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28: Bell's Infamous Theorem (Bell's Theorem)
490 Plays6 years ago
The history of physics as a natural science is filled with examples of when an experiment will demonstrate something or another, but what is often forgotten is the fact that the experiment had to be thought up in the first place by someone who was aware of more than one plausible value for a property of the universe, and realized that there was a way to word a question in such a way that the universe could understand. Such a property was debated during the quantum revolution, and involved Einstein, Polodsky, Rosen, and Schrödinger. The question was 'do particles which are entangled "know" the state of one another from far away, or do they have a sort of "DNA" which infuses them with their properties?' The question was thought for a while to be purely philosophical one until John Stewart Bell found the right way to word a question, and proved it in a laboratory of thought. It was demonstrated to be valid in a laboratory of the universe. So how do particles speak to each other from far away? What do we mean when we say we observe something? And how is a pair of gloves like and unlike a pair of walkie talkies?
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Transcript
Introduction & Correction
00:00:00
Speaker
Hey everyone, it's Jon from Breaking Math. Before this episode begins, let me just correct an error I made about 10 minutes in so that you're ready for it when it comes and it doesn't throw you for a loop. I said that two entangled photons, photons that have the special property that they act like one another even at a distance, go through two polarizing filters. I meant to say that if one entangled photon goes through a polarizer, then a photon entangled with it will go through a similar filter. And if the first one doesn't go through, then the second one won't go through either.
00:00:29
Speaker
Got it? Good. Now on to the episode.
History of Physics & Entanglement
00:00:34
Speaker
The history of physics as a natural science is filled with examples of when an experiment will demonstrate something or another, but what is often forgotten is the fact that the experiment had to be thought up in the first place by someone who is aware of more than one plausible value for a property of the universe, and realize that there is a way to word a question in such a way that the universe could understand.
00:00:54
Speaker
Such a property was debated during the Quantum Revolution, and involved Einstein, Poladsky, Rosen, and Schrodinger. The question was, do particles which are entangled know the state of one another from far away, or do they have a sort of DNA which infuses them with their properties?
00:01:09
Speaker
The question was thought for a while to be purely philosophical until John Stuart Bell found the right way to word a question and proved it in a laboratory of thought. It was demonstrated to be valid in a laboratory of the universe later. So how do particles speak to one another from far away? What do we mean when we say we observe something? And how is a pair of gloves unlike a pair of walkie-talkies? All of this and more on this episode of Breaking Math.
Guest Introduction & Collaboration
00:01:32
Speaker
Episode 28 Bell's infamous theorem.
00:01:41
Speaker
I'm Jonathan and today we have on my cousin, Adam. Hello. And Adam, how are you involved in the sciences? So I have been studying engineering at New Mexico state for about nine years now, working on my master's in mechanical engineering and should be done in the next year or so.
00:02:01
Speaker
Awesome, and today we're gonna be talking, of course, about Bell's theorem, but before we do that, I'm gonna give a quick plug to Arts Academy in the Woods in Fraser, Michigan. Breaking Math is doing a little bit of, somewhat of a collaboration with David Fuchs, who contacted us, and it has to do with prerequisites and standards-based grading. More information on that as it unrolls. All right, so polarization.
Understanding Light Polarization
00:02:30
Speaker
Polarization is light going the same way, but I think we could be a little more specific than that. What do you know about polarization? So if you can imagine light being a wavelength going up and down, that light isn't necessarily going up and down in the same plane. If you have a ray of light, a light could be rotated. You're talking about rotating the light like a screw. So would you consider light to be flat?
00:03:01
Speaker
No, you can consider like all of the waves kind of like a tube, like a 3D tube, vibrating light. So there's something to be said for a circularly polarized light, which is light traveling like a slinky. But I mean, for the purposes of this metaphor, we don't I mean, for this problem, we don't have to be concerned with that light, we just have to be concerned with, like, if you draw a wavy line with a pen, that is the kind of shape that we're
00:03:29
Speaker
saying that light has. And there's an instrument called a polarizer that lets through half of light, like the brightness of light, and it changes it to polarized light in whatever direction. And you could rotate this polarizer. How would you explain a polarizer?
