I've known about the theory for a while but for some reason I found myself desperately wanting to properly understand the underlying logic because our fundamental understanding of reality hinges on this proof. So thank god for this video because I finally get it.
Well good that Bendy understood it. I did not understand it at all and so I watched it almost ten times to find out why I did not under stand it. The crucial point is at minute 15:30 where suddenly the experiment done was changed. Before, it was clear that A and B choose detector settings 1,2 and 3. So this should result in 9 different situations, because A can choose settings 1..3 and B likewise. 3x3 is 9 different situations. But now you switch to results being same or different for settings 1..3. When you say 1 is same, what does it mean? Is this the polarizer setting for A or for B or both? If its only A, then what is the setting for B? That's the confusing point.
I see a big part of your problem. It is not a 3*3 Combination Matrix. It is a 2*3 Permutation Matrix, where on one side you have either it did or did not pass through the Polarizer (Yes No) and on the other side you have 3 Polarizers each set at different angles (1 2 3). If you list out all the possible Permutations you get a total of 8: YYY (1) YYN (2) YNN (3) NNN (4) NNY (5) NYY (6) NYN (7) YNY (8) There are no others. Also, notice (1) and (4) are statistically meaningless since either the photon will go through all 3 (1) or it will go through none (4). That leaves 6 outcomes that are of interest. But this table is meaningless by itself. We need to extrapolate another table that allows us to conclude the probabilities that yield a value of 33% To do that we need to remind ourselves of the actual experiment. Alice and Bob each receive one of a pair of matched photons that each have the same polarity. Alice and Bob will each choose a Polarizer at random (1 2 or 3) and then see if their photon goes through it or not. If they randomly choose polarizers that not from permutations (1) or (4) then we can see that 1/3rd of the time they will get the same results. eg 1/3rd of the time the photon will go through for both Alice and Bob. The other 2/3rds of the time they will get different results, eg it went through for Alice but not for Bob, or vice versa. This is the heart of Bells Inequality. It means if you run enough tests then 33% of the time Bob and Alice will get the same results if "Hidden Variables" is how the Quantum world works. But that's not what they get. they get the same result only about 25% of the time, which is what Quantum Mechanics predicts in a universe where entangled particles are in a super-position wave of possibilities right up until the moment you detect them (eg did it go through or didn't it). If you did this same experiment with pairs of gloves, which are left or right handed right from the start, Bells Inequality is not violated. This means we live in a fucked up universe where very small things don't seem to follow common sense.
ps. To be explicit about the value of 1/3 lets consider permutation (2) YYN. There are 3 polarizers, 1 and 2 will let the photon pass through and the 3rd one will not. Alice and Bob must randomly pick one of the 3. If they pick the same one, then the result of the test will be meaningless, but if they pick different ones, then it will be useful. The only combinations that matter are 1 and 2 (YY) 1 and 3 (YN) 2 and 3 (YN). From this list of 3 possibilities 1 of them will yield the same result (YY) and the other two will yield different results (YN). Hence we get a value of 1/3 or 33%. This holds true for all the other permutations except (1) and (4).
i had been searching explanation how we can devise experiment (The Bell's inequality) to prove argument between Einstein and Bohr. Tried most-viewed on TH-cam still hard to grasp the idea. Until i found this (very underrated one - too few viewers). It's very clear and comprehensible. Thanks for your effort. Keep it up! God bless you!
Hello Sir, Thank you so much for this explanation. I have searched a lot of sources but no one has explained it in the concise and clear manner that you have. I felt like the conclusion was absolutely a natural consequence of your amazingly well laid arguments. You are a great teacher. Thank you for igniting more curiosity in me about physics and the strange nature of quantum particles. Keep doing your amazing work sir!!!
Thank you so much. I have been trying to understand Bell's Inequality for awhile outside of a formal academic setting). This is by far the best explanation especially for a non-scientist! I appreciate you!
2022 here... and this is finally the one video that lets me understand what this year's Nobel prize was all about. DrPhysicsA has always been the best. Brought me through a third of my exams as well.
Bells inequality was explained very well. The experiment was explained very well. What was lacking was showing clearly how the table of results can be mapped onto the 3 sets of Bells inequality. I basically am struggling to understand where A not B and B not C etc is in the table of results because none of that was mentioned in the end. Apart from that, it did help me to understand some of the issues.
Very Nice Video. Although there were some "bumps" on the road, still it was very clear. The best one I found on the web to explain well Bell's inequality. Thanks.
I think you have it right. What I was trying to say was that altho Bob can obviously make a measurement he wont get a conclusive result if he measures the x component of the spin after Alice has measured the y component of the spin of the entangled particle.
I shall do another video on this shortly during the series on quantum mechanics concepts. In essence, Bob can certainly get a result from such a measurement that since the entangled state of the two spins has been affected by Alice's measurement, Bob's result is not a true result that he would have got if Alice had not made her measurement first.
Hi there. I am big fan of the way you deliver (convey) the message. But this time, I felt as if you had to give a try, indeed. It is not your fault of course. Things here start to become unstable, we may all more or less guess, so it is not your fault at all. Would you like to have a look at my Open Letter where I express question as for QM convincibility? Perhaps it will provide you some ideas. Thanx!
There have been many years since that video was out and many other TH-camrs have made elegant videos about the Bell's inequality but this is still the one that helps you understand the whole idea more clearly and in depth. That is an unusual phenomenon by itself in the TH-cam world.
Thanks for making more clear what Bell's Theorem is all about. I've been struggling to understand what this is about for some time. Even though this is not a rigorous formalized presentation, I now can try to take on the more technical discussions with much more ease. Thank you once again.
I think I understand it now. For any *one* of the eight decision schemes (hidden variable) of the photon pair, the chance of (A and B) getting the same outcome is at least 1/3, since 6 of those schemes give a chance of 1/3 and the other 2 give a chance of 1. I was calculating the probability over *all* the combinations, which is the average (1/3 * 6 + 1 * 2)/8 = 1/2. Thanks.
Brilliant- this simple analysis cuts through all the other confusing analogies and I FINALLY understand it! (Although, of course, I don't understand the true, quantum nature of those darned photons!)
It is pairs of photons that are entangled rather than beams. But if photon A passes thro a 45deg polariser it would be possible for the entangled photon B to pass thro the horizontal polariser. There's a little more about this in my EPR Paradox video.
But is it a 100% certanty that photon B passes through the horizontal polarizer? Isn't there a fallacy assuming that all 8 scenarios have the same probability? As in if we have same filters then the photn passes 100% of the time. But if it's different filters then probability may not be the same in different combinations. Would that not possibly explain discrepancy between theoretical 1/3 and observed 1/4?
Why do you expect 1/3 of the times to get the same result? Shouldn't it be 1/2? You can account for using the same polarizer experimentally but getting rid of the case were they go through every polarizer is something you don't know, you cannot possibly take the data and say "this are the same because is rule number 1 or 8", do you?
