Dear Flavio
Thank you for your kind remarks. Nicolas Gisin and I have already discussed some of the matters discussed in your essay and whilst I do agree that your and Nicolas's ideas are very thought provoking, I would say that we are not in complete agreement.
Let me start by remarking that I fully agree that it is possible to treat chaotic classical deterministic systems by some finite indeterministic approximation. In fact this is exactly what we do in modelling climate:
https://www.nature.com/articles/s42254-019-0062-2
which is to say that we approximate a set of deterministic chaotic partial differential equations by a finite deterministic numerical approximation and represent the unresolved remainder of the system by constrained stochastic noise. It works well!
However, I do not believe this approach will work for quantum physics, if one believes that the complex Hilbert Space of quantum theory is somehow fundamental, the reason being (Lucien) Hardy's Continuity Axiom. By virtue of this axiom, the continuity of Hilbert Space is fundamental to quantum theory.
Put this way, the continuum appears to play a more vital role in quantum theory than it does in classical theory. This suggests that if we seek some finite theory of quantum physics - which I certainly do seek - then the resulting theory will have to be radically different from quantum theory (even with a stochastic collapse model) and will not be just some approximation to it.
I can in fact state this a little more precisely. I believe that by virtue of Hardy's Continuity Axiom, quantum theory will have to be a singular limit and not a smooth limit of a finite discretised theory of quantum physics, as the discretisation scale goes to zero.
In my essay I attempt to suggest a deterministic (i.e. not indeterministic) alternative to quantum theory in which quantum theory is a singular limit (as a certain fractal gap parameter goes to zero). However, until potential departures from quantum theory can be experimentally tested, and perhaps this day is not so far away, who knows whether this really is the right way forward.
Having said this, there are clearly many points of commonality between our essays and I look forward to discussing these with you sometime!
Best wishes
Tim