In this paper we show that the three main equations used by Bohm in his approach to quantum mechanics are already contained in the earlier paper by Moyal which forms the basis for what is known as the Wigner-Moyal approach. This shows, contrary to the usual perception, that there is a deep relation between the two approaches. We suggest the relevance of this result to the more general problem of constructing a quantum geometry.

This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics.In it, I aim to review, in a way accessible to foundationally interested physicists as well as physics-informed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to (...) modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the "traditional" formulation of the problem. (shrink)

Motivated by the question what it is that makes quantum mechanics a holistic theory, I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these (...) resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed. (shrink)

This paper argues for a broadly dispositionalist approach to the ontology of Bohmian mechanics . It first distinguishes the ‘minimal’ and the ‘causal’ versions of Bohm’s theory, and then briefly reviews some of the claims advanced on behalf of the ‘causal’ version by its proponents. A number of ontological or interpretive accounts of the wave function in BM are then addressed in detail, including configuration space, multi-field, nomological, and dispositional approaches. The main objection to each account is reviewed, namely the (...) ‘problem of perception’, the ‘problem of communication’, the ‘problem of temporal laws’, and the ‘problem of under-determination’. It is then shown that a version of dispositionalism overcomes the under-determination problem while providing neat solutions to the other three problems. A pragmatic argument is thus furnished for the use of dispositions in the interpretation of the theory more generally. The paper ends in a more speculative note by suggesting ways in which a dispositionalist interpretation of the wave function is in addition able to shed light upon some of the claims of the proponents of the causal version of BM. (shrink)

Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics. Of course, at the nuclear level, because of some complications, it is not clear that we can claim the same confidence. One way of taking these complications and corrections into account seems to be a modification of the standard quantum theory. In this (...) paper and its follow ups we consider a straightforward way of extending quantum theory. Our method is based on a Bohmian approach. We show that this approach has the essential ability for extending quantum theory, and we do this by introducing “non-Bohmian” forms for the quantum potential. (shrink)

Experimental situations in which we observe quantum effects that deviate from the intuitive expectations of the classical world call for an interdisciplinary discussion, and one fundamental issue to be considered is the compatibility between the description of phenomena and the assumption of an objective reality. This paper discusses the ontological interpretation of Bohmian quantum mechanics, focusing on the use of the term “trajectory” and the difficulties associated with its connection to a “real” (objective) trajectory. My conclusion is that the intended (...) realistic interpretation of Bohmian trajectories is highly questionable.Los contextos experimentales que permiten la observación de efectos cuánticos contrarios a los esperables según la intuición clásica son especialmente adecuados para una discusión multidisciplinar, en particular sobre la compatibilidad entre la descripción fenomenológica y una pretendida realidad subyacente. Este artículo discute la interpretación ontológica de la mecánica cuántica en la interpretación de Bohm, centrándose principalmente en su uso del término “trayectoria” y las dificultades inherentes a su conexión con un concepto “real” (objetivo) de la misma. La conclusión es que la pretendida interpretación realista de las trayectorias bohmianas es muy cuestionable. (shrink)

We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed. The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find it (...) explanatorily redundant (in particular for dBBT’s solution of the Measurement Problem, which only requires that the corpuscles possess definite positions), and subject to a number of difficulties. Following a suggestion from Bell, we propose to abandon the Guidance Equation, whilst retaining dBBT’s point particle-based Primitive Ontology, with positions as local beables. The resultant theory, which we identify as a stochastic, minimally deBroglie-Bohmian theory, describes a random walk through configuration space. Its probabilities, we propose, are best understood as dispositions of possible corpuscle configurations to manifest themselves. We subsequently evaluate the merits of sdBBT vis-à-vis dBBT, such as the justification of the Symmetrisation Postulate and the violation of the Action-Reaction Principle. Not only is sdBBT an attractive Bohmian theory that, whilst retaining dBBT's virtues, overcomes many of its shortcomings; it also sparks off a number of exciting follow-up questions, such as a comparison between sdBBT and other stochastic hidden-variable theories, e.g. Nelson Stochastics, or between sdBBT and the Everett interpretation. (shrink)

Bohmian mechanics faces an underdetermination problem: when it comes to solving the measurement problem, alternatives to the Bohmian guidance equation work just as well as the official guidance equation. One way to argue that the guidance equation is superior to its rivals is to use a symmetry argument: of the candidate guidance equations, the official guidance equation is the simplest Galilean-invariant candidate. This symmetry argument---if it worked---would solve the underdetermination problem. But the argument does not work. It fails because it (...) rests on assumptions about how Galilean transformations (especially boosts) act on the wavefunction that are (in this context) unwarranted. My discussion has larger morals about the physical significance of certain mathematical results (like, for example, Wigner's theorem) in non-orthodox interpretations of quantum mechanics. (shrink)

The idea of obtaining a pilot-wave quantum theory on a lattice with discrete time is presented. The motion of quantum particles is described by a \-distributed Markov chain. Stochastic matrices of the process are found by the discrete version of the least-action principle. Probability currents are the consequence of Hamilton’s principle and the stochasticity of the Markov process is minimized. As an example, stochastic motion of single particles in a double-slit experiment is examined.

The paper presents an inquiry into the question regarding the compatibility of Bohmian mechanics, intended as a non-local theory of moving point-like particles, with background independence. This issue is worth being investigated because, if the Bohmian framework has to be of some help in developing new physics, it has to be compatible with the most well-established traits of modern physics, background independence being one of such traits. The paper highlights the fact that the notion of background independence in the context (...) of spacetime physics is slippery and interpretation-laden. It is then suggested that the best-matching framework developed by Julian Barbour might provide a robust enough meaning of background independence. The structure of Bohmian dynamics is evaluated against this framework, reaching some intermediate results that speak in favor of the fact that Bohmian mechanics can be made background independent. (shrink)

Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown that the explanation does not make use of the full probability measure, but rather of a suitable set function deriving from it, which defines relative typicality between single-time cylinder sets. Such a set function can also be derived directly (...) from the standard quantum formalism, without the need of an underlying probability measure. The key concept for this derivation is the quantum typicality rule, which can be considered as a generalization of the Born rule. The result is a new formulation of quantum mechanics, in which particles follow definite trajectories, but which is based only on the standard formalism of quantum mechanics. (shrink)

I consider the fact that there are a number of interesting ways to ‘reconstruct’ quantum theory, and suggest that, very broadly speaking, a form of ‘instrumentalism’ makes good sense of the situation. This view runs against some common wisdom, which dismisses instrumentalism as ‘cheap’. In contrast, I consider how an instrumentalist might think about the reconstruction theorems, and, having made a distinction between ‘reconstructing’ quantum theory and ‘reinventing’ quantum theory, I suggest that there is an adequate instrumentalist approach to the (...) theory that invokes both. (shrink)

I briefly sketch Bohm's causal interpretation (BCI) and its solution to the measurement problem. Crucial to BCI's no-collapse account of both ideal and non-ideal measurement is the existence of particles in addition to wavefunctions. The particles in their role as the producers of the observable experimental outcomes render practical considerations, such as what observables can be reasonably measured or how to get rid of interference terms in non-ideal measurements, secondary to BCI's account of measurement. I then explain why it is (...) not easy for BCI to justify its statistical postulate. To successfully justify the postulate would be to solve the distribution problem. Two proposed deterministic solutions to this problem are only briefly set out and not discussed in detail. BCI can solve the measurement problem whether or not the distribution problem is solved. However, if the distribution problem is not solved, BCI cannot be shown to be empirically adequate. (shrink)