Gamification of Bell's Theorem
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- Опубликовано: 25 июн 2024
- This video shows a gamified version of Bell's Theorem called the "CHSH Game".
The theorem proves the non-local nature of quantum physics, known sometimes as "Spooky action at a distance". The gamified version further shows that quantum entanglement can be useful.
See more about the usefulness of quantum entanglement in this video about the relation of such games and interactive proofs, and a recent result related to the halting problem:
• Halting Problem & Quan...
Some history:
Bell's Theorem is due to John Stuart Bell in 1964.
The CHSH inequality, by John Clauser, Michael Horne, Abner Shimony, and Richard Holt, improved on it in 1969.
The CHSH game by R. Cleve, P. Hoyer, B. Toner and J. Watrous in 2004.
About "Bell Locality":
The formal statement of it is this requirement of the probability distribution:
P(x,y|a,b,particle1,particle2)=P(x|a,particle1)P(y|b,particle2)
This means that the outcomes are independent given the input bits and the respective particle statements.
Another way to say that is as stated in the video: that given the particle the top player has, we can specify the table P(x|a,particle1), and it makes no difference what happens with the bottom player (or the other way around of course).
Bell's theorem proves this is not what's happening.
As stated in the closing slide, this conclusion relies on a few more background assumptions:
* Each measurement has one outcome. According to the "many-worlds" theory a measurement can have multiple outcomes, and Bell locallity may still hold with this interpretation.
* The referee can choose random bits. According to "superdeterminisim" world view, there's no such thing as randomness, and it might be that the referee chooses bits somehow pre-determined to match the particles held by the players.
Some more links:
A primer on quantum physics: • Visualization of Quant...
A more rigorous explanation of quantum spin (Physics Videos by Eugene Khutoryansky): • Quantum Spin - Visuali...
Chapters:
0:00 Part 1: Decision problems
1:56 Part 2: Classical bound
6:20 Part 3: Quantum spin
13:44 Part 4: A Quantum Strategy
16:10 Part 5: Local realism
18:48 Part 6: No signaling
22:45 Part 7: Bell locality
![Halting Problem & Quantum Entanglement 2020 Breakthrough result [MIP*=RE]](/img/1.gif)
6:10 that escalated quickly. If coins and dice don't work, try ENTANGLED PARTICLES.
Seriously though, this was a very clear and well done video.
Thanks! :)
But I think your comment reveals a point not stressed enough in the video:
This 2x2 table is the most general way to describe a player's behavior. No matter what kind of device is used, or how the decision process works, it can be summarized with such a table. So by proving that a table is equivalent to dice we basically prove that any device is equivalent to dice.
The implicit assumption of course, as revealed later, is that the 'dice' can't affect each-other from afar, which is the assumption that the quantum entagled particles break.
I mean, when part 2 said "classical bound", it was pretty clear that some quantum stuff is coming.
I've paused the video because that turnaround was a massive left field jump for me, and it was really good! It got it's fundamental point across, and then moved onward, it is just humorous to have such an expressive jump from "oh let's use dice" to *quantum entanglement required*
@@mooman1017 that part had me laugh "since we can only win 75% with dice, how about we give them some entangled particles" *cheerful quantum music*
... I can also offer you these hyper-cubes, take two and it'll take you to the 5th dimension... eheheh
the whiplash i got when you went from coins to using quantum physics to decide which strategy to use is indescribable
well done
6:08 "it seems there is nothing we can do to get better performance" ok reasonable
"so let's give the player entangled particles and see what happens" well, that escalated quickly :0
It's nice to see udiprod is back. Their videos explaining the difference between the different types of sorting algorithms were very enlightening.
Thanks. More of these coming soon.
they're not really "back", they never really left. They just post at an incredibly slow rate
@@udiprod we love you
" Don't call it a comeback, I been here for years
I'm rockin' my peers, puttin' suckers in fear
Makin' the tears rain down like a monsoon
Listen to the bass go boom"
@@ativjoshi1049 Ahh, a fellow LL Cool J fan, I see.
i love how this video characterises measuring quantum behaviours not as a passive look-and-check but something you actively need to do, it really helps people understand that to measure a quantum thing really does change how it will act in future, something that's really often overlooked and/or misunderstood
udiprod is probably my favorite underrated channel about computer science and physics
Oddly specific
@@MayorVideo you're right. should have used and/or since I meant logic gate OR
@@lemonice heh
Some technical remarks for those interested: There's some really deep and fascinating amount of physics and philosophy about this stuff! The "magical non-signaling box" is known as Popescu-Rohrlich boxes, if anyone wants to look it up. It's basically just a probability distribution p(a,b|x,y) (probability of a,b outcomes given x,y inputs/settings) which are non-local, but also obey non-signaling conditions. The values of x/a and y/b are assumed to be in "separate laboratories".
