Do we know how magnets work yet?

0:00 Imagine you are in empty space and you fire off a stream of electrons.

0:05 Well then, according to most physics textbooks,

0:07 the only way to change how those electrons behave is

0:10 by applying an electric or magnetic or gravitational force to them.

0:14 But most physics textbooks are wrong.

0:17 In the 1950s, two physicists came up with a clever experiment.

0:21 You could have electrons travel through a region

0:23 with no electric or magnetic fields whatsoever,

0:26 and yet by flipping a switch, you could change their behavior.

0:31 The magnetic field could be just zero,

0:33 and yet the presence of some quantity could actually lead to observable effects.

0:39 That wasn't supposed to happen, right?

0:41 This experiment split the physics community in two.

0:44 It made them question whether fields

0:47 are fundamental or whether something that was

0:49 supposed to be just an abstract mathematical

0:52 tool was actually more core to reality.

0:56 This tool was first introduced in an attempt

0:58 to solve one of the hardest unsolved problems in physics,

1:02 the three-body problem.

1:05 That is if you have three bodies

1:07 and you know their initial positions and velocities,

1:09 how will they move under the influence of each other's gravity?

1:13 It's a juicy, juicy problem, which occupied literally generations,

1:17 hundreds and hundreds of years of incredibly ambitious,

1:20 talented mathematicians, physicists, and astronomers, and beyond.

1:25 The fact that this problem is so difficult to solve should

1:28 at least be a little surprising because if you have just two bodies,

1:32 then the solution is easy to find.

1:34 In fact, the general case was already

1:36 solved over 300 years ago by Newton himself.

1:40 But when Newton added a third body, well, that's when everything fell apart.

1:46 In the two body case, the forces behaved predictably,

1:48 always pointing where the system's shared center of mass.

1:52 But with three bodies, this is no longer the case.

1:55 When you try to calculate the forces, they end up being extremely dynamic.

1:59 In addition to worrying about the magnitude of the forces,

2:01 you also have to worry about their direction.

2:04 So you end up with this chaotic mess of vectors.

2:08 For the next hundred years, everyone who tried to solve this problem failed.

2:12 But what if there was some other way to approach it,

2:16 a way to simplify the math and not

2:18 have to worry about these three-dimensional vectors?

2:21 Well, that's where Joseph-Louis Lagrange comes in.

2:24 In the 1770s, he was also trying to solve the three-body problem,

2:28 and he came up with a new approach.

2:30 It works something like this.

2:33 Say you've got a single mass like a star,

2:36 Lagrange imagined assigning a value to each point in space around the star.

2:40 The value is determined by the star's mass and the distance from the star.

2:44 You can think of each value as a height,

2:47 and if we then turn this into an altitude map,

2:49 you can see how the star creates this sort of well.

2:52 What Lagrange had developed was the gravitational potential V.

2:56 And what's important to note is that V is a scalar,

2:59 it has a magnitude but no direction.

3:02 So the genius in Lagrange's idea is this.

3:06 At any given point, we can draw an arrow pointing directly downhill where

3:10 the size of the arrow corresponds to the steepness of the hill at that point.

3:14 We can repeat this process at every point,

3:16 and if we then shift our perspective to two dimensions,

3:18 look, what we've got is the gravitational field of the star.

3:22 Mathematically, we say that the gravitational field G

3:25 is equal to the negative gradient of V.

3:29 So Lagrange had found a way to switch the problem

3:31 back and forth between one of vectors and one of scalars.

3:34 And while adding up vectors is hard, adding scalars is a piece of cake.

3:39 To find the combined potential landscape of any number of bodies,

3:42 you just add up their individual potentials.

3:45 And then you can always use that to get back to forces if you want.

3:49 For a simple two body system like the Earth orbiting the sun,

3:53 that combined potential look something like this.

3:56 If you look closely,

3:57 you see that there are five points where the gradient is zero.

4:00 And so Lagrange realized the forces there are also zero,

4:04 which means that at each of these points, you could place a tiny third body

4:08 and it would maintain a perfectly stable orbit.

4:11 That is if it isn't disturbed.

4:13 These points are now known as the Lagrange Points.

4:16 And while they didn't help solve the three-body problem,

4:19 Lagrange was developing more sophisticated tools.

4:22 In fact, he developed an entirely new way of doing mechanics.

4:26 But for that to work, he didn't just need the potential,

4:29 he needed the potential energy and the kinetic energy too.

