Bell's Experiment demonstrates the phenomenon of quantum entanglement, where two entangled photons are emitted in opposite directions and exhibit correlated spin states. When one photon is measured, the spin of the other photon is instantly determined, regardless of the distance separating them. The excitement surrounding Bell's Theorem arises from its implications for local realism, challenging the classical understanding of physics by showing that quantum mechanics cannot be reconciled with predetermined outcomes. The experiment's results violate Bell inequalities, indicating that quantum mechanics predicts correlations that classical theories cannot explain.
PREREQUISITESStudents, educators, and anyone interested in quantum physics, particularly those seeking to understand the foundational concepts of quantum entanglement and its challenges to classical physics.
Did you try reading it through? The reasoning is actually pretty basic in that post, but if you have questions about any part of it I can explain.MEMoirist said:
That's not all there is to it, if your read my analogy through you'll see why. The idea is that the experimenters have multiple detector settings (they can measure spin along different axes), and they choose randomly which one to use on each trial. On some trials they happen to choose the same setting and they always get identical (or opposite, depending on the type of particle and how it was prepared) results on these trials, but the "weird" part is the statistics they get on the trials where they chose different settings. In terms of my analogy, this is just like how Alice and Bob choose randomly which of the three boxes to scratch on their cards, and on any trial where they both choose the same box they always find the same fruit revealed when they scratch it. But if you just imagine that the two cards were printed with an identical set of hidden fruits behind all three boxes, some simple arithmetic shows that on the trials where they chose different boxes to scratch, you should expect that they'll see the same fruit at least 1/3 of the time; this is known as a type of "Bell inequality". It's violated in my imaginary scenario by the fact that they actually find the same fruit only 1/4 of the time when they scratch different boxes, and similarly in QM if you pick the right combination of three detector angles, you can get it so they have a 100% chance of same (or opposite) result when they pick the same angle, but only 25% chance of same (or opposite) result when they pick different angles.MEMoirist said:
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There are many different types of Bell-style experiments, I'm not that familiar with the specifics of most so I haven't seen one with a "pion splitter" or a "photon interrupter", can you link to whatever you're talking about?MEMoirist said:
OK, but if I can make a request, if you have trouble understanding any sentence or idea could you please quote the ones that you don't understand and ask me to elaborate, rather than just asking me to start over from the beginning?MEMoirist said:
Why not start by trying to just visualizing the analogy on its own, without trying to understand for now how it connects to a Bell experiment? Just imagine the lotto cards sent to Alice and Bob at different locations, forget what they might stand for in terms of particles. It sounds like you're just shutting down without trying to follow it, because it isn't quite the sort of explanation you had in mind. But trust me, if you take the time to understand the analogy on its own, it really will make understanding the Bell experiment much easier.MEMoirist said:
Sorry about that, I should have mentioned that "QM" is the common abbreviation for "Quantum mechanics". That's the only acronym I used, but of the others DrChinese mentioned, EPR stands for a thought-experiment about entanglement that Einstein, Podolsky and Rosen came up with. In that paper they were trying to argue for "hidden variables" to explain the correlations in quantum entanglement. What Bell did was to show that even a hidden variables theory can't explain these correlations, as long as you assume that the particles can't influence one another faster than light (by the way "FTL" is also a common acronym used for faster-than-light). It's not that important that you know about the EPR paper though, it's just part of the history. As for cos^2, that's just a mathematical term, it stands for the square of the cosine of an angle. This term appears in the equation for the probability both experimenters will get the same result when they set their detectors to different angles, but you don't really need to know the details to start with.MEMoirist said:Also, if you could take the time to use words rather than acronyms, it would be helpful. I’m only in fifth grade, remember. Terms like QM, EPR, cos/\2 left right for light are WAY beyond me, but I believe you can explain this to me without them. You’re so close. We’re even entangled
MEMoirist said:If you could put your answers into shorter sentences and shorter paragraphs, it would be easier to understand. And if you could avoid mixing metaphors (cherries/lemons=+/-) it would be easier to visualize. Also, if you could take the time to use words rather than acronyms, it would be helpful. I’m only in fifth grade, remember. Terms like QM, EPR, cos/\2 left right for light are WAY beyond me, but I believe you can explain this to me without them. You’re so close. We’re even entangled
A mirror doesn't split a single photon into a pair of entangled photons, to do that you need something like spontaneous parametric down-conversion.MEMoirist said:
Why 55%? I guess from your next comment you are talking about what would be predicted by a theory that obeyed local realism, not what is predicted by quantum physics. If so, probably you're talking about the local realist prediction that over the course of many trials, the frequency of getting the same color should be greater than or equal to 5/9, which is 55.555... %. But do you understand the reason for this prediction? This is really the most important part if you want to understand Bell's theorem. It has to do with the idea that, under local realism, we should expect that each photon just had an identical set of three predetermined responses to the three settings A,B,C. Again it's equivalent to the idea in my lotto card analogy that each card had an identical set of hidden fruits under each box (if you prefer, we could say that under each box is either a green patch or a red patch, to make the connection to the quantum experiment more clear).MEMoirist said:
Yeah, the idea is that you get a number smaller than the minimum predicted under local realism. It could be 50% or it could be something else, would depend on the exact details of the experiment. You didn't explain what's inside the "interceptor box" and I don't think there's any standard piece of lab equipment that goes by that name, I would imagine that inside the box is supposed to be something like a polarizer that has a certain chance of allowing the photon to pass through (so it goes towards a detector which causes the green light to come on) and a certain chance of reflecting the photon at some other angle (so it goes towards a different detector which causes the red light to come on). In that case, the probability that the two boxes will show the same color depends on the specific choice of angles for the polarizers in settings A, B, and C.MEMoirist said:
