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Quantum Measurement and Initial Conditions

International Journal of Theoretical Physics volume 55, pages 1897–1911 (2016)Cite this article

Abstract

Quantum measurement finds the observed system in a collapsed state, rather than in the state predicted by the Schrödinger equation. Yet there is a relatively spread opinion that the wavefunction collapse can be explained by unitary evolution (for instance in the decoherence approach, if we take into account the environment). In this article it is proven a mathematical result which severely restricts the initial conditions for which measurements have definite outcomes, if pure unitary evolution is assumed. This no-go theorem remains true even if we take the environment into account. The result does not forbid a unitary description of the measurement process, it only shows that such a description is possible only for very restricted initial conditions. The existence of such restrictions of the initial conditions can be understood in the four-dimensional block universe perspective, as a requirement of global self-consistency of the solutions of the Schrödinger equation.

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Notes

  1. Patching local solutions together to obtain global solution, and the obstructions preventing this, are studied in sheaf theory [43].

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Acknowledgments

The author cordially thanks Eliahu Cohen, Hans-Thomas Elze, Florin Moldoveanu, and the referees, for very helpful comments and suggestions.

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  1. Horia Hulubei National Institute for Physics and Nuclear Engineering, Bucharest, Romania

    Ovidiu Cristinel Stoica

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  1. Ovidiu Cristinel Stoica
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Correspondence to Ovidiu Cristinel Stoica.

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Stoica, O.C. Quantum Measurement and Initial Conditions. Int J Theor Phys 55, 1897–1911 (2016). https://doi.org/10.1007/s10773-015-2829-2

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Keywords

  • Foundations of quantum mechanics
  • Measurement theory
  • Contextuality
  • Entanglement and quantum nonlocality
  • EPR paradox
  • Bell inequalities
  • Quantum mechanics