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EPR, Faust, and the Cat

Jim Baggott, John L. Heilbron

Published Apr 25, 2024• 0 citations
Publisher

Abstract

Abstract ‘At the next meeting with Einstein at the Solvay Conference in 1930 our discussions took quite a dramatic turn’, Bohr wrote. Bohr turned Einstein’s ‘photon box’ experiment on its head to defend the uncertainty relations. But Einstein’s purpose was more subtle, arguing that quantum theory implied that the properties of a photon are governed by the choice made by an experimenter, no matter how distant. This argument resurfaced in his epoch-making paper with Boris Podolsky and Nathan Rosen. The experimenter chooses what kind of measurement to make on one of a pair of correlated particles, instantly determining the properties of the distant other. Schrödinger called it ‘entanglement’, and exposed the theory’s absurdities in his paradox of the cat. As the founders were rewarded with Nobel prizes, Pauli resolved the problem of nuclear beta-decay by proposing the neutrino, inspiring a witty parody of Goethe’s Faust performed in Bohr’s institute in 1932.

DOI
10.1093/oso/9780192846105.003.0008

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Abstract ‘At the next meeting with Einstein at the Solvay Conference in 1930 our discussions took quite a dramatic turn’, Bohr wrote. Bohr turned Einstein’s ‘photon box’ experiment on its head to defend the uncertainty relations. But Einstein’s purpose was more subtle, arguing that quantum theory implied that the properties of a photon are governed by the choice made by an experimenter, no matter how distant. This argument resurfaced in his epoch-making paper with Boris Podolsky and Nathan Rosen. The experimenter chooses what kind of measurement to make on one of a pair of correlated particles, instantly determining the properties of the distant other. Schrödinger called it ‘entanglement’, and exposed the theory’s absurdities in his paradox of the cat. As the founders were rewarded with Nobel prizes, Pauli resolved the problem of nuclear beta-decay by proposing the neutrino, inspiring a witty parody of Goethe’s Faust performed in Bohr’s institute in 1932.
In 1930, Einstein argued against the consistency of the time–energy uncertainty relation by discussing a thought experiment involving a measurement of the mass of the box which emitted a photon. Bohr seemingly prevailed over Einstein by arguing that Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit this thought experiment from a modern point of view at a level suitable for an undergraduate readership and find that neither Einstein nor Bohr was correct. Instead, this thought experiment should be thought of as an early example of a system demonstrating nonlocal 'EPR' quantum correlations, five years before the famous Einstein–Podolsky–Rosen paper.
The Bohr–Einstein photon box thought experiment is a forerunner of the EPR experiment: a packet of radiation escapes from a box, and the box-plus-radiation state remains entangled. Hence, a measurement on the box makes a difference for the state of the far-away radiation long after its escape. This consequence is analogous to the EPR experiment, but an additional aspect of the Bohr–Einstein box is that complementary magnitudes of the escaped radiation seem correlated to jointly measurable box quantities, which appears to imply a violation of the uncertainty relations. We show how the details of the dynamics make this latter paradox disappear. This calculation makes Bohr’s qualitative arguments in defense of the uncertainty relations precise and reinforces the EPR-like behavior that Einstein later claimed to have had in mind. The calculation reveals that the quantum description of the far-away radiation depends on exactly when the box measurement is performed.
The third round of the Bohr-Einstein debate was conducted by way of the journals rather than in person. Five years after Bohr’s victory at the Sixth Solvay Conference, Einstein, working with two younger colleagues, Boris Podolsky and Nathan Rosen, finally achieved a sharp formulation of the argument that quantum mechanics is an incomplete description of reality. They published in the American journal The Physical Review , in 1935. As one expects in a paper bearing Einstein’s name, the argument is simple but very clever. An improvement by Schrödinger speeds up the exposition. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The first round of the Einstein–Bohr debates took place when Einstein challenged Bohr’s principle of complementarity at the Solvay conference in 1927 and Bohr successfully defended it. The most serious challenge, however, came in 1935 when a paper by Einstein, Podolsky, and Rosen (EPR) argued that quantum mechanics was incomplete through a gedanken experiment motivating an approach based on hidden variables. In this chapter, EPR’s arguments about the incompleteness of quantum mechanics and Bohr’s reply to them are presented. The ultimate answer came almost 30 years later, almost ten years after Einstein’s death, and was nothing that Einstein would have expected. Bell’s inequality and the subsequent Bell-CHSH inequality, that are satisfied by all theories based on the “self-evident truths” of reality and locality are discussed. The startling results that quantum mechanics violates Bell’s inequality and the experimental results are in agreement with the prediction of quantum mechanics are presented.
Meanwhile, on 18 September 1931, Heisenberg wrote to Bohr that ‘my work seems to be somewhat gray on gray’ (Pauli, 1985). By 1931 the bright future for quantum physics that seemed just over the horizon in the fall of 1927 paled with the formulation of relativistic quantum mechanics. Besides the as yet uninterpreted negative energy states, there was the electron's divergent self-energy and the continuous energy spectrum of β-particles in the supposedly two-body final state of nuclear β-decay, which implied that energy was not conserved in nuclear reactions (Bohr, 1932) and that perhaps quantum mechanics was not valid within the nucleus (to be discussed in Chapter 5). Measurement problems in a quantum theory of the electromagnetic field At the 20–25 October 1930 Solvay Conference, Bohr, Dirac, Heisenberg and Pauli concurred that fundamental difficulties in quantum electrodynamics might be clarified by investigating measurability of electromagnetic field quantities. Upon his return to Copenhagen from Brussels, Bohr continued discussing field measurements with Lev Landau, who happened to be visiting at Bohr's institute. In December 1930 Landau went on to Zürich, where he interested Pauli's assistant Rudolf Peierls in field measurements. Their deliberations led to a joint 1931 publication entitled ‘Extension of the uncertainty principle to relativistic quantum theory’ (Landau and Peierls, 1931). Measurement of an electric field can be accomplished through measuring the change in momentum of a charged test body placed in the field.
In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) published a thought experiment that is entirely correct, has been demonstrated in real experiments, and is now the most famous in quantum physics. Their pioneering work described, for the first time, quantum correlations and can be regarded as a very early glimpse into today's 'deep' quantum technologies, by which I mean those that enhance functionality by making use of quantum correlations. However, their work also contains a paradox that Erwin Schroedinger had already recognised as such in 1935 and which has since been cemented by the so-called Bell experiments. Here, I am now able to pinpoint the origin of the paradox within the chain of reasoning, which ultimately resolves the paradox.