Proof of Bell's theorem
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- Опубліковано 9 лют 2025
- Watch the video I made about the significance of Bell's theorem first: • Is Quantum Mechanics T...
The spin video is here: • Things we know about s...
This video is based on the fantastic discussion of Bell's theorem by my favourite physicist, David Mermin. Is the Moon there when nobody looks? cp3.irmp.ucl.a...
I couldn't watch because of the slide that said "entangled particles communicate faster than light," because that is incorrect. They simply share a quantum state that forces the spin (or other property, such as linear polarization) of one to be the opposite of the other. There is no communication of the spin information. You cannot set the spin of one entangled particle in order to communicate the opposite spin to the other particle.
Hey guys, sorry but I'm going to be on holidays for 3 weeks so I won't be making videos till I'm back- sorry!
Back :)
ua-cam.com/video/rbRVnC92sMs/v-deo.html
"Just the place for a Snark!" the Bellman cried,
As he landed his crew with care;
Supporting each man on the top of the tide
By a finger entwined in his hair.
"Just the place for a Snark! I have said it twice:
That alone should encourage the crew.
Just the place for a Snark! I have said it thrice:
What I tell you three times is true."
If you can, please consider watching:
Classical Violation of Bell Inequalities, by qmiscm.
This is not a critique of your interpretation of Bell's theorem - you do a beautiful job in explaining it and your explanation corresponds to other interpretations of the theorem I have read. It is a critique of the assumptions/predictions of Bell's theorem.
Bell’s (or Bell’s interpreter’s) assumptions in his theorem are supposed to be EPR assumptions which can be reduced to absurdity, but they are not EPR assumptions. They are quantum and random assumptions.
1>EPR assumptions/predictions: When particles are created or entangled, they immediately have opposite spin 100% of the time which is necessary to preserve angular momentum. The angle of spin (somewhere between 0 and 360) is set at the time of entanglement and embedded in the twin particles, so that even if they are separated, this information remains in the particles. If one particle is spin up, the other will be spin down in the same line such as 0/180 - not in any combination of lines. There is no half-down, ¾ down correlation - there is only fully down (180-degrees apart) correlation. The whole point is to conserve angular momentum, and you can’t conserve momentum half-way or ¾ of the way. Given this interpretation, all particle pairs will have opposite and equal spin, that is, they will always be measured to have different states (A up/B down or A down/B up) and will never show the same states (A up/B up, or A down/B down). If particles show the same states, then they were not entangled to begin with.
2>Quantum (Copenhagen) assumptions/predictions: When particles are entangled, they acquire some basic information, that is, to always have opposite spin when measured, but the direction or angle of spin is undetermined until measured. The superposition interpretation is that the particles have all possible angles of spin until measured - the other interpretation is that they have no definite direction of spin before measured. So, in Q-M, half the information (particles will have opposite spin) is embedded locally, but the other half (angle of spin) is not. Since the constraint to be measured with opposite spin, even in the quantum interpretation, is built into the entanglement process to conserve angular momentum, then the prediction should be the same as EPR’s prediction - that 100% of the time the entangled particles will show opposite spin to conserve angular momentum when measured. If the pair shows the same angle of spin, then they were not entangled. However, the interpreters of Bell tell us that the odds are 50% for same spin and 50% for opposite spin. Of course, entanglement means particles will have opposite spin or different spin when measured at a distance. Is there any other meaning to the word “entanglement?” If spin is not entangled, then what is? Entanglement means that particles have mirror-correlated DNA.
3>Random pairing of particles without entanglement: The real assumption of the interpreters of Bell are that the particles are independent of each other so that sometimes particle A can be spin up and particle B can be spin up also and vice versa. If this same behavior occurs, then there is no entanglement and the odds would be 50/50 of getting a same response or getting a different response. After all, the experiment boils down to the fact that either the pair is opposite in spin or the same in spin. There are two ways of getting same spin (particle A up and particle B up or, vice versa, particle A is down and particle B is down). And, there are two ways of getting a different measurement (particle A up, particle B down or particle A down, particle B up). So, regardless of the number of detectors, it boils down to a 50/50 chance of getting the same or different response. As can be seen, the Random pairing of particles gives the same prediction as the quantum (Copenhagen) prediction - 50/50 either way. Since the quantum interpretation does not differentiate itself from the random interpretation, it is not a scientific theory because one could attribute a 50/50 result to either interpretation. There is an equality here - not an inequality. The inequality exists between the EPR interpretation and the random/quantum interpretations.
The fact that EPR, even in the flawed experiment, gives a 55+% result in particle-pairs showing opposite spin says that EPR is in the direction of its 100% prediction. At least it beats the odds. The fact that quantum theory does not beat the chance expectation of 50/50 shows that it does not really predict anything that a flip of a coin would predict. Most theories predict that the results will be a deviation from chance. To sum it up, this experiment does not differentiate between EPR and quantum interpretations.
Mr. Reinhardt, you explanation is practically flawless, and I wish most dilettantes in quantum mechanics had the discipline and research motivation to knuckle down to the hard observed facts.
Many thanks for the crystal clarity, albeit a long explanation.
Question::
Special relativity and quantum mechanics are two theories developed separately and independently, and QM doesn't have the assumption or limitation that nothing can travel faster than the speed of light.
So how does this limitation creep into qm?
How can an electron have spin "up" in all 3 axis 120 degrees apart in classical mechanics?
That's not what the 3 up arrows represent. The 3 up arrows represent that the electron will be measured as up in those axes.
We never know the true spin of the electron. If I give you an electron and ask you in which axis is it spin up, you won't be able to tell me. Theoretically, all axes besides the direct opposite will have a nonzero chance of measuring spin up
@@jakebrowning2373 Can't we know the spin by measuring in "classical mechanics"? And we're only making 2 measurements, one in each detector. Where does the third arrow come from? I'm out of my depth here, but I'm not getting this experiment. It looks like a neat trick to me.
Love these old videos. No janky music drama. Just pure educational stuff ❤
I think this is the most well explained and well vulgarized channel about quantum physics. Be sure I'll be recommending it to anyone who has interest in these subjects. Keep up the good work and can't wait to see more videos.
I think it would be nice to know a little bit more about you, your educational background / work. Anyway.
Oh and maybe a subject matter for a future video: without going too much metaphysical, your thoughts on what may link the Universe (stars, infinity and stuff) with quantum mechanics. Cheers!
Thank you!
