What is 'Hidden Variable theory?
It is the idea that the behavior of quantum particles is actually determined by even smaller particles (or something) that we've not yet detected. Probably the most popular example is quantum entanglement. A mated pair of photons are emitted from a light source and travel in opposite directions away from one another, both at lightspeed (obviously). Yet, altering the state of one of the pair can have an effect on the other. There is no obvious mechanism through which this alteration is transferred from one to the other, and it should be impossible for any kind of effect to reach from one to the other, as the information would have to exceed the speed of light. Hidden Variables Interpretation (it's not really considered a "theory", BTW) says that the change to one photon has an effect on the other by means of some physical connection the two have, and usually proposes that connection is the exchange of very small particles that travell faster than light.
Obviously, any model that involves faster-than-light travel of particles or information has a tremendous burden of proof wieghing against it, and Hidden Variables is not the most widely-accepted interpretation of QM.
A hidden variable theory is a QM interpretation that postulates that there are particle properties that cannot be measured, or are unknown, but that, none-the-less affect the behavior of the particle. The notion that something cannot be measured, but has noticable effect, is of course, self-contradictory which is, really, what the problem with these interpretations generally comes down to in one way or another.
Generally, hidden variable interpretations are divided into local hidden variable interpretations where these unknown quantities are tied to a particular particle, and globabl hidden variable interpretations where the state is universal. Local hidden variable interpretations have been largely falsified by the combination of Bell's Theorem, and a series of experiements, the most famous of which is Aspect et al. The most well-known global hidden variable interpretatation is apparently Bohmian mechanics.
There are a number of good resources on the net for this topic.
N.B. Lurch's post is confusing:
This is poorly phrased, it would probably be better to say something like:
Hidden variables are one of several interpretations used to explain quantum phenoma such as the behavior of entangled particles.
This is a common misconception or, at best very misleading. It is only true for an unusual notion of effect. (If you pull a shoe out of a shoe box, does noticing it is the right show cause the other shoe in the box to be the left one?)
Welcome to physicsforums kiru!
I'd like to recommend this paper to you:
"The mystery of the quantum cakes", P.G. Kwiat, L. Hardy, American Journal of physics, Volume 68, No. 1, January 2000.
In my understanding the Hidden Variable theory says, that the outcome of a measurement is not determined by the quantum mechanical state of a system but by a local hidden variable.
Basically the question is whether the only way to describe a system (for example a particle) is the wavefunction [tex] \Psi [/tex] with it's superpositions or does the system have a definite value [tex] \lambda [/tex]?
What does this mean exactly?
In the first case with the wavefunction a certain value is not determined until the measurement. But in the latter the value exists before the measurement.
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