[SideQuark]

There can be no proof, in the mathematical sense, of anything about the physical world, so radioactive decay being provably random in the most tested, accurate model of the world we have is as close to certainty as anything known about the physical world.

Semi-related is this year's Nobel Prize for experiments showing Bell's Theorem is physically true. This rules out hidden variable theories.

[agalunar]

I believe Bell's theorem specifically rules out local hidden variable theories, not all hidden variable theories.

[a1369209993]

Technically, even then it only rules out efficient local hidden variable theories. A theory where every particle carries a local hidden variable containing the entire state of the universe can (obviously?) emulate any other theory, quantum or otherwise (with a bit of finangling for things like quantum field wierdness).

[SideQuark]

Yes, you're correct. However, nonlocal hidden theories bring other issues that don't seem plausible. That's why the best current quantum field theories do make radiation a purely random event. None use nonlocal hidden variables.

[amelius]

Hmmm.

First you say that there can be no proof of anything about the physical world.

Then you tell about a Nobel prize for showing Bell's Theorem is physically true ...

[Timon3]

You left out the parts which answer your question. GP specifically wrote:

> There can be no proof, in the mathematical sense, of anything about the physical world[...]

followed by:

> Semi-related is this year's Nobel Prize for experiments showing Bell's Theorem is physically true.

The first quote refers to "mathematical proof", the second to "physical proof". They are different categories.

[amelius]

Ok, what is a physical proof then, apart from strong evidence?

[icegreentea2]

Mathematical proofs are in escapable conclusions of your choice of axioms (assumptions).

Negative physical proofs is evidence showing that a particular model (assumption) about the physical world does not hold. Negative physical proofs are relatively straightforward. Take your model, make a prediction, and then show the prediction is untrue in the physical world. This is more or less how the Bell Inequality test was supposed to be.

Positive physical proofs (for example, prove that radioactive decay is random), is in general not "actually possible". We can only show that physical reality is sufficienty compatible with your model.

[amelius]

So I take it that that Nobel prize was for a negative physical proof?

[icegreentea2]

Yes more or less. Bell's Theorem stated that if local realism holds (very roughly things continue existing separate from observation, and things can't influence other things faster than the speed of light), then certain measurements cannot correlate at higher than a certain rate. The relevant experiments show that for increasingly well designed and controlled cases, that these measurements correlate above the limit, and therefore local realism cannot be true.

[atoav]

Physical proof is not the same as mathematical proof. It is strong evidence for a mathematical model to be an adequate description of reality.

But that means we did not proof that the mathematical model is reality. There might be some weird edge case looming around the corner under which our model utterly fails to describe the physical world. Then we have to adjust the model or find a new one.