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I have to say right off the bat, I'm a little frustrated that there seem to be very contradictory answers about this, at least to a layman like me. If two particles are entangled and you separate them by some huge distance, and you measure one of the spins, you know the other particle must be spinning the opposite direction.

The usual analogies I hear are things like, well if you have a blue and red marble, you scramble them in a bag and then take one blindly, and give the other to your friend, if you look at your marble and see blue, you know your friend must have red.

To me this sounds like "boringly classical pre-determination." Like this whole spooky action at a distance is really just "the spins were already opposite to begin with and we just separated them," as if we had a machine that spat out pairs of opposite-colored marbles and now we're surprised that they're always opposites regardless of how far apart we are when we see them.

At the same time people say it's not like that either (Bell's inequalities). In quantum mechanics the state of something is in this weird superposition where it's not known for sure -- it's sort of everything at the same time and it only takes on a particular state according to a probability distribution. So the two particle spins are unknown and yet somehow when you observe one, it "communicates" to the other (regardless of distance) what its state is so it "knows" to become to opposite.

But apparently it's not that either and there's no communication actually taking place or information passing from one to the other, and this is what really gets my goat. The usual response is that we cannot choose what the state is or input any kind of information that can come out the other end.

I feel this answer is a bit of a cop-out because it doesn't address the confusion, just sort of attacks low-hanging fruit over some semantic difference in the word "communication" even though what is really being asked is the sort of cause-effect relationship going on. I am fine with the idea that we can't directly input what we want or use it to communicate. But how is it not a form of "the particle is communicating something" or "causing" or "influencing" something to happen in the other?

Normally this discussion goes nowhere and someone inevitably says "Well you just have to learn quantum mechanics." I always find this answer deeply unsatisfying. It feels like the other person is giving up on you and can't be bothered to explain it.

So... what's going on? I'm not stupid but I'm also frustrated that these two interpretations both seem to be wrong and yet no one can actually seem to address the core point of confusion despite Googling this question across blogs, news articles, Reddit, Physics forums, Quora, etc.

It's always the same back-and-forth. "There's no communication... but it's not like the states were known to begin with either." How on earth is there a third possibility to this?

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    $\begingroup$ This is really the key though. It is neither FTL communication, nor just revealing pre-existing information. Bell's theorem says that any theory of the latter type has to be nonlocal, which is considered to be quite ugly even if it can't be used for FTL communication. $\endgroup$ – knzhou Feb 7 at 18:09
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    $\begingroup$ You might ask, intuitively, how could this possibly be true? After all, classically it has to be one or the other. Unfortunately the simple answer is that it has no classical explanation, because quantum mechanics just isn't the same thing as classical mechanics. I could give a nice-sounding argument using only classical intuition for what is going on here, but it would necessarily be wrong because the world isn't actually classical. To get the real story, you're going to have to learn quantum mechanics. $\endgroup$ – knzhou Feb 7 at 18:10
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    $\begingroup$ Any correct explanation, purely at the verbal level, is going to feel like a "semantic copout" because language was invented to describe ordinary experience, i.e. classical physics. Common English simply does not have words to explain what is going on correctly, but the language of mathematics does. $\endgroup$ – knzhou Feb 7 at 18:12
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    $\begingroup$ (c) none of the above. $\endgroup$ – WillO Feb 7 at 19:08
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    $\begingroup$ You might benefit from reading my answer here: physics.stackexchange.com/a/330571/4993 $\endgroup$ – WillO Feb 7 at 19:12
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So is quantum entanglement actually FTL “communication” or is it mundane pre-determination?

In short:

  • It is not "mundane pre-determination".
  • Whether it is "actually" some form of FTL communication depends on which interpretation of quantum mechanics you prefer.
  • However, regardless of interpretation, if there is some form of FTL communication between the parties, then it is completely inaccessible to us.

