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From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every time that measurement of one particle affects the other.

In my head, there is a less magic explanation: the entangling measurement affects both particles in a way which makes their states identical, though unknown. In this case measuring one particle will reveal information about state of the other, but without a magical instant modification of remote entangled particle.

Obviously, I'm not the only one who had this idea. What are the problems associated with this view, and why is the magic view preferred?

Emilio Pisanty
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Andrey Tatarinov
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Entanglement is being presented as an "active link" only because most people - including authors of popular (and sometimes even unpopular, using the very words of Sidney Coleman) books and articles - don't understand quantum mechanics. And they don't understand quantum mechanics because they don't want to believe that it is fundamentally correct: they always want to imagine that there is some classical physics beneath all the observations. But there's none.

You are absolutely correct that there is nothing active about the connection between the entangled particles. Entanglement is just a correlation - one that can potentially affect all combinations of quantities (that are expressed as operators, so the room for the size and types of correlations is greater than in classical physics). In all cases in the real world, however, the correlation between the particles originated from their common origin - some proximity that existed in the past.

People often say that there is something "active" because they imagine that there exists a real process known as the "collapse of the wave function". The measurement of one particle in the pair "causes" the wave function to collapse, which "actively" influences the other particle, too. The first observer who measures the first particle manages to "collapse" the other particle, too.

This picture is, of course, flawed. The wave function is not a real wave. It is just a collection of numbers whose only ability is to predict the probability of a phenomenon that may happen at some point in the future. The wave function remembers all the correlations - because for every combination of measurements of the entangled particles, quantum mechanics predicts some probability. But all these probabilities exist a moment before the measurement, too. When things are measured, one of the outcomes is just realized. To simplify our reasoning, we may forget about the possibilities that will no longer happen because we already know what happened with the first particle. But this step, in which the original overall probabilities for the second particle were replaced by the conditional probabilities that take the known outcome involving the first particle into account, is just a change of our knowledge - not a remote influence of one particle on the other. No information may ever be answered faster than light using entangled particles. Quantum field theory makes it easy to prove that the information cannot spread over spacelike separations - faster than light. An important fact in this reasoning is that the results of the correlated measurements are still random - we can't force the other particle to be measured "up" or "down" (and transmit information in this way) because we don't have this control even over our own particle (not even in principle: there are no hidden variables, the outcome is genuinely random according to the QM-predicted probabilities).

I recommend late Sidney Coleman's excellent lecture Quantum Mechanics In Your Face who discussed this and other conceptual issues of quantum mechanics and the question why people keep on saying silly things about it:

