# Lon-local hidden variable theories?

#### venkat

Bell thought that maybe non-local hidden variable theories might have something to say, even though local hidden variable theories have been shown to be unable to properly describe nature.

well, what exactly would you mean by a non local hidden variable theory?

where exactly does the assumption of locality come,in the proof of Bell's theorem? does it arise when we say that in a hidden variable theory( in the proof of Bell's theorem), even non-commuting variables have simultaneous reality?

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Bohm's theory is a non-local hidden variable theory. The unobserved pilot wave (hidden variable) interacts with the particle at FTL speeds (non-local). This of course violates relativistic locality, which is what non-local means.

#### slyboy

Assumption of locality

The assumption of locality in Bell's theorem is that the probability of measurement outcomes of all measurements at one site is not affected by the choice of measurement made at another, spacelike separated, site.

For a choice of two measurements at two different sites, A_1 or A_2 at the first site and B_1 or B_2 at the second site, this amounts to saying that the probabilities of the different measurement outcomes satisfy:

p(A_1,A_2,B_1,B_2)

= sum_\lambda p(\lambda) p(A_1 , A_2 | \lambda) p(B_1, B_2 | lambda)

where \lambda is a hidden variable.

Standard QM asserts that the joint probability p(A_1,A_2,B_1,B_2) does not exist in general if the pairs of measurements (A_1, A_2) and (B_1,B_2) are incompatible (i.e. the Hermitian operators that represent them do not commute). It only makes sense to consider the marginals p(A_1,B_1), p(A_1,B_2), p(A_2,B_1) and p(A_2,B_2) which do not have to result from a joint distribution.

On the other hand, a non-local hidden variable theory would assert that a good joint probability can be defined if we include the choices of measurement as variables in the distribution as well.

#### DrChinese

Gold Member
Originally posted by venkat
where exactly does the assumption of locality come,in the proof of Bell's theorem? does it arise when we say that in a hidden variable theory( in the proof of Bell's theorem), even non-commuting variables have simultaneous reality?
Bell's assumption of locality rested on the idea that a measurement at one point in space could not affect a measurement at another point sufficient distant. Bell said in part:

"...the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past..."

In the Innsbruck experiments, the distance was 400 meters of separation. The Bell inequality was found to be violated by 30 standard deviations.

M

#### mhernan

##### Guest
nonlocal hiden variables a violation of relativity theory?.

Bohm's theory is a non-local hidden variable theory. The unobserved pilot wave (hidden variable) interacts with the particle at FTL speeds (non-local). This of course violates relativistic locality, which is what non-local means.
I don't quite agree that nonlocality is a phenomenon that violates relativity theory. RT, as I understand the system, merely prohibits massive 'stuff' from propagating faster than light. An effect at long range, instantaneously with an observed event, does not suggest that matter, or mass, or energy that we are all familiar with was the cause. Of course then we are at the brink of a other way of looking at things.

Did not Bohm insist that his 'pilot-wave ' was real and that his version of Schroedinger's equation worked perfectly well and that the matter of nonlocality was an essential and even uintuitive aspect pof his construct? When one reviews the limitations on viewing the real world imposed by QT, personally nonlocality seems infinitely more real, or of a common experience than QT. Here, we must remember that the 'piolot wave did not come about because someone discoverd the PW in an experiment. The PW theory was imposed to explain diffraction and the motion of the electron through two-hole experimental arrangements. The PW was, is, a theoretical convenience to clear the slates of doubt and to impose a form of "truth" that allows the serious scientist to "progress" with the development of her science with a clear professional conscience.

Nonlocality is a channel of information exchange, where matter is connected by a detailed time-ruled system void in spatial significance. Uniting space and time in some droll relativity mechanism is to arbitrarily cut off scrutiny with complacent axiomatic dogma.

For instance if we considered a simple EPR experiment where two "twined photons" move apart at the speed of light and measuring the polarization of one photon immediagtely set the twin photon to its proper predicted value, then we could look at the problem as the photons taking advanmtage of Mother Nature's zeal at maintaining efficiency. Here, both photonf could represent both ends of a vector system that share a common vector attribute. Using the analogy of a school yard teeter-totter where the ends of the TT are exposed to space time reality, the unexposed center board would be functional to both ends. Measuring one end by simply grabbing the TT and stopping it would have the effect of instantaneously stopping the other end. Nothing moved from one end to other. The polaization vectors simply share 'nonlocal attributes'.

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It is a fact of relativity that if you can send information, bits, FTL then you can arrange inertial frames moving with respect to each other at less than c that will reflect those bits back to the worldline of their origin, at a time BEFORE THEY WERE SENT. Thus you have violated causality. Every ansible is potentially a time machine, and it doesn't require any outre physics to convert it to one.

#### slyboy

Bohmian mechanics does not violate relativity because it is assumed that the probability density over position is always |\psi|^2. This is called the equilibruim assumption (in analogy with thermal equilibrium) and it ensures agreement with QM and rules out non-local signalling. One can show that for a wide class of non-equilibrium states, the system tends to relax towards a |\psi|^2 distribution over time. This has lead some people to claim that perhaps the early universe did not obey the equilibrium assumption and that we might be able to detect the effects of this, by looking at the details of the cosmic microwave background radiation for example.

