The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account has three desirable features that the standard account lacks: it does not refer to any abstract mathematical objects, it is free from the usual arbitrary conventions, and it explains why the wave function has its gauge degrees of freedom, something that are usually (...) put into the theory by hand. Hence, this account has implications for debates in philosophy of mathematics and philosophy of science. First, by removing references to mathematical objects, it provides a framework for nominalizing quantum mechanics. Second, by excising superfluous structure such as overall phase, it reveals the intrinsic structure postulated by quantum mechanics. Moreover, it also removes a major obstacle to ``wave function realism.''. (shrink)

This book seeks to work out which commitments are minimally sufficient to obtain an ontology of the natural world that matches all of today’s well-established physical theories. We propose an ontology of the natural world that is defined only by two axioms: (1) There are distance relations that individuate simple objects, namely matter points. (2) The matter points are permanent, with the distances between them changing. Everything else comes in as a means to represent the change in the distance relations (...) in a manner that is both as simple and as informative as possible. The book works this minimalist ontology out in philosophical as well as mathematical terms and shows how one can understand classical mechanics, quantum field theory and relativistic physics on the basis of this ontology. Along the way, we seek to achieve four subsidiary aims: (a) to make a case for a holistic individuation of the basic objects (ontic structural realism); (b) to work out a new version of Humeanism, dubbed Super-Humeanism, that does without natural properties; (c) to set out an ontology of quantum physics that is an alternative to quantum state realism and that avoids any ontological dualism of particles and fields; (d) to vindicate a relationalist ontology based on point objects also in the domain of relativistic physics. (shrink)

It is generally argued that if the wave-function in the de Broglie–Bohm theory is a physical field, it must be a field in configuration space. Nevertheless, it is possible to interpret the wave-function as a multi-field in three-dimensional space. This approach hasn’t received the attention yet it really deserves. The aim of this paper is threefold: first, we show that the wave-function is naturally and straightforwardly construed as a multi-field; second, we show why this interpretation is superior to other interpretations (...) discussed in the literature; third, we clarify common misconceptions. (shrink)

Quantum philosophy, a peculiar twentieth-century malady, is responsible for most of the conceptual muddle plaguing the foundations of quantum physics. When this philosophy is eschewed, one naturally arrives at Bohmian mechanics, which is what emerges from Schrodinger's equation for a nonrelativistic system of particles when we merely insist that 'particles' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. The quantum formalism emerges when measurement situations are (...) analyzed according to this theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with quantum theory simply evaporate.Bohr's ... approach to atomic problems ... is really remarkable. He is completely convinced that any understanding in the usual sense of the word is impossible. Therefore the conversation is almost immediately driven into philosophical questions, and soon you no longer know whether you really take the position he is attacking, or whether you really must attack the position he is defending. (shrink)

The deBroglie–Bohm quantum potential is the potential energy function of the wave field. The quantum potential facilitates the transference of energy from wave field to particle and back again which accounts for energy conservation in isolated quantum systems. Factors affecting energy exchanges and the form of the quantum potential are discussed together with the related issues of the absence of a source term for the wave field and the lack of a classical back reaction.

The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? I review the debate between 3N-Fundamentalists and 3D-Fundamentalists and evaluate it based on three criteria. I argue that when we consider which view leads to a deeper understanding of the physical world, especially given the deeper topological (...) explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons in favor of 3D-Fundamentalism. I conclude that our evidence favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I outline lines of future research where the evidential balance can be restored or reversed. Finally, I draw lessons from this case study to the debate about theoretical equivalence. (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.

Here the philosopher and physicist David Z Albert argues, among other things, that the difference between past and future can be understood as a mechanical phenomenon of nature and that quantum mechanics makes it impossible to present the entirety of what can be said about the world as a narrative of “befores” and “afters.”.

The most puzzling issue in the foundations of quantum mechanics is perhaps that of the status of the wave function of a system in a quantum universe. Is the wave function objective or subjective? Does it represent the physical state of the system or merely our information about the system? And if the former, does it provide a complete description of the system or only a partial description? We shall address these questions here mainly from a Bohmian perspective, and shall (...) argue that part of the difficulty in ascertaining the status of the wave function in quantum mechanics arises from the fact that there are two different sorts of wave functions involved. The most fundamental wave function is that of the universe. From it, together with the configuration of the universe, one can define the wave function of a subsystem. We argue that the fundamental wave function, the wave function of the universe, has a law-like character. (shrink)

