Abstract
The symmetries that govern the laws of nature can be spontaneously broken, enabling the occurrence of ordered states. Crystals arise from the breaking of translation symmetry, magnets from broken spin rotation symmetry and massive particles break a phase rotation symmetry. Time translation symmetry can be spontaneously broken in exactly the same way. The order associated with this form of spontaneous symmetry breaking is characterised by the emergence of quantum state reduction: systems which spontaneously break time translation symmetry act as ideal measurement machines. In this review the breaking of time translation symmetry is first compared to that of other symmetries such as spatial translations and rotations. It is then discussed how broken time translation symmetry gives rise to the process of quantum state reduction and how it generates a pointer basis, Born’s rule, etc. After a comparison between this model and alternative approaches to the problem of quantum state reduction, the experimental implications and possible tests of broken time translation symmetry in realistic experimental settings are discussed.
Highlights
The physical laws of nature typically possess a great amount of symmetry
We have recently shown that this is not a necessary constraint, and that it is possible to give a dynamical description of spontaneous symmetry breaking in quantum mechanics which does allow even the time translation symmetry to break down [5,6]
If we assume that the order parameter field results from the incompatibility of general covariance and unitarity, as we argued before, the combination of ω 2 = Gρ and M is of the correct order of magnitude to ensure that elementary particles, molecules and even supercurrents should be considered microscopic, while tables, chairs and pointers should be treated as macroscopic objects
Summary
The physical laws of nature typically possess a great amount of symmetry. We expect Newton’s laws for example to give an adequate description of the motion of a pendulum, irrespective of its precise position on earth or the time of day. The understanding of the mechanism of spontaneous symmetry breaking, explaining how symmetry-broken states can result from the symmetric laws of nature, is one of the highlights of modern quantum physics [2,3]. It was originally formulated in the context of magnetism in solid state theory, but is a general phenomenon that is central to many of the ideas in other fields of physics, including elementary particle physics and cosmology [4]. The central concepts in this description are the order parameter field, the singular nature of the thermodynamic limit and the so-called ‘thin’ spectrum We illustrate these notions using the elementary example of a harmonic crystal which breaks translational symmetry. We conclude with a summary and outlook to future experiments
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