Yaa....

You are right.....

Actually I have gone through this and found same quest....

Like a clarification....

Thanks Mrutunjaya

Thinking about hidden variables misses the point if it does not include Bohmian particles. Positions and momenta of these hypothetical particles turn orthodox quantum mechanics into a deterministic theory that includes the measuring process. It has been given an interesting type of concreteness by the many Wolfram Demonstrations by Klaus von Bloh (see e.g. the link below). Although a natural idea, Bohm's particles don't fall in any category of parameters with which the hopelessly abstraction-ill hidden-parameter-researchers concern themselves.

http://demonstrations.wolfram.com/BohmTrajectoriesForQuantumParticlesInATimeDependentLinearPot/

Ulrich, indeed, I wouldn't call the de Broglie-Bohm theory a 'hidden variables' theory in the sense I meant here.

The dB-B theory is a pilot wave theory based on non locality and Schrödinger (some of its elements are widely accepted but sometimes called differently) and on its degree of coherence with the wider environment (to wit, the whole universe) The 'hidden variables' are not hidden at all, they're fundamentally the effect of the environment.

The Bohm theory is non relativistic and isn't generalizable in relativity. In addition, it requires a non-local "quantum force." It is not deterministic since it implies an ensemble of particles.

Local hidden variables have been excluded by the Bell theorem and experiment, that is to say, only *local* hidden variables. That is in the philosophy of Einstein's "element of reality." But other types of hidden variable, or concepts making quantum mechanics complete, aren't ruled out. They only are not possible in the current theories, but theories are made to change. There is no really general theorem like the Bell's one that can prevent it, whatever the claims of the contrary.

As a non-physicist, the simplest possible explanation for entanglement seems to be that particle properties are determined during the process of entanglement. At that moment, both particles are localized together.

Perhaps especially in the case of photons split by an optical beam-splitter that allows a portion of a photon wave to pass through while reflecting the other portion, the reflected photons' spin, for example, is configured as the compliment of its entanglement partner photon that passed through.

Unfortunately I cannot assess or explain the probabilistic distribution of properties detected, except that perhaps not all particles are entangled, again using the example of an optical beam splitter, perhaps some distribution of photon waves pass through without reflection, or are reflected without being passed through.

There may also be an issue with detection, as I think that all particles cannot possibly be detected, possibly affecting the distribution of detected particle properties. However, I'm just guessing. At any rate, the hidden variable in this case would be the probabilistic determination of entangled particle properties as they are physically entangled. I understand this scenario has been ruled out, however, by applying Bell's theorem to experimental results...

James, particles are not 'localized together' during the process of entanglement (if that were the case, fermions could then never become entangled because of the Fermi exclusion principle, and the world as we know it would not exist.)

Even 'near localization' (as a way to circumvent the FEP) does not work, such a concept is actually meaningless (you'd have to first work out precise boundaries or alternatively statistical distance thresholds defining near localization, in any event Bell's theorem demonstrates the irrelevance of spatial separation.)

The process of entanglement arises not because of space or spacetime localization or near localization, it's more complex than that.

There is one important hidden variable in quantum theory that is seldom mentioned: the wave function. It is hidden, because it cannot be measured.

H Chris Ransford,

As I understand, particles can only become entangled when they are at least in very close proximity. Is there any process of entangling two particles that can be imparted when they are separated by any significant distance?

For example, please see http://en.wikipedia.org/wiki/Quantum_entanglement#Methods_of_creating_entanglement

"Entanglement is usually created by direct interactions between subatomic particles. These interactions can take numerous forms. One of the most commonly used methods is spontaneous parametric down-conversion to generate a pair of photons entangled in polarisation.[52] Other methods include the use of a fiber coupler to confine and mix photons, the use of quantum dots to trap electrons until decay occurs, the use of the Hong-Ou-Mandel effect, etc. In the earliest tests of Bell's theorem, the entangled particles were generated using atomic cascades."

