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Decoherence, Quantum Measurement Problem, and Spontaneous Symmetry Breaking

Yuanxin Li

Published Sep 30, 2024• 0 citations
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Abstract

In this paper, we propose a mechanism analogous to the spontaneous symmetry breaking to explain quantum measurement. It is actually a supplement to the decoherence theory. We introduce the effective potential between eigenstates and show that a wave function in a superposition of several eigenstates reduces to a single eigenstate due to the spontaneous-symmetry-breaking-like kinetic effect.

DOI
10.20944/preprints202409.2405.v1

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In this paper, we propose a mechanism analogous to the spontaneous symmetry breaking to explain quantum measurement. It is actually a supplement to the decoherence theory. We introduce the effective potential between eigenstates and show that a wave function in a superposition of several eigenstates reduces to a single eigenstate due to the spontaneous-symmetry-breaking-like kinetic effect.
Quantum mechanics cannot be applied within a closed system. Inevitable measurement process in quantum mechanics is usually treated separately from the basic principles of the framework and requires outside observer of the system. In this paper, we propose that the quantum measurement process is actually a physical process associated with the ubiquitous mechanism of spontaneous symmetry breaking. Based on this proposal, we construct a quantum measurement model in which the mixed state evolves into a pure state as the dynamical pro-coherence process. Furthermore, the classically distinguishable pointer parameter emerges as the c-number order parameter in the formalism of closed time-path quantum field theory. We also discuss the precision of the measurement and the possible deduction of the Born probability postulate.
We present a mathematically simple procedure to explain spontaneous symmetry breaking in quantum systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a symmetry broken state in crystals, antiferromagnets, and even superconductors. It has the advantage that it automatically brings to the fore the main players in spontaneous symmetry breaking: the symmetry-breaking field, the thermodynamic limit, and the global excitations of a “thin” spectrum.