Journal of Statistical Physics

, Volume 53, Issue 1–2, pp 323–344 | Cite as

Equivalence relations between deterministic and quantum mechanical systems

  • Gerard't Hooft


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 words

Hilbert space massless fermions extensive Hamiltonian primordial observables reversible cellular automaton Baker-Campbell-Hausdorff expansion discrete time 


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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Gerard't Hooft
    • 1
  1. 1.Institute for Theoretical PhysicsTA UtrechtThe Netherlands

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