00:03:45
Speaker
So a polarizer, as far as I know about it, I don't know much. I'm only a mechanical engineer, so don't do much with light. But it forces the light to either go in the direction the polarizer is being polarized, or it doesn't allow the light that is not going in that direction to pass through the direction the slits of the polarizer are facing.
00:04:09
Speaker
Well, I know that's almost, the only addendum is that because it's quantum mechanics, you get a little bit of weirdness because if we had like a grate that let through, that if we drop coins on top of it, most of the coins wouldn't be going exactly up and down.
Polarizers & Quantum Measurement
00:04:27
Speaker
So you'd expect the vast majority.
00:04:29
Speaker
of coins to not fall through the grate but about half of light gets through the polarizer so what it does is it sort of creates a potential for light to be up and down and depending on how up and down the light already was it either does that or not and it's a form of quantum measurement polarization so you're measuring something when you polarize it and that's essentially what polarization is all about and um
00:04:56
Speaker
So if you polarize light and you have, say you had like just spectrum visible light, could you polarize it to only say have green light be the wavelength that you're allowing through and could you make like light that's on the fringes of the green wavelength kind of rotate to become in the green wavelength or does it just reject all of the other wavelengths if you have it that at that direction?
00:05:21
Speaker
I think that, uh, that would just be a filter. Oh, that makes sense. Okay. Yeah. So then how does a polarizer, how is it different than the filter for, for that? I think the difference is that a polarizing filter filters, uh, out basically a specific angle of light, a gel filter filters out wavelength instead. Okay. So like a polarizer will have a slit and only light vibrating on that plane will get through and it can be any kind of wavelength.
00:05:49
Speaker
Yeah, although I think that they work best for specific, like I think that there's like a specific polarizers for like, I know that there's some antennas that take advantage of polarization, things like that. So, and they have a different structure entirely than optical polarizers that deal with visible light. What it does is it doesn't not let other stuff through, but it just doesn't affect it in the same way. It doesn't collapse the wave function for different, for higher or lower wavelengths.
00:06:17
Speaker
Okay, and so like if you have a light bulb or any other kind of source of light, is stuff ever coming out of that source polarized or do you have to interact with it after it's been, say, emitted?
00:06:26
Speaker
Usually radiated light is decoherent by my understanding. There are interesting ways of polarizing though. Like if you use a quarter wave plate you can polarize light rotationally so that it doesn't just have an up and a down component but has an out of sync left and right component so it's traveling like a slinky.
Quantum Entanglement & Nonlocality
00:06:46
Speaker
And so is this the kind of stuff that Bell's theorem has to do with?
00:06:50
Speaker
Yeah, what it has to do with is entanglement. And entanglement, you could generate certain particles with the property that they're kind of like brothers. And there's like some crystals, for example, that if you shoot light through it, you'll get two different beams of light coming out. But the photons that make up those two beams of light are entangled with one another. So if you just fire one photon at a time at this crystal, two photons at a time will come out.
00:07:17
Speaker
And if one photon passes through a vertical polarizer, for example, the other one will too. It gets weird when the polarizers are at different angles because the thing is about the entanglement property is that Einstein thought that it was like a pair of gloves where the gloves are like a pair to one another. So the particles have all the information in them that they need to know when to pass through a polarizer or not. So if they had the DNA that said they would pass through a vertical polarizer, they both would. And if not, then they both wouldn't.
00:07:47
Speaker
Einstein is saying like a pair of gloves, like if I start to move my hand in a certain way, then the other hand would also move exactly the same way? Not necessarily, like a pair of gloves in a box. Because the whole thing about locality is that things can only interact if they're like basically right next to each other. So he's saying that when these photons get entangled, they're imbued with the DNA, just like a glove has its pair.
00:08:15
Speaker
So it's just a way of looking at it. It's not like you move one and not the other, but it has to do with, I think with electrons, you actually get like opposite properties or something, but I'm more familiar with the photon example. So I guess a better way of saying that would be that you just have two books that represent all the information. And when they pass through a polarizer, they look up if they're supposed to go through or not.