http://motls.blogspot.com/2010/11/sidney-coleman-quantum-mechanics-in.html

Luboš Motl
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    " But there's none " - have you ever read "Road to reality" by Penrose? – Terminus Feb 25 '12 at 01:09
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    Yes, it's one of those hundreds of wrong popular books written by people who don't really understand quantum mechanics whom I was referring to. – Luboš Motl Apr 18 '12 at 08:04
  • Your explanation make sense, but there are many interpretation of the Quantum Mechanics itself right? From Wikipedia, which one your explanation belongs to? – tia Feb 25 '13 at 00:15
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    This question is a question about foundations of quantum mechanics itself - using the sloppy popular language, about interpretations. The phrase "interpretation of quantum mechanics" itself is strongly misleading. As Sidney Coleman and others would say, if there's something to be interpreted, it's classical physics, not quantum mechanics. Quantum mechanics is a well-defined theory containing both the dynamical laws and their maths and the rules how to connect them with observations and the answer was about the latter. No room for vague excuses or "interpretations" here. – Luboš Motl Feb 25 '13 at 05:49
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    I don't know .. but your answer seems to contradict itself. if there's no magic transfer of information, and if the outcome is genuinely random, then it should be possible in principle to violate certain conservation laws, no? (since, as far as I can tell, entanglement is mostly about conserving things like angular momentum, etc) – hasen Jan 12 '14 at 05:21
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    No, it is easy to prove that the conserved quantities are indeed conserved. It boils down to the zero commutator between them and the Hamiltonian. The error you're probably making is that you are computing the conserved quantity from the observed values of e.g. $x,p$ etc. and assuming that it was the energy before that and after that. But it's neither. The conserved quantity in general doesn't commute with the observed observables so its value before as well as after the experiment is different than a classical function with the measured values substituted. There is no contradiction. – Luboš Motl Jan 12 '14 at 07:17
  • In other words, you are trying to deny the uncertainty principle for the measured quantities and the conserved ones. Otherwise for the angular momentum of the 2 photons, the angular momentum conservation and parity conservation law is the very tool that allows us to derive the entangled state! – Luboš Motl Jan 12 '14 at 07:18
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    "Entanglement is just a correlation" that doesn't fit with Bell's theorem. – ike Apr 24 '14 at 19:14
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    +1 Excellent answer. This is the first thing that makes sense about quantum entanglement. – vgru Jul 28 '14 at 08:23
  • One question: is your opinion that Bell inequality experiments are inherently flawed, or is there a different explanation to their results which doesn't involve non-locality? (that explanation would then be non-realism I presume?) I am referring to experiments which claim to have shown that different measurements of the spin of an entangled particle A show larger correlation with measurements of particle B, when taken under certain relative angles (although, I still don't understand why this relation should be linear according to classical physics). – vgru Jul 30 '14 at 13:59
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    There is nothing flawed about these experiments, and the right explanation is indeed the quantum mechanics - realism is wrong in Nature while locality is correct. – Luboš Motl Jul 30 '14 at 15:56
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    @LubošMotl Thanks for linking to the video with Sidney Coleman. What a lecture, and the analysis he presents consides with my understanding perfectly. However, I disagree with your statement here "The wave function is not a real wave". It seems that SC's standpoint was that there is nothing more real than quantum states. – Per Arve Aug 23 '14 at 15:21
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    Your viewpoint is biased. There are many valid ways to interpret quantum mechanics, but you have chosen to go the route of saying that you know the right way, and everyone else is wrong. While there are certainly many people that don't understand quantum mechanics, it is absolutely the case that there are many mathematically and experimentally valid alternative theories and scientific interpretations. Saying there is only one is quite simply false. – B T Aug 06 '15 at 00:39
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    There is only one theory of quantum mechanics and it is well-defined. To "interpret" means to describe what the theory requires to know and what it predicts and how. All these scientifically meaningful questions are unambiguously answered in quantum mechanics - like in other theories - and one either knows it or not. One may describe the predictions in different languages and/or with different mathematically equivalent pictures or formalisms or focuses but there's only one theory - including all the rules what is observable, what is not etc. - and diverging from this truth means to be wrong. – Luboš Motl Aug 06 '15 at 09:01
  • @LubošMotl, what I don't understand from your answer is why Einstein called this "spooky action at a distance". Is it that Quantum Mechanics wasn't a complete science back then so there was no theory to explain it yet? – GetFree Dec 25 '15 at 19:47
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    Einstein called it "a spooky action at a distance" because he didn't understand how quantum mechanics worked and always implicitly and incorrectly assumed that the fundamental theory had to be classical. The correlation in QM occurs without any action at a distance, there is nothing spooky about the entanglement, it's how Nature works all the time, and QM is perfectly compatible with locality and Lorentz symmetry and relativity. Quantum mechanics is consistent and complete and it is the theory. Theories explain Nature. Nothing else may explain a fundamental enough theory such as QM. – Luboš Motl Dec 27 '15 at 08:42
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    Your assumption that "something else should explain quantum mechanics" is pretty much exactly the same mistake that was done by Einstein when he invented his misleading terminology - and it's done by virtually all other people who have some psychological problem with quantum mechanics. You are just not willing to accept the essential, established scientific fact about Nature that the most fundamental theory describing Nature may be something else than a classical theory describing the "objective state of affairs". But the fundamental theory of Nature is quantum i.e. non-classical! – Luboš Motl Dec 27 '15 at 08:43
  • @LubošMotl, the last "it" in my previous comment refered to quantum entanglement, not quantum mechanics. I understand that QM is a self-contained theory, it doesn't need another theory to make sense of it. – GetFree Dec 28 '15 at 13:02
  • Dear @GetFree, it doesn't matter whether "it" represented "quantum mechanics" or "quantum entanglement". The latter is just an unavoidable omnipresent feature of the former. Almost all states in the Hilbert space are entangled; almost all predictions for pairs of quantities in almost all "composite" QM problems show entg.-like correlations. The word entanglement hasn't been coined up to 1935 but the predictions of quantum mechanics we categorize as "implications of entanglement" today have been known since 1927 if not 25. The EPR+Schrödinger's 1935 contributions were just in terminology. – Luboš Motl Dec 29 '15 at 05:13
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    When you say "this probability is realized", the issue is that it is realized, globally, for the entire wave function. The corrolorary is that you can't transmit information this way, but it's unambiguous that applying an interaction hamiltonian locally will change the wavefunction everywhere and break the coherence, per Bell's theorem. You can say "this isn't action at a distance", and in terms of signal transfer, you'd be right, but there is something strange happening in the formalism if you're anything but a radical positivist. – Zo the Relativist Apr 07 '16 at 16:34
