I bet the automatic response to my question would be "Bell's theorem" and of course I am not disputing Bell's proof. I am however uncertain of one of his assumptions.
The so called "no conspiracy" assumption states that we somehow posses this magical thing called free will which makes us able to break free from the causal chain of events that make us measure the $y$-axis instead of the $x$-axis and so on in experiments. Obviously this makes little sense once reviewed under the light of logic.
What this naturally implies is that, if a theory is fully deterministic, it is instantly super-deterministic.
Simon Kochen and John Conway published a theorem in 2009, "The Strong Free Will Theorem", which simply-put states: either everything is deterministic (super-deterministic) or every particle has free will.
Among the few who accept this to the fullest extent is Gerard 't Hooft.
He has proposed that what we call sub-atomic particles are really just templates and that there is a realm beneath the quantum where the true fabric of reality is "hidden". By accepting determinism he escapes Bell's theorem (due to not having to accept the "no conspiracy" assumption) and can construct a local, deterministic and realist hypothesis of reality. In Gerard 't Hooft's model there is cellular automata somewhere near the Planck scale which gives rise to the "emergent quantum mechanics".
This means that there exist no superpositions in objective reality, the cat is always either dead or alive, no collapse of wave functions, no branching universes, non-locality or retro-causality.
The big question for me is basically: Why do people have such a hard time accepting determinism? Some will object and say "oh but it's SUPER-determinism", but that makes no sense whatsoever, either everything is determined (determinism) or only somethings are (quasi-determinism). By accepting it we escape Bell's theorem. Bell himself was well aware of this and mentioned it a few times in interviews in the 80's.
I know some are concerned that if we accept complete determinism we can no longer do science because it's all a HUGE CONSPIRACY. Gerard 't Hooft has answered critics who bring up this here: arXiv:1112.1811, section 6.
Additionally, another author who has taken a deeper look into the worries of "conspiracies" in QM interpretations is Peter J. Lewis in his paper "Conspiracy Theories of Quantum Mechanics" (also here).
So to all of you who dismiss local hidden variables I ask: Why?
Best Answer
The idea of my latest paper is simple. I experienced in other blogs that most people refuse to go with me all the way. I'll give my argument step by step and you may choose where you want to step out.
Consider superstring theory, in its original, completely quantized version. Many people believe it might have something to do with the world we live in. It has interesting low energy modes that show some resemblance with what happens in the Standard Model: fundamental fields for particles with spin 0, 1/2 and 1, as well as gravitons for the gravitational field, as gravitinos. The theory is not universally accepted, but it is an interesting model with many features that look like our world. Certainly not obviously wrong, and certainly very much quantum. There is a Hilbert space of states. I only use it as a model to illustrate my ideas. But step out here if you want.
The transverse coordinates of the string form a simple integrable quantum field theory on the string world sheet. This integrable system has left-movers and right-movers, forming quantum states, the string excitations. Now, I discovered a unitary transformation that transforms the basis of this Hilbert space into another basis. In QM, we do this all the time, but what is special in the new basis is that it is spanned completely by a set of left-movers and right-movers that are integer-valued, in units whose fundamental length is $2 \pi \sqrt{\alpha^\prime}$. Thus, we have operators taking integer values, and they are all commuting. What's more, they commute at all times. The evolution operator here translates the left-movers to the left and the right-movers to the right. Intuitively, you might find that the result is not so crazy: these integers are of course related to particle occupation numbers in quantum theory. I still have Hilbert space, but it is controlled by integers. If you don't like this result, please step out.
Do something similar to the fermions in the superstring theory. They can be transformed into Boolean variables using a Jordan-Wigner transformation. The superstring theory of course has supersymmetry on the world sheet. That does not disappear, but does become less conspicuous. Also the fermions are transversal. The Boolean variables also commute at all times. Next stop.
Realize that, if Nature starts in an eigen state of these discrete operators, it will continue to be in such an eigenstate. There is a super-selection rule: our world can't hop to another mode of eigen states, let alone go into a superposition of different modes. Thus, if at the beginning of the universe, we were in an eigenstate, we are still in such an eigenstate now. Step out if you want.
I can add string interactions. My favorite one is that strings exchange their legs if they have a target point in common. This is deterministic, so the above still applies. This is a stop where you may get out.
Rotations and Lorentz transformations. To understand these, we need to know the longitudinal coordinates. The original, completely quantized superstring tells you what to do: the longitudinal coordinates are fixed by solving the gauge constraints (both for the coordinates and the fermions). The superstring has only real-number operators, of course non-commuting. This step tells us that only 10 dimensions work, and fixes the intercept a. Don't like it? Please step out.
What I have here is a Lorentz invariant theory equivalent to the model generated by the original superstring theory, but acting like a cellular automaton. It IS a cellular automaton. Any passengers left?