In [3] John S. Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |Ψ|2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; such processes we call Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of (...) jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to “second quantization.” As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field. (shrink)

Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...) random, with probability density ρ given by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements.” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. (shrink)

A Philosopher Looks at Quantum Mechanics’ (Putnam [1965]) explained why the interpretation of quantum mechanics is a philosophical problem in detail, but with only the necessary minimum of technicalities, in the hope of making the difficulties intelligible to as wide an audience as possible. When I wrote it, I had not seen Bell ([1964]), nor (of course) had I seen Ghirardi et al. ([1986]). And I did not discuss the ‘Many Worlds’ interpretation. For all these reasons, I have decided to (...) make a similar attempt forty years later, taking account of additional interpretations and of our knowledge concerning non-locality. (The Quantum Logical interpretation proposed in Putnam [1968] is not considered in the present paper, however, because Putnam [1994b] concluded that it was unworkable.) Rather than advocate a particular interpretation, this paper classifies the possible kinds of interpretation, subject only to the constraints of a very broadly construed scientific realism. Section 7 does, however, argue that two sorts of interpretation—ones according to which a ‘collapse’ is brought about by the measurement (e.g. the traditional ‘Copenhagen’ interpretation), and the Many Worlds interpretation or interpretations—should be ruled out. The concluding section suggests some possible morals of a cosmological character. Background Scientific realism is the premise of my discussion What ‘quantum mechanics’ says—and some problems Other interpretations of quantum mechanics The problem of Einstein's bed Classification of the possible kinds of interpretation Which interpretations I think we can rule out The ‘moral’ of this discussion. (shrink)

I argue that the wave function ontology for quantum mechanics is an undesirable ontology. This ontology holds that the fundamental space in which entities evolve is not three-dimensional, but instead 3N-dimensional, where N is the number of particles standardly thought to exist in three-dimensional space. I show that the state of three-dimensional objects does not supervene on the state of objects in 3N-dimensional space. I also show that the only way to guarantee the existence of the appropriate mental states in (...) the wave function ontology has undesirable metaphysical baggage: either mind/body dualism is true, or circumstances which we take to be logically possible turn out to be logically impossible.“While our theory can be extended formally in a logically consistent way by introducing the concept of a wave in a 3N-dimensional space, it is evident that this procedure is not really acceptable in a physical theory... ” (Bohm 1957, 117). (shrink)

In Bohmian mechanics elementary particles exist objectively, as point particles moving according to a law determined by a wavefunction. In this context, questions as to whether the particles of a certain species are real---questions such as, Do photons exist? Electrons? Or just the quarks?---have a clear meaning. We explain that, whatever the answer, there is a corresponding Bohm-type theory, and no experiment can ever decide between these theories. Another question that has a clear meaning is whether particles are intrinsically distinguishable, (...) i.e., whether particle world lines have labels indicating the species. We discuss the intriguing possibility that the answer is no, and particles are points---just points. (shrink)

Spontaneous collapse theories of quantum mechanics require an interpretation if their claim to solve the measurement problem is to be vindicated. The most straightforward interpretation rule, the fuzzy link, generates a violation of common sense known as the counting anomaly. Recently, a consensus has developed that the mass density link provides an appropriate interpretation of spontaneous collapse theories that avoids the counting anomaly. In this paper, I argue that the mass density link violates common sense in just as striking a (...) way as the fuzzy link, and hence should not be regarded as a problem-free alternative to the fuzzy link. Hence advocates of spontaneous collapse theories must accept some violation of common sense, although this is not necessarily fatal to their project. (shrink)

Once upon a time, the twentieth-century investigations of the behaviors of sub-atomic particles were thought to have established that there can be no such thing as an objective, observer-independent, scientifically realist, empirically adequate picture of the physical world.

Despite its extraordinary predictive successes, quantum mechanics has, since its inception some seventy years ago, been plagued by conceptual di culties. 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?

We are often told that quantum phenomena demand radical revisions of our scientific world view and that no physical theory describing well defined objects, such as particles described by their positions, evolving in a well defined way, let alone deterministically, can account for such phenomena. The great majority of physicists continue to subscribe to this view, despite the fact that just such a deterministic theory, accounting for all of the phe nomena of nonrelativistic quantum mechanics, was proposed by David Bohm (...) more than four decades ago and has arguably been around almost since the inception of quantum mechanics itself. Our purpose in asking colleagues to write the essays for this volume has not been to produce a Festschrift in honor of David Bohm or to gather together a collection of papers simply stating uncritically Bohm's views on quantum mechanics. The central theme around which the essays in this volume are arranged is David Bohm's version of quantum mechanics. It has by now become fairly standard practice to refer to his theory as Bohmian mechanics and to the larger conceptual framework within which this is located as the causal quantum theory program. While it is true that one can have reservations about the appropriateness of these specific labels, both do elicit distinc tive images characteristic of the key concepts of these approaches and such terminology does serve effectively to contrast this class of theories with more standard formulations of quantum theory. (shrink)

