Abstract
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the equations to be considered. Special attention is given to the notion of `locality'. Various examples are worked out, followed by a systematic procedure to generate classical evolution laws and quantum Hamiltonians that are exactly equivalent. What is new here is that we consider interactions, keeping them as general as we can. The quantum systems found, form a dense set if we limit ourselves to sufficiently low energy states. The class is discrete, just because the set of deterministic models containing a finite number of classical states, is discrete. In contrast with earlier suspicions, the gravitational force turns out not to be needed for this; it suffices that the classical system act at a time scale much smaller than the inverse of the maximum scattering energies considered.
Highlights
We do things that are normally not considered: allow for evolution laws that directly exchange ontological states. Perhaps, this leads to interaction Hamiltonians that are as general and as complicated as what we usually only encounter in genuine quantum systems
We find that by including ontological exchange interactions between the ontological states, and by adjusting the speed of the evolution, we can create a quite generic quantum mechanical Hamiltonian
We find that one can postulate the existence of “cells” that each contain one or more variables; these variables are postulated each to move in periodic orbits as long as other interactions are absent
Summary
Discussions of the interpretation of quantum mechanics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] seem to be confusing and endless. If temporarily we limit ourselves to a single, isolated, elementary building block of a more general quantum system, allowing for only a finite number of states, we may assume it to be periodic in time. We do things that are normally not considered: allow for evolution laws that directly exchange ontological states Perhaps, this leads to interaction Hamiltonians that are as general and as complicated as what we usually only encounter in genuine quantum systems. The only way to register what happens when they interact, is to project away the ultra fast time components of both systems This can only be done by selecting sufficiently low energy eigen states of the Hamiltonian, which is a procedure that can only be done by introducing Hilbert space. We leave it to the philosophers to expand on such observations or suspicions
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