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Is the randomness that can be extracted from thermal noise "as random" (that is, even theoretically inaccessible to measurement according to our knowledge of quantum mechanics, and not just random for practical purposes) as the one that comes from "true" quantum phenomena, like radioactive decay of nuclei?

Due to the uncertainty principle, we can't predict both a particles position and speed infinitely accurate, and therefore we shouldn't be able to predict thermal noise, so it would seem that there is at least some level of quantum mechanics involved, but is that the same randomness that dictates the decay of nuclei, tunneling and other quantum phenomena?

So, is there a true distinction between thermal and "quantic" noise on a theoretical level, or are they basically the same? In other words, is the thermal movement of atoms and molecules fundamentally deterministic or indeterministic?

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2 Answers

A common way of answering is something is a quantum effect is to see what would happen if Planck's constant was zero. In this example, it was Planck himself who did this in 1900 when he explained the observed formula for black-body radiation. Without quantization of the radiation, the formula would have an ultraviolet catastrophe. So without the exchange of photons for thermal radiation, the observed behavior would differ markedly for our current experience, as described by the attempted classical explanations for black-body radiation.

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This is true, but you should say "yes, thermal noise is quantum random, as best as we understand physics today". –  Ron Maimon Sep 9 '12 at 7:29
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In general, thermal noise is simply the noise due to a macroscopic point of view, which neglects microscopic (classical and/or quantum) features and only describes these statistically.

Thermal noise is not intrinsically quantum as it also arises in the statistical mechanics of classical systems. However, classical and quantum statistical mechanics often differ in their macroscopic predictions, which means that part of the thermal noise is due to quantum phenomena (i.e., cannot be explained on a classical basis). As everywhere when classical and quantum contributions must be distinguished, the classical part is that proedicted by the classical theory, whereas the quantum correction (the ''truly quantum part'') is the difference between the classical and the quantum result. Thermal noise is not special in this respect.

One of the typical forms of quantum noise is shot noise. See http://en.wikipedia.org/wiki/Shot_noise

The introduction ''In other words'' of your last question ''In other words, is the thermal movement of atoms and molecules fundamentally deterministic or indeterministic?'' is misleading, as you are not rephrasing what you had asked before. The answer to the last question is ''indeterministic'', according to the main stream interpretations of quantum mechanics. But this has nothing to do with thermal noise.

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If as you said microscopic has (classical and quantum) features, then there is no way to isolate both effects, then thermal noise can't be nor classic nor pseudorandom. Do you accept that there may be a quantum random component in whatever distribution it to be? –  HDE Sep 27 '12 at 1:43
@HDE: In principle, one can get the classical part of the noise by calculating it with classical statistical mechanics. The pure quantum contribution is then the correction obtained by repeating the calculation with quantum statistical mechanics. But I didn't claim that this separation can always be done in practice. It works only for sufficiently simple systems. –  Arnold Neumaier Sep 27 '12 at 7:24
The quantum part is usually considered as being irreducibly random, but its distribution is usually far from simple, so that using it for the construction of a true random number generator for uniform or normally distributed random numbers is hardly possible. –  Arnold Neumaier Sep 27 '12 at 7:25
Good point, surprisingly enough both answers have same amount of votes stating the opposite! I think this lead to a deeper issue, i.e. what we refer as "true random". Is it linked to any particular distribution?, I mean, given any matter system, you can think there is a wave funtion for that and so a probability density function, but more atoms you add, less "quantumness is detectable", so I think you should add this to the answer, there is always a true random behind everything (included thermal noise), but it's not accesible/detectable, so this accesibility is classic-quantum distance. –  HDE Sep 28 '12 at 15:13
@HDE: It wasn't asked to give a definition of truly random. I don't even think that there is a well-defined notion of that, apart from being not reducible to an underlying deterministic description. –  Arnold Neumaier Sep 28 '12 at 17:10
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