00:08:43
Speaker
So until you had these two photons, both going at a polarizer, and you only have like one slit, what does the other photon go? Does it just hit the wall and kind of not get absorbed by it or what? Oh, you're combining the entanglement of the double slit experiment? What was the question again? So if you have two photons and they're entangled,
00:09:04
Speaker
But you only have one slit, where does the other photon go if one photon goes through the slit? Oh, the other one might not go through the slit because their position isn't entangled, it's just their properties are entangled. So if you make them go through a polarizer,
00:09:22
Speaker
Like let's say we have two vertical polarizers on the table and we redirect the photons to go through them. If the polarizers are at the same angle relative to one another, then the photon will go through both or go through neither. Once the photons get entangled, I mean like once you interact with one of the photons, they're no longer entangled. But you also know the property of the other one.
00:09:44
Speaker
Now here's where it gets weird, you can't communicate faster than light using this, and you think you might be able to, because if you know the state of the other one as soon as you measure the one that you have, you might think that you have information from far away, but you can't do anything with that information, you still have to send a photon to the other person to tell them what the outcome was, and by that time, you're not violating causality at all.
00:10:08
Speaker
That's why that kind of quantum communication doesn't actually make sense. Yeah. In a communicating type of way. Yeah. Plus, I mean, plus you could set up a bunch of spaceships going nearly the speed of light and create a paradox using that, which I'm sure they did in many of their discussions. Cause they'd have information reaching people before they got there.
00:10:35
Speaker
Yeah. Yeah. You would have something happening before it happened, which can't happen. Okay.
Set Theory & Food Categories
00:10:43
Speaker
And the last thing that we're going to talk about before we talk about the inequality is the double slit experiment. Are you familiar with the double slit experiment? Yeah. Is that like where you have like the two slits and then you have a distribution behind the slits of where the photons kind of end up and it's not quite distributed the way that classical physics would predict that.
00:11:04
Speaker
Yeah, so it's kind of like if I had a pool or a bathtub and in the middle of the bathtub, I put a wall with two holes in it so that waves can go through the two holes, but not other part of the wall. If I turned on the water, then it would cause a bunch of waves to go outward and then.
00:11:23
Speaker
when it went through the two holes, you would see the waves going up and down and they would interact with each other so that they would cause, so if you looked at the waves, they would kind of be all over the place. It would be like a crisscross pattern. It was thought that atoms had to be, not atoms, that photons had to be a wave because they, when you fire it through a double slit, you get that distribution. So they thought, okay, if they're particles, then they wouldn't interact with each other in that way. They would have kind of a,
00:11:52
Speaker
it would look like a flashlight on the opposite side, but they don't. Oh, so they distribute in the way that the wavelength is in the shape of the wavelength. Yeah. So these slits have to be very small and very close together. So it doesn't look like a shadow on the other end. It looks like their wavelength.
00:12:10
Speaker
What it looks like is the shadow of a jack-o'-lantern if the jack-o'-lantern had closed teeth. So it's like brightest in the middle, it just kind of like a pattern of waves, yeah. It doesn't look like a shadow of two slits. Right, right, okay. So it looks like a banded line after the slits. Yeah, with the brightest bands near the center.
00:12:35
Speaker
Okay. If you only fire one photon at a time through, you'll still get this pattern, which means that the photon must interact somehow with itself through both slits, which is called the wave-particle duality because sometimes things act like a particle sometimes act like a wave. That's the quantum weirdness that
00:12:55
Speaker
It seems to require faster than light communication because once it gets to the wall, how does it know that it's touching the wall? There's so many questions that you could ask about quantum physics that people have tried to ask and you can't really answer with concepts that are familiar to people. People don't have the hardware for it. But math has been used since the beginning of quantum mechanics very heavily to understand it.
00:13:19
Speaker
So to delve into what Bell's inequality and Bell's theorem really is, we're going to talk a little bit about a property of inequalities themselves. This is pretty much pure math at first.
