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arXiv:2206.10595 · Symmetry

A Time-Symmetric Resolution of the Einstein’s Boxes Paradox

Michael B. Heaney

Published Jun 13, 2022• 1 citation
arXivHTMLPDF

Abstract

The Einstein’s Boxes paradox was developed by Einstein, de Broglie, Heisenberg, and others to demonstrate the incompleteness of the Copenhagen Formulation of quantum mechanics. I explain the paradox using the Copenhagen Formulation. I then show how a Time-Symmetric Formulation of quantum mechanics resolves the paradox in the way envisioned by Einstein and de Broglie. Finally, I describe an experiment that can distinguish between these two formulations.

DOI
10.3390/sym14061217

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The Einstein’s Boxes paradox was developed by Einstein, de Broglie, Heisenberg, and others to demonstrate the incompleteness of the Copenhagen Formulation of quantum mechanics. I explain the paradox using the Copenhagen Formulation. I then show how a Time-Symmetric Formulation of quantum mechanics resolves the paradox in the way envisioned by Einstein and de Broglie. Finally, I describe an experiment that can distinguish between these two formulations.
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.
At the 1927 Solvay conference, Albert Einstein presented a thought experiment intended to demonstrate the incompleteness of the quantum mechanical description of reality. In the following years, the experiment was modified by Einstein, de Broglie, and several other commentators into a simple scenario involving the splitting in half of the wave function of a single particle in a box. This paper collects together several formulations of this thought experiment from the literature, analyzes and assesses it from the point of view of the Einstein–Bohr debates, the EPR dilemma, and Bell’s theorem, and argues for “Einstein’s Boxes” taking its rightful place alongside similar but historically better known quantum mechanical thought experiments such as EPR and Schrödinger’s Cat.
As it is well-known one of the most fascinating examples in remarkable discussion between Einstein and Bohr on the conceptual foundation of the quantum mechanics (Heisenberg energy-time uncertainty relation especially) was an experimental device representing a box hanged on an elastic spring. The pair of similar devices is used in this work for formulation of a classical and (implicitly) quantum mechanical analog of the famous two capacitors paradox. It admits a simple solution of the paradox since energy difference or seeming paradoxical "loss" can be explained by work of the elastic force for moving of the boxes in the gravitational field. (Obviously, original two capacitors paradox can be explained in the analogous way.)
The problems of modern physics are man made. The Copenhagen version of quantum mechanics is formulated in a vague prosaic way, inconsistencies and paradoxes are the price. New interpretations try to solve the problem, however a reformulation rather than an interpretation is needed. In this manuscript I will point out, where the Copenhagen formulation of quantum mechanics is flawed and how one can make sense out of it. Then I will show, that it is possible to give a precise formulation of quantum mechanics without losing its compelling ability in describing experiments.
The problems of modern physics are man made.The Copenhagen version of quantum mechanics is formulated in a vague prosaic way, inconsistencies and paradoxes are the price.New interpretations try to solve the problem, however a reformulation rather than an interpretation is needed.In this manuscript I will point out, where the Copenhagen formulation of quantum mechanics is flawed and how one can make sense out of it.Then I will show, that it is possible to give a precise formulation of quantum mechanics without losing its compelling ability in describing experiments.