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    Dear Jerry, the wave function isn't "localized to places" in any simple way. The wave function is the description of the whole knowledge. It is not a function of space, like fields are functions of space. For 2 particles, it is a function of both vectors $r_1$ and $r_2$. So it's nonsense to say that "the wave function changes everywhere". What's relevant is whether the observables change somewhere. And locality of QFT guarantees that they won't. Moreover, I only used the word "realized" after "outcome", not "probability", so you're just distorting everything I wrote. – Luboš Motl Apr 10 '16 at 08:41
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    There is nothing strange or nonlocal happening in quantum field theory at all and one may explicitly, rigorously, and precisely prove from the actual quantum formalism. To be sure that nothing strange or nonlocal takes place QFT means to understand QFT fully without defects. It doesn't involve being any "radical positivist" or any other bizarre philosophical statement. These are just totally sharp physics questions in QFT that have nothing whatever to do with philosophy as long as one remains a scientist. – Luboš Motl Apr 10 '16 at 08:43
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    The active link is because Bell showed the correlations can't be do to pre-existing properties. If it was, there are 2^3 = 8 possible "unknowable" configurations in the Bell thought experiment. He showed that repeatable experiments distinguished between "unknowable" and "non-existent" which also shows your blog post on "ignorance and uncertainty are synonyms" is wrong. He showed it's not due to ignorance of some "unknowable" properties. He showed they don't exist prior to the measurement. The spooky action immediately follows to make sure the photons know what to do since it's not pre-planned. – user7348 Jun 08 '16 at 03:41
  • Dear Luboš, I understand your explanation I think. The other commenters seem not to understand it. There is only one, Jerry Schirmer, who states that the wavefunction has to be changed 'everywhere', since the wavefunction has the probability distribution for all the space, and if it changes for one particle, the other's wave function needs to be changed too, even if they are in separate places in space. But can you please tell me something about that a little bit more explained and can you please explain what the experiment itself says in QM and EPR, we measure what first and then what? – Árpád Szendrei Nov 30 '16 at 20:05
  • Thank you for this, i finally ALMOST understand. Now to me it seems like, if " If Bob takes a measurement in y-direction, Alice' measurements will be uncorrelated. If Bob takes a measurement in x-direction (corrected), results will be correlated: Alice will always measure the opposite spin." If Bob measure y, Alice still has to measure x right(you said Alice always measures x)? So it will be then uncorrelated(what will be, the x and y spin will be uncorrelated?). Why, is there a correlation between x and y spin? – Árpád Szendrei Nov 30 '16 at 21:19
  • I don't understand this point of view at all. In particular, the statement that "is just a change of our knowledge ". No it's not! we know that the experimenters choice of what to measure on one end necessarily affects the result of the experiment on the other end. There has to be some form of information propagating unless you believe in superdeterminism. The point of view that "well this is just how QM works" is fine, nobody debates that, but this particular piece is far from understood and something is waiting to be understood here. – elelias Apr 17 '18 at 18:17
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    Dear @elelias - it's not a shame, most laymen and even lots of those who don't consider themselves to be laymen but they should fail to understand these basic points about quantum mechanics. The wave function is a complexified counterpart of the probability distributions (on phase spaces in classical physics). It reflects the observer's incomplete knowledge. When the observer learns something about the outcome of a measurement, the knowledge increases and the wave function therefore tautologically changes - collapses. There is no nonlocality or action at a distance in our quantum world. – Luboš Motl Apr 18 '18 at 04:58
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    @Luboš Motl : If it's just an update of knowledge, then why is it that the measurement seems to have a physical effect? In particular, if you do serial measurements of the right type on identical repetitions of the same experiment, then the statistics of the final measurement may be different from the case if the intermediate measurements were missing, as though the collapse were "really happening" (and this will work even if you don't "look at" the results of them and update YOUR knowledge, but only record the final)? – The_Sympathizer Jun 27 '18 at 23:35
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    And thus it seems the measurement both updates your knowledge AND it has a physical effect. – The_Sympathizer Jun 27 '18 at 23:39
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    Dear @The_Sympathizer - all physical effects are encoded in the observer's knowledge. So updating one's knowledge and experiencing a physical change are exactly the same thing. Like millions of others, you assume that "the reality" and "the knowledge about reality" are two separate things. But in quantum mechanics, they're simply not. The only way how reality can have some properties is for the reality to be measured by an observer. – Luboš Motl Jun 28 '18 at 03:54
  • @Luboš Motl: So how do the "observers" come to be, then, if there was no reality without them - i.e. before humans or other suitably competent creatures evolved? Doesn't this effectively shrink the age of the Universe from 13.8 billion years to a much smaller value? – The_Sympathizer Jul 09 '18 at 02:35
  • If you talk about the period in which it was possible to perceive and discuss observations and deduce the laws of Nature that govern them, indeed, that was only a period much shorter than 13.8 billion years - the recent periods in which an observer existed. The previous sentence just says that when an observer exists, an observer exists. It's a tautology. Do you doubt it's true? When asking about the "rise of observers", you're completely missing the point. – Luboš Motl Jul 21 '18 at 13:35
  • You miss the point because the observer is the subject that observes the world, not someone who should be looked at from outside. If something is looked at from outside, it doesn't deserve the status of the observer in that situation. You're programmed to push for this external, "objective" view on the Universe but quantum mechanics shows that it's wrong (although it used to be OK in classical physics). Only the observer's viewpoint on the world is correct and the observations are constrained by the probabilistic laws of quantum mechanics. – Luboš Motl Jul 21 '18 at 13:37
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    @The_Sympathizer The observer doesn't need to have a capacity to understand the observation. For example, an atom that gets transmuted due to accepting a neutron from a spontaneous decay of another atom would be an "observer". The reason why we focus so much on human observers is that, well, we can observe and share our experience with other humans very easily. And since all science ultimately comes from observation (that is, being entangled with our surroundings), it is the most relevant to science. But that doesn't mean that atoms don't decay if there's no human to watch them do so :) – Luaan Nov 07 '18 at 15:59
  • @Luboš Motl , others - I think I've finally managed to pin down what all is going on with this. The key trick is that quantum mechanics describes, as you say, a viewpoint of the Universe that is from the perspective of what I'd call an active, participatory agent, and not a classical "separable" observer. Philosophically, we have to abandon the usual normative subject/object distinction where the subject is some all-seeing "viewer from nowhere" which is apart and independent from the object observed. (cont'd) – The_Sympathizer Nov 08 '18 at 01:23