4:33 I think when people hear potential, they think potential energy.

4:38 And while they're very similar, there is a subtle difference.

4:41 If you have the potential that's basically

4:44 the field corresponding to a single body,

4:47 then it will have some potential field around it,

4:50 which is described as V equals minus G M over r,

4:56 where this is the mass of the sun.

4:58 But to get the potential energy, we need to add in a second body.

5:01 So let's say that's the Earth.

5:04 The potential energy, let's call it U,

5:07 is basically just the potential times the mass of the second body.

5:11 So they're very similar, but they're slightly different.

5:14 And the kinetic energy of the Earth is simple.

5:16 That's of course 1/2 mv squared.

5:20 So now we have everything we need to try this new method.

5:23 In fact, we made a whole video on this over a year ago, but for now,

5:26 all we need to know is that we can write down

5:28 the kinetic minus potential energy to find what's known as the Lagrangian.

5:32 Then you sub that in to the so-called Euler-Lagrange Equation,

5:35 and out comes your solution.

5:38 For example, predicting the motion of a double pendulum

5:41 by using this standard forces approach is infamously hard.

5:45 Because as one pendulum is swinging,

5:47 it provides the attachment point for the pendulum hanging below it.

5:50 And so that pendulum is in this moving reference frame as it's swinging.

5:54 [Casper] But if you pluck the kinetic

5:56 and potential energy into the Euler-Lagrange Equation,

5:58 then you can quickly get to a solution at least numerically.

6:02 That's actually how we made this simulation.

6:05 I remember thinking, man, force is like hard to get the right answer.

6:08 You can do it if you're good, and people who are good at mechanics can do it.

6:12 But with the Lagrangian approach, you could just write down the energy,

6:15 which is a scalar not a vector, plug it into the Euler-Lagrange Equation,

6:19 and you get the right equation to motion

6:21 and you don't have to be a good physicist.

6:24 But for all its usefulness,

6:25 the potential wasn't enough to help Lagrange solve the three-body problem.

6:29 In 1887, mathematician Heinrich Bruns finally

6:33 proved that the three-body problem is unsolvable.

6:37 There are simply too many unknowns and no

6:40 way to simplify the problem to reduce them.

6:42 So the best we've got are computer simulations,

6:44 which compute the potentials from moment to moment,

6:46 and use that to predict how the system will evolve in time.

6:51 And so that's where we come to realize

6:53 that the three-body problem is beautiful for what it's taught us.

6:57 Even though we now recognize that we can't actually solve

7:00 for this exact problem as many folks had hoped to do.

7:03 And in doing that, they merely gave

7:04 us the machinery of modern mathematical physics.

7:07 So I'm pretty happy they tried.

7:09 The potential helped simplify a wide array of problems.

7:13 For many physicists, it even replaced forces as their primary tool.

7:17 It became so useful that people started to wonder

7:19 if other forces in nature might have a corresponding potential,

7:23 starting with the electric force.

7:26 If you look at the formula for the electric force,

7:28 you notice that it's remarkably similar to that for gravity,

7:32 just with masses and charges swapped.

7:35 In the 1810s, Simeon Denis Poisson,

7:37 one of Lagrange's students also noticed the similarity.

7:41 And he realized that you can define

7:43 an electric potential phi in a very similar way.

7:46 But there is one important difference.

7:49 And that is while two masses can only attract, two charges can attract or repel.

7:55 So now, with the potential you don't only get pits, you also get hills.

8:01 But one force was much trickier to find

8:03 the potential for, and that was the magnetic force.

8:06 And that's because magnetism is a fundamentally

8:08 different beast from the gravitational and electric force.

8:12 Take a bar magnet, we can draw the magnetic field it produces.

8:16 It looks something like this.

8:17 Now at first glance, this looks very similar to the electric scenario

8:21 where we have a positive and negative charge,

8:24 but this picture doesn't look at what's going on inside the magnet.

8:27 So if we reveal what's inside and you see that these lines actually continue,

8:31 but now they point from south to north.

8:34 So magnetic field lines are actually loops,

8:36 they don't have an origin or endpoint.

8:39 And that fundamentally changes things.

8:41 So physicists needed a new way to describe the magnetic potential.

8:45 [Derek] The breakthrough came in the 1840s

8:47 from an undergraduate student named William Thomson.

8:50 His day job as an undergraduate was to learn as much fancy calculus as possible.

8:54 And then when he learned that he invented more.

