Einstein thought that quantum mechanics was incomplete because it was nonlocal. In this paper I argue instead that quantum theory is incomplete, even if it is nonlocal, and that relativity is incomplete because its minimal spatiotemporal structure cannot naturally accommodate such nonlocality. So, I show that relativistic pilot-wave theories are the rational completion of quantum mechanics as well as relativity: they provide a spatiotemporal ontology of particles, as well as a spatiotemporal structure able to explain quantum correlations.

Recently doubts have been raised about the ability of pilot wave theories with field ontology to recover the predictions of quantum field theory. In particular, Struyve has questioned that the overlap between wave functionals of macroscopically different states with fixed particle number is really non-significant.With numerical computations and some further plausibility arguments we show that the overlap between n-particle states in field theory decreases almost exponentially with the number of particles and becomes non-significant already for small particle (...) numbers. (shrink)

The de Broglie–Bohm pilot-wave theory provides an illuminating candidate solution to the philosophical problems that plague orthodox quantum theory. But the pilot-wave theory also has the potential to be of practical use to, for example, quantum chemists and condensed matter physicists who study many-body problems. In particular, the proprietary pilot-wave concept of the “conditional wave function” provides a novel perspective on and justification for a standard approach to many-body quantum systems in which the (...) N-particle wave function is replaced by N single-particle wave functions. Moreover, this uniquely Bohmian “small entanglement approximation” can be understood as the most basic level in a hierarchy of well-defined approximation schemes. Here we explain all of this theoretical background and then explore several of these approximation schemes numerically in the context of a simple toy model system. (shrink)

The representation of a quantum system as the spatial configuration of its constituents evolving in time as a trajectory under the action of the wave-function, is the main objective of the de Broglie–Bohm theory. However, its standard formulation is referred to the statistical ensemble of its possible trajectories. The statistical ensemble is introduced in order to establish the exact correspondence between the probability density on the spatial configurations and the quantum distribution, that is the squared modulus of the (...) class='Hi'>wave-function. In this work we explore the possibility of using the pilot wave theory at the level of a single Bohm’s trajectory, that is a single realization of the time dependent configuration which should be representative of a single realization of the quantum system. The pilot wave theory allows a formally self-consistent representation of quantum systems as a single Bohm’s trajectory, but in this case there is no room for the Born’s rule at least in its standard form. We will show that a correspondence exists between the statistical distribution of configurations along the single Bohm’s trajectory and the quantum distribution for a subsystem interacting with the environment in a multicomponent system. To this aim, we present the numerical results of the single Bohm’s trajectory description of the model system of six confined planar rotors with random interactions. We find a rather close correspondence between the coordinate distribution of one rotor, the others representing the environment, along its trajectory and the time averaged marginal quantum distribution for the same rotor. This might be considered as the counterpart of the standard Born’s rule when the pilot wave theory is applied at the level of single Bohm’s trajectory. Furthermore a strongly fluctuating behavior with a fast loss of correlation is found for the evolution of each rotor coordinate. This suggests that a Markov process might well approximate the evolution of the Bohm’s coordinate of a single rotor and, under this condition, it is shown that the correspondence between coordinate distribution and quantum distribution of the rotor is exactly verified. (shrink)

It’s generally taken to be established that no local hidden-variable theory is possible. That conclusion applies if our world is a _thread_, where a thread is a world where particles follow trajectories, as in Pilot-Wave theory. But if our world is taken to be a _set_ of threads locality can be recovered. Our world can be described by a _many-threads_ theory, as defined by Jeffrey Barrett in the opening quote. Particles don’t follow trajectories because a particle in our (...) world is a set of _elemental_ particles following different trajectories, each in a thread. The “elements” of a superposition are construed as subsets in such a way that a particle in our world only has definite position if all its set-theoretic elements are at corresponding positions in each thread. Wavefunction becomes a 3D density distribution of particles’ subset measures, the stuff of an electron’s “probability cloud”. Current Pilot-Wave theory provides a non-relativistic dynamics for the elemental particles (approximated by Many Interacting Worlds theory). EPR-Bell nonlocality doesn’t apply because the relevant measurement outcomes in the absolute elsewhere of an observer are always in superposition. (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.