That said, you're certainly correct in one respect: there's a lot of very poor descriptions of what entanglement is and how it works in the popular-science press. In particular, these two paragraphs do a very good job of summing up a very common misconception that arises from poorly-written material:

The usual analogies I hear are things like, well if you have a blue and red marble, you scramble them in a bag and then take one blindly, and give the other to your friend, if you look at your marble and see blue, you know your friend must have red.

To me this sounds like "boringly classical pre-determination." Like this whole spooky action at a distance is really just "the spins were already opposite to begin with and we just separated them," as if we had a machine that spat out pairs of opposite-colored marbles and now we're surprised that they're always opposites regardless of how far apart we are when we see them.

Your interpretation of that description is indeed correct. However, quantum-mechanical entanglement goes much further than that property, and this is exactly the content of Bell's theorem.

To be more precise, Bell's theorem is a description of systems that use "boringly classical pre-determination" (known in the technical lingo as Hidden-Variable Theories) to produce correlated outcomes, and it makes quantitative statements about which kinds and what amounts of correlations you can expect from such a system.

Bell's bigger argument then goes on to construct quantum-mechanical states that break those bounds, and which therefore (provably) cannot be explained with "boringly classical pre-determination" at all. And, when we talk about Bell-test experiments, we refer to experiments that implement those states and show that you do indeed get more correlations than classical pre-determination can produce.

This does raise the question about how your initial model,

you have a blue and red marble, you scramble them in a bag and then take one blindly,

fails to describe the quantum systems at play. The answer is that this classical model is unable to describe superposition states between the blue-marble and red-marble states of each bag, and for the quantum-mechanical description to work at a level where it can exceed the classical bounds on correlations, it needs to be able to measure on the superposition state $$ |\text{blue marble}⟩ + |\text{red marble}⟩ $$ and to distinguish it from the 'conjugate' superposition state $$ |\text{blue marble}⟩ - |\text{red marble}⟩, $$ where that $-$ sign is a truly new, fully quantum-mechanical ontological feature that doesn't exist in classical mechanics.


OK, so it's not classical pre-determination. But is it faster-than-light communication, then?

Well... also no, this time because of another theorem of quantum mechanics - the No-Communication Theorem. This theorem states that, if you have any arbitrary entangled states linking two parties, and you allow them to perform any arbitrary physical operation on them, it is provably impossible to transmit a message in any way other than classical communication.

But that's at the level of the (ostensibly human) operators of the experiment, though. Do the particles themselves communicate?

And the answer here is that yes, it's not inconceivable that they do. More to the point, it is a consistent interpretation of quantum mechanics to suppose that there is a hidden-variable theory that underpins QM. Since Bell's theorem rules out hidden-variable theories which are 'local' and 'realist', the price for doing so is that those variables need to be 'non-local', which basically means that changes in those variables can propagate at FTL speeds.

However, the price for that is that the No-Communication Theorem requires that, to be consistent with QM, such a hidden-variable theory needs to somehow make that FTL communication completely inaccessible above the quantum-mechanical layer of the description. And that then means that, when you build those theories, they come out looking extremely contrived and artificial.

And here is where it gets subjective: most working quantum mechanicists are extremely uncomfortable with those theories as models of what reality is "really like". There are very good reasons to be uncomfortable with them, but $-$ as in all things where the interpretations of quantum mechanics are concerned $-$ this is ultimately a subjective thing.


Now as for the bulk of the text that you've written $-$

Normally this discussion goes nowhere and someone inevitably says "Well you just have to learn quantum mechanics." I always find this answer deeply unsatisfying.

Your observation is correct: this is indeed unsatisfying. But the hard truth is that, while it would be wonderful to know what's "really going on" between two entangled particles, we simply don't know. There's a broad array of proposals of how one should understand this, but they all have serious drawbacks and for each of them there's multiple reasons to think that it's completely bonkers.