We say a probability distribution is local if it can be written as a probabilistic mixture of local probability distributions. Mathematically: p(a,b|x,y) = Σ_i pᵢ p(a|x,i) p(b|y,i), where pᵢ is a probability, and p(a|x,i) and p(b|y,i) are the local distributions depending on this i variable. Σ_i is "sum over the values of i". Classical physics restricts us to these.
A probability distribution is non-signaling if the outputs of one side don't depend on the inputs and outputs on the other, that is, if you compute the marginal (sum over "the other side"), you get a distribution that can be written as: p(a|x) = Σ_b p(a,b|x,y), for all a,x,y and similarly for the other side: p(b|y) = Σ_a p(a,b|x,y), for all b,x,y. This means the local probability distributions carry no information "coming from the other side".
So the distributions of these "magical non-signaling boxes" (or "PR boxes") is non-local, but it's still non-signaling. That's a VERY surprising result, because we sort of hoped that non-signaling was a property of locality, that is, non-signaling is a physical consequence of a finite speed of light. But what the (mathematical) existence of PR boxes show is that non-signaling is an independent property of locality, so we currently have no physical argument to deny the existence of such weird things.
(Mathematically, what all of these results show is that: Local Correlations ⊂ Quantum Correlations ⊂ Non-Signaling Correlations, where ⊂ denotes a strict subset.)
Woah it's wikipedia math man
its funny to think what magical physics object could have such property?
20:23 The top coin flips when both handles are set to be 1. That means the bottom handle is sending signal to the top coin!
@@beijingchef2745 the coin is an intrinsic state of the device, there is no way for an observer to see that the coin flips, thus signaling between coins does not matter. It is indeed weird, but If the state can't be physically observed in any way, it may violate any laws, and it's fine from physics standpoint.
Such as blackholes for example, singularities in the centers of those allow for some serious violations of a lot of laws, but because a singulatiry can't ever be observed due to the event horizon, it's completely fine, because those violations can't affect anything observable.
@@beijingchef2745 that what's I thought as well. How would one machine know other one is 1.
6:10
I got so excited the moment you brought this out. That came outta nowhere.
This is a great video!
There is still a third hidden assumption regarding Bell's theorem, in the particular case of the video, it is that input bits from the referee are uncorrelated from from the particle outcome. So, from a physical point of view, it is possible to imagine local and deterministic strategies that should still be coherent with the 85% winning quantum strategy observation, granted this correlation exists and originates in the common past of all the matter composing the game elements. This possibility is defended by Gerard 't Hooft, among others.
Thanks! Right, I just added it to the description as the "superdeterminism" option.
Omg THANK. YOU. *hits table*
Presumptions are always ignored, I can't accept the theorem for several of them!
So the creation of the entangled particles could send some kind of hidden signal to the referee and influence the "secret answer". Did I get that right? Or the creation of the secret answer could influence the entanglement, whichever happens first. Or there could be some other cause, even further back, that sends messages to both. -----
Another thought that I had about the parallel-worlds interpretation: Does the "world splitting" happen when the particle is measured, or does it happen when the secret answer is picked? Is it possible to make the math work? I don't know the math well enough, but it feels like there is some kind of dualism, where the referee creates something and the quantum measurement destroys that same something.
The basic problem with superdeterminism, at least in my opinion, is that there's no obvious physical mechanism for those correlations to arise. Why should the referee's input bits have anything to do with the entangled particles? They are (at least in the real-life experiments which the video alludes to) produced by entirely unrelated processes, and it's really hard to come up with an explanation for why they should agree with each other, aside from "the results of the experiment travel back in time and retroactively change the referee's choice of bits." But a retrocausal explanation is just FTL signalling in fancy dress.
@@NYKevin100 t'Hooft says you only need some kind of conservation law that ensures superdeterminism at the particle level and eventually propagate to macro scale observations, like here. Then, since all the matter we know originate from a distant common past, all particules must be correlated through this conservation law. That would include the referee's input bit and all of the matter making up the physical processes of the experiment.
The most comprehensive explanation of Bell's Theorem by far. Well done !!!!
I like how you represented a biased coin by bending it :D
After gaining a bit of background on Bell's Theorem, this finally clicked for me. Well done!