  • (cont'd) Agents, however, are not necessarily humans - they are instead just systems which we can ascribe a very general sense of "knowledge" as in "possessing information", and capable of processing and storing new information that they retrieve from interactions with other systems. How exactly they do this is not important, and the "agent" in the theory is a bit of a fictive construct, just as "particles" and all the rest are: they are scientific models. The agent's information is modeled by the wave function, $\psi$ (or more generally the ket vector, $|\psi\rangle$). (cont'd) – The_Sympathizer Nov 08 '18 at 01:23
  • (cont'd) It describes all physical parameters simultaneously and complementarily. The amount of information available for each parameter, in bits (or other informatic units), is given by the negated Shannon entropy for that parameter. "Wave function collapse" means simply the update of information with new information coming in. However that doesn't also mean that the acquisition of information is passive - the fact that the evolution "starts over again" from the collapsed wave function - or, at least, we model it as starting from there, but it definitely starts over from (cont'd) – The_Sympathizer Nov 08 '18 at 01:24
  • (cont'd) something different - and this is observable with serial queries ("measurements") as a difference in statistics of the later queries depending on whether or not the earlier ones were present in many repeated trials, means there is a real physical effect upon the system. The laws of quantum theory, moreover, constrain these effects so that the only way to eliminate them is for the agent to receive zero information. – The_Sympathizer Nov 08 '18 at 01:24
  • And because the agents aren't necessarily humans, per se, the theory isn't inapplicable to describing the Universe earlier than that, but whenever we do so, we are presuming it is the viewpoint from at least some fictive agent that is present there, not a view "from nowhere". – The_Sympathizer Nov 08 '18 at 01:25
  • And this also addresses why that, say, the idea about decoherence, where that a physically-instantiated agent only evolves into a superposition of pointer states and not a unique one: because the view of the physically-instantiated agent that we are describing with the superposition belongs to some OTHER agent, and the superposition here simply means that the latter agent is unsure as to the former agent's state. – The_Sympathizer Nov 08 '18 at 01:26
  • The ultimate collapse is subjective to the second agent when it interacts with the first agent and acquires the state of the pointer. A third agent would see the same superposition process repeated for the second. The trick is remembering that every time we introduce a $\psi$-description we are also introducing another agent, we aren't getting "outside" the Universe. Many-worlds and other theories are more attempts to try and re-establish such an "outside" view, and they all require compromises of some kind, and moreover are untestable because we cannot actually get to that outside. – The_Sympathizer Nov 08 '18 at 01:27
  • And also, despite that the collapse seems "dramatic", the acquisition of the pointer state from the macroscopic other agent is actually only a very slight interaction, as measured by the number of bits it acquires versus the total number of bits to describe the entire macroscopic agent. So "Schrodinger's cat"'s "collapse" is actually not as dramatic as it first seems, it's just our intuition that makes us think this is something "severe". – The_Sympathizer Nov 08 '18 at 01:30
  • No, @The_Sympathizer - it is simply not true that quantum mechanics only uses the term "observer" for stupid reasons. The application of the laws of quantum mechanics depends on the existence of observations - conscious observations, if you wish. In classical physics, observers may be eliminated and made irrelevant, but that is simply not the case in QM. – Luboš Motl Nov 08 '18 at 12:01
  • @Luboš Motl So then if it does require a conscious observer, then does that make it technically meaningless to speak about a time in the Universe that pre-dated conscious observers, and thus one has to qualify any talk about "13.8 billion years of cosmic time" or the "4.6 billion year history of the Earth" and so forth? – The_Sympathizer Nov 08 '18 at 12:14
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    No, it just means that it only makes scientific sense to talk about properties of the early Universe as they are derived by actual observations done by actual observers - i.e. recently. These properties didn't have particular values "independently of observers". The shape of the galaxy clusters, as originating from quantum fluctuations during inflation, was unknown and "its particular values" therefore didn't exist prior to an observation. – Luboš Motl Nov 08 '18 at 15:01
  • @Lubos Motl : So if it literally did not exist, then is it sensible to say the "true" age of the universe - measured by the duration of what actually exists - is really only as long as that of humans, or even human consciousness? – The_Sympathizer Nov 10 '18 at 16:10
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    No, the true age of the Universe is another physical quantity that may be - and that is actually - reconstructed from measurements=observations (of the rate of the expansion of the galaxies, and other things). So if no observation of that took place 5 billion years ago, it just means that the age of the Universe was unknonwn, not that it was zero. – Luboš Motl Nov 12 '18 at 05:34
  • It is incorrect to say Nature is quantum i.e. non-classical! Nature encompasses all aspects of itself including functions of the human mind. – Wookie Jan 22 '20 at 20:17
  • This fails to allow for MWI, pilot-wave, and some other deterministic interpretations so mustn't some part be incorrect? Does your use of probability allow for an underlying deterministic script where probability only exists for local observers ? These are all consistent interpretations, and yet you seem to know more than all their proponents? – J Kusin Mar 27 '20 at 19:15
  • Dear Kusin, no, physics doesn't allow for MWI, pilot waves, or any underlying determininistic script. No, they are not "consistent interpretations". They are both internally inconsistent and incompatible with the empirical data and the broad principles and patterns that have been extracted from those data. – Luboš Motl Mar 29 '20 at 03:39
  • Very disappointing answer Lubos, can you explain how a local non realist statistical model can reproduce QM correlations that violate what you can get with a local model? –  Dec 25 '20 at 08:42
  • Dear Jonny, the purpose of science is to look for correct answers, not "not disappointing" answers. Your question is equivalent to "why quantum mechanics works". It just does. Quantum mechanics (in versions like quantum field theory) is a local non-realist theory. No realist theory, whether it's local or non-local one, can work. – Luboš Motl Dec 26 '20 at 07:41
  • @LubošMotl You state: "In all cases in the real world, however, the correlation between the particles originated from their common origin - some proximity that existed in the past." You answered in 2011, so you are forgiven if you were unaware of experiments such as https://arxiv.org/abs/0911.1314 (2009). However, there's no requirement that entangled photons (for example) need to have interacted in the past. In fact, there is no requirement that the photons ever even co-exist, and in fact they can be entangled after detection (when they no longer exist). So... no common origin required. – DrChinese May 27 '23 at 19:20
  • It is required by causality. Entanglement is always a result of co-existence or interaction in the past and everyone who denies it misunderstands both relativity and quantum mechanics. – Luboš Motl May 29 '23 at 04:01
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    I really like this answer. It offers a very good insight on a very hard to understand topic. Thank you for posting this. – T. Sar Jan 02 '24 at 20:51
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I wish to complete @Luboš Motl's answer, to which I agree. My point is on why people continue to make this mistake of an active link. This mistake is connected with one of the most interesting properties of quantum mechanics, Bell's theorem. One can argue that any physical theory is an hidden variable theory, the hidden variable being the description of the state of an object as written by the theoretician describing it. For quantum theory, the wavefunction of the object is the hidden variable.

