The fallacies inherent in the Einstein's Boxes thought experiment are made evident by taking an axiomatic approach to quantum mechanics while ignoring notions not supported by the postulates or by experimental observation. We emphasize that the postulates contain everything needed to completely describe a quantum experiment. We discuss the non-classical nature of both the state vector and the experiment that it represents. Einstein's Boxes is then described by the formalism alone. We see that it is no different from any other experiment in which a two-state observable is measured.
The fallacies inherent in the Einstein's Boxes thought experiment are made evident by taking an axiomatic approach to quantum mechanics while ignoring notions not supported by the postulates or by experimental observation. We emphasize that the postulates contain everything needed to completely describe a quantum experiment. We discuss the non-classical nature of both the state vector and the experiment that it represents. Einstein's Boxes is then described by the formalism alone. We see that it is no different from any other experiment in which a two-state observable is measured.
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and ensembles, clarifies the logical relations and operations for them, and shows how they give rise to dynamics and probabilities. States are identified with maximal consistent sets of weak equalities in the algebra of observables (instead of, as usual, with the rays in a Hilbert space). This leads to a concise foundation of quantum mechanics, free of undefined terms, separating in a clear way the deterministic and the stochastic features of quantum physics. The traditional postulates of quantum mechanics are derived from well-motivated axiomatic assumptions. No special quantum logic is needed to handle the peculiarities of quantum mechanics. Foundational problems associated with the measurement process, such as the reduction of the state vector, disappear. The new interpretation of quantum mechanics contains `elements of physical reality' without the need to introduce a classical framework with hidden variables. In particular, one may talk about the state of the universe without the need of an external observer and without the need to assume the existence of multiple universes.
Shall I refuse my dinner because I do not fully understand the process of digestion? No, not if I am satisfied with the result. O. Heaviside, Electromagnetic Theory , vol. 2, 1899 Basic notions of quantum mechanics Quantum axioms Let us start with a brief recapitulation of quantum mechanics on the “how to” level. According to the standard lore, the instantaneous state of any quantum system (that is, everything that can be known about it at a given moment of time) is given by its wave function (state vector) – a complex-valued vector in some abstract Hilbert space; the nature of this space is determined by the system. All the observables (i.e., physical quantities defined for the system and determined by its state – e.g., the position or momentum of a free particle, the energy of an oscillator) are described by Hermitian operators defined in the same Hilbert space. All three elements – the Hilbert space, the state vector, and the set of observables – are necessary to describe the outcome of any experiment one could perform with the system. Since humans cannot directly observe the behaviour of quantum objects, these outcomes are also called measurements , being the result of using some classical apparatus in order to translate the state of a quantum system into the state of the apparatus, which can then be read out by the experimentalist. The classical (i.e., non-quantum) nature of the apparatus is essential, as we shall see in a moment.
This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: They are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except for very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantum mechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrödinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) may be a potential source for conflicts; various attitudes that are possible to avoid this problem are discussed in this text. After a brief historical introduction, recalling how the very special status of the state vector has emerged in quantum mechanics, various conceptual difficulties are introduced and discussed. The Einstein–Podolsky–Rosen (EPR) theorem is presented with the help of a botanical parable, in a way that emphasizes how deeply the EPR reasoning is rooted into what is often called “scientific method.” In another section the Greenberger–Horne–Zeilinger argument, the Hardy impossibilities, as well as the Bell–Kochen–Specker theorem are introduced in simple terms. The final two sections attempt to give a summary of the present situation: One section discusses nonlocality and entanglement as we see it presently, with brief mention of recent experiments; the last section contains a (nonexhaustive) list of various attitudes that are found among physicists, and that are helpful to alleviate the conceptual difficulties of quantum mechanics.
In the famous EPR paper published in 1935, Einstein, Podolsky, and Rosen suggested a thought experiment, which later became known as the “EPR experiment”. Using the EPR experiment, they posited that quantum mechanics was incomplete. Einstein, however, was dissatisfied with the EPR paper and published a second work on the EPR experiment, in which he discussed the dilemma of choosing whether quantum mechanics was incomplete or nonlocal. Currently, most physicists choose the nonlocality of quantum mechanics over Einstein’s choice of the incompleteness of quantum mechanics. However, with an appropriate alternate hypothesis, both of these choices can be rejected. Herein, I demonstrate an approach to overcome the Einstein Dilemma by proposing a new interpretation invoked by a new formalism of quantum mechanics known as two-state vector formalism.
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.