Rule number 1 and 8 already added. Each one of the 8 rule has 1/8 probability of occurrence. 1 and 8 rule has 100% probability of same result. From 2 to 7 there is 1/3 probability of same result. So, total probability of same result is 1/8 + (1/8)(1/3) + (1/8)(1/3) + (1/8)(1/3) + (1/8)(1/3) + (1/8)(1/3) + (1/8)(1/3) + 1/8 for rule number 1 to 8 respectively. So it would be 1/8 + 1/4 + 1/8. And thus 0.37. 0.37 is greater than 0.33 and that is what the rule says. Probability of same result >= 1/3. Hope this helps
Sina Gohary For each trial, no matter what the combination of polarizer is, the 2 photons share one set of hidden variables. For each combination of polarizer there are 4 sets of variables that can make a SAME observation, that makes a probability of 0.5, for each trial of the experiment. Based on this, We can forget about the probability for having each combination. So the whole statistical probability of SAME observations is 0.5. Yet In real life, the number of trials is limited, which means if the experiment never encounters hidden variables 1or8, (the number of SAME observations /the number of all observations) will be something like 2/6. Since The observed probability is less than 1/3, the hidden rules are already proved not likely to exist. I think DR might mean something like that. Please reply if you find anything suspicious.
I don't think the experiment assumes that the hidden variables are random. But if they were not, then one would expect to find some consistency of results
It starts _off_ as a good explanation, then becomes long-winded, errors creep in, they are corrected... And that's fine. But as the comments indicate, there is either something systematically wrong with the thing, or the S/N is getting incomprensibly low.
OMG! Thank you soooo much! I watched so many videos and couldn't understand why the hidden information proposition were not the right one. Such a good video!
I really enjoyed the video which explained the issues very clearly. There was one point towards the end of the video where the two possibilities were discussed and one of those possibilities was that the two particles are in constant communication. There is a third possibility, namely that the two particles must be treated as a single system extended over the space separation and that it is at the point of measurement of one particle that the whole system is affected, thus changing the possible outcomes of the measurement of the other particle. This third possibility explains the results and does not violate the rule that wave transmission in spacetime is limited to the speed of light. It does mean that a measurement of an entangled system can result in instantaneous effects over a distance but this cannot be used to transmit useful information faster than light. Richard
@@simonruszczak5563 Hi Simon. I don't know about the electric universe theories but the observations of entangled systems suggest that the requirement would be for instantaneous communication. This is a more difficult requirement than 'faster than light'. This is why I prefer to think of the measurement of the entangled system as being the cause of the change of state of the entire distributed system. Actually the idea of an instantaneous effect acting over a distance requires the specification of the frame of reference (Ref: SR/GR) in which the instantaneous effect takes place and this frame of reference is the CMB rest frame.
Thanks Doc - easily the clearest explanation on the web - and I have spent an afternoon searching - now I might go back to Prof Susskind (who was not so clear)
which is why the experiment is often described as measuring the spin of, say, an electron along the y axis. If one electron has spin up the other will be spin down.
It is generally accepted that Bell's inequality coupled with experimental observations provide no explanation for how there could be hidden variables contained within the DNA of the particles produced. It doesn't mean that there is no theory that could account for this only that we haven't found one yet. Indeed, our current understanding of quantum mechanics suggests that we just have to accept that the quantum world is different.
Has it been experimentally demonstrated/determined that, for an individual photon, the three possible polarization states that you chose for example each have equal probability of being measured? In other words, are individually emitted photons statistically weighted towards having a particular direction of polarization or another? Is that important to know for this example you have given? With that said, is it correct to say that in QM experiments and theory, that a single quantum element will have a different probability of producing a particular measurement than it will were it to be measured as part of a conjugate pair whose partner has been measured?
Yes I think that's the whole point. An individual one would display the component at that angle. Classically we actually get the component as a number between 1 and -1. Quantum particles instead show up as as probability of a qubit as in 1 or -1 discretely distributed per the component. Thus take this new state where the previous measurement outcome is erased. The recommended particle in an entangled pair shows correlation similarly as with measuring a particle twice, yes? Its worth mentioning of course that to infer a probability many repeated tests must be done the more the better. So it could never be done on a single particle much as without examining a coin used for a coin flip we would just have to flip the coin many times to get a probability. Although a coin could be examined and determined to be of a shape and weight distribution we can infer in many classical systems their pseudo random nature we cannot look at featureless particles in this way
Maybe I'm missing something. Hidden variables theorem should also imply that by definition of entanglement, possibilities for both particles are not independant - 2 and 3 should be mutually exclusive. S probability should be zero for combinations (2,3) and (3,2). What do experiments show?
Doesn't matter if they are possible, what he wrote down are all 8 classical possible options and if you say options where polarizers 2 and 3 have same result are not possible this just means options 1, 4, 5 and 8 are not possible, but the remaining options 2, 3, 6 and 7 still have a probability of 1/3.
Great video as all of yours are. I think rather than saying that Bell's Theorem shows that quantum measurements cannot be explained by hidden variables, it would be slightly more accurate to say that Bell shows that quantum results cannot be reproduced if you impose (as EPR proposed) a requirement of locality. Bell acknowledges that Bohm managed to construct a hidden variable theory but points out that it is "grossly nonlocal."
Sorry about the confusion. I should have used letters instead of numbers. I dont use them as population values. I use the numbers as a shorthand for the number of a particular category within each of the numbered sections
A brave attempt. Another good explanation can be found in Brian Greens book: Fabric Of The Cosmos. One questions what percentage of results differ from predicted results, further on what distance and expected time variables, factoring in the limits of accurate measurement and possibilities to improve on this (at least theoretically!)
What a wonderful explanation. Small side note: only local hidden variable theories are ruled out, so Pilot Wave Theory (Bohmian mechanics) is not ruled out by this (Bohmian mechanics is a nonlocal hidden variable theory), and John Bell himself actually was a fan of Pilot Wave Theory. Also, an assumption that is made in drawing the conclusion about locality, is that there is no conspiracy (the particles don't somehow know in advance what your (random) measurement orientation is going to be) and no causal effects back in time (or those kinds of things).
Now, why is it that when Alice measures one spin, bob can not measure the spin in the other axis of the other particle? Do we get scrambled data or something?
Nice video! I still have a hard time understanding the Kochen-Specker addition to Bell's theorem. If you take any request for video's I would like to see you explain the KS theorem.
Maybe space is bendable, and are these bends all around, but not perceivable by us. So there could be a 4dimensional bend/tube/wormhole, which keeps both positron and electron at exactly the same place, where they entangled in 4dimensional space, but doesn't in 3dimensional space. So the 2 entangled particles are still one object/form/energy.
2:42 Why Bob cannot measure the spin in x direction? What prevents it and what happens if he tries? Does that imply ftl communication if Alice can encode information measuring the spins of particular particles and Bob can decode it by observing spins of which particles he can measure?
Bob can measure the spin projection in any direction. He will always get a random result, just like Alice. The only difference will be the amount of correlation between the two measurements.
Thank you for the excellent explanation of Bell’s Inequality and how it ostensibly proves that there are no hidden variables-as the EPR Paradox asserts.