So you understand why it's intellectual nonsense now? ;-)
@@lepidoptera9337 Possibly,but not for reason you think
@@a2sbestos768 I didn't think that you can reason about this. That would require some serous training in physics. ;-)
Thanks, very clear, and (though occasionally tedious) I like the way you really consider all the possibilities deeply instead of handwaving, and feel I have a more solid understanding because of it.
He didn't really consider *all* the possibilities. For instance, he handwaved the statistical indipendance assumption, in favor of which we have no real evidence, and the universe could work fine without. If you search online, you'll find it's often called the "free will assumption", but that's due to unscientific misinformation. I suggest you research about superdeterminism if you want to know more about this.
@@falquicao8331 There is a version of the Bell test, where the orientation of one of the measurement devices depends on light from a very distant star. While you are technically correct that we can't be 100% certain that superdeterminism isn't causing the results we see, it is a 𝘷𝘦𝘳𝘺 reasonable assumption that the photons from that distant star weren't pre-programmed with the exact time and date, down to the microsecond, when the experiment would take place, such that the results look exactly as we would expect if the particles were entangled and their measured spins were random. The universe would literally have to conspire against us, trying its hardest to look random, never slipping up, for superdeterminism to be true! Since superdeterminism can't (likely) ever be disproven, it is borderline unscientific misinformation too...
This channel is cool
I started out wanting to see bogosort and now I'm learning physics
Thank you! I've always been struggling with bell theorem before your explanation. Finally it clicked!
Love everypart of this video. A masterpiece!!
Dude! They’re back! Thank you!
The video is incredible, but udiprod has gone above and beyond in responding to people's questions and queries about such a hard to grasp subject (even with a very helpful video such as this) :)
Thanks! My pleasure.
Once again another lovely udiprod video, while they do take a while to post, the quality is always amazing.
Great to see you're still on the platform! The last video I watched of yours was one about sorting algorithms from a few years back, so it's cool to see you still here and making content, great stuff!
Is that a homestuck reference
these are so good I can't wait to see more
Always nice to see another video, you guys have such incredible clarity when explaining things. Here's a topic suggestion: the pigeon hole principle and what it means for compression.
Great submission.
Extremely nice description. I first read the book from ginsi abou this and this video answered all the questions i still had
This is such a well made video, wow.
Wow great video
It's the first time I understood bell'S theorem
Thank you
I don’t know much about physics, but this is still very entertaining. I am happy this was on my recommended.
Love all your videos!
You're a madman udiprod. Great stuff!
6:11 Well, that escalated quickly!
Actually it's a point that I think I didn't stress enough in the video:
The 2x2 table such as the one shown at 4:13 can describe any decision process using any device. So even if the player is using some clever AI algorithm running over a supercomputer, we can still describe its behavior using such a table.
So when we prove such a table is equivalent to tossing dice, it seems like we proved the 75% barrier holds universally for everything.
The implicit assumption in this proof is what quantum entanglement breaks - the locality assumption.
Thanks for mentioning superdeterminism in the description
Very good job to explain concepts such a pleasant way. Other documentaries i watched on this subject realy not bother to explain how we come up with conclusion that qubit values not determined beforehand. Also nice touch with spooky tunes.
The legend returns
holy crap I love this channel
It's weird how the universe cares specifically about whether it's communication or not.
We found this "quantum" thing that makes something instant and tried so hard with it. Yet the universe said "nope." therefore we can't send information with it.
It's related to special relativity. According to special relativity, if A takes an action that has some instant effect on a far away object B, then some viewers will view the effect on B first, and then A taking the action. This is because of the relativity of time relations.
So from the assumptions of special relativity it follows that the actions of A can only send signals within A's light cone, or objects that are within reach of a light ray from A.
@@udiprod but assume we can't see light and only hear sound. Then if A sends an audio signal at the speed of sound and B reacts when it receives that audio signal, we observe B after A. However we now use this magic light signal that's faster than sound. Then do we observe B before A as a "viewer" near B?
@@AgentM124 No, the problems are only caused with signals that travel faster than light.
According to special relativity, two events A and B can be separated either in a "timelike" fashion, or "spacelike" fashion. If there's enough time for light to travel from A to B, then it's "timelike", otherwise it's "spacelike".
If they are 'timelike' separated, then all viewers will agree that B occurs after A. This follows from the mathematical formulation of special relativity. And this is also what happens in your example. Only two events that are spacelike separated then some viewers will see A before B and some will see B before A.
