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.
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.
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.
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.
Abstract 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 through a paper by Einstein, Podolsky, and Rosen (EPR) when they argued about the incompleteness of quantum mechanics through a gedanken experiment motivating an approach based on hidden variables. In this chapter, the EPR argument about the incompleteness of quantum mechanics and Bohr’s reply to it, are presented. The ultimate answer came almost 30 years later, almost ten years after Einstein’s death, and the answer was nothing what 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 result that quantum mechanics violates Bell’s inequality and that the experimental results are in agreement with the prediction of quantum mechanics is presented.
Einstein's 1927 argument for incompleteness A huge literature arose out of the famous ‘EPR’ paper by Einstein, Podolsky and Rosen (1935), entitled ‘Can quantum-mechanical description of physical reality be considered complete?’. The EPR paper argued, on the basis of (among other things) the absence of action at a distance, that quantum theory must be incomplete. It is less well-known that a much simpler argument, leading to the same conclusion, was presented by Einstein eight years earlier in the general discussion at the fifth Solvay conference (pp. 440ff.). Einstein compares and contrasts two views about the nature of the wave function ψ , for the specific case of a single electron. According to view I, ψ represents an ensemble (or ‘cloud’) of electrons, while according to view II, ψ is a complete description of an individual electron. Einstein argues that view II is incompatible with locality, and that to avoid this, in addition to ψ there should exist a localised particle (along the lines of de Broglie's theory). Thus, according to this reasoning, if one assumes locality, then quantum theory (as normally understood today) is incomplete. The conclusion of Einstein's argument in 1927 is the same as that of EPR in 1935, even if the form of the argument is rather different. Einstein considers electrons striking a screen with a small hole that diffracts the electron wave, which on the far side of the screen spreads out uniformly in all directions and strikes a photographic film in the shape of a hemisphere with large radius (see Einstein's figure, p. 440).
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.
ASPECTS OF THE DEBATE The debate between Niels Bohr and Albert Einstein concerning the interpretation of quantum mechanics extended from the fifth Solvay Conference in 1927 until the end of Einstein's life. The most dramatic exchange occurred in 1935, when Einstein, in collaboration with B. Podolsky and N. Rosen, published a paper in Physical Review entitled “Can quantum-mechanical description of physical reality be considered complete?”, concluding with a negative answer, and Bohr replied in the same journal, with a paper of the same title but giving a positive answer. Their arguments were restated, in some respects with greater clarity, in the Library of Living Philosophers volume on Einstein in 1949. The disagreements between Bohr and Einstein concerned not only the physical question expressed in the common title of their papers, but also philosophical questions about physical reality and human knowledge. Much light was thrown upon the Bohr–Einstein debate by the theorem of J. S. Bell (1964) and the experiments which it inspired. Bell showed that any physical theory which applies to a pair of spatially separated systems (as considered in the thought experiment of Einstein, Podolsky, and Rosen) and satisfies a certain locality condition will, in certain circumstances, disagree statistically with quantum mechanics. Consequently, the supplementation of the quantum mechanical description envisaged by Einstein and his collaborators (usually referred to as a “hidden variables theory”) must either violate the locality condition or clash with quantum mechanical predictions.