I study physics. I took half a year off, which is why I had time to make this channel, but I'm continuing studying in February :)
That's for the topic, it's a very interesting one. I won't have enough time to do it before I start studying again, but I hope I can talk about it sometime in the future :)!
Nice explanation.
Although, note that this isn't because of the craziness of spin, but rather the craziness of QM systems, since bell inequalities can be demonstrated with the polarization of two photons.
George Rickard That's right! The craziness of spins is a direct consequence of the craziness of QM.
+Looking Glass Universe it's any three measurements that bear an uncertainty relationship, spin and polarity are just examples where you can have uncertainty with three measurements. The weirdness is in uncertainty. While this is a good video, I think divorcing the conversation from uncertainty was an error. That was the crux of the Bohr/Einstein debate that lead to EPR, Bell, and everything else.
Here's an Idea. What if each particle had spin in a predetermined position anywhere from 0 to 2pi (0-360 degrees) , with the entangled parter pointing the opposite direction (rotated 180 degrees). This would make it so a particle could only be spin up in a max of 2 axis, ruling out the triple up possibility. If I'm not mistaken, this would also give a 50/50 chance of both indicators reading the same without having to include faster than light signals.
I've actually had the same Idea and programmed a little "Simulation". I am still in wonder wheter or not I have forgot something or what but. Jup, both Probabilities are 50% Iii.. have never understood why entanglement should be something special.
Also, the base principle of how to entangle stuff seems to be - "Just get them to do something together, share a state or just have them come from the same source" So... to me.. Well... two gears work in an entangled fashion... With no friction they would also keep spinning in the opposite direction with the same speed when they are disconnected. When you look at one you know the state of the other... etc. xD Nothing is different... I have a feeling that many parts of quantum physics are just quite missunderstood, even so. The doublesplit interference is still quite a wonder ^^
This. All i can see are just two particles spinning in opposite directions.
I'm absolutely new to entanglement, but I believe this might fix Bell's experiment, but break usual behaviour of spin entanglement. If that were the case, and the particles agreed to align their spins along the x axis, for instance, (one on the positive direction, the other in the negative direction) and we measured positive y axis spin, there would be a 50% chance that any one of them would result in a positive or negative measurement. That means that there would be a 25% percent chance of both being simultaneously positive and a 25% chance of them being simultaneously negative, which goes against the basic rules of spin entanglement.
@@santiagoerroalvarez7955 I do admit this case would go against the normal behavior, but I'd also argue the chances of it happening or so small that could account for us not observing it. If they were even a little off the x axis, one would point more towards one or the other, causing them to read as different states.
Now say we do get the unlikely scenario where they are close enough that minimal interference (or quantum fluctuations) caused them to both end up the same way, wouldn't that explain the entanglement "collapse" we get from interference?
From my understanding, researches go through a lot of effort to remove sources of noise that would break the entanglement. If you successfully removed all noise, then it would have a infinitesimal probability of running into the issue. This would mean to test it you would need an absolute 0 chamber infinitely far away from everything, doing countless try's hoping to happen upon an infinitesimal chance to run into this scenario.
What's your thoughts? Do any gaps in my logic stick out to you?
TL;DR I'm pretty sure noise in experiment already gives us these results. So as far as I can tell it's consistent with what we do see.
What I gathered from 3:34 to 3:43 is that the total spin is not always 0 or conserved. If A is down, B is more likely to be down also.
You measure in a different direction tho and thereby force the spin into your direction. Before you measure, the spin is conserved. As seen if you measure in the same direction.
It always amazes me how people can read Bell's paper and not notice that he invalidates it himself in the last few sentences. ;-)
The part with the vectors was confusing but I finally got it. We await your publication on what spin really is, I think you have some ideas you may be... not revealing.
Over the past few days I’ve once again thought about this video and the incorporation of the Monty Hall problem. It’s interesting that you derived a probability of ½ chance of both detectors measuring the same color. Similarly, I too derive a probability of ½ when using the Monty Hall Problem. Let me refresh from and explain.
There are two sets of three doors. Each set has the same configuration. The analogy here is that sets are “entangled” simply by way of duplicating what’s behind each of the doors of set 1, and setting the same with set 2. That is, if Set1 is Door 1:goat, Door2:car, Door3:goat, then Set2 will also be Door 1:goat, Door2:car.Alice plays the game with one set and Bob plays with the other set. In both sets the game is played the same.
The contestant (Bob or Alice) picks a door. Monty Hall then opens another door that always has the booby prize (goat) instead of the car. The contestant then either selects to switch their door choice to the other unrevealed door, or keep their original choice. Though these rules of the game are the same, Bob and Alice take different strategies.
Bob always switches doors after Monty opens the second one. Alice always retains her original choice. There Bob has a 2/3 probability of winning the car, while Alice only has a 1/3 chance. If you look at the combined “average” probability of both Bob and Alice it is ½. The same probability of each color being the same in the video. But here is a interesting pivot.
If Bob and Alice are playing the game simultaneously,
(1. ) What is the probability that both will win the same prize (either both win the car, or both win a goat)?
(2. ) Let’s say Alice picked first. What would Monty do he if knew that Bob could see what door Alice picked. If this were the case then Monty would have to change the game behind the scenes and randomly either swipe the prizes around on Bob’s two remain, unrevealed door. Or leave them as they are.
(3. But the important point is that Bob’s knowing the result of a revealed door that Alice picked, changed the behavior of Monty. That to me sounds like non-locality because Bob and Alice cannot see what Monty is doing behind the scenes. And what Monty is doing is slyly changing the rules of the game.
I don't see why it's necessary for the particles to "communicate" for states of entangled particles to be opposite. It's like if two people go into a room alone, assign each other a code word "up" or "down" and then go light years away from each other. We still know that they can retain that information. If we asked these people for these code words we wouldn't assume they had some sort of instantaneous psychic link, we'd assume they were in contact with each other at some point. Bell himself said that this interpretation was still possible if we assume that everything is deterministic. The only reason physicists shy away from models like these and pilot wave theory is because these models require us to make assumptions about what particles are doing instead of using statistical models that are required because of a lack of perfect knowledge. The natural model is probably not the theoretical models that we use to make predictions. The natural model is probably very boring.
Bells theorem does not prove the faster than light communication, it merely proves wrong the hidden variable hypothesis.. usually you are very precise
Bell's Theorem doesn't rule out hidden variables. It only rules out static hidden variables that are not functions of time. If you allow the hidden variable to be a function of time, then the derivation of Bell's Inequality cannot be carried through, unless the cosmos is presumed to be governed by a common master clock. Since there is no master clock, there can be time-varying hidden variables (such as Maxwell's Equations for photons and deBroglie's model for particles with mass).