Communication implies a sender and a receiver, which means causality is involved. The message was received because it was sent. The type of coordination in the video is permitted because the behaviours are the same no matter which one happens first. Neither party can tell whether they observed the particle first (such distinctions are reference frame dependent), so relativity is fine with it. While the behaviours are coordinated, they are not causally linked.
Great production. Very interesting. We need more. Thank you.
i just watched a whole video on quantum computing, understood none of it, but still was invested through the whole thing anyways.
this channel goes hard
So... Spooky action at a distance exists, but this gives no 'information' as the result is still 50/50, but nonetheless it can be useful, like in this game... That broke my brain. Am I wrong about it being useful?
You are definitely right, these non-local effects are useful for this game, and for practical applications as well in cryptography.
glad they're back
Great videos !
so instead of the players being able to communicate, their tools are? great video and explanation, but it still confuses me a bit.
They can't communicate but they can coordinate
One way to look it at, is to say their tool is this type of spooky action at a distance that is allowed by quantum entanglement. So the behavior of one player has some (limited) effect on the result sent by the other player. This allows them to coordinate their results according to the rules of the game.
A general mathematical way to describe their tool is the concept of "non-signaling correlations" (at 18:49) . Its saying they can be coordinated in any possible way that mathematics allows that we can prove that it can't be used for sending signals. This is an abstract description, that doesn't commit to a specific physical process that implements such a correlation. But in principle, any such non-signal correlation can be implemented by a hypothetical physical process.
It's not "communicating" for the players to exchange a bunch of entangled pairs _before_ the match starts, which is all that's required for the 85% strategy demoed here. That's no more "cheating" than exchanging pieces of paper or computers or words (which they need to do to choose a strategy) would be, _before_ the match. While the video _showed_ the players communicating between rounds, this isn't actually cheating since the game is stateless between rounds as-defined (and isn't actually necessary anyway since the players could just instead bring along a bunch of machines or entangled particle refills before the match, to avoid communicating between rounds, either)
per [19:33] “we have good reasons to believe it can't exist”: any Sophomore-level general relativity course will show how faster-than-light communication _implies_ time travel by explaining just exactly how to bootstrap the former into the latter-this would allow _impossibilities_ such as going back in time to kill your own father), so there's _no way_ that any device that *actually exists* (such as the green measurement boxes from the 85% strat) is communicating, so long as the players are placed far enough away.
sheesh welcome back udiprod
So, if one particle is in our galaxy and the other particle is in Andromeda, does this game still work?
It seems like the implications of this is that: we can't communicate faster than the speed of light, yet at the same time we can because of quantum physics?
Yes, it works for any distance. But it can't be used for communication, as explained in 18:49. It can be used for coordination, as is done in the CHSH game. And using this same kind of coordination, it also has cryptographic uses.
Yes it appears to work no matter the distance. But every theory so far we have for quantum entanglement includes multiple presuppositions and that is a problem.
They say* it can't be used for communication, and so far no one's been able to come up with a way it could, so therefore it "doesn't violate the speed of causality/speed limit of light"
@@SolidSiren There is the no communication theorem. It isn't just that no one has found a way to communicate with it yet.
It's interesting, right? It seems like you could use these boxes to send information, say, by intentionally 'winning' or 'losing' the CHSH game a certain number of times. But the kicker is that the other player won't know what message you've sent _until they get the results from the referee_, which still has to be done at the regular old speed of light.
@@nycki93 Another way to view that is that if you're stuck in Andromeda with your chain of entangled particles, you can arrange to win or lose games corresponding with events on Earth all you'd like and you *can* know that the "win" signals the other person is trying to send are winning 85% of games while the lose signals are only winning 15% of games.. but you still have no way to know *which* games won or lost.
The same is even true of the unrealistic Popescu-Rohrlich boxes "100% win" boxes described: you could know that 100% of the games where Earth wants to send you a "win" signal win, and that 0% of the "lose" signal games win.. but even *that* doesn't tell you *which* games are which. You get a bit from the referee, you figure out your own bit and send it back, but your own bit still always has 50% chance of being a one or a zero as does the ref's bit.
Just commenting to help this get popular soon
Incredible video! This is always a good channel.
That was so cool!
Awesome video
thanks for come back, I apreciade a lot your work, may be you can obtain support with an account in patreon.
I think this cheats the hypothetical. If this was a programing solution it would still require a reference which is the entire point. One player is dependant on information from the other player, even if it's built into the fabric of the universe, they are still communicating.
Yes, absolutely, but that’s kind of a moot point. The purpose of the hypothetical is to demonstrate this interesting fact.
is the behavior of the "undefined" spin particle still indistinguishable from one that we have recently measured but forgot the orientation of?
