Why quantum mechanics cannot be formulated as a Markov process

Daniel T. Gillespie
Phys. Rev. A 49, 1607 – Published 1 March 1994
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Abstract

Both quantum mechanics and Markov-process theory deal with dynamical systems whose behaviors can be predicted only probabilistically. The question therefore arises as to whether Markov-process theory, a theory that is firmly rooted in the common-sense laws of probability, can provide a generally adequate mathematical framework for quantum mechanics, a theory whose predictions often seem to defy common sense. It is shown here that the measurable behavior of a certain elementary quantum system that oscillates between two discrete states cannot be modeled as a Markov process. That this will also be true for most other quantum systems is shown to follow from the same property of quantum mechanics that is responsible for the so-called quantum Zeno effect. The conclusion that quantum behavior cannot generally be modeled as a Markov process underscores the truly mysterious nature of quantum mechanics when viewed in common-sense terms.

  • Received 7 September 1993

DOI:https://doi.org/10.1103/PhysRevA.49.1607

©1994 American Physical Society

Authors & Affiliations

Daniel T. Gillespie

  • Research Department, Naval Air Warfare Center, China Lake, California 93555

Comments & Replies

Comment on ‘‘Why quantum mechanics cannot be formulated as a Markov process’’

Piotr Garbaczewski and Robert Olkiewicz
Phys. Rev. A 54, 1733 (1996)

Reply to ‘‘Comment on ‘Why quantum mechanics cannot be formulated as a Markov process’’’

Daniel T. Gillespie
Phys. Rev. A 54, 1737 (1996)

Reply to “Comment on ‘Why quantum mechanics cannot be formulated as a Markov process’ ”

Daniel T. Gillespie
Phys. Rev. A 56, 3304 (1997)

Comment on “Why quantum mechanics cannot be formulated as a Markov process”

L. Hardy, D. Home, E. J. Squires, and M. A. B. Whitaker
Phys. Rev. A 56, 3301 (1997)

Original Article

Realism and the quantum-mechanical two-state oscillator

L. Hardy, D. Home, E. J. Squires, and M. A. B. Whitaker
Phys. Rev. A 45, 4267 (1992)

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Issue

Vol. 49, Iss. 3 — March 1994

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