We do know a lot about entanglement:

  • we know how to formulate the quantum-mechanical laws that define it, and which are unbeaten in their ability to match experiments
  • we know how to operate on those quantum-mechanical laws and the concepts within them
  • we know how to perform experiments that are able to probe those laws and their differences to more 'reasonable' theories
  • we know for sure that it goes well beyond 'classical pre-determination', and we have verified that experimentally multiple times
  • we also know for sure that it does not allow us, as operators, to use it for FTL communication
  • we also know that if it does involve some "back-end" FTL communication between the systems, then that requires additional "protective" layers in the theory that can fairly be described as completely bonkers
  • (but then again, every way to interpret QM does things that can fairly be described as completely bonkers)

But as to what's "really going on", we just don't know.

Judging from your text, it sounds like you already have a pretty decent understanding of the epistemology around entanglement, and that you've reached the kind of grounded frustration at the weirdness of the theory that's widely shared among working physicists. We know it's weird. We agree that it ultimately makes very little sense. We absolutely would like a better answer. We are actively searching for better answers, and we are making decent progress $-$ we are indeed advancing the state of the theory, bit by bit, and we're getting better and better at examining single quantum systems in ways that allow us to test QM in finer and finer ways. But we've yet to find that better answer.

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  • $\begingroup$ Great answer, helps me contextualize it a bit better. As a side note, what exactly is |blue marble⟩+|red marble⟩ versus |blue marble⟩−|red marble⟩? This was the only part of the answer where I couldn't really understand the argument being made. $\endgroup$ – user222141 Feb 8 at 16:28
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    $\begingroup$ Good stuff! I think this could serve as a canonical answer. $\endgroup$ – knzhou Feb 8 at 16:30
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    $\begingroup$ @user222141 That's a much bigger question than I can answer here - for now I'll limit myself to referring you to The Talk, by Scott Aaronson and Zach Weiner-Smith. If you want more details about the difference, you should ask separately. $\endgroup$ – Emilio Pisanty Feb 8 at 16:33
  • $\begingroup$ @user222141 : This question you ask, is exactly why I think it's right to answer back at you: "Go learn quantum mechanics". If you don't know at least the basics of the formalism, you shouldn't complain too much about not understanding it. When I was a kid, I wanted to understand relativity, and I quickly figured out that not having a solid mathematical background would get me nowhere. And relativity is still quite explainable with just words if you make an effort. But with quantum mechanics, you'll eventually have to dig deeper. $\endgroup$ – Raskolnikov Feb 8 at 16:44
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A couple of thoughts.

No, entanglement is not (does not allow for) FTL communication. With this I mean that, even if you and me share an entangled system, there is no way for me to alter what you will observe on your side. Yes, the operations I perform on my part of the system will affect what you will observe on your part, but there is no way for you to realize that this correlation exists without knowing what happened on my side as well. In other words, there is no way for me to send you information using only our shared "entanglement link".

To me this sounds like "boringly classical pre-determination." Like this whole spooky action at a distance is really just "the spins were already opposite to begin with and we just separated them," as if we had a machine that spat out pairs of opposite-colored marbles and now we're surprised that they're always opposites regardless of how far apart we are when we see them.

The key point here is that it is possible to show (via Bell inequalities for example) that sometimes you and me can observe correlations between our observations that cannot be explained by any classical theory like the one you mention.

More Precisely, the gist is that if we denote with $x$ and $y$ our measurement choices (e.g. $x=0$ means I push button $A$, $x=1$ means I push button $B$, $y=0$ means you push button $A'$ etc.), and with $a$ and $b$ our observations (say $a=0$ means I see output $0$, $b=1$ means you observe output $1$ on your side, etc.), then quantum mechanics allows for correlations $p(ab|xy)$ that cannot be explained by any classical theory, in the sense that there is no way to write such correlations as: $$p(ab|xy)=\sum_\lambda p_\lambda p(ab|xy,\lambda).$$ This expression means that there is no way to describe our observations by invoking some pre-existing correlation between our shared system. For example, your proposed explanation with the marbles is such a case, with $\lambda$ representing the pre-shared correlation between the colors of our marbles.

