Foundations of Physics

, Volume 24, Issue 3, pp 363–377 | Cite as

Statevector reduction in discrete time: A random walk in Hilbert space

  • Akihiro Nakano
  • Philip Pearle


A simple model is presented in which the statevector evolves every ε seconds in one of two ways, according to a particular probability rule. It is shown that this random walk in Hilbert space results in reduction of the statevector. It is also shown how the continuous spontaneous localization (CSL) theory of statevector reduction is achieved as a limiting case of this model, exactly as Brownian motion is a limiting case of ordinary random walk. Finally, a slightly different but completely equivalent form of the CSL equations suggested by the simple model given here is discussed.


Hilbert Space Simple Model Brownian Motion Random Walk Discrete Time 
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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Akihiro Nakano
    • 1
  • Philip Pearle
    • 1
  1. 1.Department of PhysicsHamilton CollegeClinton

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