Bell’s theorem and local realism
Bell's theorem rules out local hidden variables as an explanation for quantum entanglement. The core idea: Einstein insisted that entangled particles must carry pre-set properties (local realism), while Bohr held that no definite spin exists until measurement. John Bell's 1964 paper showed that by giving Alice and Bob each a choice of measurement direction, the joint probability distributions predicted by quantum mechanics exceed the upper bound that any local hidden variable theory can produce. That gap between the two predictions makes the question experimentally testable rather than merely philosophical.
- Bell wrote his paper during a one-year sabbatical in the United States, with the published affiliation listed as the University of Wisconsin-Madison.
- The EPR paper (Einstein, Podolsky, Rosen, 1935) was the earlier work that framed the hidden variable argument Bell later addressed.
- When Alice and Bob measure entangled particles along only a single direction, the classical and quantum predictions are identical, which is why the debate seemed unresolvable for decades.
- Adding a second measurement direction for each observer creates a matrix of outcomes whose correlations can be checked against Bell's factorability condition.
- John Clauser tested Bell's inequality experimentally at Berkeley and found results that violated the local realism bound.
Transcript
This chapter, from the episode video's captions · 1,570 words
10:46Um this is a photo of our America 250 timeline that we had prepared for the celebration of America's 250th birthday. We had done a giant timeline of some 400 accomplishments that America was responsible for. A lot of people think that John Bell was mostly at CERN, but actually he took a one-year sbatical and he came to the United States in 1964. He visited Stanford University and the University of Wisconsin. And during that sbatical is when he wrote the seminal paper that he is most well known for. It showed definitively that local hidden variables cannot account for the richness of the observed phenomenon that
11:28we see in quantum mechanics. So I want to dive a little bit into that because I think that is going to be the foundation for understanding why Fineman got into it. A lot of people just start with Fineman. >> Mhm. >> There's a lot of stuff that happened before Fineman. Okay. And I don't want to be a podcast that is the cult of Fineman. There's plenty out there. Um Fineman is a great man as we will see. um in the talk that he gives, but there was a lot of stuff that happened before then that enabled him to think about those problems. >> And for anyone who actually is interested in checking out that America 250, you can go to ffpod.com/amea250. It's an interactive timeline that covers
12:08some of the stuff you just mentioned. That's prefineman as well as many of the other great discoveries in our history. Um and it's I think a really humbling experience to go through it in that format. >> Yeah. Um and Fineman is mentioned a lot on that timeline because he did a lot of really cool things. So let's start with um our entanglement experiment that everyone gets to know. Alice and Bob. Okay. They always use Alice and Bob. I don't know why. I think it's because A and B. Um maybe if somebody has an idea of of historically why we always use Alice and Bob in these entanglement thought experiments, please let us know.
12:48So here's the idea. Suppose I create two particles with spin and they're entangled. So I don't know um maybe like a photon goes through a crystal and then it splits into two. So then the two photons that were created were created from the same same quantum state. So they're going to have an entangled quantum state. Okay. Now, by conservation of angular momentum, if Alice gets one of these particles and Bob gets another one of these particles and Alice observes her particle spinning one way, then by conservation of angular momentum, Bob should see his particle spinning the other direction, right? Because then the two spins cancel out. Um, but according to quantum mechanics,
13:28there's a probability that Alice is going to see the spin going one way and the other way and then a probability that Bob is going to see it going the other way. It's just that the two probabilities are correlated and that they always have to be opposite. >> Now, that begs the question, is there a spin to begin with? >> Right. >> Okay. That that was like made in the entanglement state and then got split up. Okay. Or the alternative being or is it only existent once it's been quote observed? >> Exactly. Which is that's Neil's bore >> which is a complex what is >> yeah what does that even mean? Right. So Neil's bore is like no that second thing. No that's it. Right. Uh there's no well- definfined spin and then only when you observe it the wave function
14:09collapses and then you get uh one direction or the other. Right? And Einstein's like this this is nonsense. This doesn't make any sense. He insisted on something called local realism because he one he liked local because local means that nothing travels faster than the speed of light which makes sense. Um and the physical objects possess definite properties that are independent of observation. Okay, so that's like the realism part and they can't propagate faster than the speed of light. There's no communication. Okay. So, effectively, if you've seen the the Denzel Washington movie, Deja Vu, >> he's he's effectively Denzel Washington.