It is worth noting that the possibility of (independently) choosing different measurement settings $x,y$ is crucial in this argument. If we consider fixed, pre-determined measurements, then it is always possible to find a "classical description" of the correlations (see e.g. this post about this).

So... what's going on? I'm not stupid but I'm also frustrated that these two interpretations both seem to be wrong and yet no one can actually seem to address the core point of confusion despite Googling this question across blogs, news articles, Reddit, Physics forums, Quora, etc. It's always the same back-and-forth. "There's no communication... but it's not like the states were known to begin with either." How on earth is there a third possibility to this?

The frustration is understandable. The way I personally like to state the apparent paradox is as follows: how can there be correlations unexplainable by a common cause, and yet that cannot be used to transmit information?. Note that if we admit the possibility of a common cause, that is we consider "classical" situations, then it is no surprise that we can share correlations that nevertheless do not allow for communication (your marble example is again such a case).

But it's also important to realise that this is not simply some mathematical shenanigans that people like to wonder about in the abstract. These sorts of correlations are routinely observed in the real world, and as weird as that sounds, quantum mechanics is still the best and most "natural" way we know to explain these observations.

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"How on earth is there a third possibility to this?" That is exactly the $64,000 question of entanglement, but observations show that there is indeed a third possibility. It is possible for experiments to show correlations after the fact without it being possible to ever use this to communicate information FTL. (And don't confuse it with the red and blue marble, look up "Bertlmann's socks" to show why that's not it.) It means there is some kind of holistic quality of the system that maintains correlations across huge distances, yet this holistic character cannot be understood as a form of communication from one part to the other because it is maintained in ways that cannot be used to transmit information. (Interestingly, it can be used to encode information, in such a way that to intercept that information is to prevent its transfer. That's quantum cryptology.)

To go further, you have to start thinking about what information actually is, and where it lives. Does it live in a system, or in someone's head? If I read a book, is that information carried in the book and I'm just "extracting" it, or am I an active participant because I need to interpret what I read? In the formal sense, there is less information in a book than in a list of random letters the same length (because I would need more yes/no questions answered to be able to know the second, whereas redundancies in the first make it discernible with fewer yes/no questions), so you can see that "what is information" is tricky.

But I think this fact is telling us something: you could have one part of a pair of entangled particles, and you could choose any way you like a direction. You could then test the spin of your particle along that direction, and send a single bit of information (slower than light) to the other person, and with that bit tell them how to put their entangled particle into the same spin state as yours (same axis direction, same up or down state along that axis). This holds even though you are only communicating one bit of information, yet you can choose any axis direction you like!

That sounds like communicating more than one bit, but here's the catch: they would put their particle into the same state as yours, but never have any way of knowing what that state was! In particular, they could never know the axis direction you chose. This is related to the fact that when you do a spin measurement, you don't get to know what the state was, you only get to know if it is up or down along some axis chosen by you. Plus, you only know it afterward, so much of that original information is "lost" (if it was ever really there in the first place, that's the issue of quantum information). So the limits of what you can know, versus what "information" is in a quantum state prior to measurement, is the crux of the matter. It's all connected to the quantum measurement paradox, and the issue of whether a wave function is a real thing that represents information we don't have complete access to in each individual case, or if it is just a rule about correlations in ensembles. Classically, we never make a distinction between those two possibilities (like a deck of cards we just haven't looked at yet so treat as random), but quantum mechanics challenges us to decide if that distinction needs to be made.

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You are worrying about the apparently nonlocal behaviour of physical systems (so called 'spooky action at a distance') that is implied from correlations calculated from the formalism of quantum theory. These were pointed out by Schroedinger and Einstein, Podolsky and Rosen in 30's. There was some disagreement but the matter was largely ignored by the most famouse physicists. There was no way to test those correlations.