"If you allow the hidden variable to be a function of time, then the
derivation of Bell's Inequality cannot be carried through, unless the
cosmos is presumed to be governed by a common master clock."
Why? what is the evidence for this?
It's in the mathematics of the derivation of Bell's Inequality. Bell's derivation tacitly assumes a master clock that pervades the cosmos. This is equivalent to assuming that the graphs of the twin particles are perfect mirror images of each other. With that unrealistic simplifying assumption, the presumptive hidden variable vanishes.
But there is no master clock. The graphs of the twin particles are not perfect mirror images of each other. There remains a residual non-zero "beat frequency" that doesn't vanish. That's why Bell's Inequality doesn't apply to the real cosmos, where there are pervasive gravitational gradients such that the twin particles do not age in perfect phase-locked synchrony.
It seems like Bell's Theorem can't rule out the possibility that hidden variables might lie within the scientists performing the experiment. If you treat the scientist as a quantum system, then the observation of spin at one sensor is actually the scientist becoming entangled in the system. The scientist can't observe the outcome of the other measurement faster than light, so no faster than light communication is necessary, she simply can't observe outcomes that contradict the system she's entangled with. Those "other worlds" are simply inaccessible to her.
Does that make any sense? I'm not an expert, but that's how I always thought of it.
+Barry Kort
Bell didn't assume that a "master clock that pervades the cosmos". He did what people always do in thought experiments: assume all un-specified variables are negligible. If you assume Bell's theorem takes place in some inter-galactic flat space-time such that there is no noticeable gradient, you can still use it to determine if the universe behaves according to classical or non-classical physics.
*That's why Bell's Inequality doesn't apply to the real cosmos,*
As far as I know, all attempts to test Bell's theorem have successfully shown that the universe is non-classical, so I don't understand how you can say it "doesn't apply".
It would be interesting to reformulate the experiment in curved spacetime to test for time-dependant variables, but that's a different experiment. It doesn't render Bell's theorem invalid.
I just had this thought:
If the information travels instantly, how could we tell if it ever existed somewhere in space-time?
Yep Yep there's another thought that distance is meaningless at the quantum scale for whatever reason. So instantaneous travel of information isn't encumbered by a distance that we perceive, because from the perspective of the particles it doesn't exist.
There is an utterly different way to arrive at Bell's Theorem. At the ensemble level the Schroedinger equation is super-accurate, so accurate in fact that the savvy natural philosopher will realise that modification of it is forbidden. If we want to add some randomness to the Schroedinger equation to produce what we observe below the ensemble level, then we are going to be short of degrees of freedom unless we start to look at the superluminal world. Bell's Theorem is just common sense and does not require a proof. Any local theory would be trapped in Feynman's straitjacket.
One thing is never explained in Bell's theorum that why particle would decide spins against each axis. They will just decide that I am going to point to the centroid of universe from the creation point, you be pointing in opposite direction . If they decide this the condition will be same as the first case, according to how you measure spin will be in opposite direction 50% of time.
Deciding to measure it against 3 axis just kind of recipe for failure even before measurement because particles are going to be oriented in opposite direction in space as in the first scenario, not in the each axis. Can someone explain?
Thanks for making this! You've made it easier to understand!
Glad to help :D
Remember: if you think you understand q.m, you don't understand q.m. (R. Feynman)
You should make some videos regarding the math of quantum states, for someone is really boring but if someone wants to go deeper in this field he needs to know it (at least a little)
Spin can be equated to the forces of the Right-hand-rule. This can be demonstrated by holding the pole of a reasonable sized N48-N52 magnet up to the screen of a functioning cathode ray TV with a screen projection of sufficient detail to illustrate the effects of the torsional forces of the magnets 'pole' By reversing the polar orientation of the magnet will impart the opposite torsional disturbance on the Cathode Ray TV screen. (There's more to it, with regards to the counter rotational disturbance at the boundry of the main torsional disturbance, but that's another story for another time. What is important though is the equatorial plane of the magnetic field in relation to the 'spin' properties of the 'pole' when you couple this with the affects of; 'Shielding' a single magnetic pole, or arranging a composition of magnetic fields to form a Hallbach Array, or configuring the physical structure of the magnet to produce a significantly 'imbalanced' magnetic field ie: pyramid magnet, where each pole has vastly different physical attributes, then you are producing a field that, from an external reference frame, represents a point in space that has a particular 'spin' characteristic. If this point is sufficiently miniscule, the particular 'spin' characteristic of the dominant pole would be the primarily evident 'spin' attribute of the point, regardless of which direction you approach/observe the point from. Ie; You could bring the non-dominant pole of the magnet towards the Cathode Ray TV screen and the observed disturbance would be that of the dominant pole on the further side of the magnet.
Another thing to consider. Physical spin characteristics are different from imparted spin characteristics....
Ie; imagine a steel cylinder bouncing around in an elliptical pattern inside a slightly larger rubber cylinder where each point of 'impact' from a section view, was incrementally displaced from the previous point then the imparted spin characteristics of the rubber cylinder could be mistakenly quantified as a physical spin property if the method for quantifying the cylinder properties is not adequately suited to allow for the distinguishment to be discernable.
Much in the same sense that oscillation is often mistaken/miss-characterised as spin.
Nothing is spinning it is the centripetal and/or centrifugal properties of the magnetic moment.
And just like oil, magnets ain't magnets.
(As in there is a whole array of magnetic properties and characteristics characteristics that all fit indiscernibly within that crude and rudimentary 'magnetic field' demonstration from secondary school.
The "resolution" or "explanation" cannot be that "spin is weird" because the exact same non-local correlations occur with classical observables such as position and momentum. Bell's theorem generically only requires incompatible observables, meaning the generators for the symmetry groups do not commute. But the group generators do not commute in classical mechanics either, it's just in classical mechanics we can make arbitrary precise measurements (shrinking ħ to zero in effect) so the non-commutativity can be worked around in CM. But they're still non-commutative.
The "explanation" is not understood yet, of course, but Susskind's ER=EPR Conjecture does explain entanglement, and it turns out it is just classical general relativity with a minimal extension, that being allowing wormhole topology at around the Planck scale (this is generic, an actual geometric theory of elementary particle structure would be needed to make ER=EPR particular --- Cohl Furey might be getting close to this). I have no idea how to experimentally test ER=EPR, but if you can think of a feasible test I'd urge you to quit physics-youtube for a bit and perform it!!!
