Broken Time Translation Symmetry as a model for Quantum State Reduction

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.Comment: 15 pages, 5 figure

An objective collapse model without state dependent stochasticity

The impossibility of describing measurement in quantum mechanics while using a quantum mechanical model for the measurement machine, remains one of its central problems. Objective collapse theories attempt to resolve this problem by proposing alterations to Schrödinger’s equation. Here, we present a minimal model for an objective collapse theory that, in contrast to previous proposals, does not employ state dependent stochastic terms in its construction. It is an explicit proof of principle that it is possible for Born’s rule to emerge from a stochastic evolution in which no properties of the stochastic process depend on the state being evolved. We propose the presented model as a basis from which more realistic objective collapse theories can be constructed.</p

Stochastic field dynamics in models of spontaneous unitarity violation

Objective collapse theories propose a solution to the quantum measurement problem by predicting deviations from Schrödinger's equation that can be tested experimentally. A class of objective theories based on spontaneous unitarity violation was recently introduced, in which the stochastic field required for obtaining Born's rule does not depend on the state of the system being measured. Here, we classify possible models for the stochastic field dynamics in theories of spontaneous unitarity violation. We show that for correlated stochastic dynamics, the field must be defined on a closed manifold. In two or more dimensions, it is then always possible to find stochastic dynamics yielding Born's rule, independent of the state being measured or the correlation time of the stochastic field. We show that the models defined this way are all isomorphic to the definition on a two-sphere, which we propose to be a minimal physical model for the stochastic field in models of spontaneous unitarity violation

Spontaneous Symmetry Breaking in Quantum Systems: Emergence or Reduction?

Beginning with Anderson (1972), spontaneous symmetry breaking (SSB) in infinite quantum systems is often put forward as an example of (asymptotic) emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show SSB in their ground states (or equilibrium states at low temperature), although they are finite. Thus against what is sometimes called `Earman's Principle', a genuine physical effect (viz. SSB) seems theoretically recovered only in some idealization (namely the thermodynamic limit), disappearing as soon as the the idealization is removed. We review the well-known arguments that (at first sight) no finite system can exhibit SSB, using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics (which typically forbids SSB) versus classical mechanics (which allows it). This discrepancy between formalism and reality is quite similar to the measurement problem, and hence we address it in the same way, adapting an argument of the author and Reuvers (2013) that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to (asymmetric) perturbations of the (symmetric) dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring SSB and hence restores Earman's Principle (at least in this particularly threatening case)

Decoherence and definite outcomes

This thesis has three aims: (1) to clarify in detail the relation between the decoherence mechanism and the problem of definite outcomes, (2) to dispel common misconceptions about the measurement problem in quantum mechanics, and (3) to present some recent alternative approaches in the quest for a satisfactory solution of the definite outcomes problem.Comment: 102 pages, in English. Thesis work for the "Laura Magistrale Interfacolt\`a in Logica, Filosofia e Storia della Scienza" at Universit\`a degli studi di Firenze. Supervisors: Prof. Roberto Casalbuoni and Prof. Elena Castellan

Decoherence and definite outcomes

This thesis has three aims: (1) to clarify in detail the relation between the decoherence mechanism and the problem of definite outcomes, (2) to dispel common misconceptions about the measurement problem in quantum mechanics, and (3) to present some recent alternative approaches in the quest for a satisfactory solution of the definite outcomes problem

Broken Time Translation Symmetry as a Model for Quantum State Reduction

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

Vortex Duality in Higher Dimensions

A dynamic vortex line traces out a world sheet in spacetime. This thesis shows that the information of all its dynamic behaviour is completely contained in the world sheet. Furthermore a mathematical framework for order–disorder phase transitions in terms of the proliferation of such vortex world sheets is presented, leading to the prediction of quantized vortex lines of electric current in phase-disordered superconductors.LEI Universiteit LeidenTheoretical Physic