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Kluwer Academic Publishers eBooks

Relativistic Quantum Theory with a Physical State Vector and Hypothetical Laws of Reduction

Bernd A. Berg

Published Dec 19, 2005• 1 citation
Publisher

Abstract

Evolution of a Physical State Vector (PSV) is described as governed by two distinct physical laws: Continuous, unitary time evolution and a relativistically covariant reduction process. Non-local measurements, proposed by Aharanov and Albert, are excluded when the reduction is attributed to measurement devices which are included in the PSV. The existence of a PSV allows to formulate phenomenological laws of reduction. A proposal ismade for which the collapse time is found tobe τ c = bh /Δ E , where Δ E is a difference in energy distribution between alternative world branches. Experiments yield the bounds 1.35·10 11 < b <4.5·10 18 . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/0-306-47097-7_30

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Evolution of a Physical State Vector (PSV) is described as governed by two distinct physical laws: Continuous, unitary time evolution and a relativistically covariant reduction process. Non-local measurements, proposed by Aharanov and Albert, are excluded when the reduction is attributed to measurement devices which are included in the PSV. The existence of a PSV allows to formulate phenomenological laws of reduction. A proposal ismade for which the collapse time is found tobe τ c = bh /Δ E , where Δ E is a difference in energy distribution between alternative world branches. Experiments yield the bounds 1.35·10 11 < b <4.5·10 18 . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Evolution of a physical quantum state vector is described as governed by two distinct physical laws: Continuous, unitary time evolution and a relativistically covariant reduction process. In previous literature, it was concluded that a relativistically satisfactory version of the collapse postulate is in contradiction with physical measurements of a non-local state history. Here it is shown that such measurements are excluded when reduction is formulated as a physical process and the measurement devices are included as part of the state vector.
We study the instantaneity of the state-reduction process in relativistic quantum mechanics. The conclusion of various authors that this instantaneity will restrict the set of relativistic observables to purely local ones (i.e., that the measurement of any nonlocal property of a system at a well-defined time would give rise to violations of relativistic causality) is found to be erroneous, and experiments (of a kind not encountered before in measurement theory) are described whereby certain nonlocal properties of some simple physical systems can be measured at a well-defined time without violating causality. The attempts of certain authors to reconcile the reduction process with the covariance of the relativistic quantum state are considered and found wanting, and it is argued that the covariance of relativistic quantum theories resides exclusively in the experimental probabilities, and not in the underlying quantum states. The problem of nonlocal measurement is considered in general: distinctions (which are not to be met with in the nonrelativistic case) arise in relativistic quantum mechanics between what can be measured for fermions and what can be measured for bosons, between what can be measured for individual systems and what can be measured for ensembles, and between what kinds of states can be verified by measurement and what kinds of states can be prepared by measurement; and these pose difficult questions about the nature of measurement itself.
The measurement of nonlocal properties of relativistic quantum-mechanical systems, the compatibility (or lack of it) of two or more such measurements, and various other of their characteristics are considered; and with these notions in hand an old problem (which is to produce a covariant description of the state reduction associated with the measuring process) is attacked, and succumbs. The solution requires us to depart (not as we did in part I of the present work, but in an entirely different direction) from the usual picture of the time evolution of quantum states.
It is considered to re-formulate quantum theory as it appears: A theory of continuous and causal time evolution, interrupted by discontinuous and stochastic jumps. To develop the (missing) theory of jumps a heuristic-phenomenological approach is suggested. Relying on a global reduction process, a hypothesis is introduced postulating spontaneous collapse of superpositions of states which describe spontaneous absorption or emission. The collapse probability determines a mean collapse time τc=bℏ/△Eτ^c = b \hbar / \triangle Eτc=bℏ/△E, where bbb is a dimensionless constant and △E\triangle E△E is the difference in energy distribution between alternative branches. Ramsey atomic beam spectroscopy yields a lower bound on bbb and avalanche photodiodes give an upper bound, such that 1.35⋅1011<b<3.8⋅10211.35\cdot 10^{11} < b < 3.8\cdot 10^{21}1.35⋅1011<b<3.8⋅1021. Ample opportunities for experimental improvements exist.
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.