Classical mechanics does not emerge from quantum mechanics by setting Planck's constant to zero. That's just one of many myths that are being perpetuated in poorly taught QM 101 classes. Classical mechanics emerges as the result of continuous weak observation on states with large angular momentum. This has been understood theoretically since 1929 and it has been verified experimentally on e.g. Rydberg states.
I'd like to propose a "Quantum Central" theory/theorem. This could possibly remove interference with Einstein's law of relativity. I propose that entangled particle's/waves have a "Center of entanglement" that predicts the time of observation and sends a message simultaneously to each entangled particle/wave. If all particles are equidistant, that halves the travel time of the signal. With the possibility of the central being able to predict, its able to get this message to all particles at around the same time and in time for an observer to collapse its waveform, all without breaking the theory of relativity. If this theory or one similar has already been proposed or discredited, please let me know.
+A Flaming Potato Demon no that doesnt work. Special relativity can rule that out by telling that whats simultaneous to you is not simultaneous to me
A beautiful voice with a even more beautiful mind.
4:15 How do you get 50% chance of same color? This is a "fun trig exercise", I feel I don't have enough knowledge to work out just from the information in this video. Unless I am missing something. In that case, can you help point me in the right direction?
Excellent explanation, I'm beginning to get it. Head has stopped spinning also. It suddenly starts to make sense, the explanation, not the spins. tks
Ahaha! Spins have yet to make sense to me.
Looking Glass Universe Spins are an arbitrary property, just a conventional one. "Spin" also has nothing to do with rotational motion. I just think of a light switch, on or off.
I am trying to understand this. Honestly!
However, all the explanations I have found so far seem to be of the type: "I thought apples were dearer than oranges - but they are not. So faster than light messaging must be happening!"
At 6:35 you say A and B are more likely than not to have different colors (5 out of 9) but at 6:45 you say they're more likely than not to have the same color. Am I missing something or was that just a slip of the tongue?
It's more likely to have DIFFERENT colours. 6:45 was just a slip of the tongue (watch the screen at that moment, and the added "different" at the bottom right corner is evident).
Thanks for these videos, and have a nice holiday!
Thank you! I am, hope you are too :)
when I watch your videos I feel like , Can anything be better than studying physics from you !! you're really amazing !!!
I think I am missing something. It seems that Einstein hadn't been given a fair chance here: his postulate about "hidden variables" is being tested considering a behavior where the spin is completely unrelated from the axes of choice (which is not what happens "in nature"). As far as I understood, this "spin on axis X being related to the cos(spin Y)" is not something necessarily linked to "superposition" rather than "hidden variables", so why can't we test Einstein saying "hidden variables will give us a + on axis Y, given that axis X blah blah", instead than making Einstein say that all the possibilities are equiprobable? Also, the fact that results are statistical in nature doesn't rule out hidden variables: there might be some hidden turbulence that will give a certain result most of the times but not always. I am not an expert, so probably I missed something easy
Coming here one year later, had the same doubt, and found my comment I had forgotten :D
I've never really gotten a straight answer when i ask if entanglement is about an action on one particle affecting the other or if it's about the "entangling" of particles causing each particle to "inherit" set behaviors that are always correlated after the fact. It seems like Bell's theorem says that entanglement is about a physical connection as opposed to correlated "settings".
Exactly! Hit the nail on the head.
Quite interesting. Thanks for the response :D
I found that the Monty Hall problem with a little "spin" will result a similar mindblowing problem. I made a video about it. What do you think?
Thank you for making these videos! You have found a good balance between a high-level explanation and a math-based explanation. I hate videos that focus on the 2 extremes. The "Equation Gurus" put me to sleep, and the ""Carl Sagan Wannabes" are unsatisfying. I'll keep watching & learning.
Thank you so much! I feel the same way so I try to get that balance.
I agree. Wowing people is just the first step not the only one. It also sends the wrong message of what physics research is like. It explains why so many people abandon the physics major.
Still lost.....the details are confusing and I'm missing the point. I can follow word by word but don't get the overall picture. It would be better to communicate the basic idea how to distinguish "true entanglement" and "fake entanglement" by hidden variables.
I like the idea of "Digital" physics to explain Spooky Action. The Universe as a binary system ( Occum's Razor). The Universe is in continuous flux between two parallel universes that we call The Universe (Particles continuously click "On and Off"). Scientists measure spin of a particle in space-time. They change the spin of one particle, it clicks off entering a parallel universe where the information travels instantaneously to its' entangled partner. The particles click back "on" and the spin has magically changed faster than the speed of light. FTL without breaking laws of GR.
Mr. Bodge, the 'parallel' universes you are referring to are 1) the MACRO visible world that we can see and observe out to about 40 billion light years, and 2) the microlevel of existence, called the QUANTUM, which is the 'parallel' universe everyone thinks exists 'out there' somewhere, but is actually RIGHT HERE INSIDE of us.
I don't know if this cob of tobacco will fit in your pipe. . . .or not!!!!
How would this work out if the same principle was applied to the famous "Monty Hall Problem"? That is Alice and Bob (still entangled) both have the choice of picking one out of a set of 3 doors. However if Alice decides to switch to a different door, Bob always keeps the door he originally selected.
In the "Monty Hall Problem" there's always a better chance of win the car by switching doors. But Bob always does the opposite of Alice. If Alice always switches then Alice would have a different probability of winning because Bob would always keep his original pick. Alice would have 2/3 probability of winning the car, while Bob would only have 1/3 probability.
But of course if Alice were truly a quantum being she would only switch 50% of the time thereby ensuring Bob switches 50% of the time and their probabilities then even out.
Now I've left out one crucial component in this. And this is the action of Monty himself. This difference in probability is solely due to the actions of Monty (who reveals an extra door that does not contain the car). I think maybe Monty is really the observer/measurer (or more like the decider in the Delayed Choice Quantum Eraser).
To me It almost seems that quantum randomness is a necessity because of measurement. And that they are inextricably linked.
This is very cool :) I need to have a think about it. I do agree with your conclusion though: quantum randomness only happens at the measurement stage. Before that it is purely deterministic
Looking Glass Universe I'd be very happy to hear your thoughts on this. And yes, in a very odd sense it seems that quantum randomness is needed (in this case) in order to produce classical results!
Would you be able to clarify somethings? So in your problem, what does it mean for Alice and Bob to be entangled? As there are 3 states and Alice's choice of state determines Bob's?