Dear Sir, another question, "Does the spin of A change over time, assuming no other external influence act on the two particles? I mean if the initial spin of A is up, sometime later will it change by itself to down?
There are no particles. A spin measurement is an irreversible transfer of angular momentum. Once that angular momentum has been transferred, it can't change anymore. That's the difference between classical physics that allows continuous measurement and quantum mechanics that only allows for a single measurement.
When you say he cannot make a measurement you must say what happens if he tries first. Once you do not the listener is lost and cannot listen after that.
@@rafaelclp The point is that should be explained in the video. The video isn't wrong it is incomplete. The problem is when you know the answer you don't think you have to explain. You don't think you have to explain because the answer is obvious to you but it isn't always obvious to the viewer.
Dear Professor, I'm lost. What is the relationship between the hats/scarves/gloves case and the polarizers case? How can the logic of hats/scarves/gloves violate Bell's inequality that was derived from that logic? Where does the .25 probability for hats/scarves/gloves come from?
the .25 probability cames from this experiment realized. And the relationship is that every kid has at least one of that clothes and every photon or electron will pass through at least one polarizer.
I didn't remember what my comments were about, for I had forgotten the content of the video. Upon readig your explanations, and keeping them in mind, I have watched the video again. It seems to me the video must have been altered, for now it is clear that probability 0.25 comes from an unexplained experiment and that it's never said that clothes violate Bell's inequality. However, the example of the hats/gloves/scarves remains logically unrelated to the case of the photons in the video. Thanks.
I think the problem is in describing the spin of an entangled particle at 2 different locations. The experiment is set up to determine discrete characteristics (spin direction >
Well explained. I watched the first three minutes of another 'explaination' of the same idea which was full of waffle and used a video dispaly. A 1/4 is greater than or equal to a 1/3. Mind bending.
Hi. Thanks for the clear video. When you say Bob can't measure in the x-axis. What do you mean? What would occur if bob and Alice tried to measure x and y spin simultaneously?
I would had that French physicist Alain Aspect was, in 1982, the first to do the actual experiment proving that Bell inequality was violated (Aspect found the 0,25 in the end of the video).
2024 29th of March - the lecture, the English, is very precise n clear. I think it is his native ( England) English that makes the difference. American English is very confusing. Students must need to spend a great deal of efforts to decipher Science n engineering books written by American authors. I discovered this by chance- one day I was reading a physics book from the Oxford’s series without knowing it is Oxford’s n found it’s English was precise, clear n succinct n I turned to the front pages n found out it is from the UK. Many of my good physics books are from the UK.
Great lecture, but I am missing the reasoning for having 0.25 result in the experiment. In another words, what is the quantum mechanics reason for the 0.25 measurement in the experiment?
@@elimarburger1659 I watch it again, and it's clearly the experiment result! so the only conclusion is that the pair of particles seems to"communicate" their states at the time of measurement rather carry the "hidden information". At the bottom line it solves Einstein-Podolsky-Rosen paradox by showing that the particles could not carry the information without breaking bell's inequality.
Hi, thanks for these great videos on physics very much appreciated. Now I've been trying to figure out what entanglement is for some time now & i think I've made some progress so if someone can help me out, just please dont bite my head off :) So, starting with the double slit experiment, a single slit produces random dots as would be expected of particle behavior whereas a double slit produces an interference pattern suggesting wave-like behavior..ok fine. Now, placing a detector at the slits, the interference pattern disappears & QM theory says that the "wave function" collapses as a result of the measurement effectively eliminating the superposed states etc. Now, if we generate a pair of entangled photons, A & B, and measure some property of A along an axis we shall have random results as would be expected, but when we measure its entangled partner we have 100% correlation with A (ie NOT random) implying that measuring photon A, and thereby collapsing its wave-function to a definite state, causes the wave-function of its partner, B, to ALSO collapse presumably instantaneously. According to Bell experiments all local hidden variable theories have been rendered useless, we have Bohmian non-local hidden variable theories which work as a valid interpretation but doesnt really advance our knowledge of QM. Now I have to ask this not because I think its correct but because the fact that im thinking it means theres something im not understanding. Why isnt the process of generating entangled particles the problem? I mean, during the process they simply acquire correlated polarization or whatever other property, why does there need to be this mysterious hidden variable or "pilot wave" or faster-than-light communication? Is there some experiments that have been performed that rule this possibility out even if we couldnt observe this process directly to tell for sure? Are there natural processes that produce entanglement? How do we know for sure that the entangled pair have not already experienced state-collapse as a result of whatever produces entanglement?
What you're asking about IS the idea of hidden variables. If the particles acquire definite correlated states at creation this means that there are hidden variables that define these states at the creation of the entangled pair. Bell's inequality experiments prove mathematically that this can't be the case however, so there must be something else at play here. Either instant and faster-than-light communication, or some other explanation where Bell's inequality can be violated.
@@Patatmetmayo Bell's inequality confronts a linear probability distribution with a non linear one. It's frankly obvious that polarization experiments will violate the inequality, because the polarization follow's Malus' law, which is a cosine law (i.e. non-linear). It's just wrong to think about hidden variables as a predetermined outcome for ALL polarization angles. Also notice how Bell's derivation is purely a logical statement and has fundamentally nothing to do with quantum effects. Let's say our photons are created entangled with polarization on the z axis. Every measurement along that axis (detector A) will pass. Now put the detectors at an angle, like 22.5°: every photon will pass test A, but test B has a cos^2(22.5) chance to pass, that is 85%. If detector B is instead at 45°, it will have a 50% chance. See how the "hidden variable" refers uniquely to detector A, and how the outcome of the other measurement is not independent of what we measure at A. But there's no information exchanged between the two photons, each already had all it needed to produce experimental results, namely polarization aligned with A. The fundamental problem is that we think of the light going into the detectors as single indivisible packets, but that is not true: what is quantized is the EXCHANGE OF ENERGY to matter from the field. A photon is effectively one only at the moment of detection, before it's just a normal EM wave, subject to Malus' law.
How is it possible to possessing the hidden property going through polarizer1 and polarizer3 simultaneously? Because if a Photon is polarized 45, it is certainty will be absorbed at -45.
I can count twelve 'S' from twenty four possible {S, D}, therefore the probability of obtaining an 'S', if all the combinations (1 to 8) occur with the same frequency, should be exactly 1/2. I suppose that as we cannot establish the probability of the individual combinations, we have take 1/3 as the lower limit. Thanks for the clear presentation.
I see the main error here is the assumption that there are two photons. There is just one single phenomena which propagates outward from the source like a pebble dropped in a pond, but only dual-beamed instead of circular wavefront. The measurement processes doesn't send information faster than light, but there are actually precursor ripples of the measurement which start way before the actual declared measurement begins. It's just classical wave mechanics and no mystery. It just requires ample noise. In the low noise approximation without precursors, it appears to be "mysterious". Also, please send me the specs on a polarizer that lets a photon "pass though or not". All polarizers I've encountered will absorb the photon via interaction with electrons and re-radiate a new one or not.