We illustrate, using a simple model, that in the usual formulation the time-component of the Klein–Gordon current is not generally positive definite even if one restricts allowed solutions to those with positive frequencies. Since in de Broglie's theory of particle trajectories the particle follows the current this leads to difficulties of interpretation, with the appearance of trajectories which are closed loops in space-time and velocities not limited from above. We show that at least this pathology can be avoided if one (...) adapts in a covariant form the formulation of relativistic point particle dynamics proposed by Gitman and Tyutin. (shrink)

The strange story of the von Neumann impossibility proof is recalled, and the even stranger story of later impossibility proofs, and how the impossible was done by de Broglie and Bohm. Morals are drawn.

Many agree that the pilot-wave theory is to be understood as a first-order theory, in which the law constrains the velocity of the particles. However, while Dürr, Goldstein and Zanghì maintain that the pilot-wave theory is Galilei invariant, Valentini argues that such a symmetry is mathematical but it has no physical significance. Moreover, some wavefunction realists insist that the pilot-wave theory is not Galilei invariant in any sense. It has been maintained by some that (...) this disagreement originates in the disagreement about ontology, as Valentini, contrary to Dürr, Goldstein and Zanghì, has been taken to endorse wavefunction realism. In this paper I argue that Valentini’s argument is independent of the choice of the ontology of matter: it is based of the notion of natural kinematics for a theory, and the idea that the kinematics should match the dynamics. If so, I also argue that there are several reasons to dispute Valentini’s claim that the kinematical symmetries should constrain dynamical ones. (shrink)

In 1927 Louis de Broglie proposed an alternative approach to standard quantum mechanics known as the double solution program (DSP) where particles are represented as bunched fields or solitons guided by a base (weaker) wave. DSP evolved as the famous de Broglie-Bohm pilot wave interpretation (PWI) also known as Bohmian mechanics but the general idea to use solitons guided by a base wave to reproduce the dynamics of the PWI was abandoned. Here we propose a nonlinear (...) scalar field theory able to reproduce the PWI for the Schrödinger and Klein–Gordon guiding waves. Our model relies on a relativistic ‘phase harmony’ condition locking the phases of the solitonic particle and the guiding wave. We also discuss an extension of the theory for the N particles cases in presence of entanglement and external (classical) electromagnectic fields. (shrink)

Recently it was shown that certain fluid-mechanical ‘pilot-wave’ systems can strikingly mimic a range of quantum properties, including single particle diffraction and interference, quantization of angular momentum etc. How far does this analogy go? The ultimate test of quantumness of such systems is a Bell-test. Here the premises of the Bell inequality are re-investigated for particles accompanied by a pilot-wave, or more generally by a resonant ‘background’ field. We find that two of these premises, namely outcome (...) independence and measurement independence, may not be generally valid when such a background is present. Under this assumption the Bell inequality is possibly violated. A class of hydrodynamic Bell experiments is proposed that could test this claim. Such a Bell test on fluid systems could provide a wealth of new insights on the different loopholes for Bell’s theorem. Finally, it is shown that certain properties of background-based theories can be illustrated in Ising spin-lattices. (shrink)

The symmetries of the wavefunction for identical particles, including anyons, are given a rigorous non-relativistic generalisation within pilot-wave formulations of quantum mechanics. In particular, parastatistics are excluded. The result has a rigorous generalisation to _n_ particles and to spinorial wavefunctions. The relation to other non-relativistic approaches is briefly discussed.

We briefly review the history of de Broglie's notion of the “double solution” and of the ideas which developed from this. We then go on to an extension of these ideas to the many-body system, and bring out the nonlocality implied in such an extension. Finally, we summarize further developments that have stemmed from de Broglie's suggestions.