The entanglement has to be created through certain processes, and the creation of the entanglement is local. For example, if a particle with 0 spin split into two you’d know that the total spin has to be the same, so if one is +1 the other must be -1
@@btd6vids yes i think i understand that already, i don't see how that answers my question
@@bpansky It means that once you’ve measured the particle they’re no longer entangled so it doesn’t matter whether you personally forgot the information, as far as I know
I always see entanglement on the same plane as Maxwell’s Demon. Insofar as the idea of the “demon” performing a function, as a meta for the system. “Entangling” automatically comes as prepackaged info, before you even entangle it, that measuring one bit will simultaneously let you know the state of the other. Which takes me back to the interpretation of the “pair of gloves.” The simple knowledge alone of what is being measured before hand is the “demon.”
If two beings at the opposite ends of the universe already knew about gloves and how they are paired, left hand and right hand gloves, and that pairing them (entangling), as proper entangling would be proper pairing. If at opposite ends of the universe, one observer gets a left hand glove, he will automatically know that the other is a right handed and vice versa. You know this instantaneously, thanks to the “demon” which is the foreknowledge. You can’t actually confirm this instantaneously, but what you know about glove pairings, it must be true. The information always existed in the pairing, when it was paired. The actual observation seems arbitrary.
The knowing what to look for before and after entanglement is the demon in the problem. You won’t know which glove you have before the observation, but when you do, you’ll know the state of yours and the other’s and when you meet up with your partner from the opposite end of the universe, you’ll find that your measurements coincided. Since the gloves can’t travel faster than the speed of light anyhow, nothing is violated causally. You can’t know which glove you’ll have until you measure it, but when you do you’ll know the nature of the entangled partner.
My issue is you can’t say you are “entangling” particles, and negate that information was put into entangling them. When you entangle them, you are essentially tying an equilateral knot. Pull on one end or the other, you will have an end in your hand or your partners hand, but the knot (entanglement) will be gone. Tying the knot, didn’t change anything about the nature of the reality of either end. You just paired opposite ends, with foreknowledge that what even end you measured, you knew there was another end that would be opposite. You knew that when you entangled them and you knew what to look for measuring them and what the conditions would be. The demon.
This world view is the "local realism" view, explored at 16:10.
The players are given particles that contain some information locked within, and they are prepared so that they'll have opposite spins.
But this doesn't work - it still can only win at most 75% of the time.
The issue you raise is a good one, in that most people seem to neglect the fact that the knowledge of entanglement is related to a greater system… “we can prepare particles that are entangled!” is usually all the depth given to that topic.
But the point with the gloves is that, once observed, the glove must be either left and right and the other glove state can be known via inference. But before it is observed, the glove is neither a left or right glove, but a single “superposition” glove. This distinctly different third state of the glove isn’t observable to our most direct experimental methods (such as “looking at it”) but it IS observable via more indirect, roundabout ways. Bell’s theorem is one such way; the two slit experiment is another.
@@dialectphilosophy I guess the “problem” I have with my correlation to the glove, analogy is that it isn’t a 1:1 for the experiment. Simply due to it not being binary as a left or right glove, as what is being measured, photons, are being measured of 1:3 states, left hand, right hand, and a third “hand” glove, but not necessarily a superimposed state of the two. In the Venn Diagram Paradox version of this experiment, the filtering of the light fundamentally changes the light passing through it.
I picture light passing like a bullet from a gun, if you will. At 0 degree’s between two filters, you have a “100%” pass through. I always feel like the like being filtered isn’t really explaining how the filtering affects what is actually being measured. Now when you pass light through 0 degree and a 45 degree angle on the polarizer, you have a 50% pass through. So I picture half those bullets being changed going through (path wise) differently than the 0 degree pass through, and the “filtering” by absorption, has to do with filtering light interfering with each other, other than just simply acting as a “strainer” for light. Which is why when you introduce another filter in the middle a 22.5 degrees, between the 0 and 45, you get more light at the end than just the two. Altering the path of the light isn’t a simply binary function, and the information being changed between filters is more complex than just saying the light passes through or it doesn’t, it is what is being imparted by the measurement itself. I picture light traveling in a pack of bullets, twisting about their axises, while tumbling forward, each filter, depending on it’s orientation changes that orientation and it’s interference pattern(s) with itself, leading to different pass through.
I hate to invoke “hidden” variables, but that is what I feel makes things “random” in these experiments. “Random” simply means (to me) that the function unfolds faster than we can predict or that making measurements of the function, changes the function itself, which also propagates faster that we can analyze it. That is all “random” means to me. That the “hidden” variable(s) are only hidden by virtue of measuring them changes the result and/or calculations over time compound faster than can be measured as it propagates and compounds.
