# Pure chance question

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1. Nov 15, 2015

I recently had a discussion with someone about Quantum Mechanics. His story was confusing to me but I could detect that he made an error in his thinking
which I proceeded to explain :

You are trying to reason from the idea that the 'collapse of the wave-function', which precedes the measurement, is something you can reason about in the
first place. The wave-function allows us to determine the probability of detecting a particle in a certain place and time. It's a probability distribution
function which means the reason a particle appears, is measured, in a certain place and time is determined by pure chance only. It's just that the
chance can vary from place to place and in some places the chance might be zero. So reasoning about how the wave-function 'collapses' equates to reasoning
about something that per definition is determined by pure chance only. This is invalid, since pure chance cannot be defined. Hence, you end up with paradox galore.

My question is, doesn't that mean that physics, once it exposes this 'problem' of pure chance ultimately determining everything, has reached its philosophical
limit already at that moment, since once it reaches pure chance, it has basically reached undefinability.
Doesn't it just stop there? No matter which way you shake it, you always have to make the assumption that you can still 'get' something from pure chance,
which is invalid per definition. Or you could assume that it's not pure chance, but why the hell are you using a probability distribution function then?

Ideas?

2. Nov 15, 2015

There's also no way out of using a PDF! From Feynman, Lectures on Physics vol. III :

'The uncertainty principle 'protects' quantum mechanics. Heisenberg recognized that if it were possible to measure the momentum and the position simultaneously with a
greater accuracy, the quantum mechanics would collapse. So he proposed that is must be impossible. Then people sat down and tried to figure out ways of doing it,
and nobody could figure out a way to measure the position and the momentum of anything - a screen, an electron, a billiard ball, anything - with any greater accuracy.
Quantum mechanics maintains its perilous but still correct existence.'

3. Nov 15, 2015

### DrChinese

You don't need to make an assumption when there is empirical evidence. That being our world exists and we are having this discussion! There is plenty of evidence for the laws of chance as being fundamental, not so much for the other side.

There is no known cause for the value of any quantum observable I chose to measure. That doesn't mean there isn't one, and that one won't ever be discovered. But there is no particular advantage to assuming one exists. And it is definitely a stretch to assume pure chance is "invalid per definition". That remains to be seen.

In fact, any other viewpoint would actually be circular reasoning: assuming that which you wish to prove.

Last edited: Nov 15, 2015
4. Nov 15, 2015

Thanks.

'You don't need to make an assumption when there is empirical evidence.'

You're always making an implicit assumption. And then it's best to be pragmatic, which ultimately leads to the scientific method, indeed.

'That being our world exists and we are having this discussion!'

There it is!

'There is plenty of evidence for the laws of chance as being fundamental, not so much for the other side.'

I don't dispute this. But there is a problem with the concept of the 'laws of chance'.

'There is no known cause for the value of any quantum observable I chose to measure.'

There is, but it's random. That's why you use a PDF. And when you use a PDF, you're making the implicit, mathematical, assumption that it's random then, which means
it cannot be defined. That's the problem : Mathematically, you've already stated that it's undefinable.

'That doesn't mean there isn't one, and that one won't ever be discovered.'

Mathematically, you've already stated that definition of it is impossible. Reasonably, this means that there isn't one, and that one won't ever be discovered either.

'But there is no particular advantage to assuming one exists.'

Don't assume anything at all; It's undefinable per definition. Reason stops.

'And it is definitely a stretch to assume pure chance is "invalid per definition". That remains to be seen.'

I said that defining chance, as in complete unpredictability, is undefinable. If we could provide a definition in any way, it wouldn't be very unpredictable, would it?

'In fact, any other viewpoint would actually be circular reasoning: assuming that which you wish to prove.'

But we can already know that any assumption is invalid on this, for mathematical reasons. I think that that, in itself, is a better assumption.

5. Nov 16, 2015

### Staff: Mentor

Dr Chinese didn't say that.

The laws of chance are rigorously definable via the Kolmogerov axioms:
https://en.wikipedia.org/wiki/Probability_axioms

QM is actually the most reasonable extension of those axioms that allows continuous transformations between so called pure states:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks
Bill

6. Nov 16, 2015

When you try to formalize probability, you're always making the same implicit assumption that chance cannot be defined. If it could, then why are you
handling it in that way? Rigorous treatment contents itself with studying the behaviour of randomness, but makes no attempt to define it. If it would,
it would be immediately mathematically invalid.
Sometimes, this is useful in dealing with incomplete information about the world; A world that might on deeper analysis turn out to be not random.
Then it just works as a simplified model. Maybe that's where the misconception comes from.
Quantum Mechanics however would collapse if the behaviour turns out to be non-random in any way. The theory then cannot make any predictions any more.
Therefore, the undefinable pure chance concept is what you have left, when you talk about 'collapse of the wave-function' etc.
And that's invalid, because you're trespassing in the Pure Chance Zone, so to speak, beyond the math.

7. Nov 16, 2015

### Staff: Mentor

That's nonsense. I think you need to state your position with greater care.

Errrrr - because it works.

Thanks
Bill

8. Nov 16, 2015

### Demystifier

Let us suppose, for the sake of argument, that you are right that chance cannot be defined. Does it mean that it is invalid/inconsistent/paradoxical to have a theory in which chance plays a vital role? You are arguing that it is. But you are wrong. There is nothing invalid/inconsistent/paradoxical with dealing with a theory in which some elements cannot be defined.