Bell's theorem state that the prediction of quantum theory cannot be described by any local hidden variable theory. More precisely, for any entangled state, you can find a set of measurement with statistics contradicting any local hidden variable theory. The three possible explanations are:

  1. Nature is not local : your physical description is a real physical object, and there is an active non-local link between the two entangled particle.
  2. Nature is not realist : your physical state is only an approximation and has no real meaning.
  3. Nature is not quantum.

(1) is much easier to explain and appears often in popular science, mainly because (2) is much more difficult to explain and accept. But I think most researcher working with entanglement prefer explanation (2). Einstein intuition was 3 (before Bell's theorem), because he could not accept (1) and (2).

Interestingly, Einstein 1936 original paper on the EPR paradox was on a case where you can easily find a local hidden variable theory. The state described it what is now called a two-mode squeezed state. Its Wigner function is positive and can therefore be interpreted as a classical probability distribution on the quadrature (position and momentum) measurements, the only one discussed in the EPR paper. Such classical analysis of entanglement can be theoretically very useful and help the intuition in some case without needing any spooky action at distance. However, as shown by Bell, such local hidden variable theory cannot be generic enough to encompass all quantum mechanics.

stafusa
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Frédéric Grosshans
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    Exactly, +1. ;-) – Luboš Motl Jan 20 '11 at 19:34
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    This is a nice answer. I think, especially, it's good that you point out that when someone tells you to give up "local realism," the right answer is to give up the "realism" part. It's a bad choice of word anyway; the real world is quantum. – Matt Reece Jan 21 '11 at 05:38
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    This is a good answer, just nit picking on one thing not being precise, in (2) you seem to be saying that the physical state has no real meaning because it is only approximate, implying a correctable technical problem. Maybe the thing to say is it has no meaning because it has redundant information? @Matt, I like your point, strange that "realism" in this debate came to refer to an intuitive but ultimately wrong view of the world, it's like hearing about the flogiston realism. Good catch. –  Jan 27 '11 at 15:30
  • @Moshe: It is indeed difficult to be precise about (2), and I don't know what is the real meaning of the state... – Frédéric Grosshans Jan 28 '11 at 18:15
  • So far the papers by Joy Christian which claim to disprove Bell's Theorem have only made it into the External Links section of the Wikipedia link so far. – Roy Simpson Feb 17 '11 at 23:38
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    There are some recent developments that suggest that quantum state may be real. Check articles by Lucien Hardy and : PBR – Tony Mar 29 '14 at 17:26
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    +1 a great answer, but one thing puzzles me (especially in conjunction with the answer by @Luboš): you state that the wave function is the non-local hidden variable which describes probabilities for the entangled particles, implying that the act of measurement does not actually influence the other particle, but merely unravels our knowledge about its state. Now, if this is not a local theory (not contradicting Bell's theorem), why do you state that one needs to conclude that nature is not realist and the physical state has no meaning? – vgru Jul 28 '14 at 08:38
  • @LubošMotl Don't you mean "Holy words, Mattman" ? – B T Aug 06 '15 at 00:40
  • Dear Mr. Grosshans, it would be great to have your take on this recent post, on quantum scaling and memory. http://physics.stackexchange.com/questions/206492/quantum-and-classical-scaling-of-memory – user098876 Sep 22 '15 at 14:44
  • Thank you for this, i finally ALMOST understand. Now to me it seems like, if " If Bob takes a measurement in y-direction, Alice' measurements will be uncorrelated. If Bob takes a measurement in x-direction (corrected), results will be correlated: Alice will always measure the opposite spin." If Bob measure y, Alice still has to measure x right(you said Alice always measures x)? So it will be then uncorrelated(what will be, the x and y spin will be uncorrelated?). Why, is there a correlation between x and y spin? – Árpád Szendrei Nov 30 '16 at 21:18
  • 2 and 3 seem to be the same. The wavefunction as the state of the system is a fundamental concept in QM. Saying that it's only an approximation and not really true (2), is saying that QM itself is only an approximation and not really true (3) – Juan Perez Dec 01 '21 at 23:23
  • @ÁrpádSzendrei possibly adding to the confusion - most treatments of bells theorem in pop phys discuss examples with perfectly aligned polarizers (or spin angles) or perfectly orthogonal, but in these cases bells theorem is not violated. you need in fact at least one of the sides switching between two non-commuting measurements, like polarization angle 0 and 10 degrees. as Frederic writes, the EPR experiment as outlined wouldn't violate BT. the violation in the experiments is subtle and small (but can clearly be measured) – BjornW Nov 25 '22 at 15:47
  • While most physicists (that have read Bell's theorem) would go for something along the lines of (2), most physicists that I have encountered that work on entanglement dilemmas go for (1) still. Bell himself for example could not figure out what (2) means, according to him realism is not a condition in his theorem so nonlocality is the main one that is violated here and (1) is the only possibility (not everyone agrees of course). – Mauricio Nov 23 '23 at 18:56
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In fact your view is quite close to the 'official' one; entanglement occurs just because both particles are described with one wave-function; the magic is in our classical habit of thinking that separate objects are described with separate "coordinates".