With reference to recently proposed theoretical models accounting for reduction in terms of a unified dynamics governing all physical processes, we analyze the problem of working out a worldview accommodating our knowledge about natural phenomena. We stress the relevant conceptual differences between the considered models and standard quantum mechanics. In spite of the fact that both theories describe systems within a genuine Hilbert space framework, the peculiar features of the spontaneous reduction models limit drastically the states which are dynamically stable. (...) This fact by itself allows one to work out an interpretation of the formalism which makes it possible to give a satisfactory description of the world in terms of the values taken by an appropriately defined mass density function in ordinary configuration space. A topology based on this function and which is radically different from the one characterizing the Hilbert space is introduced, and in terms of it the idea of similarity of macroscopic situations is precisely defined. Finally, the formalism and the interpretation are shown to yield a natural criterion for establishing the psychophysical parallelism. The conclusion is that, within the considered theories and at the nonrelativistic level, one can satisfy all sensible requirements for a completely satisfactory macro-objective description of reality. (shrink)

A new proposal for a Lorentz-invariant spontaneous localization process in the framework of relativistic quantum field theory is presented. As in all dynamical reduction models, a stochastic process is introduced, which drives the state vector towards the eigenspaces of a set of operators representing suitably chosen physical quantities. Such operators constitute a Lorentz scalar field and are built as time averages and space integrals of a local field-theoretic operator in such a way that the quantities they represent acquire a macroscopic (...) character. As always in dynamical reduction theories, the action of the process on microscopic systems takes place via the micro-macro correlations which arise, e.g., as a consequence of measurements. (shrink)

It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wave function (“statistical mixture”) or a system that is entangled with another system (“reduced density matrix”). We point out another role, previously unnoticed in the literature, that a density matrix can play: it can be the “conditional density matrix,” conditional on the configuration of the environment. A precise definition can be given in (...) the context of Bohmian mechanics, whereas orthodox quantum mechanics is too vague to allow a sharp definition, except perhaps in special cases. In contrast to statistical and reduced density matrices, forming the conditional density matrix involves no averaging. In Bohmian mechanics with spin, the conditional density matrix replaces the notion of conditional wave function, as the object with the same dynamical significance as the wave function of a Bohmian system. (shrink)

The year 2005 has been named the World Year of Physics in recognition of the 100th anniversary of Albert Einstein's "Miracle Year," in which he published four landmark papers which had deep and great influence on the last and the current century: quantum theory, general relativity, and statistical mechanics. Despite the enormous importance that Einstein’s discoveries played in these theories, most physicists adopt a version of quantum theory which is incompatible with the idea that motivated Einstein in the first place. (...) This seems to suggest that Einstein was fundamentally incapable of appreciating the `quantum revolution,’ and that his vision of physics as an attempt to reach a complete and comprehensive description of reality was ultimately impossible to obtain. Relativity theory has provided us with a picture of reality in which the world can be though as independent on who observes it, and the same can be said for statistical mechanics. Instead, quantum mechanics seems to suggest that physical objects do not exist `out there’ when someone is not observing them. In this framework, it is often suggested that any kind of causal explanation is impossible in the atomic and subatomic world, and therefore should be abandoned. This is why many think that it is in principle impossible for quantum theory to provide us with a coherent and comprehensive view of the world, in contrast with what happens with relativity and statistical mechanics. Is it really impossible to pursue Einstein’s ideal of physics also in the quantum framework? This book argues that this is not the case: the central idea is that Einstein’s vision of physics is still a live option, and indeed it is the one that best allows obtaining a unitary understanding of our physical theories. One can consider all the three theories mentioned above, suitably modified, as theories that are able to account and explain the world around us without too much departure from the classical framework. ---------------------------------------------------------------------------------------------------- -------------------------------------------------- -/- La teoria della relatività, la meccanica statistica e la meccanica quantistica hanno profondamente rivoluzionato il nostro modo di concepire spazio, tempo, materia, probabilità e causalità, nonché il rapporto tra universo fisico ed osservatore, nozioni che sono state al centro della discussione filosofica dal mondo greco fino ai nostri giorni. Questo volume, opera di Valia Allori, Mauro Dorato, Federico Laudisa e Nino Zanghì, non solo intende suggerire nuovi metodi di confronto tra fisica e filosofia, ma prova altresì a rendere espliciti i presupposti filosofici che sono presenti nell'interpretazione che i fisici stessi danno del formalismo matematico. (shrink)