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arXiv:2309.04018

Time-Symmetric Resolutions of the Renninger Negative-Result Paradoxes

Michael B. Heaney

Published Sep 7, 2023• 0 citations
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Abstract

The 1953 and 1960 Renninger negative-result thought experiments illustrate conceptual paradoxes in the Copenhagen formulation of quantum mechanics. In the 1953 paradox we can infer the presence of a detector in one arm of a Mach-Zehnder interferometer without any particle interacting with the detector. In the 1960 paradox we can infer the collapse of a wavefunction without any change in the state of a detector. I resolve both of these paradoxes by using a time-symmetric formulation of quantum mechanics. I also describe a real experiment that can distinguish between the Copenhagen and time-symmetric formulations.

DOI
10.48550/arxiv.2309.04018

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The 1953 and 1960 Renninger negative-result thought experiments illustrate conceptual paradoxes in the Copenhagen formulation of quantum mechanics. In the 1953 paradox we can infer the presence of a detector in one arm of a Mach-Zehnder interferometer without any particle interacting with the detector. In the 1960 paradox we can infer the collapse of a wavefunction without any change in the state of a detector. I resolve both of these paradoxes by using a time-symmetric formulation of quantum mechanics. I also describe a real experiment that can distinguish between the Copenhagen and time-symmetric formulations.
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I present here a thought experiment which violates the most widely accepted interpretation of quantum mechanics “The Copenhagen Interpretation” and Bohr’s complementarity which says that there is no meaning of the state of a particle until it is observed and the act of observation might change it. The experiment consists of a double slit apparatus which is modified by putting a second double slit apparatus between the source and the original apparatus with certain conditions imposed on both the apparatuses using the facts of interference and diffraction. A striking paradox emerges if we consider the arguments of Bohr’s complementarity, i.e. the photon travels through both the paths simultaneously in a double slit apparatus whenever there is interference. It turns out that this paradox can be resolved only if the photon travels through one path even if interference fringes are visible.
In the framework of an interference setup in which only two outcomes are possible (such as in the case of a Mach–Zehnder interferometer), we discuss in a simple and pedagogical way the difference between a standard, unitary quantum mechanical evolution and the existence of a real collapse of the wavefunction. This is a central and not-yet resolved question of quantum mechanics and indeed of quantum field theory as well. Moreover, we also present the Elitzur–Vaidman bomb, the delayed choice experiment, and the effect of decoherence. In the end, we propose two simple experiments to visualize decoherence and to test the role of an entangled particle. Quanta 2014; 3: 156–170.
It is argued that the conclusions obtained by Renninger (Zeitschrift fur Physik 136, 251 (1953)), by means of an interferometer thought experiment, have important implications for a number of still ongoing discussions about quantum mechanics (QM). To these belong the ontology underlying QM, Bohr's complementarity principle, the significance of QM's wave function, the "elements of reality" introduced by Einstein, Podolsky and Rosen (EPR), and Bohm's version of QM (BQM). A slightly extended setup is used to make a physical prediction at variance with the mathematical prediction of QM. An english translation of Renninger's paper, which was originally published in german language, follows the present paper. This should facilitate access to that remarkable, apparently overlooked and forgotten, paper.