quantum mechanics: probablistic or completely random?

[gib65]

So we know that quantum mechanics is a non-deterministic field. Something I've always wondered though is how to interpret "non-deterministic" in this description. Does it mean the phenomena in the quantum world are completely random or is there is there more of a fine grained level of probability? What is mean is - suppose you wanted to measure the position of a particle. Would you expect your results to be completely random (as is the particle could be anywhere) or somehwhat probablistic (as in the particle is most like to be in a particular region)?

[swansont]

The wave function (related to probability) is not, in general, flat. Positions are not all equally probable except in specific cases; a particle that can be anywhere could have a very well-known momentum, since the Fourier transfor of the delta function is a flat line.

[Sisyphus]

So we know that quantum mechanics is a non-deterministic field.

 

Either that, or it is deterministic, just in a way that we aren't yet able to determine, or even something that may be fundamentally impossible to observe, yet still be deterministic.

[gib65]

Either that, or it is deterministic, just in a way that we aren't yet able to determine, or even something that may be fundamentally impossible to observe, yet still be deterministic.

 

Yes, good point. In fact, I've always suspected that the probablistic nature of quantum mechanics - as opposed to a completely random nature - is a sign that its non-deterministic appearance is the result of too many unknown variables interacting, making it too complex to understand. Usually, high complexity with too many unknowns results in probablistic outcomes, not complete randomness (think of the social science).

[swansont]

Yes, good point. In fact, I've always suspected that the probablistic nature of quantum mechanics - as opposed to a completely random nature - is a sign that its non-deterministic appearance is the result of too many unknown variables interacting, making it too complex to understand. Usually, high complexity with too many unknowns results in probablistic outcomes, not complete randomness (think of the social science).

 

I suggest you read up on "hidden variable" experiments.

[Chupacabra]

Yes, good point. In fact, I've always suspected that the probablistic nature of quantum mechanics - as opposed to a completely random nature - is a sign that its non-deterministic appearance is the result of too many unknown variables interacting, making it too complex to understand. Usually, high complexity with too many unknowns results in probablistic outcomes, not complete randomness (think of the social science).

 

I thing hypotheses like "hidden variables" are just the results of the inability of people with a deterministic mindset to incorporate the notion of the freedom inherent in the world and the scientific discoveries refuting the concept of the "clockwork Universe" and the view that everything is just the "small flying balls running into each other".

Probabilism and randomness are not contradictory at all. You could know the definite probability that something would happen and still be unable to predict the result of the any single trial.

[gib65]

I thing hypotheses like "hidden variables" are just the results of the inability of people with a deterministic mindset to incorporate the notion of the freedom inherent in the world and the scientific discoveries refuting the concept of the "clockwork Universe" and the view that everything is just the "small flying balls running into each other".

Probabilism and randomness are not contradictory at all. You could know the definite probability that something would happen and still be unable to predict the result of the any single trial.

 

You've missed my point entirely. I'm not saying randomness and proabability are incompatible. I am saying' date=' however, that [b']complete[/b] randomness (i.e. there being perfectly equal chances of every possible outcome) is incompatible with asymmetrical probability (i.e. there being more of a chance of one outcome over other outcomes). But you're right that the latter will still fall short of having perfect predicting power, although it will be more useful in predicting outcomes than complete randomness.

 

My point is, when you have "asymmetrical probability" (my term), it's a good sign that there are at least some hidden variables bringing about the asymmetry. In other words, if the probability is leaning in a certain direction, there a pattern of outcomes emerges. This pattern may not be perfectly clear with well defined parameters, but it becomes more noticeable the more asymmetric the probability. If there's a pattern, there is probably something determining the pattern, and those are the hidden variables.

 

Note that I'm not saying that asymmetric probability MUST mean there are hidden variables, just that it's a good sign that they exist. Also note that I'm not saying ALL of it can be traced o hidden variables, just enough to account for the asymmetric probability.