8:56 Thomson found that the mathematics of his day was unable

8:59 to describe the relationship between

9:00 a magnetic field and its associated potential.

9:03 So he came up with an entirely new function, the curl.

9:07 To see how this works,

9:09 imagine the arrows of this vector field are like currents in a liquid.

9:12 If we were to place a paddle wheel right here,

9:14 it would start to rotate rapidly counterclockwise.

9:17 As Thomson defined it, this spot has high positive curl.

9:20 At this spot, it would rotate clockwise but not as rapidly,

9:24 so it has lower negative curl.

9:26 And here, the current pushes on it equally in both directions,

9:30 so it wouldn't rotate at all.

9:32 This spot has zero curl.

9:34 But Thomson realized that the magnetic vector field B could

9:37 be defined as the curl of some other vector field,

9:39 the magnetic vector potential A.

9:42 Now even though they're both vector fields, it turns out that A is often much

9:46 easier to work with than the magnetic field itself,

9:49 much like the other potentials V and phi,- Thomson was showing there was

9:53 a kind of underlying mathematical structure one

9:56 could use that would streamline the calculations.

9:59 But even Thomson thought this was a kind of device,

10:02 a helpful device, and not a substitute for like the real physics.

10:08 [Derek] Decades later,

10:08 Thomson was elevated to the House of Lords for his contributions

10:11 to science where he received a new title, Lord Kelvin.

10:15 With Kelvin's latest edition, there were now three fundamental equations

10:18 relating the potentials to their respective fields.

10:22 Thanks to each of these, you could now solve problems much easier.

10:27 And so ever since, professional physicists often use potentials instead

10:31 of forces or fields to solve the problems they're working on.

10:34 Potentials even show up in some of our best physical theories of the universe.

10:39 But that raises an important question.

10:42 If potentials pop up everywhere,

10:44 then do they actually represent anything physical,

10:47 that is, can they have a direct influence on reality?

10:50 Well, to most physicists, the answer was a resounding no.

10:54 Take the gravitational potential of a single star for example, well,

10:58 we could just add 10 to each value of the potential,

11:01 and this would shift the overall landscape.

11:04 But the change in landscape from one point to the next remains the exact same.

11:09 So the field is the same as the one we had before

11:12 and the force an object would experience at any point would remain unchanged.

11:17 In fact, we can add any constant, 10,

11:19 a hundred, a million, and the field doesn't change.

11:23 And so the forces an object would experience going around it also don't change.

11:28 There are an infinite number of ways we could write the gravitational potential

11:33 for any gravitational field and get the system to evolve in the same way.

11:38 And the same is true for electricity and magnetism.

11:41 The value of the field and thus the force is fixed,

11:45 but the value of the potential is arbitrary.

11:47 So from this, most physicists concluded

11:49 that potentials can't possibly have any physical significance.

11:53 It must just be a trick that makes the math easier.

11:56 But most physicists might be wrong.

11:59 [Derek] In 1942, 23-year-old David Bohm was hard at work on his thesis

12:03 in particle physics when one day he received an unexpected visit.

12:08 [David] Robert Oppenheimer, who was David Bohm's PhD advisor,

12:11 wanted to bring him squarely onto the new Manhattan Project efforts.

12:15 [Derek] This was a life-changing opportunity.

12:16 Bohm would be working side by side with some of the top minds in physics.

12:20 But there was a problem.

12:22 The project's military director General Leslie

12:24 Groves had to approve Oppenheimer's recruits.

12:27 And when he ran a background check on Bohm, he didn't like what he saw.

12:31 He briefly joined the American branch

12:33 of the Communist Party when he was in California.

12:35 By his own recollections, he quit pretty quickly 'cause he got bored.

12:38 He said, these people just sit around talking all day and don't do anything.

12:41 [Derek] Even so, Groves deemed Bohm a security risk

12:44 and banned him from working on the Manhattan Project.

12:46 But things got even worse.

12:48 Just as he was about to finish his dissertation in Berkeley,

12:51 the topic was then classified.

12:53 He did not have clearance,

12:55 so he couldn't even work on or even write up his own dissertation.

12:58 So Oppenheimer had to certify that Bohm had done good work.

13:02 And in 1943 in wartime, that was sufficient for Bohm to actually get a PhD.

13:07 [Derek] After the war,

13:08 Bohm became an assistant professor at Princeton University.

13:11 But fear surrounding his communist sympathies followed him wherever he went.

13:15 In 1949, he was brought before

13:17 the House Un-American Activities Committee for questioning.

