# Quantum entanglement - problem with Bell's inequality [closed]

To ask the question, I will state the scenario first. Please let me know if the scenario is not described appropriately. The question is in the scenario itself.

There are many questions marks in this text but they all basically question the appropriateness of applying Bells Inequality against hidden variables approach and so, in support of "instantaneous action at a distance".

1. Entangled particles were found to have opposite spin in each and every angle. This has been demonstrated experimentally without any doubt. And this observation required "instantaneous action at a distance".

2. Einstein (or EPR) suggested no need for "instantaneous action at a distance", the behavior can be due to hidden variables.

3. People kind of agreed with EPR till Bell came up with Inequality.

4. People have been citing Bell's Inequality to disprove "Hidden Information Approach" and been claiming therefore "instantaneous action at a distance" is real. (Well, if you ignore the loopholes, which is ok)

5. Bell's Inequality supports/proves "instantaneous action at a distance" based upon a statistical correlation between spins of entangled particles at different angles.

6. Now my problem/question with Bell's Inequality is - How by citing a statistical correlation, we can say "instantaneous action at a distance" is necessary. We all know that statistically correlation builds over a period of time. So for that correlation to build, why "instantaneous action at a distance" would be necessary. The statistical correlation can be built as the experiment progresses, without need of "instantaneous action at a distance".

7. Have people (scientists) been confusing the two things - "instantaneous action at a distance" and statistical correlation. "instantaneous action at a distance" is only necessary for the anti correlation. But anti correlation alone can be easily explained by hidden variables too!

Why statistical correlation, (which builds over time, and so, does not require FTL) has been used to support "instantaneous action at a distance"? Has anyone pointed out this loophole in the Bells Inequality?

## closed as unclear what you're asking by CuriousOne, ACuriousMind♦, Norbert Schuch, user36790, Daniel GriscomFeb 6 '16 at 16:44

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• Action at a distance was never required. People agreed with the EPR paper's physical conclusions because they are correct. Whether they agreed with its philosophical conclusions is both questionable and irrelevant. There was never any scientific need for Bell's equation and it doesn't solve any pressing physical problems with quantum mechanics. Bell's equation doesn't prove anything relating to quantum mechanics proper and it certainly does not introduce instantaneous action, so your "question" does not make any sense. – CuriousOne Feb 5 '16 at 6:34
• If I am not wrong, Bell's inequality is sighted numerous places to disprove hidden variables approach. Disproving hidden variables mean proving/supporting instantaneous action (or saying the entangled particles are one system). What I am saying is that only anti correlation requires the (one system) because they can be measured with a gap which is not enough for light to reach the other particle. But anti correlation is also explained by hidden variables very easily. The hidden variables are disapproved by different angle correlation which is statistical and does not need FTL (or one system). – kpv Feb 5 '16 at 7:16
• To me it is not clear what you are asking. What do you mean by "We all know that statistically correlation builds over a period of time."? Testing of Bell's inequality requires measurements which are space-like separated (or, instantaneous). That is what you meant? By the way: violation of Bell's ineq disproves (locality+realism), together, I meant. – ophelia Feb 5 '16 at 8:07
• If we measure spin of 1 million pairs of entangled electrons at angle 0 and 60 degrees, they will be correlated (same spin) sin(30) squared times = quarter million times. 1 Million pairs are measured over a period of time. Statistical correlation is built during that time. That is what I mean by "We all know that statistically correlation builds over a period of time.". Suppose nature knows past measurements & generates new pairs such that they are anti correlated but adjust to fulfill quantum mechanics predictions in previously measured angles. This way no need for the pairs to be one system. – kpv Feb 5 '16 at 8:37
• I'm sorry, but I have no idea what you actual question about physics is. Correlation is not "action at a distance". – ACuriousMind Feb 5 '16 at 14:26

The physical description of what Bell's inequality is about is as follows. Suppose that the outcomes of measurements are described by stochastic variables. That is, each quantity has a value that is some number picked at random in some way. And suppose that for each system the quantities influencing how the numbers are picked are determined locally. That is, whatever information is used is either carried there by the system, or just happens to be around in that region so that it won't be correlated with your system. You can then put some constraints on how much correlation can arise between two systems: Bell's inequality.

A rough indication of the problem that leads to ruling out local hidden variables theories would be the following. If you measure the same observable on both systems they are anti-correlated. If you measure a different observable, then they may be uncorrelated. So then how does each system know what the other is doing to determine the degree of correlation?

