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Quantum theory without measurement or state reduction problems

Alan Macdonald

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

There is a consistent and simple interpretation of the quantum theory of isolated systems. The interpretation suffers no measurement problem and provides a quantum explanation of state reduction, which is usually postulated. Quantum entanglement plays an essential role in the construction of the interpretation.

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Physics Today•Mar 1, 2000•348 citations
The problem of measurement taken at face value shows clearly that there is an inconsistency inside the quantum formalism.The phenomenon of decoherence is often presented as a solution to it.A widely debated question is to decide between two different interpretations.The first one is to consider that the decoherence process has the effect to actually project a superposed state into one of its classically interpretable component, hence doing the same job as the reduction postulate.For the second one, decoherence is only a way to show why no macroscopic superposed state can be observed and so, to explain the classical appearance of the macroscopic world, while the quantum entanglement between the system, the apparatus and the environment never disappears.In this case, explaining why only one single definite outcome is observed remains to do.In this paper, we examine arguments for and against both interpretations and defend a position according to which the outcome that is observed is relative to the observer in close parallel to the Everett interpretation.
It is well known, that the causal Schrödinger evolution of a quantum state is not compatible with the reduction postulate, even when decoherence is taken into account. The violation of the causal evolution, introduced by the standard reduction postulate distinguishes certain systems (as the measurement devices), whose states are very close to statistical mixtures (as the ones resulting from the process of decoherence). In these systems, this violation has not any observable effect. In arbitrary quantum systems, the transition from the initial density matrix to a diagonal matrix predicted by the standard reduction postulate, would lead to a complete breakdown of the Schrödinger evolution, and consequently would destroy all the predictive power of quantum mechanics. What we show here, is that there is a modified version of the postulate that allows to treat all the quantum mechanical systems on equal footing. The standard reduction postulate may be considered as a good approximation, useful for practical purposes, of this modified version which is consistent with the Schrödinger evolution and via decoherence with the experimental results. Within this approach, the physical role played by the reduction postulate is as a tool for the computation of relative probabilities and consequently for the determination of the probabilities of consistent histories.
The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of considering the quantum state description to apply only to an ensemble of similarily prepared systems, rather than supposing, as is often done, that it exhaustively represents an individual physical system. Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretation. The introduction of hidden variables to determine the outcome of individual events is fully compatible with the statistical predictions of quantum theory. However, a theorem due to Bell seems to require that any such hidden-variable theory which reproduces all of quantum mechanics exactly (i.e., not merely in some limiting case) must possess a rather pathological character with respect to correlated, but spacially separated, systems.
We suggest solving the measurement problem by postulating the existence of a special future final boundary condition for the universe. Although this is an extension of the way boundary conditions are usually chosen (in terrestrial laboratories), it is our only deviation from standard quantum mechanics. Using two state vectors, or the "two-state", to describe completely the state of systems of interest, we analyze ideal and "weak" measurements, and show the consistency of our scheme. If the final state of a measuring device is assigned to be one of the possible outcomes of the measurement, an effective reduction is observed after an ideal measurement process. For final conditions chosen with an appropriate distribution, the predictions of standard quantum mechanics may be reconstructed, thus eliminating probability from the description of any single measurement. The interpretation attained, the Teleological Interpretation, is an ontological one; it is local and deterministic. Other special assumptions in the choice of the final boundary condition may explain certain unaccounted for phenomena, or even supply a mechanism for essential free will. In this context we believe that a new conception of time should be adopted.