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Bell's theorem - for or against Hidden Variables?
#1
The violation of Bell's inequality is considered by many scientists as one of the strongest arguments against Hidden Variable Theories. Last but not least, it forbids a whole class of  such Hidden Variable Theories, usually named (I think misleadingly) "local realistic theories".  

So, it may be a surprise for many people that Bell himself was one of a few, at this time, almost the only one, defender of the most famous Hidden Variable Theory, de Broglie-Bohm theory (dBB), also known as Bohmian mechanics.  How is it possible that a defender of a Hidden Variable Theory is the one who has found one of the most important theorems against Hidden Variable Theories?  A theorem which, as many think, proves that dBB theory is wrong?  This sounds like if the best argument against a theory comes from the only defender of that theory.

Of course, the situation is a little bit different.  Bell's theorem is a problem only for a very special class of Hidden Variable Theories, and the theory defended by Bell is not in this class, thus, not endangered at all by his theorem.  Instead, this theorem solves, in an indirect way, one powerful objection against dBB theory:  The problem is that dBB theory requires a preferred frame. What happens here and now immediately influences what happens far away - immediately, that means, without caring about the speed limit of causal influences imposed by Einstein causality.  

But to violate Einstein causality is a strong argument against a theory - even if it is a Hidden Variable theory.  Hidden or not, the relativistic metaphysics postulates that everything should follow relativistic symmetry. So, the question arises if one can improve dBB theory in such a way that it becomes Lorentz-symmetric too, that means, if there exists an Einstein-causal Hidden Variable Theory.  What Bell has proven is that such a theory does not exist.  So, one cannot make dBB theory Lorentz-symmetric.  It violates Lorentz symmetry, because all Hidden Variable Theories have to violate Lorentz symmetry, because improving it in this direction is impossible.  

As a side effect, Bell's theorem connects the two otherwise quite different classes of Hidden Variable Theories we consider here: Those of quantum theory, which try to revive the classical ideas about reality by introducing hidden trajectories of physical objects, and those of relativity, which try to revive classical ideas about space and time by introducing a hidden preferred frame: If you want hidden variables for quantum theory, you have to have also hidden variables for relativity. 

But there is another aspect, which transforms Bell's theorem even into a strong argument in favour of Hidden Variables. This aspect is hidden behind a popular but wrong simplification of Bell's theorem, namely, that it presupposes the existence of Hidden Variables.  It doesn't.  The existence of these hidden variables is derived in the first part of the theorem.  This is usually ignored, because this first part was only shortly mentioned in Bell's paper - with a reference to the EPR argument.  This first part is, essentially, the EPR argument that Quantum Theory is incomplete, a conclusion derived from a different assumption - the EPR criterion of reality.  

So, Bell's theorem derives Bell's inequality from Einstein causality, together with the EPR criterion of reality.  Once Bell's inequalities are violated, one of the assumptions has to be false.  So, if we postulate the EPR criterion of reality, and use the violation of Bell's inequality as a fact, we can derive that there exists a preferred frame - the Hidden Variable for relativity.  

Even more, for those who think realism is a dubious, questionable assumption, there is a variant which does not mention even realism, but is based on causality alone.  All it needs is Reichenbach's principle of common cause:  If we observe a correlation, there has to exist a causal explanation.  And there are two possible causal explanations: either one event is the cause of the other, or they have a common cause.  What is excluded by Bell's theorem is the causal explanation by a common cause in the past. What remains as a causal explanation is one event causally influencing the other.  Which is the cause, which is the effect, remains unknown by the nature of the argument.  But, if the two events are space-like separated, above remaining explanations violate Einstein causality.  So, there have to exist hidden causal influences violating Einstein causality. 

So, it appears that Bell's theorem provides strong arguments in favor of a hidden preferred frame.
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#2
Dear Schmelzer, I would like to react with a question I've asked myself for long.

Let us imagine that the universe was immerged in a constantly-changing-random number, called X, complex number of the form exp(i. theta).

Now let us imagine that a physical property, say vertical polarization of 2 photons, could be initially bound so that their wavefunctions are equal to (X) and (-X).

Lately, say that measuring the vertical polarization of the particle, anywhere, anytime, would really mean to measure the X parameter. That would be, to bind the measurement instrument and everything around, to the still-everchanging-value of X. Same for the second measurement on the second particle.