In 1964 John Bell came with his revolutionary analysis of quantum theory and nonlocality

J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics, 1, 195-200 (1964)

(copy here https://drchinese.com/David/Bell_Compact.pdf)

which brought a way (at least in principle) to test whether nature really behaves in such a strange way. Bell shows that quantum theory does not obey Bell's inequalities and therefore it is (in Bell's terminology) not a local theory. The inequalities provide a statistical test to decide in experiment with particle spins, whether particle spins behave in such non-local way or not.

This experiment is difficult to do and as far as I know, it was never done.

But other experiments on correlations of light, motivated by Bell's theorem, were done and are currently accepted in mainstream as a proof that nature behaves in a way that Bell called nonlocal, although the conclusion is sometimes contested (the experiments have various loopholes).

https://en.wikipedia.org/wiki/Bell_test_experiments

Also, there is some disagreement on terminology, there is another school of thought where experts prefer to say that quantum theory is still local, but not realist. Anyhow, all agree that quantum theory does not obey Bell's inequalities, which makes it very strange.

The accepted status of this question is that there can be correlations between distant systems that violate the inequalities or their analog (which is used in experiments with light), but at the same time, there is no known way to use these correlations for superluminal action at a distance or communication.

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Let me give you a simple example with a quantum mechanical particle called $π^0$.

The $π^0$ is a neutral meson, has a specific mass $~135$MeV and spin $0$, and inevitably decays into two $γ$ (photons).

Angular momentum is a conserved quantum number so the spin of the two photons,no matter how far they may travel in the cosmos has to add up to zero. So one only has to measure the spin of one photon, to immediately know the spin of the other.

The knowledge is an association in the experimenter' head read off from the spin detection of one of the photons. The previous experiments with $π^0$ 's established its spin, so it is in the data bank, the previous experiments with photons established their spin, the mathematics of angular momentum is in the books, so the quantum mechanical wavefunction describing the decay process mathematically contains the entanglement .

The decay of the $π^0$ follows the probability distribution given by the $Ψ^*Ψ$ where the wavefunction $Ψ$ is given by the theoretical mathematical model. The distributions which describe the decay, time, angles of decay, spin distributions between the two photons are controlled by $Ψ$ . Each individual decay has to obey the conserved angular momentum law.

It is not known what the spin of each photon will be, unless one measures it, but measuring one of them, because of angular momentum conservation, means that the other has been simultaneously measured.

So is quantum entanglement actually FTL “communication” or is it mundane pre-determination?

There is no predetermination for observables in the quantum mechanical framework where entanglement is discussed. All measurements of observables, have a probabilistic distribution. And there is no communication except in the mathematically imposed "knowledge" from the conservation of angular momentum.

Edit after the following comment :

@a1s2d3f4 I agree with user222141. You haven't addressed the confusion. In the last paragraph you suggest that there is simultaneously no predetermination and no communication. The OP is asking how that is possible.

It is possible because it is in the mathematics that models the data. The only value that is communicated is the measurement from the detector of the gamma. The rest is mathematics of the quantum mechanical model.

Example of a classical probabilistic model:

Take a rod and paint one end white and the other black and cover the ends.

Whirl it in the air and throw it. Open the end that is closer to you.

Do you need to open the other if you see your end is white, to know that the other end is black?

That is how probability enters, and the mathematics is in the length of the rod, that tells you if you have one end the other has to be there by conservation of shape and mass.