James,

Entanglement is caused by the establishment of a correlation - at some point in time - between particles or sets thereof. In formal mathematical terms it means the establishment of a valid multi-variable Schrödinger equation binding up these particles. The now-correlated entities will then remain entangled as long as decoherence does not occur.

This means that the now entangled particles will stay entangled at any distance whatsoever, as long as they are represented by variables a, b, c ... bound up within a valid Schrödinger equation governing a multivariable wave function ψ(a,b,c...) : this is exactly what is confirmed by experiments confirming Bell's inequality (see Alain Aspect's and Nicolas Gisin's experiments).

Bell's inequality works because a particle B reacts instantly to any change occurring upon A, however distant. This is caused by the necessity for Schrödinger's equation to continue to hold (in the absence of decoherence , of course.) Distance does not intervene anywhere in the equations, and the above-cited experiments have demonstrated the real-world validity of the equations.

@H Chris, don't you think that the phrase "a particle B reacts instantly to any change occurring upon A, however distant..." is a very 'hard' one? And what is the so mythical for a second degree partial de like Schroedinger's? Equations and other math tools are just tools, not self-existent beings, I think.

Demetris, this is exactly why experimentation is always needed. The instant reaction irrespective of distance has been repeatedly documented.

The explanation above is so far the only one that has ever been ventured for the repeated outcomes of Nicolas Gisin's experiments, which were a series of experiments done under watertight conditions to duplicate the foregoing experiments by Alain Aspect and others.

If you have another explanation or interpretation, all would be extremely curious to know of it?

For the moment I'd like to share my Einsteinian education of the limited speed of the information transmission. I shall be back later for more arguments. (But, we have to agree that :(1)either information propagates with v=c (2)either c is not the upper velocity limit here).

Well, that's why Einstein dubbed 'spooky interactions at a distance'

However, we need to think out of the box - no interactions faster than light take place at all.

The mechanism of entanglement demonstrably does not use a communication channel between the two locations. Entanglement does not work in 'communicative' mode.

Different workable mechanisms have been proposed by a number of physicists, but for some reason these are not accepted by a majority of the physics community? So we keep looking, in vain, for other answers - seemingly because we for some reason do not like the workable answers put forward thus far....

As I previously stated, it appears that physical interaction between particles is necessary to produce the entanglement of their property states.

That measurement of one entangled particle's state probabilistically establishes the state of the other is an enormously interesting phenomena, but I think the critical factor is that physical _interaction_ is necessary to initially establish state entanglement. This suggests to me that there is not any communication between particles that occurs across spatial dimensions, but rather a synchronicity or communication between propagating waves - that previously directly interacted - that is distributed in time...

I think that modern Physics has end up with many self- inconsistencies:

1)the light speed c is 'holy quantity', a limit and so on, but

2)when we find things difficult we are ready to accept instant interaction!

I don't know, probably all the building is ready to crash and the careers of their supporters prevent it from collapsing...

I understand that the question here is about non-local hidden variables and what for they can be useful. I regret that I see this question after so much time. I agree that they don't solve the problem of how the correlations are preserved at a distance.

First of all which variable is non-local? What is it? Did somebody see a nonlocal variable?

Let's though assume that such variables exist, and let's denote such a nonlocal hidden variable by λ, and let's denote the measurements on two distant particles as MA and MB, where A and B are the two labs. Then the result of a joint measurement has to be a pair (a, b) with 

(1) a = fA(MA, MB, λ), and b = fB(MB, MA, λ).

It has to be clear that λ is a variable independent of MA and MB, i.e. for one and the same pair MA, MB, one can obtain different pairs (a, b), according to the different values of λ.

From the equations (1) it is understood that at the location A and at the location B are available all three data, MA, MB, and λ. How is that possible without transmission of the datum MA to the location B and MB to the location A? So, the hypothesis of non-local hidden variables is good only for removing the indeterminism of having different results (a, b) for the same pair MA, MB, but not for explaining how the correlations are respected at a distance.