46] the electromagnetic and gravitational potentials even when all the fields are exactly zero. So does that mean that most physics textbooks are wrong

[35:00] They're beautiful. And we should be open to surprise. roughly between say Lagrange and Aharonov-Bohm,

[35:14] in beautiful and surprising and very powerful ways. the reason you decided to do the AB effect was

[35:27] something that was just a mathematical tool - That is correct. Sometimes it's good not to know too much.

[35:42] (gentle music)