There is a lot of confusion about what this result actually means. There are people who seem to think it means that quantum mechanics is non-local. But this conclusion is wrong. Quantum mechanics does not describe the world in terms of stochastic variables, so Bell's inequality is irrelevant. Quantum systems are described by Hermitian operators, each of whose eigenvalues represents a possible measurement result, and those operators change locally. When a measurement is performed, each of the possible measurement results occur and the correlation is established after the measurement is over, see

tl;dr: Your points 1 to 5 are misunderstandings. The answer to your question follows from a better understanding: Entanglement is no active link, hence there is no need for instantaneous action. However, if you want a certain kind of ontology, then you must accept a certain kind of instantaneous action/non-locality (which doesn't necessarily violate information causality).

Disclaimer: I'm neither and expert in philosophy nor in what people think. So if anybody finds faults in my descriptions, please do correct them.

1. Entangled particles were found to have opposite spin in each and every angle. This has been demonstrated experimentally without any doubt. And this observation required "instantaneous action at a distance".

This is both historically and factually wrong. Entanglement is defined as "not separable", where separable has a precise mathematical definition as being a convex combination of product states (see here). In an experiment, this can be seen in many different ways - especially since entanglement can exist between arbitrary many parties. A special scenario is the case of two people sharing a maximally entangled state that is perfectly correlated. This is the scenario you describe which can be produced and tested experimentally.

An observation as such doesn't "require" anything only an intepretation does. However, when people discovered entangled state (i.e. EPR), it seemed to them that it does indeed require instantaneous action at a distance because they were making other implicit assumptions about what should be the case. This is what Einstein described to Bohr in some of their letters and what he didn't like at all (according to Wikipedia, you can read about it in the book Albert Einstein, Max Born: Briefwechsel 1916–1955).

Let me stress already at this point that today we understand entanglement as nonclassical form of correlation which does not in any way need action at a distance.

1. Einstein (or EPR) suggested no need for "instantaneous action at a distance", the behavior can be due to hidden variables.

No, this is not what the paper suggested at all. The paper is concerned with the question of whether the wave function is "real" and in particular the reality of the wave function. The question is the following: If we think that the wave function is the "real thing" and describes complete reality, then this should mean (definition in the paper) that for every measurable quantity we should be able to predict its outcome definitely if we know the wave function.

The paper shows that this is not possible with entangled states. There are (at least) two ways to interpret this: One can say that this reality as Einstein wants it doesn't exist or that the wave function is just not the full description of reality. If you endorse the latter, the next question is what the full reality is and whether you can know it (philosophically, this is the difference of epistemology and ontology).

Einstein deeply believed that there is an underlying reality (ontology) and therefore he needed hidden variable models. However, the paper clearly states that the authors do not possess such a hidden variable model at the time.

While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.

In other words, what Einstein felt is: We need another theory "hidden variables" because quantum theory is not complete. The wave function is not what we are after.

1. People kind of agreed with EPR till Bell came up with Inequality.

Not really and I strongly suspect that most people just didn't care. The physics was universally agreed upon but the equipment could not test it yet. The phenomenon was only tested in the lab in the late seventies and the paper has slumbered for decades. Also, the underlying questions people might differ upon (as pointed out above) are philosophical and were not accessible to experiments, so people just waited. Most others who cared went with Bohr and just held the view that such a realistic description was not possible. Some, such as Bohm tried to vindicate Einstein's views and suggest a completely deterministic hidden variable theory (see Bohmian mechanics).

1. People have been citing Bell's Inequality to disprove "Hidden Information Approach" and been claiming therefore "instantaneous action at a distance" is real. (Well, if you ignore the loopholes, which is ok)

Once again: No. One of the main problems is that you confuse two concepts: hidden variables and local hidden variables. The distinction is extremely important.

Essentially, Bell made the following two assumptions:

• We want a theory that is "real" in approximately the sense that Einstein wanted (I paraphrased above).
• We want a theory that is also "local" in that causes must propagate with a certain speed and cannot be instantaneous.

People (especially Einstein) want the first, because it is ontologically nice and people want the second, because it seems to be required by relativity and our knowledge of how the world works.

What Bell did was to device an experiment that could prove that one of the two assumptions must be wrong (ignoring loopholes). A (deterministic) hidden variable (information) theory would be a theory of the first kind and therefore what Bell claims is that you can make an experiment that would show that the world cannot be described by a local hidden variable theory.

What does this say and what not (also see the abstract of the original paper)?

1. It does not say that hidden variable theories are impossible - indeed Bohmian mechanics provides such a concept, although they have troubles incorporating relativity.
2. It does say that any such theory must be nonlocal (as indeed Bohmian mechanics is).
3. It says that we cannot have a theory such as classical mechanics for quantum mechanics.

What does locality say? How does it connect to "spooky action"? People have understood nowadays that a nonlocal theory might not necessarily violate observed causality in that we might never be able to devise an experiment that violates causality although the theory is nonlocal. This is possible if we cannot achieve perfect knowledge of the universe and boils (once again) down to a philosophical difference of ontology versus epistemology.