We would have a X-depending, continuum universe containing all possibilities of consequences of both measurements. If such consequences are incompatible with the preservation of quantum coherence, X would "have to fall to a fixed value" as well as Higgs boson fell to a fixed value in the whole universe. This would propagate at the speed of light and finally resolve. Hopefully (but we don't know how).

It could create a conflict with another measurement, from the other particle, and this conflict would have to end to only one value of X ; thus, to "reverse time" of what had "started to happen" (this is hard to imagine). Though it's the same process for the Higgs boson whose final value is fixed and constant everywhere. But really, this would not mean to reverse time, only to throw away a macroscopic possibility so that the coherence of the X value can be resolved.

Of course lots and lots of "variables" would be necessary to allow this process in the world. Is it so scary ?

Then it should also be scary, that when you detect a 13-billion-year old photon, a whole 13-billion-lightyear-radius sphere "switches immediately" from the state of "maybe the photon is here" to "no photon left", this happens for every photon ever absorbed since the holy creation of light.

So. In conclusion we could state :
- Causality is respected in such process
- Polarization is not a hidden variable
- The speed of light is not violated
- That there is no need for nonlocality, (NB : did someone try to prove that GR forbids this sort of "uniform scalar 3D wormhole" ?)


But somewhere in the universe, there could be a Shrödinger's cat being at the same time dead and alive in a box, as a situation that nobody could ever notice without being himself as "seeing a dead cat while also seeing a living cat" until the universe, with all the time it needs at speed of light, resolves this in a Higgs-like process, and avoids us to believe in a quantum multiverse idea...

Where am I wrong ?
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#3
First, the explanation for the large scale homogeneity, which includes the constant value for the Higgs particle, is given by "inflation" (better would be accelerated expansion,  "inflation" is misleading), and this explanation is causal, compatible with usual Einstein causality. And it is this requirement for Einstein causality, which is the main, and imho the only decisive, argument for this accelerated expansion in the early universe.   

Then, of course, the idea of a photon which "switches immediately" from the state of "maybe the photon is here" to "no photon left" may be scary, but it would not need any influence backward in time. All we need is a classical absolute time (not a directly measurable one because of distortion by gravity, but this does not make it scary, only hidden) where this causal influence happens with almost infinite speed but forward in time.

Your idea could not only create a conflict with another measurement of the other particle, it actually creates one. This is what the experiments which test violations of Bell's inequality are about: To have two experiments so that a light ray emitted at the begin of each of them could not reach the other part before the end of the experiment, before the measurement result became macroscopic and irreversible. So, to "revert time" one would really have to undo an actual macroscopic event, not only to reject a yet unrealized possibility.

This process of undoing would have to violate causality, classical causality, not only Einstein causality. One would need a causal influence into the past, not only one faster than light but into future in some hidden preferred time.

In the last part you introduce something many-worlds-like. Many worlds is nothing I would like to comment, the main problem is imho that it simply does not make sense. Probability is the probability that something happens, and this makes sense only if only one thing really happens and everything else not.
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#4
(05-19-2016, 09:49 PM)John Duffield Wrote: No, Einstein's ether isn't much to do with do with dBB and quantum hidden variables, but take a look at Travis Norsen's paper http://arxiv.org/abs/0707.0401 : "Many textbooks and commentators report that Bell's theorem refutes the possibility (suggested especially by Einstein, Podolsky, and Rosen in 1935) of supplementing ordinary quantum theory with additional ("hidden") variables that might restore determinism and/or some notion of an observer-independent reality. On this view, Bell's theorem supports the orthodox Copenhagen interpretation. Bell's own view of his theorem, however, was quite different..." As for how different, I don't know, but I see this, and I wonder: "It may well be that a relativistic version  of [quantum] theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level".  

A very good article from Travis Norsen. He is, in my humble opinion, one of the best writers about the EPR-Bell question.
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#5
I presume you know all about Joy Christian too. He had an article in New Scientist and ended up getting slated. I didn't like that, all the more so because I refuse to believe in magic.
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#6
Of course I know him, I have already had some longer discussions with him in his forum. (Ok, it is not his, but of one of his supporters.) The article you have linked is weak:

Quote:There is no competing theory that banishes the weirdness and embraces a reality that exists independent of our observations of it. The spookiness, it seems, is here to stay.

You see, it already starts with a lie. There are realistic theories equivalent to quantum theory, and I have only started here with dBB, because it is the oldest and most well-known. There are others, and imho better, like Nelsonian stochastics and Caticha's entropic dynamics. If I find time I will present them here too.