However, if it were possible to generate non-equilibrium states, where the position probability density is different to |\psi|^2, then Bohmian mechanics would give different predicitions to QM and also allow non-local signalling.

#### NateTG

Homework Helper
Originally posted by venkat
well, what exactly would you mean by a non local hidden variable theory?
A hidden variable is a variable that cannot be measured.

Another example of a non-local hidden variable theory might, for example, be the many worlds theory where every particle interaction would involve hidden parameters that indicate which universe the particles are in.

Non-local effectively means that the quantity is not a property of the particle that is being measured, but some wierd universal property, or that "information" about the quantity is propagated at faster than light speed.

Bell's theorem is essentially a proof by contradiction that the quantum behavior cannot be explained by non-local hidden variable. Thus the assumption of locality in Bell's theorem is by contradiction.

As an aside, Bell's theorem also assumes that the probability function for the hidden variable's state is measurable, so really, it only rules out 'nice' local variable theories.

#### TeV

It is a fact of relativity that if you can send information, bits, FTL then you can arrange inertial frames moving with respect to each other at less than c that will reflect those bits back to the worldline of their origin, at a time BEFORE THEY WERE SENT. Thus you have violated causality. Every ansible is potentially a time machine, and it doesn't require any outre physics to convert it to one.
SR says 3-dimensional space is mathematicaly isotropic.Togather with time that would make 4-dimensional Minkowski space isotropic too.But physical realm show phenomena that cannot be described just in a frame of a simple Minkowski space.Causality principle is probably the strongest principle in a whole physics.Stronger even than the law of conservation of energy or momentum.To explain mathematical formalism of QM that corresponds to observable reality where FTL signaling between two "Minkowski space" points HAS BEEN observed ,it is necessary to postulate higherdimensional spacetime in a first step as a physical reality.(How to proceed mathematicaly and arrange everything to fit togather and to causaly work is a big question.) Otherwise,explanation of FTL signaling by absorber theory would lead to the violation of causality (which is unexceptable).Then there is also "spooky instantenous action at distance" as Einstein would call it and there is also big issue of "reality" of time direction in cosmology.Recent findings seems to indicate that universe is opened after all.If it were true then there is a real truth in saying that it is dumed to thermodinamical death and absorber theory would be nothing else than a neat theoretical trick without any physical sense.
Matter of fact ,in words of entropy language,both retarded and advanced waves would appear as if travell backwards in time.

#### slyboy

As an aside, Bell's theorem also assumes that the probability function for the hidden variable's state is measurable, so really, it only rules out 'nice' local variable theories.
Whilst Bell's proof does assume this, there is an alternative proof due to Pitowski that allows an arbitrary probability function.

M

#### mhernan

##### Guest
It is a fact of relativity that if you can send information, bits, FTL then you can arrange inertial frames moving with respect to each other at less than c that will reflect those bits back to the worldline of their origin, at a time BEFORE THEY WERE SENT. Thus you have violated causality. Every ansible is potentially a time machine, and it doesn't require any outre physics to convert it to one.

It is a fact of experimental results, Clausen et al, that one activity at one detector had an immdiate effect at another "far removed". No relativity violation here as no ". . .information, bits . ." were "sent". The effect is immediate, which is certainly not "faster than light". Immediate means "now". The results of the Clausen experiments are not "outre" physics, if this is what you are saying, and need nothing to convert physics or to add any explanation.

Mother Nature doesn't have to justify herself.

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Originally posted by mhernan
It is a fact of experimental results, Clausen et al, that one activity at one detector had an immdiate effect at another "far removed". No relativity violation here as no ". . .information, bits . ." were "sent". The effect is immediate, which is certainly not "faster than light". Immediate means "now". The results of the Clausen experiments are not "outre" physics, if this is what you are saying, and need nothing to convert physics or to add any explanation.

Mother Nature doesn't have to justify herself.
Google didn't show me any experiment by Clausen. Did you mean Clauser?

"Right now" means elapsed time = 0, and this can easily be shown to entail closed timelike paths.

M

#### mhernan

##### Guest
Originally posted by mhernan
It is a fact of experimental results, Clausen et al, that one activity at one detector had an immediate effect at another "far removed". No relativity violation here as no ". . .information, bits . ." were "sent". The effect is immediate, which is certainly not "faster than light". Immediate means "now". The results of the Clausen experiments are not "outre" physics, if this is what you are saying, and need nothing to convert physics or to add any explanation.

Mother Nature doesn't have to justify herself.
Google didn't show me any experiment by Clausen. Did you mean Clauser?

"Right now" means elapsed time = 0, and this can easily be shown to entail closed timelike paths.
mhernan replies

Clauser is correct, my mistake.

There is a collection of papers by J.S. Bell that describes the question of “action at a distance”, “local and nonlocal” etc: Speakable and Unspeakable in Quantum Mechanics”. The proofs are clearly stated.
See Proceedings of the Symposium on Frontier Problem in High Energy Physics, Pisa, June 1976, 33-45 for a discussion on the Einstein, Podolsky and Rosen paradox.

