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A critique of the disturbance theory of indeterminacy in quantum mechanics

Abstract

Heisenberg'sgendanken experiments in quantum mechanics have given rise to a widespread belief that the indeterminacy relations holding for the variables of a quantal system can be explained quasiclassically in terms of a disturbance suffered by the system in interaction with a quantal measurement, or state preparation, agent. There are a number of criticisms of this doctrine in the literature, which are critically examined in this article and found to be ininconclusive, the chief error being the conflation of this disturbance with the projection postulate. We present a critique of the disturbance theory based on the fact that the required disturbance will in general depend on the interaction time of the system and state-preparer. This point is exploited in the construction of a spin-interaction model which acts as a counterexample to the disturbance doctrine, while remaining faithful to the spirit of Heisenberg'sgedanken experiments. Several consequences of this result are discussed.

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This work formed part of a thesis submitted by one of us (HRB) in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the University of London.

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Brown, H.R., Redhead, M.L.G. A critique of the disturbance theory of indeterminacy in quantum mechanics. Found Phys 11, 1–20 (1981). https://doi.org/10.1007/BF00715192

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Keywords

  • Quantum Mechanic
  • Quantal System
  • Interaction Time
  • State Preparation
  • Quantal Measurement