Thanks for these truly intelligent lectures, Phil! I love your knowledge but I don't understand the vast majority of your information! I wonder, just out of curiosity, if you know also Goethe's 'Theory of Colours', I think I can grasp that. Although sometimes it seems my mind is so slow I only understand in science Plato's 'Wax Tablet Hypothesis' and Aristotle's 'Theory of Everything'. Lol!
I don't really get the first part about simultaneously measuring "spin in both X and z axes". Afaict electrons only have one spin direction, and if you try to measure it with magnets you have a certain chance of getting that spin or the exact opposite, depending on the previous spin. I.e. measuring with magnets reorientates the electron. In fact spin is just an emergent property of electrons in the presence of measurement apparatus
Thanks for this clear explanation. I'm not a physicist but love it. My question is as follows. According to the experiment setting, It seems to me that ruling out the existence of any hidden variables is based on the entangled particles, i.e., quantum entanglement is taken for granted. What would happen if the quantum entanglement itself does not always happen? Could the entanglement phenomenon be also probabilistic?
Not unless you are prepared to throw out conservation of angular momentum and many other conservation laws. One example of entanglement is the consequence of a particle with no spin decaying into 2 particles with spin, such as an electron and a positron. Conservation of angular momentum requires that they have opposite spin. Yet, uncertainty requires that each one's spin is all possibilities until it is measured. Only then does the wave function collapse. Entanglement means that it collapses for both particles at the same time. Put another way, these properties are probabilistic until they are measured. The spin of an electron could end up either way depending on when it is measured. It didn't start out with an up spin and it's partner a down spin. Measuring it makes the spin definite and makes its partner's spin definite at the same time.
I have a question! Please someone who understands this - answer , Im so curious. In the video we assume that the photons will have EQUAL probability (12,5%) of any of the 8 possible combinations . Why is that? Why cant the porbability of the combinations 1-8 differ? Why do we assume this? Could perhaps the experiment be faulty so that some angles of polarization were more probable? Or was the experiment conducted with some other particles and spins were measured and it still came out this way?
I understood for the most part though you lost me at the 1/3 part, I understand that's the probability of obtaining a different polarizer, though 1/3 seems like the probability of each individual case, all of them together on the other hand should be 6/8 or 3/4, this while taking in count the ones that are the same, what am I missing?
I think the individual case (1/3) and overall case (3/4) yield the same result because the overall case is accounting for every combination of hidden variables while in an actual experiment you would perform it once with 3 polarizers in 3 different pairs with any hidden variable combination governing that one particular experiment
In the simple case of recovering light from extra filters, I have a feeling these photons aren't blocked, but phase shifted to oppose its orthogonally polarized counterparts. The fact that you can recover the output with more filters is exactly what is seen in series resonant circuits when reactance pushes the voltage and current out of phase and then realigns it to eliminate the destructive interference of the opposing waveforms. Due to quantum wave effects, polarizing lenses probably act like the quantum equivalent of reactance rather than resistance.
I don't see why there is so much resistance to accepting nonlocality in physics at the very smallest of scales. It explains the experimental results (such as double-slit and entanglement) without contradicting our intuition of locality at larger scales, where decoherence rules. We can even, in special cases, see coherence at large scales: superconductivity, superfluidity, Meissner Effect.
Sir, you really keep on posting high quality content, even though you might have lost yourself a bit through the explanation it still remains THE BEST I´ve seen so far, and believe me, since the nobel price has been awarded, I´ve checked many... Thank you very much, keep up the great work you´re doing!
Seems to me the trials are not testing spin direction [which is the 50/50 proposition,] but instead identical polarization [which apparently should always be the same]? Also, in many cases [when Alice and Bob pick different polarizers,] the trial is not measuring spin in the same plane, which I thought was a condition for the spins of entangled particles to always be found to be opposite?
Sorry if these questions where answered but I just misunderstood them: 1:54 Does Alice shouting the result to Bob have anything to do with Bob's readings? If Bob didn't know that Alice had even measured the z direction on her side, would he still be unable to measure the x direction? In the setts of children example, he says "A not B + B not C ≥ A not C". This is obvious if A = B ≥ C, but not true if A + B < C. Are we starting with the assumption that there are equal numbers of children wearing hats, gloves and scarves. Because he does not make that distinction.
The inequality refers to the number of elements in the sets. In your example for instance A={4,2,1,3} has four elements, B={b,w,r} has three elements and C={on,off} has two elements. The set "A not B" is the set of elements that are in A but that aren't in B which in this case equals the set A since A and B have no elements in common. Letting "#S" be the number of elements of set S, then #(A not B) = #A =4, #(B not C) = #B = 3 and #(A not C) = #A = 4, which since 4+3 > 4 matches the inequality.
One of the rare, if not the only, good and clear explanation of Bell's Inequality
Dont forget concise!
*Who else is here in 2020 and still finds the video the very best.*
I am.
I've known about the theory for a while but for some reason I found myself desperately wanting to properly understand the underlying logic because our fundamental understanding of reality hinges on this proof. So thank god for this video because I finally get it.
Well good that Bendy understood it. I did not understand it at all and so I watched it almost ten times to find out why I did not under stand it. The crucial point is at minute 15:30 where suddenly the experiment done was changed. Before, it was clear that A and B choose detector settings 1,2 and 3. So this should result in 9 different situations, because A can choose settings 1..3 and B likewise. 3x3 is 9 different situations. But now you switch to results being same or different for settings 1..3. When you say 1 is same, what does it mean? Is this the polarizer setting for A or for B or both? If its only A, then what is the setting for B? That's the confusing point.
I see a big part of your problem. It is not a 3*3 Combination Matrix. It is a 2*3 Permutation Matrix, where on one side you have either it did or did not pass through the Polarizer (Yes No) and on the other side you have 3 Polarizers each set at different angles (1 2 3). If you list out all the possible Permutations you get a total of 8:
YYY (1)
YYN (2)
YNN (3)
NNN (4)
NNY (5)
NYY (6)
NYN (7)
YNY (8)
There are no others. Also, notice (1) and (4) are statistically meaningless since either the photon will go through all 3 (1) or it will go through none (4). That leaves 6 outcomes that are of interest.
But this table is meaningless by itself. We need to extrapolate another table that allows us to conclude the probabilities that yield a value of 33%
To do that we need to remind ourselves of the actual experiment. Alice and Bob each receive one of a pair of matched photons that each have the same polarity. Alice and Bob will each choose a Polarizer at random (1 2 or 3) and then see if their photon goes through it or not. If they randomly choose polarizers that not from permutations (1) or (4) then we can see that 1/3rd of the time they will get the same results. eg 1/3rd of the time the photon will go through for both Alice and Bob. The other 2/3rds of the time they will get different results, eg it went through for Alice but not for Bob, or vice versa.
This is the heart of Bells Inequality. It means if you run enough tests then 33% of the time Bob and Alice will get the same results if "Hidden Variables" is how the Quantum world works.
But that's not what they get. they get the same result only about 25% of the time, which is what Quantum Mechanics predicts in a universe where entangled particles are in a super-position wave of possibilities right up until the moment you detect them (eg did it go through or didn't it).