13:20 While Bohm was under investigation, Princeton let his professorship lapse.

13:24 And even after he was acquitted, the university refused to reinstate him.

13:28 It seemed that Bohm was destined for obscurity.

13:32 And so Oppenheimer gave him a firm recommendation,

13:35 leave the country and start fresh somewhere else.

13:38 Oppenheimer was no stranger to political persecution,

13:41 and he didn't want Bohm to suffer the same fate.

13:44 So Bohm took the advice.

13:46 His journeys brought him to Brazil and then Israel.

13:49 And though he was free from the political pressures he had felt in America,

13:52 he still found himself an outcast.

13:54 Many of Bohm's academic peers were put off by his more unorthodox ideas,

13:59 including his radical interpretation of quantum mechanics

14:01 and his new theory of human consciousness.

14:05 But there was one student who was enthralled by Bohm's approach,

14:08 and that was Yakir Aharonov.

14:11 He was, first of all, extremely, extremely bright,

14:14 and also had a very nice personality.

14:19 So it was beautiful to interact with him.

14:23 When Bohm relocated once more,

14:25 this time moving to the University of Bristol in England,

14:28 Aharonov chose to come with him.

14:30 And it was there in Bristol in the 1950s

14:32 that Aharonov and Bohm stumbled upon something huge.

14:37 For a long time, I was thinking more

14:39 and more deeply about the interpretation of quantum mechanics.

14:44 It wasn't to solve any problem, it was just curiosity.

14:48 According to quantum mechanics,

14:50 at the smallest scale, particles behave like waves.

14:53 And this behavior is governed by the Schrodinger equation.

14:57 The solution to this equation is called the wave function psi.

15:01 If you take its modulus squared,

15:02 you get the probability density of finding a particle

15:06 at a given point, at a given time.

15:08 The left side of this equation tells you

15:11 how the wave function changes over time and space.

15:14 And the right side tells you that this change depends on H,

15:18 what is known as the Hamiltonian.

15:19 It's basically just the total energy of the system.

15:22 In the case where we have both an electric and magnetic potential,

15:25 the solution to the Schrodinger equation looks something like this.

15:29 Where this is just a constant.

15:31 And this term describes the complex phase.

15:34 It looks complicated, but it's actually quite easy to get a feel for it.

15:37 So let's plot it in two dimensions for an electron moving to the right.

15:42 The different colors here represent the different phases.

15:45 And you can see how the phase evolves over time and space.

15:49 Thank you to Richard Behiel for inspiring this approach.

15:52 Now, if you look closely at the original phase term,

15:55 you see A and phi, the magnetic and electric potentials.

16:00 So watch what happens if we add a magnetic vector potential

16:03 that points in the same direction as the electron is traveling.

16:06 You can see that the wave stretches out.

16:09 So now the phase changes more slowly over space than it did before.

16:13 And if the potential points the other way,

16:15 then now the wave gets more compressed and its phase changes faster over space.

16:20 And a similar thing would happen if you change the electric potential phi.

16:25 Now, this by itself, I think wasn't shocking to most physicists.

16:28 Just as you would always use the potentials to make the math easier,

16:31 that's also why you use it in the Schrodinger equation.

16:33 But really what's responsible for these, you know,

16:36 even phase changes were still the fields.

16:39 But you spoke to Aharonov.

16:41 Yeah.

16:41 And that wasn't his take.

16:43 No.

16:44 If you look at the Schrodinger equation,

16:46 you can't just replace the potential phi with the electric field E.

16:50 Why not?

16:51 'Cause you're losing information.

16:52 Okay.

16:53 Because remember, you can define any number of potentials

16:57 for a specific electric field because you can pick an arbitrary height,

17:01 but that information is lost when you go and swap it out for the electric field.

17:06 There's another way to think about it.

17:07 Okay, okay.

17:08 It's getting real.

17:09 So if you have an expression like 5x squared plus 5,

17:12 you think you could just write this as the integral of 10x dx, right?

17:16 Because the integral is 5x squared plus.

17:20 C.

17:21 C.

17:22 Right.

17:22 C is a constant.

17:23 So it includes 5, but it also includes any other number.

17:26 But importantly, C is not 5, or at least not in every case.

17:32 So you lose this specificity when you

17:34 grow from a potential to an electric field.

17:36 And Aharonov wasn't comfortable with that.

17:38 So he thought, what if every quantum system was

17:42 actually influenced by the potential and not by the field.

