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arXiv:0708.0365 · The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Uncollapsing the wavefunction

Andrew N. Jordan, Alexander N. Korotkov

Published Jan 1, 2007• 2 citations
arXivHTMLPDF

Abstract

The undoing of quantum measurements is discussed in the broader context of irreversibility in physics. We give explicit examples of how a wavefunction can be uncollapsed in two solid-state experimental set-ups. Wavefunction uncollapse shows the quantum observer paradox in a new and significantly clearer way.
DOI
10.1364/cqo.2007.ctub1

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The Schr\"odinger equation cannot convert a pure state into a mixture (just as Newton's equations cannot display irreversibility). However, to observe phase relationships between macroscopically distinguishable states, one has to measure very peculiar operators. An example, constructed explicitly, shows that the classical analog of such an operator cannot be measured, because to do so would violate classical irreversibility. This result justifies von Neumann's measurement theory, without any hypothesis on the role of the observer.
Some of the problems connected with the interpretation of quantum mechanics are enumerated, in particular those related to some well known paradoxes and, above all, to the measurement process. We then show how the so called "Physics Laboratory Assumption" introduced in [1], which considers as "observables'' only the self-adjoint operators corresponding to existing measuring instruments, can propose a new perspective on the aforementioned problems and can replace the wavefunction collapse postulate. [1] Luigi E. Picasso, "On the Concept of State in Quantum Mechanics: Another Way to Decoherence?'' Int. J. Theor. Phys. 62 (2), (2023)
The relativity of simultaneity together with the definition of a quantum state collapse results in experimental situations where multiple measurements can be taken on an uncollapsed quantum state. The quantum state's collapse is defined to be instantaneous in a rest inertial frame of a detector performing measurements on the quantum system. The definition is consistent with the Copenhagen interpretation and in agreement with all measurements performed with detectors at rest in an arbitrary Lorentz (laboratory) frame. From the introduced collapse model follows that under certain conditions multiple measurements are allowed on the same uncollapsed quantum state. An application of the developed approach is shown on measurement of photon-pair state entangled in polarization and energy. Conditions under which two measurements can be taken on the uncollapsed photon-pair state are derived. Serious consequences follow from the allowance of multiple measurements on the same uncollapsed state. For example, the measurements taken by both detectors in this situation are uncorrelated. Moreover, all the conservation laws could be violated in individual measurements, but not in mean values. This statement is proved on the two-photon state entangled in energy. This is in contradiction with experimental results observed by the detectors in rest relative to each other. It is shown that the property of measuring uncorrelated results with detectors in relative movement is related solely to the proposed collapse model. The remaining collapse models---the preferred Lorentz frame, Aharonov-Albert, and Hellwig-Kraus---are examined and discussed with respect to the designed experiment, which involves spacelike separated measurements.