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arXiv:1103.3974 · Journal of Physics Conference Series

Relativistic state reduction model

Daniel Bedingham

Published Jul 8, 2011• 23 citations
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Abstract

In order to address the measurement problem of quantum theory we make the assumption that quantum state reduction should be regarded as a genuine physical process deserving of a dynamical description. Generalizing the nonrelativistic spontaneous localization models of Ghirardi, Rimini, Weber, and Pearle, a relativistic state reduction mechanism is proposed. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a mediating field to facilitate smearing of quantum field interactions.

DOI
10.1088/1742-6596/306/1/012034

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In order to address the measurement problem of quantum theory we make the assumption that quantum state reduction should be regarded as a genuine physical process deserving of a dynamical description. Generalizing the nonrelativistic spontaneous localization models of Ghirardi, Rimini, Weber, and Pearle, a relativistic state reduction mechanism is proposed. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a mediating field to facilitate smearing of quantum field interactions.
In order to address the measurement problem of quantum theory we make the assumption that quantum state reduction should be regarded as a genuine physical process deserving of a dynamical description. Generalizing the nonrelativistic spontaneous localization models of Ghirardi, Rimini, Weber, and Pearle, a relativistic state reduction mechanism is proposed. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a mediating field to facilitate smearing of quantum field interactions.
One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schrödinger evolution by implementing spontaneous collapses of the wave function. An explicit model of this kind was proposed in 1986 by Ghirardi, Rimini & Weber (GRW), involving a nonlinear, stochastic evolution of the wave function. We point out how, by focusing on the essential mathematical structure of the GRW model and a clear ontology, it can be generalized to (regularized) quantum field theories in a simple and natural way.
Ever since we have been in the possession of quantum theories without observers, such as Bohmian mechanics or the Ghirardi‐Rimini‐Weber (GRW) theory of spontaneous wave function collapse, a major challenge in the foundations of quantum mechanics is to devise a relativistic quantum theory without observers. One of the difficulties is to reconcile nonlocality with relativity. I report about recent progress in this direction based on the GRW model: A relativistic version of the model has been devised for the case of N noninteracting (but entangled) particles. A key ingredient was to focus not on the evolution of the wave function but rather on the evolution of the matter in space‐time as determined by the wave function.
A model of state reduction in relativistic quantum field theory involving a nonlinear stochastic extension of Schrödinger's equation is outlined. The eigenstates of the annihilation operator are chosen as the preferred basis onto which reduction occurs. These are the coherent states which saturate the bound of the Heisenberg uncertainty relation, exhibiting classical-like behaviour. The quantum harmonic oscillator is studied in detail before generalizing to relativistic scalar quantum field theory. The infinite rates of increase in energy density which have plagued recent relativistic proposals of dynamical state reduction are absent in this model. This is because the state evolution equation does not drive particle creation from the vacuum. The model requires the specification of a preferred sequence of space-like hyper-surfaces supporting the time-like state evolution. However, it is shown that the choice of preferred surfaces has no effect on perturbative results to second order in the coupling parameter. It is demonstrated how state reduction to a charge density basis can be induced in fermionic matter via an appropriate coupling to a bosonic field undergoing this mechanism.
A relativistic model of quantum state reduction involving a nonlinear stochastic extension of Schr\\"odinger's equation is outlined. The eigenstates of the annihilation operator are chosen as the preferred basis onto which reduction occurs. These are the coherent states which saturate the bound of the Heisenberg uncertainty relation, exhibiting classical-like behavior. The quantum harmonic oscillator is studied in detail before generalizing to relativistic scalar quantum field theory. The infinite rates of increase in energy density which have plagued recent relativistic proposals of dynamical state reduction are absent in this model. This is because the state evolution equation does not drive particle creation from the vacuum. It is demonstrated how state reduction to a charge density basis can be induced in fermionic matter via an appropriate coupling to a bosonic field undergoing this mechanism.
We study a proposal for the resolution of the black hole information puzzle within the context of modified versions of quantum theory involving spontaneous reduction of the quantum state. The theories of this kind, which were developed in order to address the so-called measurement problem in quantum theory have, in the past, been framed in a nonrelativistic setting and in that form they were previously applied to the black hole information problem. Here, and for the first time, we show in a simple toy model, a treatment of the problem within a fully relativistic setting. We also discuss the issues that the present analysis leaves as open problems to be dealt with in future refinements of the present approach.