Emilio Pisanty
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  • +1 well put. I think the main problem is that quantum mechanics still treats several instances of one particle kind with different wave functions, while quantum field theory kills a lot of that confusion – Tobias Kienzler Jan 17 '11 at 15:32
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    @Tobias Kienzler: That doesn't help. You can have entanglement between non-identical particles just as easily. Having widely separated positions really is enough for the correlations of identical particles to work the same way. – wnoise Dec 01 '11 at 16:26
  • @wnoise: true, though I think one can describe QFT by having a functional where the different particle fields are the "coordinates" (i.e. the particle fields themselves are "excitations" in that functional) – Tobias Kienzler Dec 16 '11 at 08:55
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Just a nice analogue Prof. Jürgen Audretsch told me once:

Imagine at home you put one glove in your coat without looking (and noticing it's only one of the two). After exiting the train you notice it's cold and you pull out that single glove. At this very instant you know it's either the left or the right glove, and you therefore know which one is left at home. However, no information was transmitted by your "measurement". Of course in quantum mechanics this is more complicated because of the not entirely measurable wave function, but this is the basic idea.

Tobias Kienzler
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    It's a little more complicated than the glove example, though, because the state of an entangled quantum system is indeterminate until the measurement is made, leading to stronger correlations than can be observed with a purely classical system like a pair of gloves. Bell's theorem shows that quantum systems can be correlated in ways that classical systems cannot, and that's a genuinely surprising result from the standpoint of classical intuition. – Chad Orzel Jan 17 '11 at 16:30
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    @Chad: Isn't everything indeterminate until a measurement is made? If no one checks either the glove at home or the glove in your pocket, then it will remain unknown which one you have. – Joren Jan 17 '11 at 16:45
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    The quantum indeterminacy is different than the classical "we don't know which glove in in your pocket" sort of uncertainty. If you reach into your pocket and pull out a left glove, you can be confident that it was the left glove when you put it there, and has been the left glove all along until you measured it. This is not the case with quantum entangled states. If you measure a photon to be vertically polarized, that does not mean it was vertically polarized when it left the source-- in fact, it can't have been vertically polarized, because that would be inconsistent with Bell's Theorem. – Chad Orzel Jan 17 '11 at 17:22
  • @Chad Orzel: that's true, I didn't want to go into detail too much. The basic problem is that the observer is still considered a classical system. Luboš' answer has the details. Basically there's a hen-egg problem that you measure yourself measuring and therefore perceive your own wavefunction collapsing in the state of having measured a collapsed state... kind of. – Tobias Kienzler Jan 18 '11 at 08:08
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    +1. Sometimes precision is the enemy of pedagogy. The next time someone asks me about this kind of thing at a cocktail party, this is exactly the analogy I'll give. It all depends on the level of the audience. –  Apr 15 '13 at 00:35
  • @BenCrowell Thanks, great to hear. Credit goes to Prof. Jürgen Audretsch, by the way – Tobias Kienzler Apr 15 '13 at 06:10
  • While I agree that Luboš's answer is superior to this one, I do wonder why it was downvoted - any improvement suggestions? – Tobias Kienzler Nov 27 '14 at 09:14
  • Thank you for this, i finally ALMOST understand. Now to me it seems like, if " If Bob takes a measurement in y-direction, Alice' measurements will be uncorrelated. If Bob takes a measurement in x-direction (corrected), results will be correlated: Alice will always measure the opposite spin." If Bob measure y, Alice still has to measure x right(you said Alice always measures x)? So it will be then uncorrelated(what will be, the x and y spin will be uncorrelated?). Why, is there a correlation between x and y spin? – Árpád Szendrei Nov 30 '16 at 21:18
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    This is a horrible analogy. It suggests that entanglement is merely classical correlations, which is a complete misconception. – Norbert Schuch Jul 21 '18 at 15:39
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    @BenCrowell "The next time someone asks me about this kind of thing at a cocktail party, this is exactly the analogy I'll give." Don't do that. It is a wrong analogy, and exactly does not capture the type of correlations which make quantum mechanics and entanglement special. – Norbert Schuch Jul 21 '18 at 15:41
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    @NorbertSchuch Well maybe it's not so much an analogy but more a lie-to-children to get started. Think elevator pitch. If it truly were as simple as that there wouldn't be multi-semester lectures and whole research branches on it... – Tobias Kienzler Jul 21 '18 at 20:04
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    @TobiasKienzler First, you shouldn't lie to children. Beyond that, the argument doesn't explain anything about quantum physics, but only why classical correlations don't involve faster-than-light. That is not the point about quantum mechanics, yet it will mislead people to think that this is the point. – Norbert Schuch Jul 21 '18 at 20:59
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    @NorbertSchuch You don't literally "lie" to children, but you start with a strong simplification to prepare them for the details. If a kid asks you why things fall down you don't start at general relativity ;) – Tobias Kienzler Jul 22 '18 at 19:31
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    Well, to be fair you don't state in your answer what it explains. What does it explain? – Norbert Schuch Jul 22 '18 at 21:47
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    This answer really is maximally wrong (as already pointed out by Norbert). Better to say nothing than to say this. It seems as if someone has read Bell's paper about Bertlmann's socks and took an anti-lesson out of it. – Ruben Verresen May 01 '21 at 14:07
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it's unobvious for me, why quantum entanglement is considered to be active link

Let's walk through a particular variant of the EPR paradoxon. You probably already know this, but I don't know how to explain the problem any other way:

Consider a source that produces entangled photon pairs polarized in z-direction with net spin 0, and two physicists Alice and Bob making measurements.