Bell's Inequality & Experimentation
00:13:34
Speaker
All right, so we've covered it on the show before, but set theory. What do you know about set theory?
00:13:40
Speaker
Well, you've just taken a bunch of, say like Venn diagrams, and you're comparing what is in a set, what is not in a set, and maybe what things are intersecting between the two sets, like where the sets intersect.
00:13:57
Speaker
Yeah, so for example, the set of all continents would be North America, South America, Europe, Africa, Asia, Australia, and Antarctica by some people's standards. But if you intersected that with the set of all countries, the only thing that would come out would be Australia, because there's no other country that's also sometimes considered a continent. Right, right.
00:14:19
Speaker
And then the set of all round numbers or whole numbers would have an infinite number of elements. And that's a discussion in itself. But what we're going to be talking about today is food. And these are going to be pretty American examples. So if you live in another country, just swap in examples of your own, you'll see as we go along. And if you do have a piece of paper and pencil handy, then I would use it, but it's not required.
00:14:45
Speaker
But if you do, we're going to be filling in a Venn diagram, so just draw three overlapping circles. Alright, so we have a list of foods, would you mind reading them? So for foods, we're going to have sandwiches, ham, iced tea, cereal, orange juice, slurpees, and coffee. These are seven foods, so that's a set in itself. But we can be more specific with the set, and we can break it down into three categories.
00:15:10
Speaker
So the three categories we're gonna have are lunch foods, breakfast foods, and beverages. So if you think about it, sandwiches are a lunch food, ham can be a lunch food, and iced tea could be a lunch food. Cereal, ham, and orange juice are the three foods that are breakfast foods. And the four things that are beverages are slurpees, iced tea, orange juice, and coffee. So there's a lot of overlap between them. So example, iced tea is both the lunch food and the beverage, you know?
00:15:39
Speaker
So we could break this down even further into seven categories. And this is going to take a little bit, so you're going to have to stay with us. So for breakfast only foods, not beverages, the only thing that comes out of that set is cereal when we overlap that with our main set.
00:15:58
Speaker
Yeah, so if you're following along with the Venn diagram, you would put cereal in one of the bubbles that's not intersecting with any of the other bubbles. And sandwiches are the only food that we mentioned that were a lunchtime only food that's not a breakfast food or a drink. And slurpees are the only drink that you don't drink for breakfast or lunch. I think that was more of maybe like a snack kind of beverage.
00:16:25
Speaker
Yeah, snack beverage. Which isn't a category that we're making, by the way. Yeah, although it could be a category if those are the only three categories because snack, I guess, is the only thing that isn't breakfast or lunch. I guess you could have dinner. This isn't a complete analogy. It is for our purposes, though.
00:16:44
Speaker
So now we have left ham, coffee, iced tea and orange juice. Now orange juice is you drink that for breakfast, not lunch, right? Generally, sure. Well, I mean, okay. Like you totally can, but most people don't. Yeah.
00:17:00
Speaker
And it's a beverage, so that would be in the part of the circle that's intersecting, the part of the circles that are intersecting where the part that's not intersecting are both cereal and slurpee. So drink and breakfast. And the thing that's a drink and for lunch is iced tea. The thing that's for lunch and breakfast could be ham. And then the thing that fits into all three categories is coffee, of course, because you can have coffee anytime. Some would disagree.
00:17:30
Speaker
Some would, but they would be wrong. So why are we talking to you about food so much? Also, please wake up.
00:17:39
Speaker
We are talking to you about this because if we, like let's say we have any three overlapping bubbles, and we call them A, B, and C, the number of things that are in A and not B, plus the number of things that are in B, not C, is always greater than the things that are in A, not C. Now that's a little hard to visualize, so we'll go through it with the example. What are the foods that are for breakfast but not lunch?
00:18:07
Speaker
food that would be for breakfast and not lunch. Um, I guess we have orange juice in that category. Yeah. Orange juice. And we got cereal. Right. Um, so we got two things now. What about the things that are for lunch, but not drinks, lunch that aren't drinks. We have sandwiches and ham.
