Conceptual difficulties still remain in quantum mechanics, even if they had already been identified by its inventors. This does not mean that the theory is not successful! The reality is quite the opposite: in fact, independently of these difficulties, quantum mechanics is certainly one of the most successful theories of all science. One can even consider that its ability to adapt to new situations is one of its most remarkable features. It continues to give efficient and accurate predictions while new experiments are performed, even in situations that the founding fathers had no way to imagine. Actually, there are very few theories that have been verified with the same accuracy in so many situations. Nevertheless, it remains true that conceptual difficulties subsist, and their discussion is the object of this chapter. As we will see, most of them relate to the process of quantum measurement, in particular to the very nature of the random process that takes place on this occasion. We have seen that, in most cases, the wave function evolves gently, in a perfectly predictable and continuous way, according to the Schrödinger equation; in some cases only (when a measurement is performed), unpredictable changes take place, according to the Von Neumann postulate of state vector reduction. Obviously, having two different postulates for the evolution of the same mathematical object is very unusual in physics. The notion was a complete novelty when it was introduced, and still remains unique, but also the source of difficulties – in particular logical difficulties related to the compatibility between the two different postulates.
Conceptual difficulties still remain in quantum mechanics, even if they had already been identified by its inventors. This does not mean that the theory is not successful! The reality is quite the opposite: in fact, independently of these difficulties, quantum mechanics is certainly one of the most successful theories of all science. One can even consider that its ability to adapt to new situations is one of its most remarkable features. It continues to give efficient and accurate predictions while new experiments are performed, even in situations that the founding fathers had no way to imagine. Actually, there are very few theories that have been verified with the same accuracy in so many situations. Nevertheless, it remains true that conceptual difficulties subsist, and their discussion is the object of this chapter. As we will see, most of them relate to the process of quantum measurement, in particular to the very nature of the random process that takes place on this occasion. We have seen that, in most cases, the wave function evolves gently, in a perfectly predictable and continuous way, according to the Schrödinger equation; in some cases only (when a measurement is performed), unpredictable changes take place, according to the Von Neumann postulate of state vector reduction. Obviously, having two different postulates for the evolution of the same mathematical object is very unusual in physics. The notion was a complete novelty when it was introduced, and still remains unique, but also the source of difficulties – in particular logical difficulties related to the compatibility between the two different postulates.
Current situation of quantum mechanics: some conceptual problems remainQuantum mechanics is one of the most successful theories of all physics.Its predictions have been verified in a huge number of situations, sometimes with a fantastic accuracy of 10 -12 .Historically, it was developed in several stages, each of them implying a different interpretation, sometimes opposite of the others.A "standard" version then emerged, in the line of the contributions of von Neumann and Dirac, which is the version generally found in textbooks.Nevertheless, real conceptual difficulties remain: we are far from a universal consensus concerning the best way to interpret the nature of the wave function, the measurement process, etc. and their possible relation with "physical reality".This is the reason why many interpretations of quantum mechanics have been proposed.A few will be described during the talk: the Copenhagen interpretation (Bohr), the statistical interpretation (Einstein, Ballentine, etc.) as well as the three most famous nonstandard interpretations: dBB (de Broglie Bohm), GRW/CSL (Stochastic Schrödinger dynamics) and Everett (sometimes described as "many worlds").Un certain nombre des difficultés conceptuelles de la mécanique quantique, déjà identifiées par ses inventeurs, subsistent à l'heure actuelle.Que le lecteur n'en retire pas l'impression qu'il s'agit d'une théorie peu solide !L'arbre ne doit pas cacher la forêt : indépendamment de ces difficultés très réelles, la mécanique quantique est assurément l'une des théories les plus couronnées de succès de toute la science.On peut même considérer que sa faculté d'adaptation aux situations les plus variées est sa caractéristique la plus extraordinaire ; elle continue à être toujours aussi efficace dans ses prédictions en accompagnant les progrès expérimentaux qui permettent constamment d'avoir accès à de nouvelles situations physiques que les pères fondateurs de la théorie n'avaient aucun moyen de prévoir.De fait, il existe très peu de théories dont la vérification ait été faite avec la même précision, et ceci dans des domaines d'application variés.Il subsiste cependant que, sur le plan conceptuel, des difficultés subsistent, et ce sont elles qui font l'objet du présent chapitre.Comme nous le verrons, la plupart mettent en jeu le processus de mesure quantique et la nature du phénomène aléatoire qui se produit à cette occasion.Dans le point de vue de Von Neumann ce n'est que lorsqu'une mesure est effectuée que des sauts aléatoires se produisent, selon le postulat de réduction du vecteur d'état.Sinon, en général la fonction d'onde évolue progressivement, d'une façon parfaitement prévisible et continue, selon l'équation de Schrödinger.Bien évidemment, utiliser deux postulats aussi différents pour l'évolution du même objet mathématique 1 est une situation tout à fait (1) Au lieu du « point de vue de Schrödinger », il est équivalent d'utiliser « point de vue de Heisenberg » ; l'évolution continue du vecteur d'état est alors transférée vers les observables du système (opérateurs agissant sur son espace des états), tandis que le vecteur d'état reste indépendant du temps en l'absence de mesure.Les observables évoluent de façon continue, que des mesures soient effectuées ou pas.Mais le vecteur d'état doit encore obéir à des règles différentes suivant la situation : la plupart du temps il reste parfaitement constant, mais lors d'une mesure il saute brusquement vers une nouvelle valeur prenant en compte l'information nouvelle.L'acquisition d'information est donc toujours considérée comme un processus physique totalement différent de l'évolution « normale », ce qui introduit la nécessité de bien définir la frontière entre les deux processus.