I can't help but feel that utilizing quantum entanglement breaks the "No communication" rule
I feel the same way, the entangled particles may be WORSE than a telephone line (which would allow them to win 100% of times) but it's still better than nothing... So it feels like cheating.
its basically a machine that helps the players win more than normal but the players aren't directly communicating through the machine so it isn't completely communication
Liked the spooky music, at a distance
While I'm glad you are back, I'm kind of sad that you changed the artstyle. I absolutely loved the "old-school" 3D look of your animations. It always made me feel nostalgic :')
Thanks. I didn't change, I'm trying out new styles, and trying to match the style to the content of the specific video. There'll be more sorting videos, and more 3D ones on other topics.
@@udiprod I'd watch them either way haha
Looking forward to see what you have in store for us!
@@udiprod I like the new style much more!
@@aBigBadWolf Which video's style do you mean?
@@udiprod the new one (as in this video) instead of the more 3d style of your sorting videos.
First vid of 2022!!! See you all in 2023!
Wow, high quality! (and first)
excellent
So "non signalling correlations" need not obey the speed of light barrier?
Right.
I believe you have a typo in the description. It says “The referee an”, and it seems it was meant to be “can”.
Thanks! Fixed.
what software do you use for these animations?
Thanks
So... basically spooky action is a thing? What happens in this game if both players try to measure at the same time?
This definitely is a tricky subject to wrap my head around.
It's easier to assume that there's never such a thing as exactly the same time. So one player always measures first, even if only slightly ahead. But even if you want it to be exactly the same time, we can still define the joint distribribution of the outcomes, as shown in 14:02. This distribution is the same regardless of which of them measures first.
@@udiprod I see. This is quite a fascinating topic! Thank you for sharing this with us!
The really weird consequence of all this in my opinion is that players can use quantum entanglement to _synchronize_ information, but not to _send_ information. You can affect whether the other player sees the same random bit as you or not, but you can't do anything that would make them roll more 1s or more 0s overall. So, the "spooky" thing is that the particles clearly have some sort of shared state, but there is no measurement that can extract even a _single bit_ of information from it.
@@udiprod One thing that nagged me about the explanation is talk like "affects instantly" with a background of putting the players a relativistic distance apart. There can't be any simultaneity in that situation, so one could say the measurements are "spacelike" to one another.. but never truly simultaneous.
Unfortunately I can't think of any superior way to phrase this for a video to people who might not find that intuition familiar, so I remain nagged without obvious resolution lol.
Anyway, great video as always. 👍
@@happmacdonald Thanks! You are right of course.
But the phrasing and presentation problem is even worse than you say: when the video shows the top box being measured first, and we even say "let's measure the top box first", this is also not something that is true for every frame of reference. In some frames the bottom box is measured first.
An accurate way would be to say: let's view this scene from a frame of reference where the top box is measured first. From this point of view it's also true to say that the other box changed instantly, because from this specific frame of reference this is what really happens.
It is interesting to me that these machines only seem to work due to the fact that the probability changes non-linearly to the angle. If the probability change was linear to the angle, this wouldn't work. Is there any theory on this?
If you mean the cos^2(theta/2) relation, it can be derived from basic Quantum mechanics. (By finding the eigenvectors of Pauli matrices in generalized polar representation)
I didn’t think about that Jonathan! Interesting
Are there other ways that you use more than one pair of particles or a different arrangement to get 100% for this game?
I don't believe so. For example, using multiple entangled particle pairs would give you no bias in results: 50% of your particles would still flip one way or the other.. but your team mate is getting *exactly the opposite* 50%. So you'd still have to boil your series of flips into 1 bit of data, as would your partner, and be stuck with the ~85% outcome.
Another one of these, oh wow.
Think about if you had shown Newton this game and just said "its possible to get 85% but no higher."
You can set it up as 100% same result and they can communicating with each other. Then player 1 can place top if he gets 1 and bottom if he gets 0. Player 2 knows what player 1 gets and what himself gets. So they use a new entangled particle and tell player 1 choosing which bit to reply. 1 or 0. Then it is 100% win rate. Although you need 2 entangled particles.
When you say "player 2 knows what player 1 gets", do you mean what player 1's input bit is? Or what the measurement outcome is?
Because here are some provable rules:
* Player 2 can never know what player 1's input bit is. This is demonstrated in the 'no signaling section' at 22:10.