Alice always measures the spin component of her photon in x-direction, whereas Bob may measure the spin component of his photon in either x- or y-direction.

Let's assume that the source, Alice and Bob are at rest relative to the lab frame, but Bob is closer to the source and makes his measurement first. If Bob takes a measurement in y-direction, Alice' measurements will be uncorrelated. If Bob takes a measurement in x-direction (corrected), results will be correlated: Alice will always measure the opposite spin.

This is paradoxical if you assume wave function collapse is real and local, however is happens (magic, decoherence, stochastic interactions or whatever else floats your boat).

Somehow, Bob's photon needs to tell its partner that it can do whatever it wants if the measurement was taken in y-direction, but force it to do the right thing if the measurement was taken in x-direction. This information needs to propagate faster-than-light so it's available before Alice makes her measurement.

There are several possible ways out of this situation, and I'll list three of them:

First, you can posit that there never was a collapse, that we're just dealing with statistical correlation and the paradox is a result of applying classical intuition to quantum systems.

Second, you can posit that the spooky action at a distance is time-symmetric, ie both Alice' and Bob's measurement will send information slower-than-light but backwards in time until it reaches the event that created the entanglement, which in turn sends information forwards in time. The photons will always have known what spin they'll need to end up with. The pseudo-time I used in my explanation is only a didactic tool: The physical process is atemporal interference across space-time.

Third, you can accept that there are indeed faster-than-light interactions, which, however, cannot be used to transmit information - they are an internal bookkeeping mechanism that keeps the universe in sync. The same thing happens in quantum field theory, which is explicit if you use the virtual particle picture, but even without it there are correlations between field excitations across space-like separation.

Árpád Szendrei
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Christoph
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    Can you confirm that all the x, y and z here are as intened? Because the "If Bob takes a measurement in z-direction" is where I get lost... – Christian Aug 04 '15 at 12:26
  • Thank you for this, i finally ALMOST understand. Now to me it seems like, if " If Bob takes a measurement in y-direction, Alice' measurements will be uncorrelated. If Bob takes a measurement in x-direction (corrected), results will be correlated: Alice will always measure the opposite spin." If Bob measure y, Alice still has to measure x right(you said Alice always measures x)? So it will be then uncorrelated(what will be, the x and y spin will be uncorrelated?). Why, is there a correlation between x and y spin? – Árpád Szendrei Nov 30 '16 at 20:47
  • @ÁrpádSzendrei - if you almost understand then you should be close to NOT understanding. There is no pattern the mind can catch hold of. – Wookie Jan 22 '20 at 21:04
  • "we're just dealing with statistical correlation" The violation of Bell's Inequalities show that there can't be any statistical correlation. – Juan Perez Dec 01 '21 at 23:51
  • And the idea that these particles could be connected to each other in another dimension? String theory postulates that there can be 10 dimensions. You could think of a world in 2 dimensions, in which we would not see what is connected in the upper world of 3 dimensions. This would avoid non-locality, since they will not have to send information faster than light. – Borja Mar 01 '23 at 15:07
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It is not really clear that cases 1,2, and 3 are exhaustive. Discussions about this phenomenon use a lot of terms which are not precisely defined. For example, 'particle' and 'system'. If there is entanglement, then there is one combined system, and it is misleading to call that one combined system 'two particles'.

The comment about realism and approximation is also inaccurate: all positions and data in classical physics are approximate too, this has nothing to do with the difference between classical and quantum or the difference betweeen using a Hamiltonian system whose states are points given by momentum and position coordinates and using a Hamiltonian system whose points are rays in a Hilbert Space.

The comment about entanglement only originating from contiguity in the past is inaccurate and even if true, proves nothing if the Big Bang is true, then nothing prevents every part of the universe from being entangled, and it probably is entangled, but in a way that has no practical importance.

People's comments here touch on the important issue of whether the wave function is objective or subjective. The view that probabilities represent our knowledge is called the 'Bayesian' view, it is the Bayesian or subjective interpretation of probability, as contrasted to the 'objective view' which has some problems. But the Bayesian view has problems as well, since you wind up linking quantum mechanics with consciousness instead of with material measuring apparati such as Geiger counters and bubble chambers.

So another answer to your question is the following: people prefer to talk about an active link because they cannot accept the subjective interpretation of probability and the wave function. There is a lot of current research studying quantum measurement as an actual physical process involving thermodynamic limits of unstable negative temperature systems (bubble chambers etc.).

To put this another way:

  1. alternative 1 implicitly assumes that in the combined system there are 'two particles', but this is probably a fallacy: quantum mechanics does not really recognize any precise notion of particle. As in thermodynamic limits, the notion of 'particle' is a useful approximation within a certain range of set-ups, and loses validity and leads to paradoxes if you attempt to use it outside the limits of its validity.

  2. Alternative 2 implicitly assumes that if something such as the wave function can only be approximately measured, it is somehow not 'physical', but this is unduly simplistic and troubles people because of the seeming necessity of dragging in the subjective Bayesian point of view.

  3. Alternative 3 is at least so open ended that one cannot find fault with it but neither is there a shred of experimental evidence for it. The only problems with QM are logical, not experimental.