If you did this same experiment with pairs of gloves, which are left or right handed right from the start, Bells Inequality is not violated. This means we live in a fucked up universe where very small things don't seem to follow common sense.
ps. To be explicit about the value of 1/3 lets consider permutation (2) YYN. There are 3 polarizers, 1 and 2 will let the photon pass through and the 3rd one will not. Alice and Bob must randomly pick one of the 3.
If they pick the same one, then the result of the test will be meaningless, but if they pick different ones, then it will be useful. The only combinations that matter are 1 and 2 (YY) 1 and 3 (YN) 2 and 3 (YN).
From this list of 3 possibilities 1 of them will yield the same result (YY) and the other two will yield different results (YN). Hence we get a value of 1/3 or 33%. This holds true for all the other permutations except (1) and (4).
The only explanation that allowed me to finally understand in what way Bell's inequality enlightened modern physics. Real gratitude.
i had been searching explanation how we can devise experiment (The Bell's inequality) to prove argument between Einstein and Bohr. Tried most-viewed on TH-cam still hard to grasp the idea. Until i found this (very underrated one - too few viewers). It's very clear and comprehensible. Thanks for your effort. Keep it up! God bless you!
Hello Sir, Thank you so much for this explanation. I have searched a lot of sources but no one has explained it in the concise and clear manner that you have. I felt like the conclusion was absolutely a natural consequence of your amazingly well laid arguments. You are a great teacher. Thank you for igniting more curiosity in me about physics and the strange nature of quantum particles. Keep doing your amazing work sir!!!
Thank you so much. I have been trying to understand Bell's Inequality for awhile outside of a formal academic setting). This is by far the best explanation especially for a non-scientist! I appreciate you!
Did this explanation ring a BELL then?
@@happylittlemonk cling
You have to be kidding? Clear as Mississippi mud!
2022 here... and this is finally the one video that lets me understand what this year's Nobel prize was all about.
DrPhysicsA has always been the best. Brought me through a third of my exams as well.
A big thank you...i was struggling to grasp bell inequality and its role to eliminate the hidden variables theory. Beautiful and lucid explanation👍
The polarisers in my example should be 60 or 120 degrees apart.
This is an important correction!!
Bells inequality was explained very well. The experiment was explained very well. What was lacking was showing clearly how the table of results can be mapped onto the 3 sets of Bells inequality. I basically am struggling to understand where A not B and B not C etc is in the table of results because none of that was mentioned in the end. Apart from that, it did help me to understand some of the issues.
Watched this video a half dozen times over the last few years and I still don’t get it, but I’m coming along! Definitely the best explanation around.
Very Nice Video. Although there were some "bumps" on the road, still it was very clear. The best one I found on the web to explain well Bell's inequality. Thanks.
I think you have it right. What I was trying to say was that altho Bob can obviously make a measurement he wont get a conclusive result if he measures the x component of the spin after Alice has measured the y component of the spin of the entangled particle.
Fantastic lecture. Great, easy to understand explanation...
I've watched so many videos trying to explain this. None made sense and I got lost. This was clear and easy to follow.
I shall do another video on this shortly during the series on quantum mechanics concepts. In essence, Bob can certainly get a result from such a measurement that since the entangled state of the two spins has been affected by Alice's measurement, Bob's result is not a true result that he would have got if Alice had not made her measurement first.
Hi there. I am big fan of the way you deliver (convey) the message. But this time, I felt as if you had to give a try, indeed. It is not your fault of course. Things here start to become unstable, we may all more or less guess, so it is not your fault at all. Would you like to have a look at my Open Letter where I express question as for QM convincibility? Perhaps it will provide you some ideas. Thanx!
Well, I pressed 'like'. Could not do otherwise.
Zero graphics... just a paper and a pen; yet I have understood it better than I did on any fancy channels..
Thankyou Sir 🙏🏼
There have been many years since that video was out and many other TH-camrs have made elegant videos about the Bell's inequality but this is still the one that helps you understand the whole idea more clearly and in depth. That is an unusual phenomenon by itself in the TH-cam world.
You are best teacher of both maths and Physics :)
Thanks for making more clear what Bell's Theorem is all about. I've been struggling to understand what this is about for some time. Even though this is not a rigorous formalized presentation, I now can try to take on the more technical discussions with much more ease. Thank you once again.
The best concise and clear explanation i have seen of the Bell's inequality...plz make videos again........
Thanks this is a very clear explanation, I think I'm beginning to understand it, must watch again.
I think I understand it now. For any *one* of the eight decision schemes (hidden variable) of the photon pair, the chance of (A and B) getting the same outcome is at least 1/3, since 6 of those schemes give a chance of 1/3 and the other 2 give a chance of 1. I was calculating the probability over *all* the combinations, which is the average (1/3 * 6 + 1 * 2)/8 = 1/2. Thanks.
I'm a 18 years old guy from Italy. Physics is my passion, and i found this video very clear and understandable.
Thats great, thank you for the upload.
I think this is the best explanation for Bell's theorem
I have a huge grin on my face because I understood! Thank you :)
This was an extremely clear and unambiguous explanation, thank you!
Brilliant- this simple analysis cuts through all the other confusing analogies and I FINALLY understand it! (Although, of course, I don't understand the true, quantum nature of those darned photons!)
I add my thanks to those of others. I've watched many videos on this subject, but this is the only one I've understood.
It is pairs of photons that are entangled rather than beams. But if photon A passes thro a 45deg polariser it would be possible for the entangled photon B to pass thro the horizontal polariser. There's a little more about this in my EPR Paradox video.
But is it a 100% certanty that photon B passes through the horizontal polarizer?
Isn't there a fallacy assuming that all 8 scenarios have the same probability? As in if we have same filters then the photn passes 100% of the time. But if it's different filters then probability may not be the same in different combinations. Would that not possibly explain discrepancy between theoretical 1/3 and observed 1/4?
u r the best sir.. how easily u r describing..
Why do you expect 1/3 of the times to get the same result? Shouldn't it be 1/2? You can account for using the same polarizer experimentally but getting rid of the case were they go through every polarizer is something you don't know, you cannot possibly take the data and say "this are the same because is rule number 1 or 8", do you?
Exactly my thoughts.
Rule number 1 and 8 already added. Each one of the 8 rule has 1/8 probability of occurrence. 1 and 8 rule has 100% probability of same result. From 2 to 7 there is 1/3 probability of same result. So, total probability of same result is 1/8 + (1/8)(1/3) + (1/8)(1/3) + (1/8)(1/3) + (1/8)(1/3) + (1/8)(1/3) + (1/8)(1/3) + 1/8 for rule number 1 to 8 respectively. So it would be 1/8 + 1/4 + 1/8. And thus 0.37. 0.37 is greater than 0.33 and that is what the rule says. Probability of same result >= 1/3. Hope this helps
@@mananpanchal261/8+1/4+1/8 is not 0.37 !
