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 soinspin 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-valued, in units whose fundamental length is $2 \pi \sqrt{\alpha\prime}$$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-movers to the left and the right movers-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-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?