00:18:25
Speaker
Yeah. And those are two completely different ones. So now we have four things. Uh, so that's a not B plus B not C or breakfast, not lunch, plus lunch, not drinks. And so how many things are breakfast, but not, uh, are for breakfast, but are not drinks for breakfast, but are not drinks. We have ham and cereal.
00:18:45
Speaker
Yeah, which is only two and four is greater than two, right? Right. Last time I checked. So, so basically we proved a category, a property of sets. Um, and this is really important, uh, when we actually get into the experiment and the reason and a little bit of a preview of the reason why is because you can, if you go back to our polarized light example,
00:19:10
Speaker
You can see, you can say that has DNA with let's say a million different variables in it, but you could make those variables fit into three different categories if you wanted to. Um, and the categories would be goes through a vertical polarizer, goes through a polarizer at 120 degrees. So one third rotation and a polarizer at 240 degrees. Um, and those could be your three categories.
00:19:35
Speaker
and those are degrees measured from a vertical ninety degree yeah exactly yeah i mean you'd still get an inequality the other way but it wouldn't be as dramatic as an inequality welcome back listeners for those of you listening we took a break so that's what's going on so now we're totally gonna cut this
00:20:00
Speaker
So let's set up the experiment. I talked about it a little bit, but I didn't go very good into it. We have to start with a crystal or something that entangles particles. So we have to start with entangled pairs of, let's say, photons. Any kind of special crystals that will entangle these photons together?
00:20:22
Speaker
So it turns out that barium borate is such a crystal that exhibits necessarily nonlinear properties. Nonlinear properties just meaning properties that don't fit nicely into differential equations that have to govern it. But yeah, you can use a crystal like that to generate entangled pairs of photons. And as a reminder, if two protons are entangled and they go through the same angle of polarizer, then they will either both go through or neither will go through, just reiterating that.
00:20:52
Speaker
And then what you do is you have three different polarizers. One at vertical angle, one at 120 degrees, and one at 240 degrees. So they're like thirds. And what you do is you measure coincidences. And coincidence here meaning when the photon goes through both or when the photon goes through neither. Now we don't have to test two types of polarizers that are the same polarizer together.
00:21:20
Speaker
Because we know that'll either the quintence will be 100% basically they'll either both go through or not go through so in this experiment Do we only have one slit at each angle? Do you mean one polarizer at each angle one polarizer? Is the polarizer not a slit?
00:21:36
Speaker
No polarizer is like a little piece of glass with like a lot of like slits in it, but so many that like, yeah. Okay. So they're like infinitesimally, like a collection of infinitesimally small slits. Theoretically. Yeah. Okay. Okay. That makes, that helps to visualize it a little bit better.
00:21:52
Speaker
Yeah, so what we do is we have three categories, and we're going to call them A, B, and C. A means this photon will pass through a vertical polarizer. B means this photon will pass through a polarizer at 1 third rotation or 120 degrees. And C means this photon will pass through a polarizer at 2 thirds rotation or 240 degrees.
00:22:12
Speaker
Now, if a photon is in category A but not B, that could be tested because we have entangled photons. And so the way we can see that result is by how they backscatter or how they end up displaying on whatever is behind the slits.
00:22:30
Speaker
Oh, there's no slits in this experiment. The double slit experiment was just mentioned because it shows a property of photons being entangled. We're just measuring it with a simple photon detector behind a polarizer.
00:22:45
Speaker
So, okay, when I say slit, I mean polarizer. Oh, I see. But I saw it saying slit is the wrong thing to say for that. Okay, so there's a photon detector behind the polarizer. And from that, we can figure out which angle of polarizer they went through. Oh, no, we know the angle of polarizer that they went through. How do we know that? We set them up that way. Oh. And we test all combinations. Okay.
00:23:12
Speaker
And, uh, we send a bunch of photons through each combination and test the percentage of time that it passes through. Okay. So you're testing, you don't have all three polarizers at the same time. No, just to polarize, like maybe we might have a vertical and a one third or a one third in a two thirds or a vertical in a two thirds. So those are the three combinations that we can have. And so when you're passing, you're passing photons through say both of those at the same time.