17:45 Right.

17:46 So it's the potential that shows up in the Schrodinger equation.

17:48 So it is what influences wave functions.

17:50 He had to find a way to prove that what we're observing

17:54 is always because of a potential and not because of the field.

17:58 How do you do that?

17:59 Complicated.

18:00 See, Aharonov had to design an experiment that would send

18:03 a particle through a region where there's no electric or magnetic field,

18:08 but there is a potential.

18:10 In such a setup, if the phase

18:12 of the particle's wave function started changing slower or faster,

18:16 that had to be the direct result

18:18 of the potential itself because there are no fields.

18:22 But that's where you run into a problem because there's no

18:25 way to directly measure the phase of a particle's wave function.

18:29 So how do you devise an experiment that can yield a measurable result?

18:33 Well, Aharonov enlisted the help of his mentor Bohm,

18:36 and together they came up with the following theoretical experiment.

18:41 It starts with a beam of electrons, which is split into two.

18:44 In the middle of these two beams is a tightly coiled wire known as a solenoid.

18:48 Now, solenoids have an interesting property.

18:51 When you run a current through one,

18:52 it produces a strong magnetic field inside the coil

18:55 and a very weak field outside the coil.

18:57 The longer the solenoid, the weaker the field in the surrounding space.

19:00 For simplicity, Aharonov and Bohm imagined a setup with an ideal,

19:04 infinitely long solenoid,

19:06 one where the magnetic field outside the coil is exactly zero.

19:10 After traveling on opposite sides of the solenoid,

19:12 the electron beams are redirected back towards each other by the researchers.

19:16 And here at this point, they intersect.

19:19 Now since electrons behave as waves, the waves from the intersecting beams

19:23 overlap and produce an interference pattern,

19:25 bright fringes with gaps in between them.

19:28 The exact pattern depends on the phase of each of these waves.

19:31 When the solenoid is off,

19:33 there is no magnetic field in the region the electrons are traveling through,

19:36 and there is no magnetic potential.

19:38 The phase of the electrons changes in the same way across both beams,

19:42 regardless of whether they pass above or below the solenoid.

19:45 And so you get an interference pattern that looks like this.

19:49 But when the solenoid is turned on, well,

19:51 there is still no magnetic field because it's confined entirely within the coil,

19:56 but there is a magnetic potential.

19:59 That may sound strange, but remember,

20:01 the magnetic field is the curl of the magnetic potential.

20:04 The curl of the potential can be zero in some region,

20:07 even when the potential itself is not.

20:10 And that's exactly what's happening here.

20:13 Now take a closer look at the vector potential.

20:16 In the space the upper beam passes through,

20:18 the potential points in the opposite direction as the beam.

20:21 So here the phase changes faster.

20:24 But below the solenoid, it points in the same direction as the beam.

20:27 So the phase changes slower.

20:29 If the phase truly depends on the potential alone and not the field,

20:33 then the phases of the two beams should evolve differently.

20:36 So as a result, the interference pattern should shift

20:39 when the solenoid is on versus when it's off.

20:43 The magnetic field could be just zero, and yet the presence of some vector

20:49 potential could actually lead to observable effects.

20:52 That wasn't supposed to happen, right?

20:54 What I love about this story is that it

20:56 reminds me that individual people can challenge entire paradigms.

21:00 For nearly 200 years, many of the smartest minds in history all

21:04 believed that potentials were nothing more than mathematical tools.

21:08 But then two outsider physicists came along and defied that interpretation.

21:13 Confident in their approach, they took on the entire scientific establishment.

21:18 That same belief in the power of the individual

21:21 is what motivated me to partner with Planet Wild.

21:24 Many of us can feel helpless when we

21:26 look at the huge problems facing the Earth today.

21:29 Deforestation, plastic pollution, and the extinction of entire species.

21:34 The easy solution is just to wait around

21:37 and hope someone else will do something about it.

21:40 Planet Wild gets boots on the ground to actually protect our planet,

21:43 and they make it easy for anyone to join the cause,

21:46 which is one of the reasons I became a member.

21:49 Another reason is that every month we

21:51 as a community fund new projects to clean up oceans,

21:55 rewild forests, protect endangered species and raise awareness.

21:59 You can think of Planet Wild as crowdfunding for nature.

22:03 My favorite part, I get to see

22:04 the impact of my contributions through outstanding monthly videos,

22:07 which are published right here on YouTube.