David Bohm published his “Suggested Interpretation of Quantum Theory in Terms of Hidden Variables” some twenty five years after Louis de Broglie first presented his similar Pilot Wave theory of quantum mechanics. In the following 30 years what became known as the de Broglie–Bohm approach to quantum theory was to a large extent ignored within the physics community. Even David Bohm himself became somewhat disillusioned with the lack of impact of his interpretation of quantum theory and he directed (...) his interest elsewhere. But some 27 years after Bohm had published his interpretation of quantum theory, interest was rekindled in part by new, detailed calculations that demonstrated clearly and graphically, exactly how his interpretation explained quantum phenomena in terms of well defined individual particle trajectories. These computations encompassed two-slit interference, quantum tunnelling, neutron interferometry, Wheeler’s delayed choice experiment, orbital and intrinsic angular momentum, quantum measurement and Einstein–Podolsky–Rosen nonlocal correlations for orbital angular momentum, intrinsic angular momentum and correlated particle interferometry. Since then, the acceptance of the validity of de Broglie–Bohm theory has steadily grown, as has the interest in the consequences of the approach. For my contribution to the current celebratory volume I was asked to provide a personal review specifically of this novel work within its historical context of the last quarter of the twentieth century. (shrink)

The ontology of Bohmian mechanics includes both the universal wave function and particles. Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated—replaced by a set of single-particle (...) class='Hi'>pilot-wave fields living in ordinary physical space. Such a re-formulation of the Bohmian pilot-wave theory can exactly reproduce the statistical predictions of ordinary quantum theory. But this comes at the rather high ontological price of introducing an infinite network of interacting potential fields which influence the particles’ motion through the pilot-wave fields. We thus introduce an alternative approach which aims at achieving empirical adequacy with a more modest ontological complexity, and provide some preliminary evidence for optimism regarding the program of trying to replace the configuration space wave function with a set of fields in ordinary physical space. (shrink)

Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, (1) Nelson, (2) de Broglie, (3) Guerra et al. (4) ), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm (5) real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations.

It is shown how, starting with the de Broglie–Bohm pilot-wave theory, one can construct a new theory of the sort envisioned by several of QM’s founders: a Theory of Exclusively Local Beables (TELB). In particular, the usual quantum mechanical wave function (a function on a high-dimensional configuration space) is not among the beables posited by the new theory. Instead, each particle has an associated “pilot-wave” field (living in physical space). A number of additional fields (also (...) fields on physical space) maintain what is described, in ordinary quantum theory, as “entanglement.” The theory allows some interesting new perspective on the kind of causation involved in pilot-wave theories in general. And it provides also a concrete example of an empirically viable quantum theory in whose formulation the wave function (on configuration space) does not appear—i.e., it is a theory according to which nothing corresponding to the configuration space wave function need actually exist. That is the theory’s raison d’etre and perhaps its only virtue. Its vices include the fact that it only reproduces the empirical predictions of the ordinary pilot-wave theory (equivalent, of course, to the predictions of ordinary quantum theory) for spinless non-relativistic particles, and only then for wave functions that are everywhere analytic. The goal is thus not to recommend the TELB proposed here as a replacement for ordinary pilot-wave theory (or ordinary quantum theory), but is rather to illustrate (with a crude first stab) that it might be possible to construct a plausible, empirically viable TELB, and to recommend this as an interesting and perhaps-fruitful program for future research. (shrink)

Bell’s inequality is an empirical constrain on theories with hidden variables, which EPR argued are needed to explain observed perfect correlations if keeping locality. One way to deal with the empirical violation of Bell’s inequality is by openly embracing nonlocality, in a theory like the pilot-wave theory. Nonetheless, recent proposals have revived the possibility that one can avoid nonlocality by resorting to superdeterministic theories. These are local hidden variables theories which violate statistical independence which is one assumption of (...) Bell’s inequality. In this paper I compare and contrast these two hidden variable strategies: the pilot-wave theory and superdeterminism. I show that even if the former is nonlocal and the other is not, both are contextual. Nonetheless, in contrast with the pilot-wave theory, superdeterminist contextuality makes it impossible to test the theory (which therefore becomes unfalsifiable and unconfirmable) and renders the theory uninformative (measurement results tell us nothing about the system). It is questionable therefore whether a theory with these features is worth its costs. (shrink)