1. Bell's Inequality supports/proves "instantaneous action at a distance" based upon a statistical correlation between spins of entangled particles at different angles.

No, see above. Also let me stress once again: You can in no way use that experiment to transmit information faster than light and this was not suggested by Bell. As far as I know, Bell was against nonlocality and favoured a nonrealist interpretation of his result, but this is completely irrelevant.

This should also render your specific question: If you want realism, Bell tells you that you have to have some form of locality. However, subsequent analysis of the experiment shows that you cannot use the nonlocality to violate causality or in other words: Bell's experiment cannot decide which of the two scenarios (nonlocal hidden variable theory OR local theory without ontological realism) is the "correct" one or whether this question even makes sense.

So what's the physics in all of this? Entanglement is correlations. We cannot use the correlations to send information faster than light, thus we don't violate this part of causality. We can use the correlations to do a whole host of other things like quantum teleportation or maybe one day even quantum computation. This is experiments, so it's physics.

Also, Bell's theorem tells us that naive classical approaches to devise a theory for this behaviour must fail. Since quantum theory works extremely well, most working theoreticians don't have to be overly concerned by this fact and so most theoretical physicists don't care. There is also the very real possibility that the two different options of Bell's theorem (if the loophole-free tests are really loophole-free) will not lead to any new physical predictions. There might be deep physics hidden that many years of trials have not revealed, but there might just as well be no physics other than the first sentence of this paragraph.

The rest is metaphysics and philosophy. Whether or not you fancy a nonlocal or a nonrealist approach is for you to decide (or not care at all since it's not physics). Maybe one day somebody actually comes up with an experiment to distinguish the two, but until then you may as well get back to doing other experiments and describing them.

• Thank you tl;dr for the detais. I am not a physicist as well and most of your points are correct due to the meaning of terminology. For example "Inst action at a distance", I mean that the "two particles are not separate" (or they are entangled). Over all, I am trying to say is that the observed behavior (50/50 in any angle(statistical), anti correlation always, and SQ(sin(A/2)) correlation (statistical)), can be explained in terms of local hidden variables, and a mechanism that only propagates at speed of light and I can simulate that all day long to generate the full QM predicted curve. – kpv Feb 5 '16 at 16:23
• I can describe (and simulate) the behavior with local variables, and a mechanism that only travel <= light speed. At randomly selected, any number of angles, with very high efficiency, to meet all three kinds of correlation (50/50 in any angle(statistical), anti correlation (always), and SQ(sin(A/2)) correlation (statistical)) and generate same curve that is generated by QM. Would this be anything new? – kpv Feb 5 '16 at 16:49
• I don't quite understand what you want - for example I don't understand what "two particles are not separate" should mean in this context. In any case, what Bell says is that you can't have a local hidden variable theory (in his definition) describing all experiments with entangled particles. This is a mathematical statement which you can't get around unless you exploit a loophole in the setting of the system. – Martin Feb 5 '16 at 17:00
• Ok, there is a lot of confusion due to me not using proper terminology. Therefore, I will post another question which would be independent of terminology. Stay tuned. Thanks. – kpv Feb 5 '16 at 17:05
• That's a good idea. Just make sure to either define precisely what you want to do or be sure to use the "usual" notation where you can point to a definition. – Martin Feb 5 '16 at 17:21

How by citing a statistical correlation, we can say "instantaneous action at a distance" is necessary.

Suppose that there is a challenge which a simple argument establishes can only be solved by a classical probability distribution with 75% effectiveness, but which a quantum team of players (i.e. a team with access to a shared quantum state) can solve with 100% effectiveness. (There is; here are the details.) By simple iteration of the challenges we can force the 75% as small as we want; after repeating 30 times we reduce the chance of winning all of the challenges "by chance" to 1 in 5,600.

Now, in the setup for this particular problem we separate three people by a spacelike relativistic interval for the duration of their individual actions, and the choice to collectively change the system is made by two of the team members without consulting either each other or the third. The common description for this problem is basically that both of the actors immediately alter the global state of the entire universe, including what it looks like in each of these other rooms.

If we take that description seriously, then there seems to be some sort of long-distance instantaneous causation which is allowed in quantum mechanics, which is not part of our model involving local hidden variables (the classical probability distribution encapsulates all possible correlations).

Of course today we understand that you do not have to take that description 100% seriously; alternate metaphysical accounts of measurement such as the many-worlds approach, though they have their own problems, can resolve this by insisting that the results themselves coming back from these rooms in so-called "classical" wires are actually deeply in a quantum superposition which entangles with us, the people who determine whether they won a game. In this sense the only time you need for the signal to propagate comes when we collect this "information" back together, and nothing truly travels faster than light per se.