Equivalence relations between deterministic and quantum mechanical systems
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Several quantum mechanical models are shown to be equivalent to certain deterministic systems because a basis can be found in terms of which the wave function does not “spread.” This suggests that apparently indeterministic behavior typical for a quantum mechanical world can be the result of locally deterministic laws of physics. We show how certain deterministic systems allow the construction of a Hilbert space and a Hamiltonian so that at long distance scales they may appear to behave as quantum field theories, including interactions but as yet no mass term. These observations are suggested to be useful for building theories at the Planck scale.
Key wordsHilbert space massless fermions extensive Hamiltonian primordial observables reversible cellular automaton Baker-Campbell-Hausdorff expansion discrete time
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