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I understand that while it is believed that there is no true randomness on the macro scale, there is true randomness on the quantum scale. A previous theory that quantum processes could be determined through "hidden variables" has been disproven (through polarizing photons and radioactive particle decay), confirming that true randomness does exist.

Now for my question. Does quantum randomness measurably affect the macro scale such that true randomness actually does exist outside quantum mechanics, or will rolling a die in identical conditions always yield the same result even after factoring quantum randomness?

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  • $\begingroup$ Two words: Schrodinger's cat. The fact that we've been able to measure and write down the results of apparently random (I'm not going to open the "is it really random" can of worms on this occasion) quantum microscale events means that the effects of those events, including their apparent randomness, can be amplified to the macro scale. $\endgroup$ – elifino Jan 4 '16 at 1:06
  • $\begingroup$ @elifino: thank you very much for the clarification. However, that can of worms is actually the true purpose of the question; I have been informed that there is true randomness on the quantum scale but none on the macroscopic scale. If what you say is true, that quantum events are as random as macro events, then which statement would prove false? $\endgroup$ – PlatypusVenom Jan 4 '16 at 5:27
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    $\begingroup$ @elifino: Schoedinger's cat is a poorly constructed Gedankenexperiment that has nothing useful to say about the matter. A superconducting magnet is in a macroscopic quantum mechanical state thanks to an energy gap in the effective potential of the quasi-particles that lead to its existence. So is all matter. As soon as you have energy gaps, the simplistic reasoning of the 1920s and early 1930s is completely out the window. $\endgroup$ – CuriousOne Jan 4 '16 at 10:56
  • $\begingroup$ @elifino I completely agree with CuriousOne. Schrodinger's cat is a fairy tale used to point out an apparently strange aspect of quantum mechanics. In fact, I think it was intended to be considered with the fact in the mind that we do not see quantum superpositions in large objects (although what "large" means is admittedly vague) and so one questions how the quantum description and the classical realities match up. $\endgroup$ – DanielSank Apr 21 '16 at 21:46
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The stochastic features of QM could leave, in principle, a "trace" at the macroscopic level.

This is because not every $\hslash$-dependent family of quantum states yields, in the limit $\hslash\to 0$, a completely deterministic classical state (phase space point). As a matter of fact:

Every possible classical phase-space probability distribution can be obtained from some suitable quantum configuration, in the classical limit.

In other words, in the classical limit the quantum non-commutative probabilities (states) become, in general, classical probabilities in the phase space (statistical states). There are quantum states that in the limit become points of the phase space (not surprisingly, this is the case for the squeezed coherent states of minimal uncertainty), but these are only special cases.

This classical statistical description, that emerges from quantum states in the classical limit, can be seen as a "trace" of the probabilistic nature of the underlying quantum theory.

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There is no randomness on the quantum scale, there is only uncertainty, which describes the information that is available to a macroscopic observer. An easy way to see that quantum processes are not random is by looking at starlight. That light has been coming to us from up to billions of lightyears away, but it doesn't show any distance dependent "random" effects that you would expect from a truly random phenomenon like scattering on particles (like in fog). We have even done interference experiments on "old light" and it interferes just as well as light from local sources.

Now, as to your question... yes, uncertainty does permeate the entire macroscopic world, but probably not in the way you might expect. It is only because of uncertainty that stable matter exists. We can not model matter correctly with any other theory than quantum mechanics. Neither classical mechanics nor electrodynamics even permit stable atoms. Light, matter, magnetic fields... these are all macroscopic quantum phenomena. The force between two magnets, that's a macroscopic quantum field at work. You can hold "it" in your hand, if you like.

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  • $\begingroup$ do you have a ref for the interference of far stars lights ? there are so few photons ... $\endgroup$ – user46925 Jan 3 '16 at 9:51
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    $\begingroup$ @igael: I have to go now, but I will look it up for you. Is that OK? $\endgroup$ – CuriousOne Jan 3 '16 at 9:58
  • $\begingroup$ I don't understand why QM isn't random (it has physical probabilities) whereas light in fog is random (which apart from physical probability from qm, has only Bayesian probabilities associated with our ignorance) $\endgroup$ – innisfree Jan 3 '16 at 11:07
  • $\begingroup$ Nor do I understand your distinction between uncertainty and randomness - given that qm has physical probabilities, randomness seems more appropriate than uncertainty (which has a more Bayesian connotation) $\endgroup$ – innisfree Jan 3 '16 at 11:09
  • $\begingroup$ "There is no randomness on the quantum scale" - Wouldn't any particle accelerator refute this? $\endgroup$ – Omry Jan 3 '16 at 11:26

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