It would be 0.5
Plz some body explain
Sina Gohary For each trial, no matter what the combination of polarizer is, the 2 photons share one set of hidden variables. For each combination of polarizer there are 4 sets of variables that can make a SAME observation, that makes a probability of 0.5, for each trial of the experiment. Based on this, We can forget about the probability for having each combination. So the whole statistical probability of SAME observations is 0.5. Yet In real life, the number of trials is limited, which means if the experiment never encounters hidden variables 1or8, (the number of SAME observations /the number of all observations) will be something like 2/6. Since The observed probability is less than 1/3, the hidden rules are already proved not likely to exist. I think DR might mean something like that. Please reply if you find anything suspicious.
Amazing, so neatly and so argumentative ly you have explained.. A big hug from me.. Thank 🙏 you
I don't think the experiment assumes that the hidden variables are random. But if they were not, then one would expect to find some consistency of results
🫡 very well explained. You sir are indeed a great teacher!
Wow, what an explanation! Thank you very much.
This intro has been THE BEST explanation of the EPR paradox I've watched!! (and I've watched quite a few!!) Thankyou
It starts _off_ as a good explanation, then becomes long-winded, errors creep in, they are corrected...
And that's fine. But as the comments indicate, there is either something systematically wrong with the thing, or the S/N is getting incomprensibly low.
OMG! Thank you soooo much! I watched so many videos and couldn't understand why the hidden information proposition were not the right one. Such a good video!
I really enjoyed the video which explained the issues very clearly. There was one point towards the end of the video where the two possibilities were discussed and one of those possibilities was that the two particles are in constant communication.
There is a third possibility, namely that the two particles must be treated as a single system extended over the space separation and that it is at the point of measurement of one particle that the whole system is affected, thus changing the possible outcomes of the measurement of the other particle.
This third possibility explains the results and does not violate the rule that wave transmission in spacetime is limited to the speed of light. It does mean that a measurement of an entangled system can result in instantaneous effects over a distance but this cannot be used to transmit useful information faster than light.
Richard
See also www.academia.edu/5927513/The_Spacetime_Wave_Theory
Richard
Fourth possibility, the Electric Universe Theory is correct, faster than light communication is possible.
@@simonruszczak5563 Hi Simon. I don't know about the electric universe theories but the observations of entangled systems suggest that the requirement would be for instantaneous communication. This is a more difficult requirement than 'faster than light'. This is why I prefer to think of the measurement of the entangled system as being the cause of the change of state of the entire distributed system. Actually the idea of an instantaneous effect acting over a distance requires the specification of the frame of reference (Ref: SR/GR) in which the instantaneous effect takes place and this frame of reference is the CMB rest frame.
Thanks Doc - easily the clearest explanation on the web - and I have spent an afternoon searching - now I might go back to Prof Susskind (who was not so clear)
Crystal clear explanation. Thank you.
which is why the experiment is often described as measuring the spin of, say, an electron along the y axis. If one electron has spin up the other will be spin down.
It is generally accepted that Bell's inequality coupled with experimental observations provide no explanation for how there could be hidden variables contained within the DNA of the particles produced. It doesn't mean that there is no theory that could account for this only that we haven't found one yet. Indeed, our current understanding of quantum mechanics suggests that we just have to accept that the quantum world is different.
Has it been experimentally demonstrated/determined that, for an individual photon, the three possible polarization states that you chose for example each have equal probability of being measured? In other words, are individually emitted photons statistically weighted towards having a particular direction of polarization or another? Is that important to know for this example you have given? With that said, is it correct to say that in QM experiments and theory, that a single quantum element will have a different probability of producing a particular measurement than it will were it to be measured as part of a conjugate pair whose partner has been measured?
Yes I think that's the whole point. An individual one would display the component at that angle. Classically we actually get the component as a number between 1 and -1. Quantum particles instead show up as as probability of a qubit as in 1 or -1 discretely distributed per the component. Thus take this new state where the previous measurement outcome is erased. The recommended particle in an entangled pair shows correlation similarly as with measuring a particle twice, yes?
Its worth mentioning of course that to infer a probability many repeated tests must be done the more the better. So it could never be done on a single particle much as without examining a coin used for a coin flip we would just have to flip the coin many times to get a probability. Although a coin could be examined and determined to be of a shape and weight distribution we can infer in many classical systems their pseudo random nature we cannot look at featureless particles in this way
Great explanation Sir .....
Bravo. A great explanation even without fancy graphics. Thank you.
Best explaination so far...for years and I am surebfor years to come!. Thankyou!
Maybe I'm missing something. Hidden variables theorem should also imply that by definition of entanglement, possibilities for both particles are not independant - 2 and 3 should be mutually exclusive. S probability should be zero for combinations (2,3) and (3,2). What do experiments show?
Doesn't matter if they are possible, what he wrote down are all 8 classical possible options and if you say options where polarizers 2 and 3 have same result are not possible this just means options 1, 4, 5 and 8 are not possible, but the remaining options 2, 3, 6 and 7 still have a probability of 1/3.
Great explanation 🙂.....A Good Teacher
Great video as all of yours are. I think rather than saying that Bell's Theorem shows that quantum measurements cannot be explained by hidden variables, it would be slightly more accurate to say that Bell shows that quantum results cannot be reproduced if you impose (as EPR proposed) a requirement of locality. Bell acknowledges that Bohm managed to construct a hidden variable theory but points out that it is "grossly nonlocal."
Your video is better than the lecture of prof.Leonard susskin
Sorry about the confusion. I should have used letters instead of numbers. I dont use them as population values. I use the numbers as a shorthand for the number of a particular category within each of the numbered sections
A brave attempt. Another good explanation can be found in Brian Greens book: Fabric Of The Cosmos.
One questions what percentage of results differ from predicted results, further on what distance and expected time variables, factoring in the limits of accurate measurement and possibilities to improve on this (at least theoretically!)
What a wonderful explanation. Small side note: only local hidden variable theories are ruled out, so Pilot Wave Theory (Bohmian mechanics) is not ruled out by this (Bohmian mechanics is a nonlocal hidden variable theory), and John Bell himself actually was a fan of Pilot Wave Theory. Also, an assumption that is made in drawing the conclusion about locality, is that there is no conspiracy (the particles don't somehow know in advance what your (random) measurement orientation is going to be) and no causal effects back in time (or those kinds of things).
Now, why is it that when Alice measures one spin, bob can not measure the spin in the other axis of the other particle? Do we get scrambled data or something?
Nice video! I still have a hard time understanding the Kochen-Specker addition to Bell's theorem. If you take any request for video's I would like to see you explain the KS theorem.
Maybe space is bendable, and are these bends all around, but not perceivable by us.
So there could be a 4dimensional bend/tube/wormhole, which keeps both positron and electron at exactly the same place, where they entangled in 4dimensional space, but doesn't in 3dimensional space. So the 2 entangled particles are still one object/form/energy.
Show me the math.
Be careful. That is how a religion starts.
you basically just stumbled upon ER=EPR (google it)
2:42 Why Bob cannot measure the spin in x direction? What prevents it and what happens if he tries?
Does that imply ftl communication if Alice can encode information measuring the spins of particular particles and Bob can decode it by observing spins of which particles he can measure?