The article sets out a primitive ontology of the natural world in terms of primitive stuff—that is, stuff that has as such no physical properties at all—but that is not a bare substratum either, being individuated by metrical relations. We focus on quantum physics and employ identity-based Bohmian mechanics to illustrate this view, but point out that it applies all over physics. Properties then enter into the picture exclusively through the role that they play for the dynamics of the primitive (...) stuff. We show that such properties can be local, as well as holistic, and discuss two metaphysical options to conceive them, namely, Humeanism and modal realism in the guise of dispositionalism. 1 Introduction2 Primitive Ontology: Primitive Stuff3 The Physics of Matter as Primitive Stuff4 The Humean Best System Analysis of the Dynamical Variables5 Modal Realism about the Dynamical Variables6 Conclusion. (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)

Is the quantum state part of the furniture of the world? Einstein found such a position indigestible, but here I present a different understanding of the wavefunction that is easy to stomach. First, I develop the idea that the wavefunction is nomological in nature, showing how the quantum It or Bit debate gets subsumed by the corresponding It or Bit debate about laws of nature. Second, I motivate the nomological view by casting quantum mechanics in a “classical” formalism (Hamilton–Jacobi theory) (...) and classical mechanics in a “quantum” formalism (Koopman–von Neumann theory) and then comparing and contrasting classical and quantum wave functions. I argue that Humeans about laws can treat classical and quantum wave functions on a par and that doing so yields many benefits. (shrink)

Properties sometimes attributed to the “particle” aspect of a neutron, e.g., mass and magnetic moment, cannot straightforwardly be regarded in the Bohm interpretation of quantum mechanics as localized at the hypothetical position of the particle. This is shown by examining a series of effects in neutron interferometry. A related thought-experiment also provides a variation of a recent demonstration that which-way detectors can appear to behave anomolously in the Bohm theory.

The paper points out that the modern formulation of Bohm’s quantum theory known as Bohmian mechanics is committed only to particles’ positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces according to which Bohm’s theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status of the (...) law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general. (shrink)

Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology approaches, which include some varieties of Bohmian mechanics and spontaneous collapse theories, are interesting in part because they hold out the hope that it should not be too difficult to make a connection between models of quantum mechanics and descriptions of histories of ordinary macroscopic bodies. But such approaches are dualistic, positing a quantum state as (...) well as ordinary material degrees of freedom. This paper lays out and compares some options that primitive ontologists have for making sense of the quantum state. (shrink)

The book comprises an enquiry into what quantum theory shows us about the world. Its aim is to sort out which metaphysical speculations are tenable and which are not. After an initial discussion of realism, the author provides a non-technical exposition of quantum theory and a criticism of the proposal that quantum theory should make us revise our beliefs about logic. He then discusses the various problems and puzzles which make quantum theory both interesting and perplexing. The text defends three (...) markedly different speculations. The first of them, the "determinate particle speculation", is shown to involve both a view which proposes determinate locations and velocities for particles and the opposite. With the "wave speculation" particles are seen as different again: here the professor proposes a radically original view of particles as polywaves. In the final chapter, he compares the competing particle theories and shows that two ostensibly opposing views are in fact compatible. He goes on to discuss the implications of quantum theory for our understanding of persons. The work assumes no prior knowledge of quantum theory and confines the necessary mathematical details to end-notes. (shrink)

In recent literature, it has become clear that quantum physics does not refute Humeanism: Lewis’s thesis of Humean supervenience can be literally true even in the light of quantum entanglement. This point has so far been made with respect to Bohm’s quantum theory. Against this background, this paper seeks to achieve the following four results: to generalize the option of quantum Humeanism from Bohmian mechanics to primitive ontology theories in general; to show that this option applies also to classical mechanics; (...) to establish that it requires a commitment to matter as primitive stuff, but no commitment to natural properties ; to point out that by removing the commitment to properties, the stock metaphysical objections against Humeanism from quidditism and humility no longer apply. In that way, quantum physics strengthens Humeanism instead of refuting it. (shrink)

The relationship between mathematical formalism, physical interpretation and epistemological appraisal in the practice of physical theorizing is considered in the context of Bohmian mechanics. After laying outthe formal mathematical postulates of thetheory and recovering the historical roots ofthe present debate over the meaning of Bohmianmechanics from the early debate over themeaning of Schrödinger's wave mechanics,several contemporary interpretations of Bohmianmechanics in the literature are discussed andcritiqued with respect to the aim of causalexplanation and an alternative interpretationis proposed. Throughout, the over-arching aimis (...) to exhibit the connections betweenmathematical, ontological and methodologicalquestions in physical theory and to reflect onthe rationality of physical theorizing in lightof the present case. (shrink)