Hidden Variables

nutgeb

I've read a lot of philosophical "blah, blah, blah" (pardon the euphemism) by QM physicists trying to noodle through why the exact location of a collapsed photon wave function is probabilistic in nature rather than determinative. One of theories I find most intuitively appealing says the collapse location is not subject to chance, but rather there are "hidden variables" which determine the outcome, whose nature and mechanics we are not currently privy to.

It seems to me that if an individual photon's EM wave has its "choice" among many target electrons into which to be fully absorbed, it would be expected to select the electron which exerts the strongest "attraction" to it at the exact instant in time when the photon is making its choice. One could imagine that a particular electron would be particularly attractive if at that instant it (a) is relatively closest to the probabilistic centrum of the photon's EM wave, (b) is at a particular point in its oscillation cycle and/or atomic orbit at which it attraction intensity is highest, and (c) is positioned consistent with the local constructive interference pattern, if applicable. Obviously I am throwing out simplistic notions, and perhaps they don't make any sense at a technical level.

I'm just wondering whether much has been done to try to find systematic "bottoms-up" attraction variables which might explain why a photon would "choose" to collapse to a particular target location. The reading I've done has turned up only theoretical mathematical work relating to broad, abstract categories of potential hidden attractors, which seems "tops down" in nature.

vanesch

Even though there is, as you say, a lot of "philosophical blah blah" concerning the probabilistic aspects of quantum theory, and concerning "hidden variables", there are also a number of hard results, as well on the theoretical side as on the experimental side.

I would say that the single most important result in this domain is what's called Bell's theorem. I've noticed that a lot of people have difficulties understanding what Bell's theorem is about, but if you understand it (as I think I do), then it is pretty "mind-boggling".

The scheme you present for instance is - if I'm not mistaking - one of the very many "explanations" that are precluded by Bell's theorem as an explanation for quantum-mechanical predictions.

gendou2

Recommended reading: Entanglement by Amir D. Aczel

jtbell

...together with the results of certain experiments...

DrChinese

As ZapperZ pointed out, it is hard to go very far on this without encountering EPR, Bell's Theorem, and related experiments (Aspect, Weihs, Zeilinger, etc.).

Your idea is that the experimental context affects the outcomes. This is consistent with what are called contextual theories. (Such theories are usually considered to be "non-realistic" in the sense that particles properties are only well-defined within the context of an observation - i.e. a measurement). This is consistent with Bell's Theorem, and standard quantum theory.

There is an additional component you should be aware of. The experimental context is actually one which depends on the future. I.e. it is not solely the context as it is now (when the EM wave/photon is emitted), but also the context at the spacetime locale of the observer that is relevant. We know this because the observational context can be changed AFTER the photon is emitted, and the result will still be consistent with Bell.

So if you want hidden variables, they must meet the criteria presented above: they must include the future context!

thenewmans

I just finished that book this morning! (Entanglement by Amir D. Aczel) I love it! It describes how the lives and motivations of physicists are intertwined. The explanations are thorough easily digested. But I think the Bell's theorem explanation could have been simpler. Personally, I prefer the wikipedia page.

http://en.wikipedia.org/wiki/Bell's_Theorem

nutgeb

Thanks folks. I've been reading about Bell's theorem. Although I see how it applies to entanglement, it's less clear to me that it applies directly to the question of the probabilistic nature of wave function collapse. Does Bell's theorem specifically rule out the possibility of Local hidden variables in wave function collapse?

Demystifier

Yes.
In fact, if you think of wave function as a physical object that objectively exists even without observations, then, by definition, the wave function itself is a hidden variable.

thenewmans

nutgeb,

What do you mean? Please explain more. The wave function is a function. You can view it as an actual wave but I don't know if that's what you're referring to when you say hidden variable. The concept of hidden variables means that the results of a test were determined at the time entangled particles split. The concept of wave collapse means that the results is determined at the time of observation. There are legitimate interpretations of QM that do not include an actual wave or collapse.

Demystifier

No it doesn't, at least not necessarily. The concept of hidden variables means that the results of a test are determined by some variables that have objective values even if tests are not performed. For example, hidden variables may have stochastic evolution with time, in which case your statement is incorrect. In particular, even the wave function may be a hidden variable if the wave function is not merely a description of our knowledge, but an objective physical entity (that sometimes randomly collapses).