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arXiv:gr-qc/9710019

Quantum Measurements, Nonlocality and the Arrow of Time

John W. Moffat

Published Oct 2, 1997• 1 citation
arXivHTMLPDF

Abstract

A theory is developed which attempts to reconcile the measurements of nonlocal quantum observables with special relativity and quantum mechanics. The collapse of a wave function, which coincides with a nonlocal measurement by some macroscopic measuring device, is associated with the triggering of an absorber mechanism due to the interaction of the apparatus with the charges in the rest of the universe. The standard retarded electromagnetic field plus radiation damping is converted, for a short time during the collapse of the wave function, to an advanced field plus radiation. The reversal of the arrow of time during the wave function reduction permits communication in nonlocal quantum experiments at the speed of light, resolving paradoxes associated with measurements of correlated quantum states and special relativity. The absorber mechanism and the advanced field solution are consistent with conventional Friedmann-Robertson-Walker expanding universes.

DOI
10.48550/arxiv.gr-qc/9710019

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A theory is developed which attempts to reconcile the measurements of nonlocal quantum observables with special relativity and quantum mechanics. The collapse of a wave function, which coincides with a nonlocal measurement by some macroscopic measuring device, is associated with the triggering of an absorber mechanism due to the interaction of the apparatus with the charges in the rest of the universe. The standard retarded electromagnetic field plus radiation damping is converted, for a short time during the collapse of the wave function, to an advanced field plus radiation. The reversal of the arrow of time during the wave function reduction permits communication in nonlocal quantum experiments at the speed of light, resolving paradoxes associated with measurements of correlated quantum states and special relativity. The absorber mechanism and the advanced field solution are consistent with conventional Friedmann-Robertson-Walker expanding universes.
Quantum mechanics implies the existence of correlations which cannot be described by any local theory. These nonlocal correlations possibly suggest the existence of particles traveling faster than light (tachyons). But the potential paradoxes associated with their existence imply that, even i f these tachyons do exist, it should not be possible to control them in a manner necessary for human superluminal (faster than light) communication. Indeed, the unitary nature of the time development operator precludes the possibility of using non-local correlations to communicate superluminally within the quantum formalism. A simplified model which preserves unitary time development i s shown to be useful in studying 'thought experiments' which appear init ially to allow for superluminal communication. The consistency of quantum mechanics is questioned when measurements of retarded fields are considered. I f certain idealized measurements are possible in principle, then the quantum formalism appears inconsistent. I f the measurements are not possible in principle, then 'state reduct ion' (non-unitary time evolution of the state operator) in a pragmatic sense can be said to have occurred. The suggestion that tachyons be used to explain the non-local correlations i s abandoned in favor of another model whose philosophy is supported by the tenets of relativity theory. Such a model may imply the existence of a more general quantum theory where a quantum system itself can be taken as a (generalized) frame of reference.
We show that quantum communication by means of collapse of the wave function is possible. In this study, quantum communication does not mean quantum teleportation or quantum cryptography, but transmission of information itself. Because of consistency with special relativity, the possibility of the quantum communication leads to another conclusion that the collapse of the wave function must propagate at the speed of light or slower. We show this requirement is consistent with nonlocality in quantum mechanics. We also demonstrate that the Einstein-Podolsky-Rosen experiment does not disprove our conclusion.
By a radical modification of statistical mechanics the measurement process of quantum mechanics can be described in terms of pure, unitary time evolution, with no wave function collapse or many‐world ideas. The key notion is “special states,” rare microscopic states of a complex system. Recovering the standard probabilities requires of this theory the appearance of Cauchy‐distributed noise in some measurement processes. This article treats experimental situations where such noise might be detected and correlated with the need or absence of need for special states. Included in this possibility are “delayed choice” experiments, in which the correlation contravenes conventional ideas on causality. Background material on all topics is provided.
The irreversible process of ‘wave packet collapse’ in quantum measurement contradicts the reversible characteristics of the Schrödinger equation and the entire quantum mechanics. This contradiction is actually the origin of measurement problems in quantum mechanics. How to resolve this contradiction is related to the understanding of some philosophical concepts. The Copenhagen School embraces the reversible/irreversible contradictions in quantum measurement through the principle of complementarity. Both von Neumann's measurement hypothesis and Everett's many world explanation adhere to the ‘universal position of the Schrödinger equation’, but due to their detachment from the thermodynamic mechanism analysis of quantum measurement processes, they fall into the dilemma of subjectivism or possible state materialization in ontology. Decoherence theory is a natural extension of dissipative structure theory in quantum mechanics, which helps to solve quantum measurement problems by combining the study of classical conversion mechanisms between reversibility and irreversibility in statistical mechanics. Due to the common statistical roots of the time arrow problem in classical mechanics and quantum mechanics, decoherence theory cannot be seen as a measurement theory that fully implements the ‘universal Schrödinger position’. Many contradictions in quantum mechanics may need to be cleverly resolved through various contradictions in classical physics.
Abstract We propose that the ontic understanding of quantum mechanics can be extended to a fully realistic theory that describes the evolution of the wavefunction at all times, including during a measurement. In such an approach the wave equation should reduce to the standard wave equation when there is no measurement, and describe state reduction when the system is measured. The general wave equation must be nonlinear and nonlocal, and we require it to be time-symmetric; consequently, this approach is not a new interpretation but a new theory. The wave equation is an integrodifferential equation (IDE). The time symmetry requirement leads to a retrocausal approach, in which the wave equation is solved subject to initial and final conditions to determine history at intermediate times. We propose that different outcomes from (apparently) identically prepared experiments may result from uncontrolled parameters; both the nonlocality and the retrocausality of the theory imply that Bell’s Theorem cannot rule out such “hidden variables.” Beginning with Hamilton’s principle, we demonstrate the construction of such a theory by replacing the action with a functional designed to give rise to a nonlinear, nonlocal IDE as the wave equation. This IDE reduces to the standard wave equation (a differential equation) in the absence of a measurement, but exhibits state reduction to a single eigenvalue when the system interacts with another system with the properties of a measurement apparatus. We demonstrate several desirable features of this theory; for other properties we indicate their plausibility and possible avenues to a proof.
Quantum physicists have made many attempts to solve the quantum measurement problem, but no solution seems to have received widespread acceptance. The time has come for a new approach. In Sense Perception and Reality: A Theory of Perceptual Relativity, Quantum Mechanics and the Observer Dependent Universe and in a new paper The End of Realism I suggest the quantum measurement problem is caused by a failure to understand that each species has its own sensory world and that when we say the wave function collapses and brings a particle into existence we mean the particle is bought into existence in the human sensory world by the combined operation of the human sensory apparatus, particle detectors and the experimental set up. This is similar to the Copenhagen Interpretation suggested by Niels Bohr and others, but the understanding that the collapse of the wave function brings a particle into existence in the human sensory world removes the need for a dividing line between the quantum world and the macro world. The same rules can apply to both worlds and the ideas stated in this paper considerably strengthen the Copenhagen Interpretation of quantum mechanics.