14:49>> Okay. There's that really funny scene where like he's looking through a wormhole or something and he's asking if the person is alive and uh the and one of the scientists like, "Well, time is not a local variable." And then he's like, it's so funny. He's like, "Let me let me say it slow so you PhDs can understand, right?" And and then he takes a a chair and destroys a monitor and he's like this monitor is now dead. It is not in a superp position of different entropy in such >> and that's Einstein. >> That's a it's such a classic scene and it's a great movie. It is really good >> and it touches on some of these subjects maybe in some ways great and in some ways not so great but it it it
15:32gives a real lived human experience to these theoretical questions in a way that you could try to kind of visualize. >> Yeah. And and honestly I was Denzel Washington before I just sort of you know succumbed to my fate and was like okay just shut up and calculate you know but when you're first learning it everyone is Denzel Washington. What are you talking about? Right. Um so effectively under local realism any correlation that's observed between Alice and Bob have to do with some kind of hidden variable. This is the famous EPR Einstein Pedolski Rosen paper that Einstein published in 1935 and he showed that you know if you have some kind of
16:14local hidden variable then you can perhaps account for the you know it could kind of make sense right and for the longest time it was like okay fine whatever the local hidden variable takes place of the wave function collapsing during observation. >> Yeah. Yeah. It's like there's something that's saved. There's like there's like a saved attribute in the two particles that then we observe on either side. Now, crucially, when we only observe like the spin in one direction, both the classical >> interpretation and the quantum interpretation are the same. >> Fine, >> right? Because we're we're going to observe them in the opposite directions. And so, for the longest time, it was like, oh, this is just like a philosophical argument. Um there's no
16:55way to prove it one way or the other. Who cares? >> Um along comes John Graham Bell. Okay, John Graham Bell has the crucial insight in this particular paper. I mean it's literally called on the Einstein Fidilski Rosen paradox. Um and crucially the affiliation there is University of Wisconsin Madison. So this is the paper for Bell's inequality and it's in America. Um and that's why it's on our uh America 250. You know it's like it hey that one year that one year was everything. Um, so he realizes that we can actually expand the Alice and Bob experiment to give Alice and Bob a choice.
17:36Instead of them only observing a single um a single direction, right, we can maybe have a filter where they they can observe the spin in the in the Z direction up and down or in the X direction sideways. Okay. So, like when the when when the light particle comes in, I can adjust my filter, my polarizer or whatever to to say, okay, what is the spin in the X direction? What is the spin in the in the Z direction? Right now, I've got two choices. Alice has the same choice and Bob has the same choice. And Alice is going to observe up and down in Z if she chose Z or up and down in X if she chose X. And similarly, Bob has two choices as well. Now, >> now we sort of have this matrix of
18:17options based based on >> Yes. Now we have a matrix of options and now we can actually disentangle is there a hidden variable or is the quantum mechanics doing crazy nonsense. Okay, >> Bell shows that in the local realism world Einstein's world >> the joint conditional probability distributions of all of these outcomes like the probability distribution of of Alice observing this way given that and Bob observing this way given his choice. it can factor out into two independent components that are local. Okay, if there's a hidden variable, I can factor it out into like this particle and Bob
18:59and that particle in Alice. Okay, >> on the other hand, quantum mechanics predicts that there is going to be certain settings where the correlation is going to exceed that bound. >> If you could factor, the correlation can only go up a certain amount. M >> but for certain angles >> the correlation is actually going to exceed. So now you've got a way to prove one way or the other is there a hidden variable or not. Okay. John Clauser very famously did this at Berkeley another one in our America 250 timeline. Um and he showed that in fact there's a
From How Quantum Computing Actually Works (Part 1)
Part I of our quantum computing deep dive traces the field from Bell and Feynman to Deutsch and Shor—and explains what quantum computers actually do differently from classical machines.