Bob can measure the spin projection in any direction. He will always get a random result, just like Alice. The only difference will be the amount of correlation between the two measurements.
Thank you for the excellent explanation of Bell’s Inequality and how it ostensibly proves that there are no hidden variables-as the EPR Paradox asserts.
Thanks for you effort sir. I am missing one thing. Why do particles have to have same polarisation in pair production process...is this a postulate?
Thank You Dr Physics I was struggling to follow the written description of Bell's Inequality and until your most enlightening video!
Dear Sir, another question, "Does the spin of A change over time, assuming no other external influence act on the two particles? I mean if the initial spin of A is up, sometime later will it change by itself to down?
There are no particles. A spin measurement is an irreversible transfer of angular momentum. Once that angular momentum has been transferred, it can't change anymore. That's the difference between classical physics that allows continuous measurement and quantum mechanics that only allows for a single measurement.
When you say he cannot make a measurement you must say what happens if he tries first. Once you do not the listener is lost and cannot listen after that.
did you find why bob cant male mesurments?
@@uvuvwevwevweonyetenyevweug7849 English isn't your first language. I don't think you understand my point. I do not know what you are saying.
@@TomTom-rh5gk I acttually ansewred to wrong comment 😂 and yes english isnt my first language
@@uvuvwevwevweonyetenyevweug7849 No problem. I do the same thing. Go in peace my friend.
@@rafaelclp The point is that should be explained in the video. The video isn't wrong it is incomplete. The problem is when you know the answer you don't think you have to explain. You don't think you have to explain because the answer is obvious to you but it isn't always obvious to the viewer.
Dear Professor, I'm lost. What is the relationship between the hats/scarves/gloves case and the polarizers case? How can the logic of hats/scarves/gloves violate Bell's inequality that was derived from that logic? Where does the .25 probability for hats/scarves/gloves come from?
the .25 probability cames from this experiment realized.
And the relationship is that every kid has at least one of that clothes and every photon or electron will pass through at least one polarizer.
I didn't remember what my comments were about, for I had forgotten the content of the video. Upon readig your explanations, and keeping them in mind, I have watched the video again. It seems to me the video must have been altered, for now it is clear that probability 0.25 comes from an unexplained experiment and that it's never said that clothes violate Bell's inequality. However, the example of the hats/gloves/scarves remains logically unrelated to the case of the photons in the video. Thanks.
Thank you. This is the first time I have seen this explained clearly.
Hellow Bob! 10 years ago.. and 10 years after... thank you for the simplified explanation ❤
I think the problem is in describing the spin of an entangled particle at 2 different locations. The experiment is set up to determine discrete characteristics (spin direction >
Well explained. I watched the first three minutes of another 'explaination' of the same idea which was full of waffle and used a video dispaly. A 1/4 is greater than or equal to a 1/3. Mind bending.
the best video ever on Bell's ineq
Hi. Thanks for the clear video. When you say Bob can't measure in the x-axis. What do you mean? What would occur if bob and Alice tried to measure x and y spin simultaneously?
My exact question plz some one explain
I would had that French physicist Alain Aspect was, in 1982, the first to do the actual experiment proving that Bell inequality was violated (Aspect found the 0,25 in the end of the video).
Thus we are free to use "Bells Hoax" instead of "Bells inequality".
I think Clauser, Shimony et al did it in 1972
2024 29th of March - the lecture, the English, is very precise n clear. I think it is his native ( England) English that makes the difference. American English is very confusing. Students must need to spend a great deal of efforts to decipher Science n engineering books written by American authors. I discovered this by chance- one day I was reading a physics book from the Oxford’s series without knowing it is Oxford’s n found it’s English was precise, clear n succinct n I turned to the front pages n found out it is from the UK. Many of my good physics books are from the UK.
BRAVO what a wonderful series of lectures.
Please write a book on the contents of this site for thd benefit if humanity
Thank you🙏
Great lecture, but I am missing the reasoning for having 0.25 result in the experiment.
In another words, what is the quantum mechanics reason for the 0.25 measurement in the experiment?
It is just the probablility of getting all same results I think.
@@elimarburger1659 I watch it again, and it's clearly the experiment result! so the only conclusion is that the pair of particles seems to"communicate" their states at the time of measurement rather carry the "hidden information".
At the bottom line it solves Einstein-Podolsky-Rosen paradox by showing that the particles could not carry the information without breaking bell's inequality.
@2:36 What you mean Bob CAN NOT make the measurement in x direction? How exactly Bob tried to measure it and what he got?
I wanna know plz someone explain what would happen
He can. His results would then be uncorrelated with Alice's results.
I think this is very useful, but a little confusing, due to the "typos". Any chance, DrPhysicsA, that you could redo it? Again, very valuable
Thank you for the video.
What is the importance of the angles of the polarizers, if any?
To distinguish between polarisations of photons.
Hi, thanks for these great videos on physics very much appreciated. Now I've been trying to figure out what entanglement is for some time now & i think I've made some progress so if someone can help me out, just please dont bite my head off :) So, starting with the double slit experiment, a single slit produces random dots as would be expected of particle behavior whereas a double slit produces an interference pattern suggesting wave-like behavior..ok fine. Now, placing a detector at the slits, the interference pattern disappears & QM theory says that the "wave function" collapses as a result of the measurement effectively eliminating the superposed states etc. Now, if we generate a pair of entangled photons, A & B, and measure some property of A along an axis we shall have random results as would be expected, but when we measure its entangled partner we have 100% correlation with A (ie NOT random) implying that measuring photon A, and thereby collapsing its wave-function to a definite state, causes the wave-function of its partner, B, to ALSO collapse presumably instantaneously. According to Bell experiments all local hidden variable theories have been rendered useless, we have Bohmian non-local hidden variable theories which work as a valid interpretation but doesnt really advance our knowledge of QM. Now I have to ask this not because I think its correct but because the fact that im thinking it means theres something im not understanding. Why isnt the process of generating entangled particles the problem? I mean, during the process they simply acquire correlated polarization or whatever other property, why does there need to be this mysterious hidden variable or "pilot wave" or faster-than-light communication? Is there some experiments that have been performed that rule this possibility out even if we couldnt observe this process directly to tell for sure? Are there natural processes that produce entanglement? How do we know for sure that the entangled pair have not already experienced state-collapse as a result of whatever produces entanglement?
What you're asking about IS the idea of hidden variables. If the particles acquire definite correlated states at creation this means that there are hidden variables that define these states at the creation of the entangled pair. Bell's inequality experiments prove mathematically that this can't be the case however, so there must be something else at play here. Either instant and faster-than-light communication, or some other explanation where Bell's inequality can be violated.
@@Patatmetmayo Bell's inequality confronts a linear probability distribution with a non linear one. It's frankly obvious that polarization experiments will violate the inequality, because the polarization follow's Malus' law, which is a cosine law (i.e. non-linear). It's just wrong to think about hidden variables as a predetermined outcome for ALL polarization angles. Also notice how Bell's derivation is purely a logical statement and has fundamentally nothing to do with quantum effects.