Therefore if one questions the implicit assumptions made about the careless use of concepts such as 'particle', 'system', and 'probability', there are many more alternatives and the final answer is not in.

vgru
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joseph f. johnson
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I think that the best picture to understand this correlation is given by many-worlds interpretation:

A singlet decomposes in a coupled pair of particles superposition $|+⟩_A|-⟩_B + |-⟩_A|+⟩_B$, so observer A sees a simple superposition of $|+⟩ + |-⟩$ (which is a partial trace of the global density matrix) and so does B.

In the many worlds interpretation, observer A will be split in a $+$ and a $-$ observer (and so will observer B). Now, where will the correlation effect manifest itself?

The 'coupling' effect is brought when observer A and observer B join together at subluminal speeds to compare notes of their measurements: (remember that according to many-worlds, we have two observers A and two observers B) .

Observer A+ is disallowed by angular momentum conservation to interact with observer B+, (otherwise they will both agree that angular momentum was not conserved). Likewise, observer A- is disallowed to interact with observer B- by the same reason.

So the remaining interactions between observers are:

  • A+ interacts with B-

  • A- interacts with B+

so the final state is a superposition of $|+⟩_A|-⟩_B$ and $|-⟩_A|+⟩_B$, which is interpreted as a 'correlation between remote observations'.

Emilio Pisanty
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lurscher
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    This is incorrect. The partial trace over $B$ of $\rho=|\Psi⟩⟨\Psi|$, for $|\Psi⟩=(|+-⟩+|-+⟩)/\sqrt 2$, is the completely mixed state, which is an evenly weighted probabilistic mixture (and not a superposition) of the A states $|+⟩$ and $|-⟩$. – Emilio Pisanty Nov 26 '14 at 13:37
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it's stated every time that measurement of one particle affects the other

Yes, this is correct. When one of the particles is measured this will secure the state of that particle and its partner.

the entangling measurement affects both particles in a way that makes their states identical, though unknown

This is not correct. The particles are entangled before the measurement. Measurement makes the state of a particle known. After measurement we find that not only is the particle's state defined but its partners is too. There is no way to measure one of them without affecting the other. The states after measurement are not necessarily identical. Measuring entangled particles yields random results that do not correlate to expectations of how they will behave.

magical instant modification of remote entangled particle

The entangled particle is not instantly modified. It will be in one of its possible states after measurement.

Quantum entanglement is considered to be an active link because the state of both particles becomes defined when only one is measured.

what are the problems associated with this view?

It "appears" that touching one particle touches the other without touching it!

Wookie
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    You state: "When one of the particles is measured this will secure the state of that particle and its partner." This is demonstrably false. They can be entangled before or after being measured. The entangled partner doesn't even need to exist when the first is measured. See "Entanglement Between Photons that have Never Coexisted" https://arxiv.org/abs/1209.4191 – DrChinese May 27 '23 at 20:25
  • @DrChinese Fundamentally, all photons coexist. – Wookie Jun 02 '23 at 13:19
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    No, that is a meaningless statement and bears no relationship to science. They don't all coexist. Regardless, it doesn't change the fact that photons can be entangled after they cease to exist. See the reference. – DrChinese Jun 02 '23 at 13:48
  • @DrChinese I mean that the entanglement exists in the relationship and nowhere else. – Wookie Jun 02 '23 at 15:53
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  1. The idea "every time that measurement of one particle affects the other" is a simplification that is often useful.  For most entangled scenarios, you can apply this and not go too wrong.  As you will see below, this simplification has been demonstrated to be false in experiments featuring photon entanglement.

  2. Your idea that measuring one particle reveals information about the already existing state of the other fails because: a) Only their joint future measurement context (settings) are a factor in the statistical outcomes (that's basic QM); and b) That context (the measurement settings) can be selected when the particles are far apart - too far apart for any relativistic signal or action to be exchanged between them.

In the past decade or so, sophisticated new experiments (I can provide references if that will help) have shown us the following to be true of entangled photon pairs:

a. They can be created from independent sources.

b. Those sources can be arbitrarily far apart.

c. They do not need to interact.

d. They do not need to have ever inhabited a common region of spacetime.

e. They do not need to have ever existed at the same time.

f. They can be entangled AFTER detection, i.e. when they no longer exist.  

Pretty difficult to reconcile this list with your view.  I don't know that invoking "magic" is an answer; I would note that all of the above a-f were deductions from quantum mechanics (and without any reference to QFT).   

PS I wouldn't normally answer an older :) question such as this.  However, it is used by the moderator in at least one question that was closed as being a duplicate of this question.  Since this question is still open, I assume another answer is fair game. 

DrChinese
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Let's try to understand through Sock Physics. Suppose you have two socks, that obey classical physics laws and they are of different colours, now you take one of them without knowing and leave one of them home without knowing which one you took. Then when you were on a different planet, you decide to look. You find it is green and can infer that the other sock must be blue. Why ? Because it's classical physics. You know that classical physics following objects behave like this through experience of classical physics.

Now, suppose there were two entangled socks that obeyed quantum physics laws. You measured one and could infer the other due to their entangled nature. Why ? Because they obey quantum laws. Quantum laws are stranger, but they tell you the outcome that occured. All the information transfer shit will come if you try to understand quantum laws through a classical picture. In quantum laws, you've information transfer as well. It turns out you don't need it here.

And the rest is understood by Lubos Motl's answer . Why the wave function isn't a real wave and hence can travel faster than light in some cases and not in some other cases. Your real particles can't travel faster than light and the wave funciton evolution will adjust automatically according to the given constraints for that, in QFT not in non relativistic quantum mechanics.

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    Sock physics? This answer goes against Bell's Theorem. We know from that there are no classical (local realistic) interpretations that can properly describe entanglement. – DrChinese May 27 '23 at 20:36