No, nothing to do with keeping a balance, it could have been 53% or 37% depending on the angles of the polarizers in the three settings A, B, C. The only thing you really need to know is that in quantum physics it can be less than the local realist prediction of 5/9 = 55.555...%MEMoirist said:
Yes, all of these would be ways of explaining how the photons managed to create those strange statistics...although I don't quite understand that very last part where you say "a common moment of now connects all particles, making the universe itself the local reality". By the way there is one other solution you didn't mention, which is that it might be that when each photon reaches the detector, the detector (and the experimenter watching it) splits into multiple parallel versions, like parallel universes. In this case until there has been time for the two experimenters to communicate (using a signal moving at the speed of light or slower) it isn't necessary to decide which parallel copy of the left-hand experimenter is part of the same "universe" as which parallel copy of the right-hand experimenter. So in a way this scenario does allow you to preserve locality, at the expense of the belief that there is a unique reality about what happened with each measurement (so it could be said to violate the "realism" part of "local realism"). This is basically the type of solution preferred by those who advocate the many-worlds interpretation of quantum mechanics, you can read my post [post=1647627]here[/post] for some more info on how this interpretation is argued to preserve locality.MEMoirist said:
There are a lot of claims to show psychic phenomena like this but they never seem to hold up under further scrutiny, and this isn't something that would be possible according to any mainstream interpretation of quantum mechanics.MEMoirist said:
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Actually, pi mesons are a different type of particle from photons.MEMoirist said:
You're getting awfully defensive, I wasn't trying to criticize you or tell you what you could or couldn't do in a science project, I was just pointing out that this part wasn't accurate because I thought you might like to know. Aren't you posting here because you want feedback on whether what you say is right or not? If you want it to be simple but don't want it to be inaccurate, you could just say something like "there's a kind of crystal that can split one photon into two identical photons".MEMoirist said:
Again I wasn't criticizing, I genuinely wasn't sure why you said 55%. Then it occurred to me that maybe you were talking about one particular way of stating a Bell inequality, in which the probability of getting the same result over all trials is greater than or equal to 5/9. I was more used to seeing it stated in terms of the probability for getting the same result on only those trials where they picked different settings (leaving aside the trials where they picked the same settings, where there's a 100% chance of same result). In that case the probability is greater than or equal to 1/3, so that's the number I was more used to seeing. Again not a criticism or saying you should do it different, just explaining why I wasn't sure initially where you had gotten that number, and double-checking to make sure my guess about where you got it was right.MEMoirist said:
I didn't really say that, I just asked if you understood how they arrived at the 55% figure, and said that this is "the most important part if you want to understand Bell's theorem". If you did understand you could just say "yes, I already understand where that number comes from".MEMoirist said:
I did try to explain it, I said "It has to do with the idea that, under local realism, we should expect that each photon just had an identical set of three predetermined responses to the three settings A,B,C." If you have trouble understanding what I mean by "predetermined responses", then just ask (it has to do with the idea that there are "hidden variables" that determine how the photon will behave...again it's easier to understand with an analogy, like the hidden fruits behind the three boxes of the lotto card)MEMoirist said:
I can't help you to "get it" if you don't tell me specifically what you don't get about it, that's why I asked before "if I can make a request, if you have trouble understanding any sentence or idea could you please quote the ones that you don't understand and ask me to elaborate, rather than just asking me to start over from the beginning?" If you want to try to understand, then just read through and copy and paste the first sentence you can't follow in the explanation, then I'll explain in more detail and we can continue from there. But if the issue is that you just don't want to put the effort to try to follow it, then I can't help you.MEMoirist said:
Same way you'd get it to produce the result of 50%, by picking the right combination of angles for the polarizers in settings A, B, C. I don't actually know what the minimum possible fraction is since I haven't checked the math on that, but certainly it would be possible in quantum physics to get results larger than 50% but still smaller than 55%.MEMoirist said:
Then you can just say something like "in quantum physics it's possible to design an experiment where you get the same result less than 55% of the time, for example it might be 50%." That way you don't have to go into details, or suggest that 50% is the unique correct answer in quantum physics.MEMoirist said:
OK, if I rewrite the whole thing with shorter sentences, will you promise to actually look through it carefully and tell me the first sentence you don't understand, like I asked? I don't want to rewrite the whole thing and just have you give another general dismissive reaction.MEMoirist said:
Again you're being really defensive, I never suggested I thought you were dumb, and if you are in 5th grade your writing is more advanced than most that age (I didn't realize you were saying you were literally a 5th grader before, maybe in part because your writing seemed too sophisticated, I thought you were just asking us to imagine you as a 5th grader as a way of making sure we kept our explanations simple). The post I linked to was mostly just meant to give references to physics papers in case you didn't trust what I was saying about the many worlds-interpretation. If you're looking for more of a conceptual explanation for how the many-worlds interpretation explains these results, I can go into that too once we've cleared up the lotto card analogy. But again, only if you're interested.MEMoirist said:
Actually it's a common confusion that human consciousness is relevant to the two-slit experiment (don't feel bad because many articles about it give this impression). Even if you just had a machine making measurements at the slits, and no human ever looked at what the machine had recorded, this would still destroy the wave pattern on the screen behind the slits. In fact if you're sending a particle with electric charge through the slits, like an electron, then you have to do it in a vacuum because if the electron interacts with air molecules as it travels, even that works the same way as an "observation" and destroys the wave pattern on the screen.MEMoirist said:
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