* Under some circumstances player 2 can know what outcome player 1 received (for example, if they coordinate in advance to measure at opposite angles). However, since they don't know the two input bits, they don't know if they should output equal bits our unequal bits, so this doesn't help them.
Yes, that sounds right. If they have a signaling device that works in p% of the games, then they can certainly win p% of the games. But of course having a signal device at all violates the rules of the games (and the laws of physics - since the players are too far away from each other to have time to send signals).
Best visulisation of quantum particles, and quantum "functions" I've seen!
What if you measure three quantum particles per game and take the most popular result?
To me it seems like quantum entanglement is still a signal. The top particle is sending information to the bottom one or vice versa. That information is, if I'm one direction, you must be the other.
Great video as always.
Also, I guess it should be "up" at 9:54, not "down"
Thanks!
Actually I considered changing this scene because it's a bit confusing, but it's actually "down", since we measure up/down relative to the device, which is upside down in this scene.
@@udiprod You should have probably said "towards" and "away". The script may have a few more words, but it's much more clear and direct with what you mean by "up" and "down".
is the word "Unequal" different to the word "different"?
Also, what way are you meaning when the players responses are "unequal"?
Do you mean, different between each of the players? Different responses that the referee receive, or something else?
I feel like I've learned so much from this video but I can't tell what it is
Today, John Clauser received the 2022 Nobel prize for Physics for inventing this experiment...
I just discovered that this upper bound of about 85% you keep mentioning, calculated by cos²(45°/2) = 1/4(2 + √2), can be rearranged in this pretty form: .5^.5*.5+.5
It is very interesting to me that this is the series of hyperoperations in decreasing order, starting at 3. What I mean is it goes exponentiation, which is repeated multiplication, then multiplication (repeated addition), then addition. I'm curious why it starts at 3, if there is any quantum-mechanical or physical significance to the same series of operations but starting at, say 2 or 4 or n, and why the term being operated upon is .5 (although for probability, 1/2 is perfectly between 0 and 1 so it comes up a lot, for example in the Riemann Hypothesis).
What's the song in the intro?
Couldn't there still be local realism since the particles were swapped out after each round or is there something that flew over my head?
A theory permitting superdeterminism can recover non locality in a hidden variable formulation of what's going on here. Philosophically I like the idea of superdeterminism, but physically it seems a tough notion to prove, and hence support. Would be interested on your take.
How do quantum particles get entangled in the first place?
Can I make quantum entangled particles out of household objects?
Man i love gabling with the bro and then we cheat and start communicating using quantum [spin]ics
I plotted the winning probability as a function of the angle of the zero-markers on the green thingies. It's (sin²((-2π+α)/2)+cos²((-(1/2)π+α)/2))/2, which is the same as (sin(α)-cos(α)+2)/4. The Maximum probability is approx 85.35534% at 135° and the Minimum is 14.64466% at 45°. (The one-markers are obviously in a 90° angle to the zero-markers)
what if you have a larger odd number of quantum bits, and used a majority vote?
Locally each bit would still be 50/50 providing no lean one way or the other
Hell yeah more udiprod
🤔 The really interesting thing is that with this system, you can pretty much guarantee a correct calculation as long as you do it a few times. It won't be 100%, but it will be so close it might as well be. Quantum computers are really fast too since they are well...always in both states at once. Spooky stuff indeed.
The quantum strategy in the video is claimed to be the best strategy at around 85%. And it is claimed that it's been proven to be the case. You can't do this process multiple times because your chances of getting 0 or 1 is always 50-50, even if the entangled probabilities vary.
the song is such a spooky banger please i need to know a name
Cool
*Starts off with classical physics*
*Goes into quantum mechanics*
*Changes to local realism with quantum mechanics*
*Straight up uses magic*
I think I can find the point where udiprod just gives up.
I don't understand how this rules out determinism rather than locality? if you assume (as we know) that measuring something affects it, then hypothetically the measurement is simply rotating the hidden information in some way, which can be deterministic. From what I understand, measuring a particle breaks entanglement because of this exact behaviour and in fact this game shouldn't even work since we can't measure the same particle multiple times?
Am I misunderstanding something?
You are right, it doesn't rule out determinism, it rules out locality (with the help of some additional assumptions). There are deterministic, non-local interpretations of quantum physics.
Like you say, each pair of particles can only be used once. The game has just one round, so the players need only one pair of particles, and measure each particle once. If we want them to play multiple games, we need to provide them with many pairs of entangled particles, one for each game.
