# How do we know that Quantum Mechanics isn't simply a theory of approximations? [duplicate]

From what I understand, QM is all about uncertainty. The wavefunction (or rather $|\Psi|^2$) gives us a probability of finding a particle at a certain point. Then, we measure the particle, and find what point it is at.

Now, here's my trouble - QM states that before we measured this particle, it was in a superposition of many states and did not have a definite position. This also implies the wave function is "perfect" because it gives as accurate information as possible about the position particle before we measure it.

So, how do we know this? Why can't there be a function $\phi$ that doesn't give probability distributions, but instead gives definite locations of particles, and we just haven't found a way of expressing or computing it? Why do we know that the position of particles is physically uncertain, and not just unknown to the experimenter? Sure, Quantum Mechanics works out beautifully and fits the results, but perhaps it is simply a very good theory of probability when we have a much more elegant and simple theory?

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• This sounds like hidden variables, which are found by Bell's Theorem and subsequent experiments to not be possible. I recommend reading the wikipedia page for this :) Hidden variables – Alubeixu Jun 17 '17 at 12:21
• Are you familiar with De Broglie–Bohm theory? – Alfred Centauri Jun 17 '17 at 12:45
• I really dont understand the downvotes to this question. Sure, the idea in the OP has been rejected by the scientific community, but that doesn't mean that the question is bad. The post is well-written, and the question is not silly. – AccidentalFourierTransform Jun 17 '17 at 12:50
• @AlfredCentauri To be honest, there was research effort, but not many results - googling this question is very tricky if you don't know the terminology (even putting it into words here was hard). The wiki page for hidden variables explains all of this, but I'll leave this up in case anyone else is having trouble finding reference on this problem. – TreFox Jun 17 '17 at 13:01
• I am closing this question as a duplicate, because the essentials ("how do we know QM isn't just a hidden-variable theory?") are so much of a well-trod ground on this site that this question should not go on the Hot Network Questions sidebar - it's just not constructive enough to be representative of this site, and to the extent that the topic is worthy of further discussion, this question is simply not couched in sufficient nuance to really advance that conversation. I'm reluctant to answer-then-close, but this one really doesn't deserve the spotlight. – Emilio Pisanty Jun 17 '17 at 16:42

We don't. It could well be the case that there is a deeper theory than quantum mechanics which makes all or most of the weirdness go away. There's a lot of people looking for those kinds of theories and in the past eight decades they've mostly come up empty handed.

What we do have is strong constraints on how that theory can look like - things like the Bell, Kochen-Specker or PBR theorems, or the far-reaching effects of nonlinearities - which make it very hard for theories to do away with the weirdness and still reduce to quantum mechanics.

Thus it's perfectly possible for someone to come up with a theory that supersedes QM, and if they do then we will all thank them for it. However, from the way things are looking like right now, that bigger theory is likely to be even weirder than QM, and it is likely to force you to give up principles that we hold even more tightly than locality and realism, such as the possibility to set up independent experiments in different places. And, if you do go that far, then many physicists will begin to question just to what extent that theory is an improvement over the weirdness of quantum mechanics.

• You link Bell's theorem to Wikipedia, and the two others to another site. But the site also has a discussion of Bell's theorem. Maybe better link it too. – Ruslan Jun 17 '17 at 16:40
• @Ruslan If you feel you can offer a better answer, you're welcome to post it. I have my reasons for linking as I did, but it appears (since you came in directly suggesting change, instead of asking questions) that you're not that interested in them. – Emilio Pisanty Jun 17 '17 at 16:46

I'm my opinion, the best bet that your suggestion may be true is Classical Stochastic Electrodynamics. This theory is not very well known, and still in its development phase. But its ideas are very interesting. See there :

https://en.wikipedia.org/wiki/Stochastic_electrodynamics

https://arxiv.org/abs/1205.0916

In brief : Stochastic Electrodynamics (SED) postulates that the vacuum is filled with zero-point fluctuations of the electromagnetic field, that can be described classicaly. It's just a stochastic field that is there, isotropic, homogeneous, and have a Lorentz invariant spectrum. Yet, this random field have an effect on the motion of particles, and the observer can only see some average behaviors. This theory suggest that QM is a kind of effective theory, valid for some time and space averages only. It can also reproduce most of the formalism of QM, but it's mathematically a very complicated theory.

The Planck constant enters that theory as a classical constant that defines the scale of the random field. All (most ?) of QM follows from that.

• Can I know why the down vote ? I think this answer fits the OP query. – Cham Jun 17 '17 at 15:32
• Maybe you should say some words about what CSE is and what drawbacks it has (nonlocality etc., maybe mentioning Bell's theorem). Otherwise it's mostly a link-only answer. – Ruslan Jun 17 '17 at 16:35
• I didn't downvote, but it really looks like a crackpot theory. Unless it predicts something new that can be experimentally tested, I'd expect that theory to stay "little known". – Magicsowon Jun 17 '17 at 16:36
• @Magicsowon Bohm-de Broglie theory isn't considered crackpot theory (it's an interpretation of QM), and CSE, according to Wikipedia, is its extension. – Ruslan Jun 17 '17 at 16:41
• Stochastic Electrodynamics is certainly not a "crackpot" theory. The reason it isn't very well known yet is it's very complicated (non-linear), and it can only do numerical evaluations. The calculations do reproduces most of the QM predictions. – Cham Jun 17 '17 at 16:41