The Einstein-Podolsky-Rosen correlations are very like many ordinary occurrences of everyday life. So it is a little difficult for the man in the street to understand immediately why there has been so much fuss about them. It must be recalled that the founding fathers of quantum mechanics had convinced themselves that it was necessary to abandon the idea of an objective reality at the microphysical level. But the correlations in question, together with the idea of local causality, were a formidable argument for such a reality. The founding fathers offered counter-arguments (neither very clear nor very convincing in my opinion) and each side held to its position. Since then it has been possible to push the analysis a little further, considering especially situations just a little different from those considered before. Then correlations appear, according to quantum mechanics, which are not at all like those of everyday life. As a result it is not now easy to believe, with Einstein, that quantum mechanical predictions are reconcilable with the notion of a Lorentz invariant objectively real microphysical world.
The Einstein-Podolsky-Rosen correlations are very like many ordinary occurrences of everyday life. So it is a little difficult for the man in the street to understand immediately why there has been so much fuss about them. It must be recalled that the founding fathers of quantum mechanics had convinced themselves that it was necessary to abandon the idea of an objective reality at the microphysical level. But the correlations in question, together with the idea of local causality, were a formidable argument for such a reality. The founding fathers offered counter-arguments (neither very clear nor very convincing in my opinion) and each side held to its position. Since then it has been possible to push the analysis a little further, considering especially situations just a little different from those considered before. Then correlations appear, according to quantum mechanics, which are not at all like those of everyday life. As a result it is not now easy to believe, with Einstein, that quantum mechanical predictions are reconcilable with the notion of a Lorentz invariant objectively real microphysical world.
Introduction The philosopher in the street, who has not suffered a course in quantum mechanics, is quite unimpressed by Einstein–Podolsky–Rosen correlations. He can point to many examples of similar correlations in everyday life. The case of Bertlmann's socks is often cited. Dr. Bertlmann likes to wear two socks of different colours. Which colour he will have on a given foot on a given day is quite unpredictable. But when you see (Fig. 1) that the first sock is pink you can be already sure that the second sock will not be pink. Observation of the first, and experience of Bertlmann, gives immediate information about the second. There is no accounting for tastes, but apart from that there is no mystery here. And is not the EPR business just the same? Consider for example the particular EPR gedanken experiment of Bohm (Fig. 2). Two suitable particles, suitably prepared (in the ‘singlet spin state’), are directed from a common source towards two widely separated magnets followed by detecting screens. Each time the experiment is performed each of the two particles is deflected either up or down at the corresponding magnet. Whether either particle separately goes up or down on a given occasion is quite unpredictable. But when one particle goes up the other always goes down and vice-versa. After a little experience it is enough to look at one side to know also about the other.
The interpretation of quantum mechanics (or, for that matter, of any physical theory) consists in answering the question: How can the world be for the theory to be true? That question is especially pressing in the case of the long-distance correlations predicted by Einstein, Podolsky and Rosen, and rather convincingly established during the past decades in various laboratories. I will review four different approaches to the understanding of long-distance quantum correlations: (i) the Copenhagen interpretation and some of its modern variants; (ii) Bohmian mechanics of spin-carrying particles; (iii) Cramer's transactional interpretation; and (iv) the Hess-Philipp analysis of extended parameter spaces.
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.
Unlike our basic theories of space and time, quantum mechanics is not a locally causal theory. Moreover, it is widely believed that any hopes of restoring local causality within any realistic theory have been undermined by Bell's theorem and the experimental investigations it has inspired. In this pedagogical paper, John S. Bell's amusing example of Dr. Bertlmann's socks to illustrate the results of these experiments is reconsidered, first within a toy model of a two-dimensional one-sided world of a non-orientable Möbius strip, and then within a real world of three-dimensional quaternionic sphere, S3, which results from an addition of a single point to IR3at infinity. In the latter quaternionic world, which happens to be the spatial part of a solution of Einstein's field equations of general relativity, the singlet correlations between a pair of entangled fermions can be understood as classically as those between Dr. Bertlmann's colorful socks.
Two problems with the Einstein-Podolsky-Rosen argument originate from the difficult-to-explain continual dismissal of Minkowski’s demonstration that the concept of spacetime represents a real four-dimensional world and is not just a mathematical space. The uncritical employment of the traditional three-dimensional language to the description of this argument leads (e.g., in its Bohm's version) to those problems: (1) due to the collapse of the common wavefunction of the constituents 1 and 2 of a disintegrated system, caused by the measurement of 1's spin (event E1), and due the conservation of the total spin, 2's spin is \textit{instantaneously} determined (event E2), which in three-dimensional language inescapably means that E2 is \textit{caused} by E1 (using merely a different word -- `correlation' -- does not explain anything in three-dimensional language); (2) events E1 and E2 are simultaneous \textit{only} for an observer A, who was at rest with respect to the disintegrated system, and therefore the total spin is not conserved for arbitrarily large periods of time for all observers in relative motion with respect to A and there exists a class of observers B for whom event E2 occurs \textit{before} E1, which demonstrates the inadequacy of the fundamental implicit assumption that the physical world is three-dimensional. When the reality of spacetime is explicitly recognized, (1) the paradoxes of the non-conservation of the total spin and that E2 happens before E1 for observers B do not arise (because there is no `before' and `after' in spacetime) and the statement that there is a correlation between E1 and E2 makes a perfect sense, and (2) a spacetime model of the quantum object can then be considered (by also taking into account the non-fully-realized experimental fact that the quantum object \textit{actually} exists everywhere where its wavefunction is different from zero) in order to address the fundamental incompleteness of quantum mechanics -- that it deals not with the quantum object itself, but only with its states. The paper ends with a discussion of a prediction by the proposed spacetime model of the electron that can be tested experimentally probably by the quadratic Stark effect.
On 25 March 1935, the Physical Review received a paper from Albert Einstein, Boris Podolsky, and Nathan Rosen, with the title “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” A few days later, on 30 March 1935, I was born. My life with Einstein was off to a promising start. Some would call it an inauspicious start. Abraham Pais, for example, says in his otherwise admirable biography of Einstein [1] that “the only part of this article that will ultimately survive, I believe, is this last phrase [ No reasonable definition of reality could be expected to permit this ], which so poignantly summarizes Einstein's views on quantum mechanics in his later years.” But today, in this centenary of the Einstein annus mirabilis, as the EPR paper and I both turn 70, it is, in fact, the most cited of all Einstein's papers [2]. The debate over its conceptual implications rages hotter than ever, and for the first time, practical (well, for the moment still gedanken practical) applications of the EPR effect have emerged in cryptography and in other areas of quantum information processing. Being only five weeks old, I was unprepared to pay attention to the article that appeared in the New York Times on 4 May 1935 under an elaborate set of headlines and subheads: And I was completely oblivious to the stern rebuke from Einstein himself, published three days later in the Times , which declared that “any information upon which the article … is based was given to you without my authority. It is my invariable practice to discuss scientific matters only in the appropriate forum and I deprecate advance publication of any announcement in regard to such matters in the secular press.” Apparently Podolsky had tipped off the Times to the article, which did not appear in the sacred press until the 15 May issue of Physical Review. It is not clear that Einstein ever forgave him, and I wish I had been old enough to send Podolsky a cross letter myself. Anyone growing up in America in the 1940s knew that the preeminent genius of our age, and perhaps of any other, lived in Princeton, New Jersey, had a predilection for baggy sweaters, and was always badly in need of a haircut—as far ahead of his time in dress and grooming as he was ahead in science during his 1905 annus mirabilis.