You said that
"Before the game Alice and Bob decide that no matter what door each of them chooses, Alice will switch doors and Bob will not switch."
But then later that
"Sometimes Alice would switch while Bob didn’t. And sometimes Bob would switch and Alice would not."
So I am confused. Do you mean that they are in the entangled state where neither of them know whether they'll switch ahead of time, but when Bob is asked ("measured") by his host, he randomly picks to switch say, and then Alice does the opposite? If so, yes, I agree, they are in an entangled state.
Then you say that Albert and Niels think this is a classical state. Do you mean that they don't realise that Alice and Bob are entangled- instead they think that each round Alice and Bob decide before hand who switches and who doesn't?
So then we might want to experimentally test if Alice and Bob are really entangled or merely classically correlated.
Cool set up :) This is really reminiscent of the scenario I'm doing for my next video. Well, I talk to you about that then I suppose.
I'm interested to see how you will bring Albert and Niels' choices into this.
Is it the case that Niels and Albert's games both always have the prize behind the same door as each other?
When we measure spins along different axis, it seems that, in the short run, some spin conservation law is being broken.
For instance, say 1 photon became 2 particles with opposite charges and spins. You measured one using axis 1 and the other using axis 2. They can't cancel each other out since the 2 vectors have same module, but different directions. So the total amount of "spin up" in the universe either increased or decreased, didn't it?
What exactly do u mean by talking? U seem to be directly implying that there exists a hidden variable which allows for FTL interactions between the two entangled pairs. However, aren't they just correlated instead of hving any sort of causal relation?
Mr. Chang, with due respect to your question, if there is communication between distant particles, then, by DEFINITION, there is a 'hidden variable' which cannot be explained. To even imply that particles KNOW what is happening between them is high blasphemy in scientific circles.
These are so delightful. Thank you.
The more I watch your videos the more I convince myself that you are Australian.
I can confirm its true
edit: See my latest comment with updated numbers.
How does any of this change if A and B have decided beforehand, what spin they will have?
If A says I'll be down in 1, then B has to be up in 1, exactly like in the first example.
John Doe idk what you're talking about but
There's 4 possible things the particles could agree on
110 and 001
101 and 010
110 and 001
101 and 010
If the particles did agree on something, they should be different most of the time.
Stephen Kamenar Why would particles agree on anything? They would just keep on spinning the way they did after splitting.
John Doe Because if both machines measure in direction 1, the particles HAVE to be different.
Stephen Kamenar
If A measures spin down in 1 then the particle could actually spin up in 2.
For B that would result in up in 1, down in 2, up in 3.
If the pilot wave is guiding the particle, could spin represent how the wave exerts that guidance upon the particle? And then, since the wave is interacting with other waves, could that be why the spin is different depending on how/when it is measured?
Could one argue, that if two things were moving apart from each other at near-light speeds (A and B), B would be moving with a faster velocity than the speed of light, from A's perspective?
nup, because at those speeds Relativity becomes important, and the effects from that ensure that even in A's perspective, B isn't moving faster than the speed limit.
Sorry I can't elaborate much, I'm not that comfortable with relativity! Maybe in the future..
Looking Glass Universe Maybe then. :)
I think that that's when special relativity comes into play and time and space change by perspective to keep it at up too c.
I will not die. Allow me to prove you wrong. * ten minutes later *. Here lies a random stranger that we somehow managed to set up a funeral a few minutes after he died.
I love your voice. Awesome explanation.
Thank you :)
+ Looking glass Universe.
Which software did you use to make these images?
It will be very helpful.
Maybe strings give particles spin from outside our dimension. Could this also be how particles communicate over long distances, sharing information. The particles themselves do not know which spin they will take until told by vibrations sent through strings??
4:17 - Choosing axis 2 &(or) 3, more often than not 'same' --> But the 'same' here is equivalent to 'different' when 1 is chosen. ie, when entanglement is assumed, 1-1 should give 'different' and 1-2, 1-3 should give 'same' from the arrangement. Anything less than 100% for 'different' result for 1-1 and anything less than 100% 'same' for 1-2, 1-3 needs explanation!!
Thanks a lot, you really helped me out on a seemingly dead end :)
Doesnt the standard quantum mechanics chose to preserve locality instead of realism when faced with the implications of bells theorem? And ismt bohmian mechanics the interpretation that chosen to preserve realism by saying particles exist at definite positions but there is non locality by means of the pilot wave?
What happens if you introduce a 4th axis or more what are the ratios then. ?
isn't the main question whether the change of spin of one particle causes instantaneous change of spin of the other ? Does this really happen ? And if so then how do they measure it ?
I'm not sure what laziness is, when applied to "mystery physics". This is like listening to my wife telling me about shopping for handbags, dresses and shoes, the results might look good, but the details are irrelevant? You can tell I'm just old in the shopping for ideas based on loose premises department.
Amplitudes and frequencies modulation in a 0-1 probability spectrum of Superspin means one "end" = Centre of Gravity vanishing point of a paired identity, is looped together at one constant resonance frequency, and symmetrical timing modes/modules are opposed. The imaginary pictures tell the story, I'm too lazy.
How can you have spin up in all three axes?
I'm confused on how the particles are entangled in the first place… Are they both ejected from an atom at the exact same time, therefore are considered entangled? If so, wouldn't they already carry information depicting any reaction thereafter? I am having a hard time understanding the point at which their reactions are considered bizarre. If you spun two pinballs in different directions down opposite paths with opposite forces… wouldn't they mirror each other classically? If one bounced and went left, the fact that the other mirrored that exact motion doesn't seem crazy to me.
What about using Newtonian Mechanics to explain Spin? If you consider a Photon as an ultra small plasmoid, then, orbiting photons are possible, and they do it so fast that a Planck Second is, still, too long, too large.
It's 4:20 am im drunk and still followed most of that. Good fucking job.
if you have a sample size 9, ofc you cant get a result of 50%. that does not prove anything? iam confused
so what is traveling faster than light?
GeekJokes Information
Lucas Carrijo you mean anything but information.
Two entangled particles can be collapsed instantaneously whatever the distance but you can't use it to share information
I dunno why, but somehow you are now #1 in my sexiest women alive category.
I read Bells non-local reality theorem back in 1989... I was only 19. I've been suffering since then to grasp the implications, ever churning in the back of my mind, whether proof was possible. All along, entanglement started to make more sense, and I'm now starting to make some sense of the nonsensical quantum "rules". It appears god does play dice, and has a gambling addiction.
