This paper discusses questions concerning the foundations of quantum mechanics (entanglement, wave collapse, irreversibility) with reference to the issues raised during a Minisymposium held in Helsinki, 1.6-3.6 in 1992, where A Shimony, A Peres and B d'Espagnat were invited to lecture. The measurement problem is related to the phenomenon of irreversibility which is known not to follow from any fundamental theory; e.g., the law of exponential decay does not follow from the Schrödinger equation in senso stricto. The approximations that lead to irreversibility are related to some form of ''forgetting'', or coarse graining. Some approaches to the question, why these approximations can be justified, are reviewed. The paper also discusses dynamical reduction schemes and it is suggested, that the corresponding non-linear modifications of the Schrödinger equation -- which lead to non-conservation of energy -- are actually ''effective'' Schrödinger equations for open systems (in analogy with the ''effective'' Lagrangians in QFT). Thus these modifications should be derived from a fundamental theory of interactions. The paper ends with some brief comments on the mind-body question in the quantum mechanical context. A postscript has been added (2006).
This paper discusses questions concerning the foundations of quantum mechanics (entanglement, wave collapse, irreversibility) with reference to the issues raised during a Minisymposium held in Helsinki, 1.6-3.6 in 1992, where A Shimony, A Peres and B d'Espagnat were invited to lecture. The measurement problem is related to the phenomenon of irreversibility which is known not to follow from any fundamental theory; e.g., the law of exponential decay does not follow from the Schrödinger equation in senso stricto. The approximations that lead to irreversibility are related to some form of ''forgetting'', or coarse graining. Some approaches to the question, why these approximations can be justified, are reviewed. The paper also discusses dynamical reduction schemes and it is suggested, that the corresponding non-linear modifications of the Schrödinger equation -- which lead to non-conservation of energy -- are actually ''effective'' Schrödinger equations for open systems (in analogy with the ''effective'' Lagrangians in QFT). Thus these modifications should be derived from a fundamental theory of interactions. The paper ends with some brief comments on the mind-body question in the quantum mechanical context. A postscript has been added (2006).
This volume offers discussions on foundational problems of quantum mechanics and other fundamental physical theories, taking into account new experimental developments. The surveying of the progress with respect to fundamental questions of the quantum theory of measurement forms the guiding line of thought of this Symposium, the main themes of discussion being: the inter-relation of quantum measurement and irreversability; the physics of information (concerned with questions of information processing and quantum noise); quantum interference and mesoscopic quantum effects (searching for the micro-macro borderline); and the quantum-classical relationship (the need for classical pointer and their realization).
Some of the quantum mechanical conceptual problems, their current status, and related theoretical developments are reviewed. The characteristics of the entangled quantum states are analyzed, and new experiments and quantum information applications involving such states are discussed. The well-known paradox of Schroedinger's cat (the impossibility of observing superpositions of macroscopically distinct states that are predicted by quantum mechanics) is discussed. It is shown that decoherence (arising when a quantum system is measured in such a way that some information about its state is recorded in its environment) prevents the distinguishing of a superposition and the corresponding mixture. This overcomes the difficulties associated with the paradoxical nature of quantum measurement provided we remain within the framework of the theory of open systems. Other conceptual difficulties, while actually lying outside physics, are now the subject of much research and have already led to new interesting interpretations of quantum mechanics. The suggestion of Wigner and others that the observer's consciousness be included in the theory of quantum measurement is discussed in this context. A hypothesis is put forward which might enable the functioning of consciousness to be described in quantum measurement terms.
In this article, I shall focus on two of the main problems raising interpre-tational issues in quantum mechanics, namely the notorious measurement problem (discussed together with the theory of measurement in section 4) and the equally important but not quite as widely discussed problem of the classical regime (discussed together with decoherence in section 3). The two problems are distinct, but they are both intimately related to some of the is-sues arising from entanglement and density operators, which are thus briefly reviewed in section 2. A few fundamentals are rehearsed in section 1. The article will aim to be fairly non-technical in language, but modern in out-look and covering the chosen topics in more depth than most introductory treatments. The philosophy and foundations of quantum mechanics offer many more examples of live research issues, and much progress has been achieved re-cently in such traditional approaches as collapse theories, pilot-wave the-ories and Everett interpretations, and in the (time-honoured but recently revived) area of axiomatic reconstructions of the theory. Recent years have
Nonintegrable Poincaré systems with continuous spectrum (so-called Large Poincaré Systems, LPS) lead to the appearance of diffusive terms in the framework of dynamics. These terms break time symmetry. They lead, therefore, to limitations to classical trajectory dynamics and of wave functions. These diffusive terms correspond to well-defined classes of dynamical processes (i.e., so-called “vacuum-vacuum” transitions). The diffusive effects are amplified in situations corresponding to persistent interactions. As a result, we have to include already in the fundamental dynamical description the two aspects, probability and irreversibility, which are so conspicuous on the macroscopic level. We have to formulate both classical and quantum mechanics on the Liouville level of probability distributions (or density matrices). For integrable systems, we recover the usual formulations of classical or quantum mechanics. Instead of being irreducible concepts, which cannot be further analyzed, trajectories and wave functions appear as special solutions of the Liouville-von Neumann equations. This extension of classical and quantum dynamics permits us to unify the two concepts of nature we inherited from the 19th century, based on the one hand on dynamical time-reversible laws and on the other on an evolutionary view associated to entropy. It leads also to a unified formulation of quantum theory avoiding the conventional dual structure based on Schrödinger’s equation on the one hand, and on the “collapse” of the wave function on the other. A dynamical interpretation is given to processes such as decoherence or approach to equilibrium without any appeal to extra dynamic considerations (such as the many-world theory, coarse graining or averaging over the environment). There is a striking parallelism between classical and quantum theory. For LPS we have, in general, both a “collapse” of trajectories and of wave functions for LPS. In both cases, we need a generalized formulation of dynamics in terms of probability distributions or density matrices. Since the beginning of this century, we know that classical mechanics had to be generalized to take into account the existence of universal constants. We now see that classical as well as quantum mechanics also have to be extended to include unstable dynamical systems such as LPS. As a result, we achieve a new formulation of "laws of physics" dealing no more with certitudes but with probabilities. The formulation is appropriate to describe an open, evolving universe.
Ever since the beginning of quantum mechanics, the measurement problem has been a subject of sometimes discontinued but nevertheless recurrent concern. As students, most physicists have raised questions about it, but the spectacular and renewed successes of quantum theory were a strong incentive for them to work out applications without further worrying about foundations. In each generation, however, some dissatisfaction reemerges, which leads to slow progress, and we may expect that the measurement problem will some day be cleared up rather than forgotten. The situation recalls statistical mechanics, the foundations of which still give rise to scientific discussions, in spite of more than one century’s achievements. Actually, the paradoxes of irreversibility and of Maxwell’s demon share some common features with quantum measurements, to wit, they involve probabilities in a crucial fashion and their explanation requires elucidating the role of the observer.