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Nonobservable space dimensions and the discreteness of time

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  • Boyarsky, Abraham
  • Góra, Paweł

Abstract

We present a simple dynamical system model for the effect of nonobservable space dimensions on the observable ones. There are three premises. A: Orbits consist of flows of probabilities [Ilya P. The end of certainty. NY: The Free Press; 1996] (which is the case in the setting of quantum mechanics). B: The orbits of probabilities are induced by (continuous time) differential or partial differential equations. C: The observable orbit is a flow of marginal probabilities where the nonobservable space dimensions are averaged out. A theorem is presented which proves that under certain general conditions the transfer of marginal probabilities cannot be achieved by continuous time dynamical systems acting on the space of observable variables but can be achieved by discrete time dynamical systems.

Suggested Citation

  • Boyarsky, Abraham & Góra, Paweł, 2005. "Nonobservable space dimensions and the discreteness of time," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 13-18.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:1:p:13-18
    DOI: 10.1016/j.chaos.2004.09.033
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