In fact any theory (about anything) must eventually be reducible to something which cannot be defined. This should be clear even at the linguistic level: To define some word, you must use some other more fundamental words. And to define those more fundamental words, you must use some even more fundamental ones, etc. But you must stop at some point, as the number of words is not infinite. And when you stop, your most fundamental definition will contain some words which cannot be defined. Such words which cannot be defined by other words are called primitive words.

Take for example the Newton law $F=ma$. The quantities $F,m,a$ are defined as real numbers. Real numbers can be defined in terms of rational numbers (e.g. via a Dedekind cut), and rational numbers can be defined in terms of integer numbers. The integer numbers can be defined by Peano axioms, in terms of sets. But sets, according to modern mathematics, cannot be defined. A set is a primitive concept in mathematics. So Newton law is based on something which cannot be defined. But, my point is, that does not mean that Newton law is invalid/inconsistent/paradoxical.

Just as "set" is a primitive concept, it is possible that "chance" is also a primitive concept. But that does not mean that there is something invalid/inconsistent/paradoxical with a theory based on chance, just as there is nothing invalid/inconsistent/paradoxical with a theory based on sets.

9. Nov 16, 2015

### Demystifier

Suppose, for the sake of argument, that it is not a pure chance. Then why one uses a probability distribution function? For the same reason one uses a probability distribution function when flipping a coin: Because it's practical.

10. Nov 16, 2015

Ok, then, show me a formula for true random behaviour that I can call in a computer program. Like so :

int getRandom()
{
...
}

I don't mean pseudo random numbers, for obvious reasons, nor do I mean random numbers obtained by some physical process, like Linux does, since that also
ends up being without a definition then. I mean an algorithm, self-contained, that's purely random.
And because that's not possible, formal treatments don't attempt this. Hence, the implicit assumption that chance cannot be defined.

I'm not disputing that it works. But to get it to work, pure chance is required as the final 'decision maker'.
If this is anything but pure chance, QM is invalid; It relies on this assumption, to make predictions at all.

Basically, I'm just saying that QM works as math. Any interpretation always ends up trying to understand/define pure chance.
Therefore all interpretations of QM are nonsense, unreasonable. This is why Feynman took the 'shut up and calculate' approach : That, at least, works.
But to continue with this theory philosophically is nonsensical. You're not going to get anything any more once you reach the undefinable.

I'm also not disputing that everything turns out to be ultimately undefinable, therefore base, elementary, assumptions are required. Pure chance is one of them,
a base concept that cannot be broken up in simpler elements. It's just that, once you reach that, you can't reason any further, unless you maintain
that it's not purely random, which QM cannot do. Bayesians can do that, not Quantum Mechanics.

Practically, sure. If you stick to measurement and math, and stay the hell away from 'collapses of wave-functions', 'many worlds' etc.
Philosophically, it cannot be anything else than nonsense.
In my opinion, this has always been the big problem with it.

11. Nov 16, 2015

### Staff: Mentor

A program is deterministic. By definition random behaviour isn't. So you can't do it - obviously.

But interestingly there are pseudo random number generators that pass even the most sophisticated tests we have for randomness - but it is an evolving area as the tests get more sophisticated.

Its impossible, utterly impossible, to tell pseudo random behaviour from truly random behaviour.

Its also irrelevant to QM.

That's false.

Thanks
Bill

12. Nov 16, 2015

### Demystifier

The Adversary, if I understood you correctly, you are effectively saying the following:
Pure chance is either true on not true.
If pure chance is not true, then we should try to find out what is true.
If pure chance is true, then we cannot say anything more about that, in which case we should stop talking about it.

Am I correct?

13. Nov 16, 2015

I'm basically saying that when it comes to QM, we should shut up and calculate. I'd advise against any philosophical interpretation because that's
always going to be invalid, for the reasons I've been arguing.
It's a matter of whether or not you care about the philosophical void. It's probably why Feynman hated philosophy :)

14. Nov 16, 2015

### Demystifier

I thought you are arguing only against pure-chance interpretations. How can your arguments be used against interpretations which do not assume pure chance?

15. Nov 16, 2015

### haushofer

If Bell would have done just this he would never have found his inequalities. Physics is more than just bookkeeping, imho.

I have a feeling that it could well be that quantum gravity is not well understood because we don't understand the underlying principles of quantum mechanics, but that's just a gut feeling. In any case, i think the shut-up attitude is not very scientific, unless you see physics merely as a device to reproduce experimental results.

16. Nov 16, 2015

### gill1109

17. Nov 16, 2015

Bell : 'No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.'

In other words, pure chance cannot be defined. 'local hidden variables' is an attempt to define pure chance, which is impossible, as the theorem states.

'How can your arguments be used against interpretations which do not assume pure chance?'

QM has to assume pure chance. Remember the uncertainty principle? If that's false, so is the entirety of QM!

18. Nov 16, 2015

### Heinera

No, local hidden variables is not an attempt to define pure chance. In fact, most of the local hidden variable models that have been proposed use "pure chance", i.e. randomness, at the source.

19. Nov 16, 2015

### gill1109

Looking for local hidden variables is not, IMHO, an attempt to define pure chance. It's an attempt to avoid deciding whether or not "pure chance" is a fundamental physical feature of the universe.

In other words, if we could "explain" quantum mechanics through (preferably local) hidden variables theory, we wouldn't need to worry about whether or not pure chance exists.

20. Nov 16, 2015

### Staff: Mentor

Its got nothing to do with it.

Because they have nothing to do with it.

It simply has to assume the Kolmogorov axioms. How you interpret it is irrelevant ie if you assume the events defined in those axioms are random or psuedo random the axioms do not care.

Thanks
Bill