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  • $\begingroup$ How does this address the point of confusion? It only seems to suggest that "You measure one, you know the other," which I am already familiar with / this isn't quite what I am asking $\endgroup$ – user222141 Feb 7 at 19:58
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    $\begingroup$ That there is no communication, just conservation laws . like "beauty is in the eyes of the beholder" communication is in the head of the experimenter. $\endgroup$ – anna v Feb 7 at 20:00
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    $\begingroup$ But if it's just mere conservation then how is this any different from "the states are already decided at the beginning / mundane predetermination"? "Communication in the head of the experimenter" is precisely the kind of definition I am speaking out against in the original post and is not what I am asking about. $\endgroup$ – user222141 Feb 7 at 20:01
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    $\begingroup$ In quantum mechanics states are probabilistic, as I say in my last paragraph, following the mathematics of the physics of the decay. $\endgroup$ – anna v Feb 7 at 20:04
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    $\begingroup$ @annav I agree with user222141. You haven't addressed the confusion. In the last paragraph you suggest that there is simultaneously no predetermination and no communication. The OP is asking how that is possible. $\endgroup$ – a1s2d3f4 Feb 7 at 20:43
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You need to divide entanglement in two parts -

1) Perfect Anti correlation (Bell's states) - This is what (I think) Anna v has described. This is direct consequence and instantaneous observation of conservation laws. The quantities are conserved from on set and they have to measure opposite. So you measure one and know the other.

2) Statistical correlations - These are used to disprove classical/local nature of entanglement by applying Bell's inequality to the statistical correlation percents. In my opinion, the application of Bell's inequality to statistical correlations is a faulty method. Because applying Bell's inequality requires you to assume equal likely hood of all possible outcomes, which is not necessarily true throughout the experiment.

It is pretty normal to get confused and even get frustrated if you try to scrutinize the entanglement because, all you get is religious kind of answers which can not be proved or disproved.

As far as learning quantum mechanics is considered - yes, you will be told this, so that the mathematics conditions your mind to start believing the mysterious nature.

In my opinion, the mathematics gives the correct predictions and are confirmed experimentally, but it also gives rise to superposition etc kind of non-verifiable nonsense. I have never seen a cat dead and alive ever. So, to a large extent, it is a mathematical camouflaging, which gives some correct predictions but also creates some mysteries. I think statistical correlation matching with QM predictions is a coincidence due to some classical mechanism that is yet to be discovered. The entities involved are so small that it has been very difficult to uncover the reality. Moreover once you learn the QM mathematics, you get conditioned to it and never doubt, let alone scrutinizing entanglement. You can judge it from the kind of responses to such basic questions by "partial experts" on the topic, mostly they will sing the Bell song, nothing else. The matured ones are more broad in their responses. To date, I have not heard a single "public" response that says, yes, the phenomenon/mystery needs further scrutinisation. Just watch down votes to my answer!

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  • $\begingroup$ "Just watch down votes to my answer!" is a remarkable thing to say when you start your text with an utterly (and undebatably) incorrect statement. Bell states need not be anti-correlated - the term refers to four separate states, only two of which fit that description. Trying to dress yourself up in martyr robes is a nice move, but you need to get your basics right to start criticising the 'establishment'. $\endgroup$ – Emilio Pisanty Feb 8 at 16:40
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    $\begingroup$ As for "To date, I have not heard a single "public" response that says, yes, the phenomenon/mystery needs further scrutinisation" - how many (public) grant proposals on quantum information and quantum foundations have you read recently? The fact that you don't look in the places where these things are discussed does not mean they don't happen - it just means that you're not qualified to talk about them. $\endgroup$ – Emilio Pisanty Feb 8 at 16:41
  • $\begingroup$ @EmilioPisanty: You prove my point. I do not claim to be "qualified" to claim I understand reality. But I am qualified to raise doubts. There are two states (out of four) that fit the description. And see what point you made? If two fit the description, then those are the two I meant, is not it simple? but you have to go an extra mile to find a fault. Did I say 1, or 2, or all the Bell's states? No! I swear, I did not. I really do not even know what the hell they mean, but all I picked from pieces, is that some perfect anti correlation states are referred to as Bell's states in academia. $\endgroup$ – kpv Feb 8 at 20:53
  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – ACuriousMind Feb 10 at 14:03

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