Let's say our photons are created entangled with polarization on the z axis. Every measurement along that axis (detector A) will pass. Now put the detectors at an angle, like 22.5°: every photon will pass test A, but test B has a cos^2(22.5) chance to pass, that is 85%. If detector B is instead at 45°, it will have a 50% chance. See how the "hidden variable" refers uniquely to detector A, and how the outcome of the other measurement is not independent of what we measure at A. But there's no information exchanged between the two photons, each already had all it needed to produce experimental results, namely polarization aligned with A.
The fundamental problem is that we think of the light going into the detectors as single indivisible packets, but that is not true: what is quantized is the EXCHANGE OF ENERGY to matter from the field. A photon is effectively one only at the moment of detection, before it's just a normal EM wave, subject to Malus' law.
How is it possible to possessing the hidden property going through polarizer1 and polarizer3 simultaneously? Because if a Photon is polarized 45, it is certainty will be absorbed at -45.
Say it’s polarized at 90 degrees. Then it has a chance of passing through both 45 and -45.
I can count twelve 'S' from twenty four possible {S, D}, therefore the probability of obtaining an 'S', if all the combinations (1 to 8) occur with the same frequency, should be exactly 1/2. I suppose that as we cannot establish the probability of the individual combinations, we have take 1/3 as the lower limit.
Thanks for the clear presentation.
Awesome explanation
I see the main error here is the assumption that there are two photons. There is just one single phenomena which propagates outward from the source like a pebble dropped in a pond, but only dual-beamed instead of circular wavefront. The measurement processes doesn't send information faster than light, but there are actually precursor ripples of the measurement which start way before the actual declared measurement begins. It's just classical wave mechanics and no mystery. It just requires ample noise. In the low noise approximation without precursors, it appears to be "mysterious". Also, please send me the specs on a polarizer that lets a photon "pass though or not". All polarizers I've encountered will absorb the photon via interaction with electrons and re-radiate a new one or not.
Thanks for these truly intelligent lectures, Phil!
I love your knowledge but I don't understand the vast majority of your information!
I wonder, just out of curiosity, if you know also Goethe's 'Theory of Colours', I think I can grasp that.
Although sometimes it seems my mind is so slow I only understand in science Plato's 'Wax Tablet Hypothesis' and Aristotle's 'Theory of Everything'. Lol!
Great explanation! Thanks!
Thank You, this is the best video on Bell's Inequality I have found so far!
I don't really get the first part about simultaneously measuring "spin in both X and z axes". Afaict electrons only have one spin direction, and if you try to measure it with magnets you have a certain chance of getting that spin or the exact opposite, depending on the previous spin. I.e. measuring with magnets reorientates the electron. In fact spin is just an emergent property of electrons in the presence of measurement apparatus
Thanks for this clear explanation. I'm not a physicist but love it. My question is as follows. According to the experiment setting, It seems to me that ruling out the existence of any hidden variables is based on the entangled particles, i.e., quantum entanglement is taken for granted. What would happen if the quantum entanglement itself does not always happen? Could the entanglement phenomenon be also probabilistic?
Not unless you are prepared to throw out conservation of angular momentum and many other conservation laws. One example of entanglement is the consequence of a particle with no spin decaying into 2 particles with spin, such as an electron and a positron. Conservation of angular momentum requires that they have opposite spin. Yet, uncertainty requires that each one's spin is all possibilities until it is measured. Only then does the wave function collapse. Entanglement means that it collapses for both particles at the same time.
Put another way, these properties are probabilistic until they are measured. The spin of an electron could end up either way depending on when it is measured. It didn't start out with an up spin and it's partner a down spin. Measuring it makes the spin definite and makes its partner's spin definite at the same time.
I have a question! Please someone who understands this - answer , Im so curious.
In the video we assume that the photons will have EQUAL probability (12,5%) of any of the 8 possible combinations . Why is that? Why cant the porbability of the combinations 1-8 differ? Why do we assume this?
Could perhaps the experiment be faulty so that some angles of polarization were more probable?
Or was the experiment conducted with some other particles and spins were measured and it still came out this way?
Thanks DrPhysics...but is there any reason that why the result is always less than 1/3? if you please explain...
I understood for the most part though you lost me at the 1/3 part, I understand that's the probability of obtaining a different polarizer, though 1/3 seems like the probability of each individual case, all of them together on the other hand should be 6/8 or 3/4, this while taking in count the ones that are the same, what am I missing?
I think the individual case (1/3) and overall case (3/4) yield the same result because the overall case is accounting for every combination of hidden variables while in an actual experiment you would perform it once with 3 polarizers in 3 different pairs with any hidden variable combination governing that one particular experiment
In the simple case of recovering light from extra filters, I have a feeling these photons aren't blocked, but phase shifted to oppose its orthogonally polarized counterparts. The fact that you can recover the output with more filters is exactly what is seen in series resonant circuits when reactance pushes the voltage and current out of phase and then realigns it to eliminate the destructive interference of the opposing waveforms. Due to quantum wave effects, polarizing lenses probably act like the quantum equivalent of reactance rather than resistance.
I don't see why there is so much resistance to accepting nonlocality in physics at the very smallest of scales. It explains the experimental results (such as double-slit and entanglement) without contradicting our intuition of locality at larger scales, where decoherence rules. We can even, in special cases, see coherence at large scales: superconductivity, superfluidity, Meissner Effect.
It's trivially incompatible with relativity. All the people who think that physics is non-local simply don't understand physics. :-)
Sir, you really keep on posting high quality content, even though you might have lost yourself a bit through the explanation it still remains THE BEST I´ve seen so far, and believe me, since the nobel price has been awarded, I´ve checked many... Thank you very much, keep up the great work you´re doing!
Good explanation. Like it.
This's amazing. Love it so much.
Seems to me the trials are not testing spin direction [which is the 50/50 proposition,] but instead identical polarization [which apparently should always be the same]?
Also, in many cases [when Alice and Bob pick different polarizers,] the trial is not measuring spin in the same plane, which I thought was a condition for the spins of entangled particles to always be found to be opposite?
And i hope that my professors will be as amzing as you!
Ok I understood fairly enough. Just one question, What is the relation between polarization and spin direction? Ain't a physicist so...
Sorry if these questions where answered but I just misunderstood them:
1:54 Does Alice shouting the result to Bob have anything to do with Bob's readings? If Bob didn't know that Alice had even measured the z direction on her side, would he still be unable to measure the x direction?
In the setts of children example, he says "A not B + B not C ≥ A not C". This is obvious if A = B ≥ C, but not true if A + B < C. Are we starting with the assumption that there are equal numbers of children wearing hats, gloves and scarves. Because he does not make that distinction.
The inequality refers to the number of elements in the sets. In your example for instance A={4,2,1,3} has four elements, B={b,w,r} has three elements and C={on,off} has two elements. The set "A not B" is the set of elements that are in A but that aren't in B which in this case equals the set A since A and B have no elements in common. Letting "#S" be the number of elements of set S, then #(A not B) = #A =4, #(B not C) = #B = 3 and #(A not C) = #A = 4, which since 4+3 > 4 matches the inequality.