00:23:40
Speaker
Yeah, the entangled pairs. We send one in one direction, one in the other direction, and then they go through the polarizers and then hit the photon detector. Okay, so you're saying we also have that fine-grained level of control over beams of light that we can... Oh yeah, we do. That's amazing. Yeah, isn't it? That kind of blows my mind a little bit.
00:24:04
Speaker
Yeah, we can send single photons through at the same time and count their coincidences. And we know when we're sending them and where we're sending them pretty precisely? Well, interestingly enough, we don't know exactly when we're sending them because we know exactly what energy they're at. And the Heisenberg's uncertainty principle says that the more you know about the time, the less you know about the energy and vice
Hidden Variables in Quantum Mechanics
00:24:29
Speaker
versa. So when you measure something or know something, you destroy something else?
00:24:33
Speaker
Yeah, but we do know generally that it does go through at some point in time. And we do know that a photon probably happened after a certain amount. So there's a little bit of engineering that goes into it. So we know enough that we can make pretty good measurements about this stuff.
00:24:47
Speaker
Oh yeah, they're getting better and better all the time.
00:25:06
Speaker
Actively working through this section cements a good foundation for learning more complex quantum mechanics. To support your educational journey in math and physics, go to brilliant.org slash breakingmath and sign up for free. The first 200 breaking math listeners get 20% off the annual subscription, which we have been using. And now, back to the episode.
00:25:26
Speaker
If we could set the photons into these three categories, then we could kind of see if a photon, this is the classical view, by the way, if a photon is in category A, meaning vertical, but not B, meaning one third, if we send the particles through and we count how many go through the vertical and not the polarizer at one third, or I guess vice versa. It's just a not case, right?
00:25:53
Speaker
Yeah, just the opposite case. So then we have category B, not C, which means the photon passed through the one-third polarizer and not the two-thirds rotated polarizer. And then A, not C means a photon passed through the vertical polarizer while it's passed through the polarizer at two-thirds.
00:26:11
Speaker
So we're just doing all three combinations, but we have to stress that this is classical mechanics because quantum mechanics says that we can't know the exact state that the photon was in because the state that the photon was in has data that we cannot access after a measurement.
00:26:31
Speaker
and polarization does these measurements. So this is where Bell's test experiments come into play, because since the categories are, if A, B, and C are like the DNA of the particle, then we could test this by testing it in this clever way, by entangling photons and then checking the likelihood that they're going to pass through things. We get more information than quantum mechanics says that we can.
00:26:56
Speaker
So when you say A, B, and C are the DNA of the particle, are you talking about like the angle that the wavelength is kind of vibrating on?
00:27:07
Speaker
Well, it's more like we're just talking about hidden variables. These are like, these are specifically variables that we know nothing about necessarily. So if we're talking about the book example where the photons are like, until photons are like books that have the same information in them, A would be a way of reading the book, B would be a different way of reading the book, and C would be a different way of reading the book.
00:27:28
Speaker
So it's kind of like saying you send these two particles, and then you want to see if the book says that they should pass through A, and you want to see if the book says that they should pass through B. If you want both that information, you have to measure at the same time, or not at the same time, but you have to measure the same photon, which seems like you could do with entangled pairs of photons.
00:27:50
Speaker
but quantum mechanics states that since you can't know everything about these, then that theory fails. But what that implies is that non-locality exists, that these photons must be communicating at some point.
00:28:02
Speaker
When you say non-locality, I'm not quite sure what you mean by that. Let's say that, well, a quick example is like, let's say we're playing a game of cards with the devil, and the devil can look at, and then the devil can not look at the card, so you're just playing a fair game of cards with the devil, and that's classical mechanics. But quantum mechanics says that the devil
00:28:26
Speaker
after drawing the cards can change their value. That's non-locality? That's non-locality, meaning that a measurement causes the information to exist in a way versus the information always, quote unquote, having been there, even though it is there in a quantum way, but those variables are complex. So is that different than the uncertainty principle?