If one starts from de Broglie's basic relativistic assumptions, i.e., that all particles have an intrinsic real internal vibration in their rest frame, i.e., hv 0 =m 0 c 2 ; that when they are at any one point in space-time the phase of this vibration cannot depend on the choice of the reference frame, then, one can show (following Mackinnon (1) ) that there exists a nondispersive wave packet of de Broglie's waves which can be assimilated to the (...) nonlinear soliton wave U 0 introduced by him in his double solution model of wave mechanics. (2) Since de Broglie's linear pilot waves can be considered to be real waves propagating as collective motions on a covariant subquantum chaotic “aether,” (3) these new solition waves can be considered as describing the particle's immediate neighborhood, i.e., the aether's reaction to the particle's motion in the stochastic interpretation of quantum mechanics. The existence of such a physical aether (which provides a perfectly causal interpretation of the action-a-distance implied by the Einstein-Podolsky-Rosen experiments) can now be proved by establishing the reality of de Broglie's waves in realizable experiments. (shrink)

We present a classical hydrodynamic analog of free relativistic quantum particles inspired by de Broglie’s pilot wave theory and recent developments in hydrodynamic quantum analogs. The proposed model couples a periodically forced Klein–Gordon equation with a nonrelativistic particle dynamics equation. The coupled equations may represent both quantum particles and classical particles driven by the gradients of locally excited Faraday waves. Exact stationary solutions of the coupled system reveal a highly nonlinear mechanism responsible for the self-propulsion of free particles, (...) leading to the onset of unsteady motion. Although the model is essentially nonrelativistic, a stabilizing mechanism for any particle traveling close to the wave signaling speed emerges through the coupling with the wavefield. Consequently, inline particle oscillations comparable to de Broglie’s wavelength are realized through this fully-classical model, suggesting a new classical interpretation for the motion of relativistic quantum particles. (shrink)

The de Broglie–Bohm interpretation is a no-collapse interpretation, which implies that we are in principle surrounded by empty waves generated by all particles of the universe, empty waves that will never collapse. It is common to establish an analogy between these pilot-waves and 3D radio-waves, which are nearly devoided of energy but carry nevertheless information to which we may have access after an amplification process. Here we show that this analogy is limited: if we consider empty waves in configuration (...) space, an effective collapse occurs when a detector clicks and the 3ND empty wave associated to a particle may not influence another particle (even if these two particles are identical, e.g. bosons as in the example considered here). (shrink)

If the energy-absorbing radio-frequency spin-flipping device used in perfect crystal neutron interferometry is an intermediate measuring device, then the experimental results contradict the associated wave packet collapse and support the real existence of the de Broglie pilot waves in both arms while the neutron travels in only one.

In this paper we consider the prehistory of quantum gravity (1916–1930) from two perspectives. First, we investigate how this research field constituted itself and we propose for the first time a red thread to trace its evolution in this earliest period. Second, we focus on a case study: the earliest work of Léon Rosenfeld. In 1927 he tried to merge wave mechanics with general relativity in the context of a five‐dimensional universe. We describe how Oskar Klein, Louis de Broglie, (...) and Théophile De Donder influenced Rosenfeld's work and analyze how and why Rosenfeld attempted to reconcile Einstein's theory with quantum phenomena. We argue that Rosenfeld investigated for the first time the corrections to a classical space‐time metric generated by a quantum source. As far as we know, Rosenfeld's approach has been largely ignored until today: he himself considered it “an accident.” After having reconsidered its connection with de Broglie's ideas and Rosenfeld's interpretation of the wave function in 1927, we argue that Rosenfeld's work can be interpreted as a first attempt to introduce the pilot‐wave theory in the context of quantum gravity and we infer that this was one of the reasons that ruled it out. (shrink)

One of our most sophisticated accounts of objective chance in quantum mechanics involves the Deutsch-Wallace theorem, which uses state-space symmetries to justify agents’ use of the Born rule when the quantum state is known. But Wallace argues that this theorem requires an Everettian approach to measurement. I find that this argument is unsound. I demonstrate a counter-example by applying the Deutsch-Wallace theorem to the de Broglie-Bohm pilot-wave theory.