22:10 Take this for instance.

22:11 This is a Planet Wild mission in Mumbai.

22:14 It's a scalable technology that stops plastic at the source,

22:17 preventing 10 tons from reaching the ocean every month.

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22:27 it came from ordinary people like you and me.

22:31 You can sign up for whatever amount feels right for you and cancel any time.

22:36 The first 150 people to sign up using my code

22:40 VERITASIUM1 will get their first month paid for by me.

22:43 Just scan this QR code or click the link in the description.

22:47 If you're interested in the science behind their projects,

22:50 then go check out their YouTube channel.

22:52 I'm leaving the link to the plastic cleanup mission in the description.

22:56 And now back to the mystery of the potential.

23:00 Aharonov and Bohm published their findings in 1959 and the reception was mixed.

23:06 Certainly in the beginning, many people thought that it can't be true.

23:10 So there were many people that tried to write articles against it.

23:16 Even Niels Bohr, one of the founding fathers of quantum mechanics,

23:19 found it impossible to accept that a particle could be

23:21 influenced by a potential in the absence of any force.

23:24 But some physicists supported Aharonov and Bohm.

23:27 Richard Feynman wrote,

23:28 "The fact that the vector potential appears in the wave equation

23:31 of quantum mechanics was obvious from the day it was written.

23:34 It seems strange in retrospect that no

23:35 one thought of discussing this experiment until 1959,

23:38 when Bohm and Aharonov first suggested it and made

23:41 the whole question crystal clear." Feynman included himself that statement.

23:46 He later wondered why he had never noticed the effect.

23:49 Physicist Victor Weisskopf had a similar response.

23:52 "The first reaction to this work is that it's wrong.

23:54 The second is that it's obvious." Ultimately,

23:57 there was only one way to settle the debate.

24:00 Someone had to actually do the experiment.

24:03 The first to try was a colleague of Aharonov

24:06 and Bohm's at the University of Bristol, Robert Chambers.

24:10 Chambers experiment largely followed the setup Aharonov

24:13 and Bohm proposed with one notable exception.

24:16 An ideal solenoid would have to be infinitely long,

24:18 which is physically impossible.

24:20 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.

24:28 When this iron whisker was magnetized,

24:30 it produced a magnetic field that was strong within the metal itself,

24:33 but negligible outside of it,

24:35 as well as a magnetic potential in the surrounding region of space.

24:39 To get a baseline interference pattern,

24:41 Chambers fired two beams of electrons around an empty region of space.

24:45 And then he added the magnetic whisker.

24:48 When he fired the beams again, the interference pattern shifted.

24:52 It seemed that Aharonov and Bohm were right.

24:55 But critics were unconvinced.

24:59 People objected to it because since the whisker is finite,

25:04 there is always some magnetic field that will go out.

25:09 Maybe a stray field was responsible for the effect, not the potential.

25:13 And that's showing, throwing no shade

25:15 on their colleague who did these cool experiments.

25:17 It's like it's hard, right?

25:18 It's really hard.

25:19 And so it went for several decades.

25:21 Experimentalists repeatedly tested the Aharonov-Bohm effect,

25:25 but each trial had flaws that left the result open to debate.

25:30 Until in 1986, a team of Japanese researchers led by Akira

25:34 Tonomura came up with a new way to do the experiment.

25:37 See, they used a tiny donut-shaped magnet to make their magnetic field.

25:42 With a perfect torus, all the magnetic field is contained within the loop.

25:46 Outside it, it's absolutely zero.

25:49 And as an added layer of protection,

25:51 the team also coated the entire magnet in a layer of superconducting niobium,

25:55 which would block out any leaking fields.

25:58 Now, previous experiments relied on turning a magnetic field on or off,

26:03 but Tonomura's team took on a different approach.

26:05 In their case, the magnet is always on, but because of its unique shape,

26:09 the potential outside the torus is different from the one in the center.

26:13 It points towards us on the outside and away from us on the inside.

26:18 And the team realized they could take advantage of this.

26:21 They started by firing off an electron beam,

26:23 which was actually wide enough to be treated as two separate beams.

26:27 Part of it traveled along through empty space and functioned as the control,

26:31 whereas the other part washed over the entire torus.

26:35 And what's important here is that the beam is wide enough so

26:37 that part of it passes around the torus and part of it passes through.

26:41 Then at the end, a biprism deflects the electron beams toward each other,

26:46 they intersect, and this is where they create an interference pattern.

