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.
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.
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.
Ultimately, any explanation of quantum measurement must be extendable to relativistic quantum mechanics (RQM), since many precisely confirmed experimental results follow from quantum field theory (QFT), which is based on RQM. Certainly, the traditional "collapse" postulate for quantum measurement is problematic in a relativistic context, at the very least because, as usually formulated, it violates the relativity of simultaneity. The present paper addresses this with a relativistic model of measurement in which the state of the universe is decomposed into decoherent histories of measurements recorded within it. The approach is essentially Everettian, in the sense that it uses the unmodified, unitary quantum formalism of RQM. But it addresses the difficulty with typical "many worlds" interpretations on how to even define probabilities over different possible ``worlds''. To do this, Zurek's concept of envariance is generalized to the context of relativistic spacetime, giving an objective definition of the probability of any one of the quantum histories, consistent with Born's rule. It is then shown that the statistics of any repeated experiment within the universe also tend to follow the Born rule as the number of repetitions increases. The wave functions that we actually use for such experiments are local reductions of very coarse-grained superpositions of universal eigenstates, and their "collapse" can be re-interpreted as simply an update based on additional incremental knowledge gained from a measurement about the "real" eigenstate of our universe.
We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse takes place. A suitable use of the causal structure of the devices involved in the measurement process allowed us to introduce a covariant notion for the collapse of quantum states. However, a fully consistent description in the relativistic domain requires the extension of the interpretation to quantum fields. The extension is far from straightforward. Besides the obvious difficulty of dealing with the infinite degrees of freedom of the field theory, one has to analyse the restrictions imposed by causality concerning the allowed operations in a measurement process. In this paper we address these issues. We shall show that, in the case of partial causally connected measurements, our description allows us to include a wider class of causal operations than the one resulting from the standard way of computing conditional probabilities. This alternative description could be experimentally tested. A verification of this proposal would give stronger support to the realistic interpretations of the states in quantum mechanics.
We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse takes place. A suitable use of the causal structure of the devices involved in the measurement process allowed us to introduce a covariant notion for the collapse of quantum states. However, a fully consistent description in the relativistic domain requires the extension of the interpretation to quantum fields. The extension is far from straightforward. Besides the obvious difficulty of dealing with the infinite degrees of freedom of the field theory, one has to analyze the restrictions imposed by causality concerning the allowed operations in a measurement process. In this paper we address these issues. We shall show that, in the case of partial causally connected measurements, our description allows us to include a wider class of causal operations than the one resulting from the standard way for computing conditional probabilities. This alternative description could be experimentally tested. A verification of this proposal would give a stronger support to the realistic interpretations of the states in quantum mechanics. 1
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 problem of quantum state reduction The fundamental problem of quantum mechanics, as that theory is presently understood, is to make sense of the reduction of the state vector (i.e. collapse of the wave function ), denoted here by R . This issue is usually addressed in terms of the ‘quantum measurement problem’, which is to comprehend how, upon measurement of a quantum system, this (seemingly) discontinuous R -process can come about. A measurement, after all, merely consists of the quantum state under consideration becoming entangled with a more extended part of the physical universe, e.g. with a measuring apparatus. This measuring apparatus – together with the observing physicist and their common environment – should, according to conventional understanding, all also have some quantum description. Accordingly, there should be a quantum description of this entire quantum state, involving not only the original system under consideration but also the apparatus, physicist, and remaining environment – and this entire state would be expected to evolve continuously, solely according to the Schrödinger equation (unitary evolution), here denoted by the symbol U . Numerous different attitudes to R have been expressed over many years, ever since quantum mechanics was first clearly formulated. The most influential viewpoint has been the ‘Copenhagen interpretation’ of Niels Bohr, according to which the state vector │ψ〉 is not to be taken seriously as describing a quantum-level physical reality, but is to be regarded as merely referring to our (maximal) ‘knowledge’ of a physical system, and whose ultimate role is simply to provide us with a means to calculate probabilities when a measurement is performed on the system.