How do we know if its faster than the speed of light if we can't see it?
Mr. 'Broke' with due respect, you cannot even see an object traveling at, or near the speed of light without very special equipment.
HOW, then, could you possibly see something traveling FASTER than the speed of light?????
What if you made this experiment not with electrons but with very small and light bar magnets that have precise orientation in space, but when you try to measure orientation using magnetic field they align themselves with the field. Since they are very light they oscillate a bit before that so the measured orientation is somewhat random. Wouldn't that setup produce same results as QM even though there is a hidden variable, initial orientation of the pair of bar magnets. It's just continuous not discrete as you assume.
Wouldn't it give QM like statistic results even if the magnets are not perfectly anti-correlated all the time, just initially?
Okey, I also do not understand 2:41, why is it 50%? I think it is more like 5/9.
When Alice measures the electron at Axis 1 and if it was ↓, probability for each axis at Bob is following
Axis 1 - 3/3 ↑ and 0/3↓ = 100% ↑
Axis 2 - 1/3 ↑ and 2/3↓ = 33% ↑
Axis 2 - 1/3 ↑ and 2/3↓ = 33%↑
Therefore, probability that direction is ↑(different from Alice) is...
(1/3) * 100% + (1/3)*33% + (1/3)*33%
= (1/3*1)+(1/3*1/3)+(1/3*1/3)
= 5/9
The probabilities don't work that way in quantum mechanics. Spin up state |↑> and spin down |↓> state can both be written in terms of spin left |←> and spin right state |→>, more precisely:
|↑> = 1/√2 |→> + 1/√2 |←>,
|↓> = 1/√2 |→> - 1/√2 |←>.
Of course from these you can work out |→> and |←> in terms of |↑> and |↓>. Using these relations you can actually work out superposition of any spin direction in terms of |↑> and |↓>, simply by decomposing the spin vector to (for example) up- and left- component and then expressing the left component in terms of |↑> and |↓>. The probability to measure spin up is the factor of |↑> squared, and the probability of spin down is obtained the same way. As an example, if our state is
√(1/3) |↑> - √(2/3) |↓>,
probability to measure spin up is 1/3 and spin down is 2/3. I don't feel like solving trigonometry problems right now, so I leave the solution to Bells theorem as an excersice to the reader ;)
@@tetraedri_1834
For axis 2, the probability of obtaining up of axis 1 is up is 1/3.
Same for axis 3. It’s 1/3
However, for axis 1, the probability of obtaining up is 100% if axis 1 is up.
Therefore, the probability is (1/3 + 1/3 + 3/3)/3 = 5/9.
It’s still 5/9.
An unbiased perusal of Bell's proof shows that the proof is wrong in the very first line - his first assumption is mathematically incorrect.
Why 120 degree apart? Is there some assumption I'm missing?
Mr. Millem, there are 360 degrees in a full circle. 120 degrees represents exactly one third (1/3) of the distance between the axes X, Y, and Z - X going from left to right, Y going from down to up, and Z going from back to forward.
If you have a protractor you can easily draw the X, Y, Z axes at the angles indicated. Don't forget that ALL the axes start at the same point and move in the directions I indicated above.
who are you? and how have you managed to explain this stuff so well?
I've been looking for accessible books on quantum mechanics but your videos are too good!!!
really really grateful
What if space-time has 2 dimensions, and the measurement of the first particle determines in what dimension the second particle will be measured? In this particular case, they must be measured at the same time, because the distance must be exactly the same and the dimensions must affect the spin.
We can't measure them at the same time, because we can't even know if speed of light is the same both ways
Why 3 axis instead of 4, considering the orientation is otherwise the same...
I've found veritasium explanation so much easier to understand. Maybe because of his visual approach to the subject matter. Thanks though.
Particles do not communicate with each other faster than speed of light, this is false description of non-locality that I hear over and over again. What happens in entanglement is just blind conservation of energy or conservation of angular momentum. Particles has nothing to do with non-locality.
Particles do not have faster than speed of light walkie talkie (particle A: I will go right. particle B: affirmative I will go left!!)
Entanglement is an emergent phenomena and a consequence of conversational laws!
I hope that physicists will start thinking this way, because physics today is full of myths and misconceptions even among physicists community.
Deep Blue, you have a little more research to do before you can make such statements.
The very real telepathic communication displayed by identical twins (EVEN fraternal twins) in distant parts of the world is incontrovertible proof that entanglement is a COMMUNICATIVE phenomena - whether or not it is AT the speed of light or FASTER than the speed of light is irrelevant to the actual phenomenon itself.
You may want to start with the Wigner's Friends experiment - repeatedly demonstrate at large distances from each other with the EXACT same results.
I assume if machines are opposite side of world are the machines orientated to be parallel
I assume if machines are opposite side of world are the machines orientated to be parallel in space initially for reference or do they take horizontal relative to earth as reference ? In other words does gravity come into this ?
At 6:47, you said: "as we already know this isn't the right result."
How?
tanvi gandhi in the initial part she showed that the result that we should get is 50%, while we got something > 50%
"Relativity is too classical to explain quantum effects*
I think this could be a way to count dimensions.... figure how to throw electrons as waves and see how many variations pop up.
at 5:06, I see 8 possibilities for the spin and I cannot understand what kind of spin can generate (↓,↓,↓) or (↑,↑,↑). If this is impossible to happen, I don't get why it is on the list. Can someone please explain this for me?
TooTooToooo why not?
It's just a question of probability, if the vector of the spin (working in vectors like in the video) is like 1, 0 (arrow right) then you have some probability that you get up even in the two other directions (even if it is lower)
@@lorenzorossi2000
I'm so sorry that I reply to you after 5 years, but I would answer your question.
Its because I can't find a value for θ at which the vector will point up in all three axis.
- Can I ask you a question?
Please give me a number between 0 deg to 360 deg at which the vector will point up in all axis.
@@TooTooToooo So, in a weird turn of events, I'm now in a Quantum Information Processing course at university xD.
Not that it matters, just thought it was weird.
Regarding your question: you should not think of "what state vector could give me this result", because in the proof we are analyzing hidden-variable (local) theories that do not work with state vectors.
Regardless of how, every hidden-variable (local) theory in this setting can be summarized as "what does the quantum state do if we measure it in this direction?".
And since the quantum state is random, any possibility has the same probability, we just know that the entangled state must be opposite.
