How do we know that Quantum Mechanics isn't simply a theory of approximations? 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? 
 A: 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.
A: 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.
