# Naive question: Macroscopic implications of quantum probability

1. Oct 27, 2014

### Nick O

My question will probably be enough to make this obvious, but I should start by saying that I have not formally studied quantum mechanics, and I know little more about it than the wave equation as a function of x and t.

Does the inherently probabilistic nature of quantum mechanics have some (vanishingly small but nonzero) implication for macroscopic physics? That is to say, if I were to continuously drop stones for a Graham's Number of years, is there some incredibly small possibility that a stone might fall up or sideways for a moment before falling down?

2. Oct 27, 2014

### Simon Bridge

Yes. Interference fringes are a case in point ... there are many others.
That is not one of them - we have yet to come up with a quantum theory of gravity and, anyway, the experiment is not well controlled: the stone is more likely to get lifted by a freak gust of wind than for an accumulated quantum fluctuation to lift it.

You want an example more surprising than interference fringes or tunnelling diodes? OK: the law of reflection is only obeyed on average.
Throw a lot of photons at a mirror, even a perfect one, and there is a chance that the angle of reflection will not be the same as the angle of incidence for some of them. It's not a small chance either - in fact it's almost certain - so that, by carefully removing parts of a mirror, it is possible to make the reflection brighter for a single colour of light. That good enough?

3. Oct 27, 2014

### Doug Huffman

See Andreas Albrecht's Origin of probabilities and their application to the multiverse.http://arxiv.org/abs/1212.0953

We argue using simple models that all successful practical uses of probabilities originate in quantum fluctuations in the microscopic physical world around us, often propagated to macroscopic scales. Thus we claim there is no physically verified fully classical theory of probability. We comment on the general implications of this view, and specifically question the application of classical probability theory to cosmology in cases where key questions are known to have no quantum answer. We argue that the ideas developed here may offer a way out of the notorious measure problems of eternal inflation.

Leonard Susskind reiterate that statistics and classical mechanics are a subset of QM

4. Oct 27, 2014

### Staff: Mentor

Yes. However, you might want to consider that you don't need quantum mechanics to construct these vanishingly small probabilities of classical forbidden outcomes. For example....

When we say that the atmospheric pressure on the top surface of my kitchen table is balanced by the pressure on the underside, we really mean that the number of molecules above the table and moving downwards is, on average, roughly equal to the number of molecules underneath the table and moving upwards. However, there is some small chance (maybe one chance in $2^{(10^{25})}$ that all the molecules underneath the table happen to be moving upwards at the same time... and if that happens the table is going to take off like a rocket.

Statistical mechanics is about how the classical behavior of macroscopic systems emerges from the random movement of large numbers of classical particles. Quantum decoherence (google for it, but be warned that some of the math is fairly heavy going) provides an analogous explanation of how the classical behavior of macroscopic systems emerges from microscopic quantum randomness.

5. Oct 28, 2014

### nikkkom

A better example is that if you would construct a machine which emits a stream of ball bearings hitting a closed box and bouncing off, after many gazillion years of operation the box will have a few ball bearings which tunneled into it instead of bouncing off. That would be a clearly "classically impossible" thing to see.

(You'd probably need to make "bounce" action magnetic, not mechanical, otherwise ball bearings will wear out the box sooner than the first tunneling would happen).

6. Oct 28, 2014

### Nick O

Thank you all for your responses!

So, to sum up: There could be some accumulated quantum fluctuations to cause such a thing, but we can't be sure because we don't even know how gravity figures into quantum mechanics. But, even if it can be caused by quantum interactions, it is much more likely to occur due to non-quantum phenomena.

I found your examples and references very interesting. Thanks for sharing!