Reviews of Modern Physics 38 (1966) 447 – 52.

Physics 1 (1964) 196-200. The seminal paper.

Bell showed that any quantum mechanical model that does not use nonlocal forces is incomplete. The “closed timelike paths” you refer need an explanation. In addition, despite the objections to the results of Bell’s inequality, such as the less than efficient detectors, the data indicates the instantaneous affect of the setting of one detector affected the state of the other particle, though far removed from the measurement of the first. This is an affect as if the particle shared hidden, nonlocal attributes that are essential to the existence of he state of the particle. I suppose some refer to the affect as ‘entanglement’ though the descriptions of entanglement vary substantially from writer to writer.

Any theoretical model used to describe the Clauser, Aspect experiments need to explain the experimental results of the instantaneous affect of measuring one particle on another particle far removed. Whatever a timlike path is, if it prohibits instantaneous action then a contradiction occurs with experimental results.

#### Arboreal

Using the analogy of a school yard teeter-totter where the ends of the TT are exposed to space time reality, The polaization vectors simply share 'nonlocal attributes'
I have heard a similar analogy. Rotating a rod (or in this case a broom handle), with a dot marked at each end to represent the "exposed" area. IN with a small epiphany, OUT with my romantic notions of FTL communication.

Arbor

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#### JohnBarchak

It is clear that the quantum mechanical world (QM) is non-
local. But that world has almost nothing to do with reality.

In "Towards Quantum Information Theory in Space and Time",
http://arxiv.org/PS_cache/quant-ph/pdf/0203/0203030.pdf [Broken]
Igor V. Volovich shows us that modern quantum information theory
deals with an idealized situation where the spacetime dependence of
quantum phenomena is neglected.

In "Local Realism, Contextualism and Loopholes in Bell`s Experiments"
http://arxiv.org/PS_cache/quant-ph/pdf/0212/0212127.pdf [Broken]
Volovich and Andrei Khrennikov demonstrate that if we include into
the quantum mechanical formalism the space-time structure in the
standard way then quantum mechanics might be consistent with
Einstein's local realism.

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#### NateTG

Homework Helper
Originally posted by slyboy
Whilst Bell's proof does assume this, there is an alternative proof due to Pitowski that allows an arbitrary probability function.
Itamar Pitowsky?

The first paper at:
http://edelstein.huji.ac.il/staff/pitowsky/ [Broken]

“Resolution of the Einstein-Podolsky-Rosen and Bell Paradoxes, Physical Review Letters 48, 1299-1302 (1982).

Contains the passage:
"...this is the first model to account for the Einstein-Podolsky-Rosen experiment without violating the principle of locality.
(my emphasis)
in the abstract.

It's entirely possible that he published something later that discounts that work, but I am not aware of it.

It should be pointed out that a non-measurable probability function requires a non-standard notion of probability in order to be meaninful, but the paper does go into that.

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#### slyboy

See paper no. 23 on that page:

“George Boole’s “Conditions of Possible Experience” and the Quantum Puzzle” The British Journal for the Philosophy of Science 45, 95-125 (1994).

as well as his book "Quantum Probability, Quantum Logic"

There is no assumption of measurability in the proofs used there, they are simply a consequence of convexity.

#### Nereid

Staff Emeritus
Gold Member
DrChinese wrote: In the Innsbruck experiments, the distance was 400 meters of separation. The Bell inequality was found to be violated by 30 standard deviations.
Could someone please provide a link to more on this experiment? Many thanks.

#### NateTG

Homework Helper
Originally posted by slyboy
See paper no. 23 on that page:

“George Boole’s “Conditions of Possible Experience” and the Quantum Puzzle” The British Journal for the Philosophy of Science 45, 95-125 (1994).

as well as his book "Quantum Probability, Quantum Logic"

There is no assumption of measurability in the proofs used there, they are simply a consequence of convexity.
You'll note that he points out that Mathematical Oddities violate Boole's conditions (page 15 of the paper). The pasage specifically refers to Lebesgue measure and the axiom of choice - which means that Boole's conditions, and AFAICT the rest of the paper about them do not apply to the model in the first paper.

It's very probably possible to create 'looser' conditions than measurability that will function for a Bell's Theorem style proof, but the (first) paper has a construction that meets all of the necessary criteria for a local hidden-variable model. It is, of course, quite ugly, in the sense leads to other conceptually problematic results.

#### slyboy

OK, it is of course very difficult to rule out every single possibility in a no-go theorem, but there comes a point where all the remaining alternatives seem very convoluted and ad-hoc. Then we resort to Occam's razor in order to rule them out. This happens in all science, but of course exactly where we put the boundary between an acceptable and an unacceptable theory is open to discussion.

I would not necessarily be against the idea of non-measurable sets being used to explain the apparent non-locality in Bell experiments, but it needs to be motivated by some physical principle and preferably also be used to derive some consequences beyond standard quantum theory. From my perspective, Pitowsky's model is more important as a proof of principle rather than as a serious model of physical reality.

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