26:50 Now think about what this interference pattern should look like.

26:54 Well, for starters, there should be a shadow of the torus,

26:56 so we can fill that in.

26:58 But the rest, well, it depends on whether

27:01 the Aharonov-Bohm effect is real or not.

27:03 If it's not real, we'd expect

27:05 to see an interference pattern that looks something

27:07 like this, where the pattern outside the torus and in the center match up.

27:11 But if it is real, then the electrons

27:14 that traveled through the center would've experienced a different potential,

27:18 which would've shifted their pattern by half a phase.

27:21 So that should look something like this.

27:24 Now here are the results from Tonomura's experiment.

27:27 You see these are the interference fringes inside and outside the magnet.

27:31 And then if you follow what is a peak

27:33 outside the torus it lines up with,- Right.

27:35 a trough inside the middle.

27:36 And then it's a peak- Yeah.

27:37 outside again.

27:38 And that's exactly what they predicted.

27:39 This is exactly what they predicted.

27:41 So it's real?

27:42 It's real- Only the Tonomura experiment

27:45 was really the final proof, experimentally.

27:50 And yet, soon a new debate emerged.

27:53 The effect is real, sure, but how should we interpret it?

27:56 What is it really telling us about the nature of the universe?

28:01 Today, physicists largely fall into one of two camps.

28:04 The first camp claims that potentials aren't just mathematical conveniences,

28:08 they can influence physical reality.

28:10 This is the perspective initially favored by Aharonov and Bohm.

28:13 As they wrote in the abstract of their paper,

28:15 "contrary to the conclusions of classical mechanics,

28:17 there exist effects of potentials on charged particles,

28:20 even in the region where all fields

28:23 vanish." Some take this position a step further,

28:26 since the potentials show up in the Schrodinger equation and the fields do not,

28:30 well, they argue that the potentials are

28:32 more fundamental to physics than fields are.

28:35 Richard Feynman supported this idea, he wrote, "A is as real as B, realer,

28:40 whatever that means."- I mean, I kind of like that interpretation,

28:45 but something about the potential bothers me.

28:47 And that's the fact that you can set the potential at any arbitrary height.

28:52 It can be plus infinity.

28:53 It can be minus infinity.

28:54 Anything in between.

28:55 So wouldn't that change, you know,

28:57 how the potential actually influences the wave function?

29:00 This bothered me too.

29:00 So much so that I actually ended up asking

29:02 a professor about this, but it turns out it can't.

29:06 It knows it's not just the potential that's entering the observable,

29:09 it's the line integral.

29:11 So it's only A that enters, it's not the magnetic field.

29:14 B vanishes, it's only A, but it's not A alone.

29:18 It gets a little technical here, but you know, if I pull up, you know.

29:24 As one does.

29:25 As one does, a flip chart.

29:27 Now we can actually run this.

29:29 So if you look at how the potential shows up,

29:33 then what's measurable is not the phase directly, but it's the phase shift.

29:37 Call it delta theta.

29:39 Then the phase shift is line integral

29:41 of A over the path or dotted with the path.

29:44 So you get this.

29:45 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,

29:53 one electron beam goes like this, and the other

29:56 one goes like this, and these are symmetric,

29:58 then the potential here will point let's say in this direction.

30:03 But here, it will point in that direction.

30:05 Let's say instead of A, we do A plus C, some constant.

30:10 Then when we're taking the path this way,

30:13 we'll be adding that C and we'll be dotting it with dx.

30:16 But because that path is the exact same when we go this way,

30:20 which is subtracted.

30:22 Mm-hmm.

30:22 So it cancels out.

30:23 So the potential, yeah, it does show up,

30:26 but in such a way that all the arbitrariness of the potential,

30:30 it cancels out perfectly.

30:32 Okay.

30:32 It's a geometrical quantity solving A that has taken care

30:37 of for which all that residual ambiguity has literally canceled out.

30:41 The potentials being physical might sound strange,

30:44 but the second interpretation is even stranger.

30:48 Physicists in camp two maintain that potentials really are just

30:51 mathematical objects and the fields are responsible for the effect.

30:55 But in Tonomura's experiment,

30:57 the magnetic field was completely confined within the solenoid.

31:00 For this interpretation to be true,

31:02 its supporters are forced to assert that fields can act non-locally.

31:05 That is a field can influence things outside

31:08 the region of space where the field itself exists.

31:11 Many physicists find this idea difficult to swallow.