Quantum mechanics is an immensely successful theory, occupying a unique position in the history of science. It has solved mysteries ranging from macroscopic superconductivity to the microscopic theory of elementary particles and has provided deep insights into the nature of vacuum on the one hand and the description of the nucleon on the other. Whole new fields such as quantum optics and quantum electronics owe their very existence to this body of knowledge. However, despite the stunning successes of quantum mechanics, there is no general agreement on the conceptual foundations and interpretation of the subject. The theory provides unambiguous information about the outcome of a measurement of a physical object. However, many feel that it does not provide a satisfactory answer to the nature of the “reality” we should attribute to the physical objects between the acts of measurement. The conceptual difficulty comes about because the wave function |ψ〉 is usually given by a coherent superposition of various distinguishable experimental outcomes. If we denote the collection of states that represent the possible outcomes of an experiment by |ψ j 〉, then |ψ〉 = ∑ j c j |ψ j 〉 where c j = 〈ψ j |ψ〉. The probability of the outcome |ψ j 〉 is P j =|c j | 2 . In the process of measurement, the so called collapse of the wave function takes place and a single, definite state |ψ i 〉 of the physical object is chosen. The difficulty comes about in the interpretation of the mechanism by which this definite state is chosen from amongst all the possible outcomes.
Introduction Despite its extraordinary predictive successes, quantum mechanics has, since its inception some seventy years ago, been plagued by conceptual difficulties. The basic problem, plainly put, is this: It is not at all clear what quantum mechanics is about. What, in fact, does quantum mechanics describe? It might seem, since it is widely agreed that the state of any quantum mechanical system is completely specified by its wave function, that quantum mechanics is fundamentally about the behavior of wave functions. Quite naturally, no physicist wanted this to be true more than did Erwin Schrodinger, the father of the wave function. Nonetheless, Schrodinger ultimately found this impossible to believe. His difficulty was not so much with the novelty of the wave function [2, page 156 of [3]]: "That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message." Rather, it was that
Quantum theory is the soul of contemporary physics. It was discovered in an adventurous way, under the urge to solve the puzzles posed by atomic spectra and blackbody radiation. But after its invention, it immediately became clear that it was not just a theory of specific physical systems: it was rather a new language of universal applicability. Already in 1928, the theory had received solid mathematical foundations by Hilbert, von Neumann, and Nordheim, and this work was brought to completion in the monumental work of von Neumann, in the form that we still study nowadays. The theory is extraordinarily successful, and its predictions have been confirmed to an astonishing level of precision in a large spectrum of experiments. However, almost 90 years after von Neumann's book, quantum theory remains mysterious. Its mathematical formulation – based on Hilbert spaces and self-adjoint operators – is far from having an intuitive interpretation. The association of physical systems to Hilbert spaces whose unit vectors represent pure states, the representation of transformations by unitary operators and of observables by self-adjoint operators – all such postulates look artificial and ad hoc . A slightly more operational approach is provided by the C * -algebraic formulation of quantum theory – still, this formulation relies on the assumption that observables form an algebra , where the physical meanings of the multiplication and the sum are far from clear. In short, the postulates of quantum theory impose mathematical structures without providing any simple reason for this choice: the mathematics of Hilbert spaces is adopted as a magic blackbox that “works well” at producing experimental predictions. However, in a satisfactory axiomatization of a physical theory the mathematical structures should emerge as a consequence of postulates that have a direct physical interpretation. By this we mean postulates referring, e.g., to primitive notions like physical system, measurement, or process, rather than notions like, e.g., Hilbert space, C * -algebra, unit vector, or selfadjoint operator. The crucial question thus remains unanswered: why quantum theory? Which are the principles at the basis of the theory? A case that is often invoked in contrast is that of Special Relativity theory, which directly follows from the simple understandable principle of relativity.
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.
From a fundamental point of view we must acknowledge that, since about 1935, our conceptual understanding of quantum mechanics has not progressed so much. Really new ideas are few and far between – except of course the major line initiated by the contribution of Bell [6]. This is in big contrast with the rest of physics, where new theoretical and experimental discoveries in many fields have flourished, very often with the help of the tools of quantum mechanics. The fantastic evolution of the experimental techniques has completely changed the situation. At the beginning of quantum mechanics, the observation of the tracks of single particles in Wilson chambers [348] played the essential role in the introduction of the postulate of state vector reduction, but otherwise it was impossible to observe continuously a single electron, atom, or ion; the experiments that theorists were proposing in discussions on the principles of quantum measurement were therefore “thought experiments” (“Gedanken Experiment”), as for instance in the famous Solvay meetings [1, 21]. But nowadays, after almost of century of experimental progress, experiments that were then unthinkable have become a reality. A huge number of contemporary experiments involves the laws of quantum mechanics in general; several books would not be sufficient to describe all of them. Nevertheless, in the majority of experiments, what is really observed is the sum over a very large number of particles of one individual microscopic observable (sum of atomic dipoles for instance), which is accurately described by the average value of this observable.