Nelson’s programme for a stochastic mechanics aims to derive the wave function and the Schroedinger equation from natural conditions on a diffusion process in configuration space. If successful, this pro- gramme might have some advantages over the better-known determin- istic pilot-wave theory of de Broglie and Bohm. The essential points of Nelson’s strategy are reviewed, with particular emphasis on concep- tual issues relating to the role of time symmetry. The main problem in Nelson’s approach is the lack (...) of strict equivalence between the cou- pled Madelung equations and the Schroedinger equation. After a brief discussion, the paper concludes with a possible suggestion for trying to overcome this problem. (shrink)

The 1927 Solvay conference was perhaps the most important meeting in the history of quantum theory. Contrary to popular belief, the interpretation of quantum theory was not settled at this conference, and no consensus was reached. Instead, a range of sharply conflicting views were presented and extensively discussed, including de Broglie's pilot-wave theory, Born and Heisenberg's quantum mechanics, and Schrödinger's wave mechanics. Today, there is no longer an established or dominant interpretation of quantum theory, so it is (...) important to re-evaluate the historical sources and keep the interpretation debate open. This book contains a complete translation of the original proceedings, with background essays on the three main interpretations of quantum theory presented at the conference, and an extensive analysis of the lectures and discussions in the light of current research in the foundations of quantum theory. The proceedings contain much unexpected material, including extensive discussions of de Broglie's pilot-wave theory (which de Broglie presented for a many-body system), and a theory of 'quantum mechanics' apparently lacking in wave function collapse or fundamental time evolution. This book will be of interest to graduate students and researchers in physics and in the history and philosophy of quantum theory. (shrink)

In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path which lies at the heart of the deBroglie-Bohm “ pilot-wave” interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths. This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, (...) and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton–Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized. (shrink)

Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952. It is the simplest example of what is often called a hidden variables interpretation of quantum mechanics. In Bohmian mechanics a system of particles is described in part by its wave function, evolving, as usual, according to Schrödinger's (...) equation. However, the wave function provides only a partial description of the system. This description is completed by the specification of the actual positions of the particles. The latter evolve according to the.. (shrink)

We construct a local \-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state \\rangle \) as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state \\rangle \) which is different from the prepared quantum state \\rangle \) and has an ontic status. The ontic state of a single particle consists (...) of two parts. First, a single particle ontic quantum state \|i\rangle \), where \\) is a 3-space wavepacket and \ is a spin eigenstate of the future measurement setting. Second, a particle position in 3-space \\), which evolves via a de Broglie–Bohm type guidance equation with the 3-space wavepacket \\) acting as a local pilot wave. The joint ontic quantum state \\rangle \) fixes the measurement outcomes deterministically whereas the prepared quantum state \\rangle \) determines the distribution of the \\rangle \)’s over an ensemble. Both \\rangle \) and \\rangle \) evolve via the Schrodinger equation. Our model exactly reproduces the Bell correlations for any pair of measurement settings. We also consider ‘non-equilibrium’ extensions of the model with an arbitrary distribution of hidden variables. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. We argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics. (shrink)

Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, nor the pilot-wave theory, nor stochastic state-reduction theories, give a satisfactory answer to the question of what objective probabilities are in quantum mechanics, or why they should satisfy the Born rule; nor do they give any reason why subjective probabilities should track objective (...) ones. But it is shown that if probability only arises with decoherence, then they must be given by the Born rule. That further, on the Everett interpretation, we have a clear statement of what probabilities are, in terms of purely categorical physical properties; and finally, along lines laid out by Deutsch and Wallace, that there is a clear basis in the axioms of decision theory as to why subjective probabilities should track these objective ones. These results hinge critically on the absence of hidden-variables or any other mechanism (such as state-reduction) from the physical interpretation of the theory. The account of probability has traditionally been considered the principal weakness of the Everett interpretation; on the contrary it emerges as one of its principal strengths. (shrink)