Quote:He claims that physicists' supposed proofs of the impossibility of more "realistic" theories rest on false assumptions and so don't prove much at all.
There is no "supposed proof of the impossibility of more 'realistic' theories". What Christian questions is Bell's theorem, which rejects only the possibility of Einstein-causal realistic theories.

Quote:"Contrary to the received wisdom," he says, "quantum theory doesn't rule out the possibility of a deeper theory, even one that might be fully deterministic."
"Received wisdom" has accepted Bohm's proof of existence, by construction, of a hidden variable theory which is fully deterministic.
Quote:Christian's conclusion follows from a relatively simple calculation using alternative mathematics, described in a paper now under review at the journal
Physical Review Letters.
There is no such animal as "alternative mathematics" (or is this the type of mathematics where 2+2=5?). And, of course, PRL has rejected this.

Quote:Bell imagined an experiment that would send particles from millions of entangled pairs to distant places around the globe, where experimenters would measure their spins. He assumed that some "real", pre-existing properties of the two particles would determine the measurement outcomes. He also assumed that relativity remains intact, so if measurements of entangled particles were made at the same moment, the properties of one particle could not possibly affect its entangled twin quickly enough. From these assumptions, Bell predicted what such experimenters would find.

What I have emphasized is wrong too - Bell has not assumed this, but derived this using the classical EPR argument. And the relativity about relativity was necessary only to prove this. But this error is already forgivable, there are too many scientists who have made the same error interpreting Bell too. (Read the Norsen paper about this, he is one of the guys who does not make this error.)

Quote:Recent experiments have gone further and tried to establish which of the two ideas has to go: locality or realism. They concluded that we have to abandon the
idea of an objective reality (New Scientist, 23 June, p 30).
More nonsense. I don't have access to this, but I would guess that this is about some small and irrelevant class of realistic theories which violates Einstein causality, but is restricted by some other conditions in such a way that one can derive also some inequality similar to Bell's, which is violated by quantum theory (and all its completely realistic interpretations like dBB) too.

Quote:Bell assumed the hidden variables in his argument would be familiar numbers, akin to the value of a velocity or a mass. Such numbers obey the ordinary rules of algebra, including a law that says that the order of multiplication doesn't matter - so that, for example, 2 × 5 equals 5 × 2. This property of multiplication is called commutation. The idea that hidden variables are commuting numbers might seem so basic as to be beyond question, but Christian argues it is important to question this point because mathematicians know that different kinds of variables needn't obey commutative algebra.
A complete misrepresentation. Bell makes no assumption at all about the hidden variables. Except that they are elements \(\lambda\) of some set of possible values of these hidden variables, \(\lambda\in\Lambda\). All what Bell assumes is that these hidden variables, together with the parameters of the measurement device a, define the result of the measurement A, which is spin up or down, or +1 resp. -1, so that \(A=A(\lambda,a)\in\{-1,+1\}\).

Quote:The debate seems likely to continue for some time while researchers puzzle over details.

No. There is no need to puzzle over details, there is also no debate - there is full agreement in the scientific community that Christian is wrong.

In the remaining part about others I have not seen obvious errors. So it may be he was simply misguided by Christian.
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#7
All points noted Schmelzer. Don't forget that the Is spookiness under threat?  article was in a popular science magazine

As for whether Christian is exactly right or dead wrong I don't know. But I welcome his contribution, because I will never accept it isn't classical, it surpasseth all human understanding, so just shut up and calculate.  
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#8
No problem, I have invited them already. But I doubt they will follow the invitation, for reasons similar to why I think Lubos Motl will not appear here.

The opposition to "shut up and calculate" I share. The difference is that I already know Christian is dead wrong.
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#9
(05-22-2016, 06:42 PM)Schmelzer Wrote: No problem, I have invited them already. But I doubt they will follow the invitation, for reasons similar to why I think Lubos Motl will not appear here.

The opposition to "shut up and calculate" I share. The difference is that I already know Christian is dead wrong.
Before we determine if Joy Christian's local-realistic model is correct (which it is), let's see if Bell was actually right. Given the CHSH string of expectation terms that can range from -1 to +1, is the following possible?

+1 -(-1) + 1 + 1 = 4
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#10
I don't understand your question. In my mathematics, +1 -(-1) + 1 + 1 is always 4, and this has nothing to do with CHSH and whatever ranges or expectation terms. So this sounds like a trick question. But so what, I will have a look at the trick.
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