In the spin-vector (or state vector) maths we can say a quantum state A has 100% probability to measure spin up in setting 1, and a 25% probability to measure spin up in setting 2 and 3. But Hidden-variables (local) theories do not use probabilities, so they should always know, regardless of measurement direction, what spin you'll measure. If in a weird theory (↑,↑,↑) where impossible to happen, it would be incompatible with state vector math. (even if improbable, we could set up a quantum state to measure always up if measured in setting 1 and still measure up in setting 2 and 3).
I'm not 100% certain since I haven't yet studied Quantum Physics so I don't have the rigorous tools to math it down.
But if you have questions I'll be happy to try answer them!
@@lorenzorossi2000
I guess your answer to my question was “The angle doesn’t exist, but in quantum mechanics, things doesn’t work the way it does in spin vector”
However, I’m not sure we you fully understand the very basic “spin vector”. For example, where did the 25% come from?
I need to know how you got the number 25% when the axis 1,2,3 are off by 120 deg.
@@TooTooToooo If the spin is up and you measure it in the spin-up basis, you 100% get spin up measurement, if the spin is down and you measure it in the spin-up basis you get 100% spin down measurement.
Otherwise, you always get up or down, but with a probability that is proportional to the angle of measurement.
I'm not the best one to answer your question since I'm only somewhat proficient in computational quantum mechanics, but using the Bloch Sphere representation in 2 dimensions (let's ignore the imaginary part) you can calculate that with a 120 degree angle, you get the wave function: sqrt(1/4) |↑> + sqrt(3/4)|↓>.
That wave function has 75% probability to measure |↓> and 25% probability to measure |↑>.
Hmmm... So is this the reason why quantum entanglement can't be used to send messages?
Nup, I haven't made that video yet- sorry!
Looking Glass Universe
O.k. I watched this a few more times and I think I get it now. Actually, I had never heard of the EPR paradox! Either I was asleep (likely) or they passed over this in College! Thank you!
They mostly passed over it or just pointed it out as vaguely interesting in my classes :/
Dear Looking Glass Universe,
can you please explain in another way, what "entangled" means.
Here you say, two electrons are entangled if they provide opposite attributes when measured at the same time.
But I don't understand if their entanglement was made sure from the beginning by some technique and is therefore a condition for the experiment or if their entanglement is just a name for the behaviour that two seemingly randomly chosen particles show in the experiment ..
If the latter was true, i sadly often read in the internet that "entangled particles are entangled" as a newsbreak for some experiments that are not so exciting at all.. somehow..
If the first one was true, i often read instead "entangled particles talk to each other faster than light which we can prove by measuring their opposite attributes that we generated in the first place" which would be stupid, wouldnt it?
and if entanglement is proven now, by the big bell test, is that big bell test really loop-hole free? can not human beings be considered as part of the experimental arrangement as well and therefore have possibly previously influenced the entangled particles? and, if that was the case, would the entanglement be a connection that travels the whole distance from particle to human being to particle? and if it was loophole-free on the other hand, what does the big bell test really prove?
i am a really big fan of bohmian mechanics but i'm still struggling a lot with spin and configuration and the whole measurement nonsense and am starving for some clear-headed human to relieve this pain..
the definition of entanglement in this video is so scarce, it just describes the particles behaviour and little of how it possibly came to this (really, not any source in the internet does it clearly).
it's like someone said the definition of flying was being in the air without touching the ground.
and then say, birds fly. and then say, because i have seen them flying, i know how they do it.
which is not true.
this is all so confusing.
Also, if qm was true and the observer was needed to define reality, would this not imply that our universe has been observed by a very big observer that must be disjunct from our universe from the beginning of it's existence?
and if so, could be postulated that our measured particles in the bell experiments do take exactly our measuring machine as the chosen observer over anyone else that could be looking at it in the very second because the bigger observer of our universe MAKES them do it, in order to drive humankind crazy?
what makes our experimental machines so different from any other object in the room and how does the concept of "observation" even apply to nature, nature such a perfect working thing vulnerable to such imperfect orientation methods of any random being of all sizes?
this sounds all very very mystical to me..
Light!! Which part?
Thanks for the clear and easy proof!
Nice video to be the 10th one on the marathon😂
Im a big fan, how do I get an autograph? :) Keep doing videos, they are excellent.
spin is as easy as having the belief that the universe is alive and quantum entanglement having affect billions of miles away from each other at the same moment is not on Lake when you have an itch on your toe in your brain registers it right when you get it open the Fest. So that said, and with this in mind you have to consider if we live inside of a living Universe then our bodies are probably a fractal kit of the universe having many separate universes inside of each other like a nesting Russian doll! So the easiest way to describe the universe is that it and everything in it is just about exactly like living Russian nesting dolls with different universes inside of each explain this result let's think about what
but what if what gets decided beforehand s just some precursor? Not all the measurements in all possible directions.
Code confirmed.
Does contextuality only apply to spin?
+Jarrod Mccarthy *Great* question. Contextuality in Bohmian mechanics applies to any variables that aren't 'classical'. For example, position and energy has classical analogs, but spin and polarization don't. To be more precise, any variables that are determined by a particles position and momentum in classical physics are not contextual. So for example, kinetic energy= p^2/2m, so it's not contextual.
the three axes are in a single plane?
Thank you! Your explanations are at the level of detail that most other UA-cam videos miss.
Unfortunately, while pleasantly articulated, the presentation was logically flawed.
All quantum filters/ measurement devices have an inherent angular tolerance for pass/fail, spin up/down, or polarization orientation. Most if not all CSHS inequality type tests take these acceptance vectors and reduce them to binary up/down results.
Photons passing through a polarizing filter can be calculated using Malus’s law. By entanglement process ( local hidden variables, like polarization orientation angle or spin direction), it quite easy to describe and predict the percentage of correlation between twin (identical) particles. No spooky action at a distance, no superposition needed. The wave function does not collapse. Everything was determined at the point of origin, and everything after that is irrational application of Bell’s Theorem.
Classical methods can consistently match QM’s 2.82 outcome of the CSHS test.
Looking Glass Universe
This doesn't seem to be right. At 2:40 you say A measured down in 1 and then assume that there is only this spin.
Can't the particle spin up in 2 (partially pointing in the negative direction of axis 1, so down in 1 - which is what A measures)
or up in 3 (again pointing partially down axis 1).
If A and B measure axis 1 then we have 3 cases, all 3 different.
If B measures axis 2 then we again have 3 cases, only 1 different, 2 same.