31:14 I think the idea of saying that these fields act

31:17 non-locally undoes the reason why we have field theory, right?

31:20 The great triad of a field theory,

31:22 which has served us so well for more than 100 years,

31:24 is this notion, stubborn notion that local causes yield only local effects.

31:29 [Derek] And yet Aharonov's own perspective has

31:31 shifted from camp one to camp two.

31:33 When we publish the article, we called it the effects of potentials.

31:38 When you use local potential and use the Schrodinger representation,

31:44 it looks as if everything is local.

31:46 But it's misleading because that local potential is really not physical.

31:52 Later, I decided that it should be called

31:55 a non-local effects of the electric or magnetic field.

32:01 The electron can feel the effect of a field that is not where it is.

32:07 While non-locality remains a controversial idea,

32:09 a sizable portion of physicists do side with Aharonov.

32:14 And the debate continues to this day.

32:18 I maybe have a third interpretation.

32:20 Good.

32:21 And I would love to get your thoughts.

32:22 And if it's bad, please tell me honestly.

32:25 Okay.

32:25 So we did this other video about particles

32:28 essentially exploring all possible paths all at once.

32:32 And so right now we're saying either

32:33 the potentials are real or fields are acting non-locally.

32:38 But what if there's a third option where the fields are

32:41 still local and it is the fields that are affecting the change,

32:45 but rather it's the particles that are exploring all possible paths all at once.

32:49 You could potentially even have some quantum tunneling effects

32:52 going inside an area where there are fields, you know,

32:55 as the electron or the wave function at least explores all possible paths,

32:59 gets influenced by those slight bits where

33:01 the wave function is inside the field.

33:04 I actually don't think that's ridiculous, Casper.

33:06 That's for a strong ringing endorsement.

33:08 I think there's a lot to that.

33:10 Okay.

33:10 If we could think about these things as it

33:13 is indeed the quantum phase that's being affected,- Yeah.

33:16 we can describe that phase in terms of quantum mechanical path integrals,

33:19 I think that's a perfectly reasonable way to to frame it.

33:23 So, yeah, I'd buy that.

33:26 That's awesome.

33:26 I'm pretty sure this isn't the complete answer,

33:29 but one thing which would be cool is if someone else takes this idea, you know,

33:33 or maybe it gets inspired by it and they're like, actually that doesn't work,

33:36 but here is how it does work and now we're closer.

33:39 That's right, that would be the best possible outcome.

33:41 Well, the best possible outcome is you're just right.

33:43 But the second best possible outcome is that that nudges

33:46 the community more broadly to ask new questions of familiar material.

33:50 That's right.

33:52 One new question the community asked was, is there also a gravitational version?

33:56 In 2022, researchers at Stanford tested this.

34:00 A simplified version of their experiment works something like this.

34:04 They shot up ultracold rubidium atoms into a tube-shaped vacuum chamber,

34:08 at the top of which was a tungsten mass.

34:11 Now atoms like electrons are also governed by a wave function.

34:15 So they split each rubidium atoms wave function into two distinct packets,

34:19 and they launched them to different heights.

34:22 One was sent really high and got close to the mass, whereas the other didn't.

34:26 And then when the two collided at the bottom,

34:28 this created an interference pattern.

34:30 And when they let this interfere and accounted for all other effects,

34:34 they could clearly see the phase shift as predicted by Aharonov and Bohm.

34:38 So it seems like the gravitational Aharonov and Bohm effect is real.

34:42 If the results hold up the scrutiny, this is a huge finding.

34:46 Because it suggests that the electromagnetic and gravitational

34:49 potentials can influence reality at the most fundamental skill,

34:53 even when all the fields are exactly zero.

34:56 So does that mean that most physics textbooks are wrong or need updating?

35:02 Don't throw out all the textbooks.

35:03 They're beautiful.

35:04 We learn a lot.

35:05 But that doesn't mean we're done.

35:06 And we should be open to surprise.

35:08 And just because things haven't changed in let's say 200 years,

35:11 roughly between say Lagrange and Aharonov-Bohm, they still could change, right?

35:15 And they can sometimes change in beautiful

35:18 and surprising and very powerful ways.

35:21 I read somewhere that the reason you decided to do the AB effect was that you

35:28 didn't really think potentials were something that was

35:31 just a mathematical tool like most scientists believe.

35:35 That is correct.

35:36 I was very ignorant, luckily.

35:38 Sometimes it's good not to know too much.

35:42 (gentle music)