David Lewis is a natural target for those who believe that findings in quantum physics threaten the tenability of traditional metaphysical reductionism. Such philosophers point to allegedly holistic entities they take both to be the subjects of some claims of quantum mechanics and to be incompatible with Lewisian metaphysics. According to one popular argument, the non-separability argument from quantum entanglement, any realist interpretation of quantum theory is straightforwardly inconsistent with the reductive conviction that the complete physical state of the world (...) supervenes on the intrinsic properties of and spatio-temporal relations between its point-sized constituents. Here I defend Lewis's metaphysical doctrine, and traditional reductionism more generally, against this alleged threat from quantum holism. After presenting the non-separability argument from entanglement, I show that Bohmian mechanics, an interpretation of quantum mechanics explicitly recognized as a realist one by proponents of the non-separability argument, plausibly rejects a key premise of that argument. Another holistic worry for Humeanism persists, however, the trouble being the apparently holistic character of the Bohmian pilot wave. I present a Humean strategy for addressing the holistic threat from the pilot wave by drawing on resources from the Humean best system account of laws. (shrink)

Recent philosophical discussions about metaphysical indeterminacy have been substantiated with the idea that quantum mechanics, one of the most successful physical theories in the history of science, provides explicit instances of worldly indefiniteness. Against this background, several philosophers underline that there are alternative formulations of quantum theory in which such indeterminacy has no room and plays no role. A typical example is Bohmian mechanics in virtue of its clear particle ontology. Contrary to these latter claims, this paper aims at showing (...) that different pilot-wave theories do in fact instantiate diverse forms of metaphysical indeterminacy. Namely, I argue that there are various questions about worldly states of affairs that cannot be determined by looking exclusively at their ontologies and dynamical laws. Moreover, it will be claimed that Bohmian mechanics generates a new form of modal indeterminacy. Finally, it will be concluded that ontological clarity and indeterminacy are not mutually exclusive, i.e., the two can coexist in the same theory. (shrink)

This paper lays out a novel proposal about the metaphysical foundations of (non-relativistic) quantum mechanics, which has some elements in common with Everett's “Many Worlds” interpretation and some elements in common with Bohm's ”Pilot Wave” interpretation. The view agrees with the Everettians that the quantum wavefunction can be interpreted be interpreted as a <em>complete</em> description of the world in fundamental terms. But it holds that this truth of this description suffices for the existence of an <em>uncountable</em> plurality of (...) “worlds” of ordinary, non-fundamental objects, where each such “world” corresponds to a mapping of points of time to points of configuration space that obeys that Bohmian “Guidance Equation”. (shrink)

This paper critically discusses an objection proposed by Nikolić against the naturalness of the stochastic dynamics implemented by the Bell-type quantum field theory, an extension of Bohmian mechanics able to describe the phenomena of particles creation and annihilation. Here I present: Nikolić’s ideas for a pilot-wave theory accounting for QFT phenomenology evaluating the robustness of his criticism, Bell’s original proposal for a Bohmian QFT with a particle ontology and the mentioned Bell-type QFT. I will argue that although Bell’s (...) model should be interpreted as a heuristic example showing the possibility to extend Bohm’s pilot-wave theory to the domain of QFT, the same judgement does not hold for the Bell-type QFT, which is candidate to be a promising possible alternative proposal to the standard version of quantum field theory. Finally, contra Nikolić, I will provide arguments in order to show how a stochastic dynamics is perfectly compatible with a Bohmian quantum theory. (shrink)

For scientific realists, quantum mechanics is unsatisfactory because it suffers from the measurement problem. However, there are at least three promising solutions: the pilot-wave theory, the many-worlds theory, and the theory of spontaneous collapse. In this paper I argue that the measurement problem is a false problem for the realist: it was proposed as the last resort to convince the positivists that the theory is not empirically adequate. Instead realists should focus on preserving the reductive explanatory schema that (...) had worked so well in physics before, which requires a theory to have a three-dimensional ontology. Incompleteness argument to this effect have been proposed in the 1920s, but effectively ignored due to the positivistic climate, other unscientific reasons, and theorems which claimed that this project was impossible. When realists re-examined quantum mechanics in the 1950s and later, they happened to focus on the measurement problem. In this paper I speculate on what would have happened if realists instead focused on finding a three-dimensional ontology to complete quantum theory. I show that most paradoxes, puzzles and mysteries connected with quantum mechanics would have never emerge, and that many of what are now considered possible ontological interpretations of the theory would have hardly been taken as viable options. (shrink)