Ok. There's still one thing that is not quite clear to me. Does this "quantum strategy" agrees with "uncertainty principle"? I mean, we have to assume that there's ALWAYS a particle inside a box. Where's always a valid object to be measured. Otherwise , if we get both "0" and "0" as results of measurement - how can we be sure that there was anything an all, not just empty box? I guess, if we consider "empty" box as a possible event, that would extend the number of losing outcomes, and reduces total win probability to 3/4 ?
The uncertainty principle doesn't say we can't be sure of anything. It says we can't have full knowledge about some specific pairs of properties, such as position and velocity. It manifests in the video as well, about the spin property: it says if we know the spin along one axis, we can't be sure about it in the other directions. That's why we have this probabilistic law instead.
So in theory we can do this experiment exactly, and reach the exact predicted 85%. In practice of course you are right, it's difficult to make sure the right particles reach the right boxes at the right times. But since the theory allows us to be accurate, it's just a matter of clever engineering to do it accurately, and there has been improvement over the years, reaching the point where we can do this experiment close enough to be sure it exceeded what classical physics allows.
@@udiprod Thank you! I just wanted to express my respect to you. Your videos are realy a masterpiece of educational work.!
Thanks :)
part 1 and 2 is what I had in school
But every time the referee sends a combination of bits, the quanum particles must be reentangled, as the entanglement is destroyed after measuring, right?
yeah, the video mentions they get replacement bits after every round
amazing stuff dude now i can brag about that i know quantum physics🤣
With the no signaling solution, aren't we just moving the problem of sharing information to the machines ? at least one of them needs know what the other's one's state is in order to change what it displays, or am I missing something ?
6:10 speedrun strategies
Some of the classical strategy pairs win 1/4 of the time, while others win 3/4 of the time. When at least one of the players works by choosing a random strategy, the expected win rate is 1/2. Please correct me if I'm wrong.
Maybe I'm not understanding something, but can't we get arbitrarily close to 100% success if we have synchronized clocks?
Algorithm: player 1 (receiving bit a) rolls alternately at 0 degrees and 90 degrees, until the reading at 0 degrees matches bit a. Each time they reroll at 0 degrees, the result should 50% 0 or 50% 1, so the probability of getting a after N cycles is 1 - .5^N. Then after some specified amount of time, player 2 reads at 180 degrees. If player 1 has successfully rolled a, then player 2 will receive a reading of (a), otherwise it will receive a reading of (1-a). Assuming enough time has passed, the probability of passing bit a nears 100% so player 2 should almost always know what was sent to player 1.
The problem is that the entanglement breaks after the first measurement. So all the re-rolls that player 1 does no longer have any effect on player 2. It's an important property of quantum entangled particles that we can't force the result to be one or the other, that's why it can't be used for communication.
@@udiprod oh of course, thanks for the response!
Bell's theorem is the physics version of "Much Ado About Nothing". :-)
okay, so you can't communicate faster than light with entanglement, but you can correlate light speed communication better than random, faster than light.
the time it takes to test that correlation is 1*distance, whereas for the parties to signal at the speed of light, it would take .5d to receive the question, +1d to communicate, +.5d to send the answers back.
that's a doubling of efficiency, with a little reduction in accuracy. you could then send a message from one player to another in 1.5d, .5d to send 2 dummy requests, the B player uses their machine to correlate or uncorrelate the response to the 2nd request, +.5d to send it to the tester, then +.5d for the tester to send that to A player... which is dumb and slow, but fun XD
The spin is not undefined entirely, it is only undefined in the rotation plane we are considering for this experiment, in fact in order to get it to such a state, we effectively perform an operation which sets the spin directly perpendicular to this rotation plane.
The measurement of the first bit does not necessarily instantaneously set the state of the second bit. In fact it is entirely possible for a pre-coordinated hidden variable set to exist. Such a set of hidden variables effectively defines a mapping of measurement direction choice to a set of weighted outcomes, fitting to the expected probability from quantum mechanics, including the 100% chance that opposite/same spins result from same/opposite measurement directions.
This is not the same as the local realism described in the video. The video shows local realism as a set of deterministic states mapped one to one to the set of measurement directions. Instead, what I am describing is that each measurement direction maps to a set of deterministic states, each weighted probabilistically. The hidden correlation between the entangled particles is this same mapping, but to flipped weights (100% - other weight).
The actual outcome may also be deterministic, influenced by the weight of the deterministic states, but ultimately determined by some local condition. This local condition need not be common between the entangled particles, as the probabilistic factor emerges from the symmetric weights.
I would love a reply to this from someone. This is exactly what I was thinking but worded far better than I could.