If B measures axis 3 it's the same story as with axis 2.
So we get different=5, same=4. Not 50%!
---
Here's the table for A:
main spin, axis 1
1d, d
2u, d
3u, d
Here for B:
main spin, axis 1, axis 2, axis 3
1u, u, d, d
2d, u, d, u
3d, u, u, d
That's the whole idea... We asume that there is hidden informantion in particles (aka they have a plan and there is no need for instant comunication) and using that asumption we calculate that the results will be diferent AT LEAST 5/9 of the time. Once we do the experiment though, we find out they are diferent only 50% of the time, which means our original asumption of hidden information was wrong. If you don't understand it yet I recommend you watch the veritasium's video as it is explained more clearly. (just search quantum entanglement on his channel)
But that is trivial to achieve statistically. The mistake is assuming that the particles have a fixed spin and that the measurement is probabilistic.
They don't need either a predefined spin nor a plan, but just react deterministically to a measurement.
Using veritasium's setup, in the following format:
A axis number & spin: B axis 1 spin, B axis 2 spin, B axis 3 spin:
1 *u*: *d*, u, u
2 *d*: d, *u*, d
3 *u*: d, u, *d*
=> 4 different, 5 same
1 *u*: *d*, d, u
2 *d*: d, *u*, d
3 *u*: d, u, *d*
=> 5 different, 4 same
===> 50% different/same overall.
This honors the "opposite spin in same axis" requirement, and all that's needed is a bunch of photons, each one reacting deterministically to a measurement.
Actual experiments need to average countless photon's results to get close to 50% .. it's always a little bit off. Of course!
There might be cases such as this:
1 *u*: *d*, d, u
2 *d*: u, *u*, d
3 *u*: u, d, *d*
=> 6 different, 3 same
and this:
1 *u*: *d*, u, u
2 *d*: d, *u*, d
3 *u*: u, u, *d*
=> 3 different, 6 same
Thanks, this is really great video. I watched many of other videos on the Internet but they did not logically and mathematically explain how "entanglement" behavior is more weird than just throwing pairs of gloves in random order to Alice and Bob, in which case the decision about spin (right or left glove) would be made at the moment of throwing and not at the moment of measurement.
Thank you! I felt that was a really important part and so I'm glad you thought it was explained ok :)
hi! i ve just discovered this channel today and i ve seen all of your videos. very good job, i guess explaining quantum is a tall order. i would like to know what does the spooky action at a distance mean for the theory of relativity? after all, it is based on the speed of light is the limit asumption...
keep up the good work!
'Spooky action at a distance' refers to entangled particles that seem to be able to affect each other instantly or very quickly over large distances :)
A few questions: How can you ensure you have precisely 120° between each measurement? How can you ensure the pick between the axis is actually random? Does fundamental randomness even matter or does it just mean the alignment of the measurement axis doesn't matter?
Neither the precise angle nor precise randomness matters. Bell's Theorem is really about _correlations,_ which are statistics, so this only requires _non-biased_ sampling. And _there is nothing special about 120deg, it just makes this version of the theorem easier to prove.
Thank you so much. Great explanation! :D I severely needed this for my honors project
waitwaitwait, you can't just ignore HOW MANY of each there are, If it can be flipped, then there's a much bigger chance that the spin patterns will contain both up & down results.
AND WHY IS MEASURE SUCH AN AMBIGUOUS TERM? THAT BREAKS LITERALLY EVERY THEORY OF ANYTHING EXCEPT THE VIRTUAL REALITY THEOREM! Just correctly try to define the term "measure" and ensure that your method of measurement doesn't influence the electrons in any way. THEN come talk to me.
But what if we treated them as the same "mathematical object"? I mean, spin, momentum and position are described in a particles wave function, right? As they are informational content, we can also take them for mathematical objects. So, if two particles are entangled maybe that just means they possess the same object (I know their spins are opposite, but so are the solutions to some equations, and those solutions both represent the same object (the variable)). As they are the same object, then there isnt really a need for information to travel between particles and the light speed limit wouldnt be violated. Locality still would, I guess, but that is a problem wich we can overlook in this hypothesis. Maybe Im talking giberish haha but let me know!
Actually the entangled pair share a single wave function. That shared wave function has all the available information about the system. In a sense, the two particles are not individualized until a measurement breaks that particular entanglement. At that time they collapse into an allowable state.
Mr. Entrudo, you have struck the nail square on the head!! The two entangled particles are really a SINGLE entity, that are physically divided - one particle on this side of the earth, and the other in India. Yet they constitute the whole entity displaying up and down spins when separated. This is the intrinsic definition of 'entanglement' meaning they are one single entity dividing itself, like a cell division, yet keeping the integrity of their 'wholeness' by displaying opposite spins.
Don't forget that identical twins ( even fraternal twins!!) exhibit telepathic behavior when they are separated by distances, and KNOW what is happening to the other twin, however distant they are apart THAT is the quintessential definition of entanglement, if I have ever heard one.
This behavior has been repeatedly confirmed and verified by the Copenhagen Interpretation, now 100 years in the raging debate that continues about what is 'real' and what is not.
thank you so much for this amazing video!
Aw, thank you :D
The more I look into this the more I disbelief it. No one can show this as an observable phenomenon yet theres tonnes of people showing mathematical proof for what is effectively a hypothetical reality. Describe one experiment that will demonstrate nonlocality exists. The nearest I've found is one guy looking at a source of same polarized photons believing it to be a source of oppositely polarised photons. Come on sciency people. Proof is built on platforms not hot air.
This is the original experiment that demonstrated Bell's theorem. journals.aps.org/prl/abstract/10.1103/PhysRevLett.47.460
But you need to pay to access this one. This is a more recent one that you can see the paper for online:
arxiv.org/abs/quant-ph/9707042
There have been many many versions of this experiment done experimentally, to get around any possible loopholes. Here's a summary en.wikipedia.org/wiki/Bell_test_experiments
FreemanStephen,
you may be interested to read Gordon Watson paper published in feb2014.
He shows the error in Bell's theorem. Not that difficult to understand.
www.fqxi.org/data/essay-contest-files/Watson_BTR201301ZA.pdf
There is a simulation showing that Bell's theorem is wrong.
github.com/minkwe/epr-simple/
A can't be up on all 3 axis. That's impossible.
For an animated debate about the validity of Bell's theorem, see www.sciphysicsforums.com/spfbb1/viewforum.php?f=6
Your vids are infused with exquisite pedagogical competence