00:28:49
Speaker
So nonlocality is when things can interact from a distance with their quantum states and the uncertainty principle is that position and momentum or energy and time are when multiplied together have a maximum uncertainty, I mean a minimum uncertainty that they have. They're related but they're philosophically different.
00:29:13
Speaker
So one thing about the inequality, we said that A naught B plus B naught C is greater than A naught C, right? In the classical sense. In the classical sense. And the way that this works out is if you manipulate these probabilities, these sets, because if you think about A naught B, it consists of the things that are solely in A plus the things that are in both A and C, but not B.
00:29:42
Speaker
for example. And the same thing with B not C, it's the things that are only in B plus the things that are only in A and C. So if you do that sort of manipulation, you get a similar probability that says that AB plus BC plus AC must be greater than one third. Now what are AB, BC and AC?
00:30:09
Speaker
AB is when it passes through A and B with the same outcome, which happens one third of the time because there's eight different possibilities. BC, one third of the time, and AC, about one third of the time, or greater than one third of the time.
00:30:26
Speaker
And the reason why it's greater than one third of the time is because you have to assume that the variables are random. Otherwise, there would be some more measurable properties about the universe. So this DNA sets them completely randomly into categories A, B, and C, right?
00:30:45
Speaker
So if they're in neither category A nor B nor C, then no matter what, we'll get the same outcome for AB, BC and AC. Right. But all the other times, except for when they're in all categories, you only get one out of three being correct. Then that's where we get the one third.
00:31:08
Speaker
Yeah, that's where the one-third comes from. And classical mechanics says that when you do this experiment, set it up that the coincidences between A and B plus the coincidences between B and C plus the coincidences between A and C are greater than or equal to one-third.
00:31:24
Speaker
So they're greater than one third because of the while being the same or all being... Yeah, exactly. But quantum mechanics, because of some math that we really can't get into, but it has to do with path integrals, it predicts one quarter. But it doesn't matter what path integrals you used to do. If you get a result that's less than one third, it means that the categories can't exist and that there has to be communication.
00:31:54
Speaker
So when you set up the experiment and run it, you get a quarter. That's what you get. So in this, we are seeing that the classical probability just doesn't hold at all. It has no bearing on this. No, this is an analytical result, meaning that it has an inequality. So yeah, then that's what it says is that it's a make or break kind of thing and it broke.
00:32:22
Speaker
Bell's theorem is the fact that nonlocality exists and Bell's inequality is the inequality that we just covered. And so because of the way that the experiment breaks, the classical probability that we're expecting, that's how we can see that the nonlocality is having an effect here.
00:32:44
Speaker
Is that, is that it? Yeah, that's exactly it. Okay, cool. And it says, it's, I mean, we've talked about how the spookiness isn't as spooky when you realize that you can't communicate faster than the speed of light, but it still is difficult to even hold in your head. And it's, and the fact that the universe is made out of quantum mechanics blows my mind personally.
Quantum Mechanics Complexity & Future
00:33:05
Speaker
Cause we don't even have the math or properly represent that stuff yet.
00:33:10
Speaker
Well, not in combination with general relativity, but it's so unintuitive that I think research is slower than it would be otherwise. That's why I'm a mechanical engineer. Quantum mechanical engineer?
00:33:27
Speaker
No, not quite. Quantum mechanics has some bizarre properties. One so bizarre that we have trouble even comprehending the mechanics, let alone the implications of them. As we evolve as a species, we will evolve better ways to understand it. One thing is for certain, however. No matter what we are in the universe, it stands that we are, and know we are. Quantum mechanics is merely the sharpest lens we have for looking at that.
00:33:50
Speaker
I'm Jonathan and this has been Breaking Math. With me I had today on... Adam! And Adam, is there anything you want to plug? Oh, I wasn't ready for this. Yeah, nobody is. No, there's nothing I want to plug right now. Alright. Anything you want to say about quantum mechanics before we sign off? It kind of breaks my head trying to think about it, so... You're in good company with pretty much everybody.