[Severian]

Well, there is structure behind the random numbers, in the sense that you mean (I think). There are laws which must be obeyed and given enough statistics the random numbers will fall in well predicted distributions.

 

So in that sense there are 'hidden variables'. If there weren't, our theory would be non-predictive and that would be bad.

 

But that is not what is meant by 'hidden variable theory' in which there are no random numbers, and everything is deterministic but we just can't see it. These sort of hidden variable theories have been disproven.

[gib65]

But that is not what is meant by 'hidden variable theory' in which there are no random numbers, and everything is deterministic but we just can't see it. These sort of hidden variable theories have been disproven.

 

Well, that's interesting. So do you mean to say that the genuine 'hidden variable' theories purport that there is absolutely NO room for randomness? How could such a theory be disproven? I can see a theory that predicts specific and well defined variables being disproven. For example, if I had a theory that little microscopic gremlins are responsible for the pseudo-random outcomes that we see in the quantum realm, then it's very possible to disprove that theory. But the idea of undefined variables that we simply haven't discovered or thought of being disproven seems logically impossible. How can you disprove that there might be an explanation for something that we just haven't figured out yet?

[Severian]

Well' date=' that's interesting. So do you mean to say that the genuine 'hidden variable' theories purport that there is absolutely NO room for randomness?

[/quote']

 

Yes.

 

How could such a theory be disproven?

 

http://en.wikipedia.org/wiki/Bell%27s_inequality

[gib65]

Ah, well I see that 'hidden variable theory' carries very specific connotations that can be disprove. I suppose I misused the phrase 'hidden variables', but the way I meant it goes beyond the scope of the conventional theory. Let me explain:

 

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

 

This is obviously from the link you provided. The key words in this quote are "physical" and "local". If hidden variable theory purports that there are physical and local - yet hidden - variables bringing about the quantum randomness, then I can see that being disproved. But what I meant by 'hidden variables' was something more abstract or metaphysical, not something that had to be physical and local. Also, I meant that such factors could not be disprove in a purely logical sense (i.e. one cannot make a purely logical argument proving that an unknown explanation doesn't exist for what appears to be random outcomes - the best you can do is show that we don't have an explanation yet).

 

An example of an abstract, non-local explanation is to suppose God decides the outcomes of quantum phenomena. Don't worry, for the moment, whether God really exists or not - I don't believe in God myself (at least, not the conventional notion of 'God'). But for the sake of argument, suppose there was a God, and He decided the outcomes of quantum phenomena based on the roll of a dice. Also, suppose that the dice adheres to all the laws of physics. That is, it falls due to gravity, it rotates in the air according to the initial angular momentum given to it by God's hand, and when it lands, it obeys the laws of collision and impact with the ground - and it finally settles on one particular side. Therefore, the outcome of the dice is purely deterministic, but too complex for any human to notice a pattern. Furthermore, suppose God never deviates from the scheme of letting the dice decide the outcome of the quantum phenomena. So here we are performing quantum experiments, and there God is watching us, saying "Oh, great, those humans are at it again. Well, better get the dice out." So we conduct the experiment, God rolls the dice, and yields a 6, and so whatever a roll of 6 dictates for the results of the experiment, God sees to it that this result is indeed what happens.

 

Now, say what you want about metaphysics. But if you keep in mind that my version of 'hidden variables' is meant in a purely logical (i.e. non-physical, non-local) sense, you see that it becomes a lot more difficult to disprove.

[Tom Mattson]

http://en.wikipedia.org/wiki/Bell%27s_inequality

 

I would be wary of any wikipedia article on Bell's inequality or the foundations of quantum mechanics. There is a battle raging behind the scenes among the editors, one of whom is the famous (infamous?) local realist crackpot named Caroline Thompson. She is constantly reverting sections of these articles towards her biased POV, and the others constantly revert them back to a more neutral, encyclopedic nature. They watch her pretty carefully but you never know what these articles are going to say on any given day.

[Severian]

Yes that is the danger of Wikipedia. To be honest, I hadn't even read it, which show how even I subconciously (and naively) trust it.