I discuss the idea of relativistic causality, i.e., the requirement that causal processes or signals can propagate only within the light-cone. After briefly locating this requirement in the philosophy of causation, my main aim is to draw philosophers' attention to the fact that it is subtle, indeed problematic, in relativistic quantum physics: there are scenarios in which it seems to fail. I set aside two such scenarios, which are familiar to philosophers of physics: the pilot-wave approach, and the (...) Newton-Wigner representation. I instead stress two unfamiliar scenarios: the Drummond-Hathrell and Scharnhorst effects. These effects also illustrate a general moral in the philosophy of geometry: that the mathematical structures, especially the metric tensor, that represent geometry get their geometric significance by dint of detailed physical arguments. (shrink)

In a recent paper, I have analysed and criticised Leggett and Garg’s argument to the effect that macroscopic realism contradicts quantum mechanics, by contrasting their assumptions to the example of Bell’s stochastic pilot-wave theories, and have applied Dzhafarov and Kujala’s analysis of contextuality in the presence of signalling to the case of the Leggett–Garg inequalities. In this chapter, I discuss more in general the motivations for macroscopic realism, taking a cue from Einstein’s criticism of the Bohm theory, then (...) go on to summarise my previous results, with a few additional comments on other recent work on Leggett and Garg. [To appear in: E. Dzhafarov, Contextuality from Quantum Physics to Psychology.]. (shrink)

We explore the possibility thatzitterbewegung is the key to a complete understanding of the Dirac theory of electrons. We note that a literal interpretation of thezitterbewegung implies that the electron is the seat of an oscillating bound electromagnetic field similar to de Broglie's pilot wave. This opens up new possibilities for explaining two major features of quantum mechanics as consequences of an underlying physical mechanism. On this basis, qualitative explanations are given for electron diffraction, the existence of quantized (...) radiationless states, the Pauli principle, and other features of quantum mechanics. (shrink)

According to Bohmian mechanics, we see the particle, not the pilot wave. But to make predictions we need to know the wave. How do we learn about the wave to make predictions, if we only see the particle? I show that the puzzle can be solved, but only thanks to decoherence.

In this work we develop a time-symmetric soliton theory for quantum particles inspired from works by de Broglie and Bohm. We consider explicitly a non-linear Klein–Gordon theory leading to monopolar oscillating solitons. We show that the theory is able to reproduce the main results of the pilot-wave interpretation for non interacting particles in a external electromagnetic field. In this regime, using the time symmetry of the theory, we are also able to explain quantum entanglement between several solitons and (...) we reproduce the famous pilot-wave nonlocality associated with the de Broglie-Bohm theory. (shrink)

This paper gives a technically elementary treatment of some aspects of Hamilton -Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the optico-mechanical analogy and the transition to quantum mechanics. Finally, I report recent work of Holland providing a Hamiltonian formulation of the pilot-wave theory.

The violation of Bell’s inequality has shown that quantum theory and relativity are in tension: reality is nonlocal. Nonetheless, many have argued that GRW-type theories are to be preferred to pilot-wave theories as they are more compatible with relativity: while relativistic pilot-wave theories require a preferred slicing of space-time, foliation-free relativistic GRW-type theories have been proposed. In this paper I discuss various meanings of ‘relativistic invariance,’ and I show how GRW-type theories, while being more relativistic in (...) one sense, are less relativistic in another. If so, the initial claim that GRW-type theories have a greater compatibility with relativity is unwarranted: both type of theories violate relativity, one way or another. (shrink)

I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite frequentism, in which Gibbs’ concept of an infinite ensemble of gases is replaced by the quantum state expressed as a superposition of a finite number of decohering microstates. It is a form of finite and actual frequentism (as opposed to hypothetical (...) frequentism) insofar as all the microstates exist, in keeping with the decoherence-based Everett interpretation, and some versions of pilot-wave theory. (shrink)