# Probabilistic vs Statistical interpretation of Double Slit experiment

Why is it assumed that the results seen in the double slit experiment are probabilistic and not just a statistical result of some unknown variable or set of variables within the system.

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I'm having difficulty distinguishing the difference between "statistical" and "probabilistic". If there is an "unknown variable or set of variables within the system" then it's just deterministic. The great irony here is that the Copenhagen Interpretation was constructed at a time when the number of elementary particles and forces was a fraction of what were discovered to date. So there were many "unknown variables" at that time and perhaps even yet. – DWin Apr 1 '13 at 17:27
Ya, in thinking how to explicitly describe the distinction, I guess I would say a system that is truly random versus one that is simply chaotic. So, yes perhaps deterministic versus non-deterministic. A chaotic system may be extremely difficult to predict, but it can still theoretically be done. A probabilistic system is complete undeterminable even with omniscience. – aepryus Apr 1 '13 at 18:22

## 2 Answers

Ever since the origination of quantum mechanics, some theorists have searched for ways to incorporate additional determinants or "hidden variables" that, were they to become known, would account for the location of each individual impact with the target.

Wikipedia

In my opinion, the "were they to become known" is the tricky bit (to put it mildly). And, as things stand, for prediction purposes one might as well assume an inherently probabilistic nature.

(I'll add to this later.)

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Actually, I think I'll leave it like this. – Keep these mind Apr 1 '13 at 16:37
I recall asking this question while studying QM and getting a stronger answer -- That there was some mathematical reason why there couldn't be unknown variables. Can the probabilistic interpretation simply be because no other variables have been found? – aepryus Apr 1 '13 at 16:55
As far as I can tell, a stronger answer always has some hidden philosophical assumptions or loopholes. As said, hidden variables have been suggested, but not how their values might be predicted. If physics is in the business of prediction, then they aren't much use. So, many physicists will tell you nature is probabilistic, but you can read this as the slightly weaker and less philosophical statement that QM is probabilistic and QM is our best and uncontested description of reality. – Keep these mind Apr 1 '13 at 17:00
@aepryus This might interest you. – Keep these mind Apr 1 '13 at 18:05
Thanks, I'll check it out. – aepryus Apr 1 '13 at 18:24

You are asking can the probabilistic results of quantum mechanics be reproduced by a deterministic classical mechanics with added random noise of some sort to reproduce the statistical results. This question has been considered in leonard susskinds lectures on quantum entanglement1 (see videos on Stanford continuing education website). The answer he gives is "no certainly not!". He points out that the logic of classical physics is the logic of set theory, states of systems being represented as points in a set; while the logic of quantum mechanics is the logic of vector spaces which is not deducible from the logic of sets. We get states (entangled states) in the latter which are impossible in the former (hence bell's inequalities which classical states must obey but which some quantum states violate) Nature has been shown to violate Bell's inequalities (Aspect's experiments etc) so the quantum description is closer to observation than classical stochastic type explanations.

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I guess at some point this question could take two forms. One form is a question about the physics involved. Another form is a question about the nature of data itself. If I were to reframe the question to ask, 'Could I create a computer program that output data in a way that precisely mimicked a quantum system, but was statistical not probabilistic?' I would argue that I could. Basically, I fail to see how one could possibly determine whether a system is statistical or probabilistic from looking at the data alone. And if we aren't looking at the data, then what are we looking at? – aepryus Nov 16 '13 at 17:30
This is not very accurate.. The logic of vector spaces is certainly deducible from set theory. In fact, all of probability can be formulated in terms of the theory of deterministic sets and deterministic real numbers. For example, no new kinds of "random" numbers need to be invented. The same holds for quantum logic: it is completely expressible in terms of ordinary Boolean logic. – joseph f. johnson Feb 8 at 15:31