It is hypothesized that de Broglie’s ‘matter waves’ provide a dynamical basis for Minkowski spacetime in an antisubstantivalist or relational account. The relativity of simultaneity is seen as an effect of the de Broglie oscillation together with a basic relativity postulate, while the dispersion relation from finite rest mass gives rise to the differentiation of spatial and temporal axes. Thus spacetime is seen as not fundamental, but rather as emergent from the quantum level. A result by Solov’ev which (...) demonstrates that time is not an applicable concept at the quantum level is adduced in support of this claim. Finally, it is noted that de Broglie waves can be seen as the “bridge of becoming” discussed by ( 2005 ). (shrink)

The author begins by recalling how he was led in 1923–24 to the ideas of wave mechanics in generalizing the ideas of Einstein's theory of light quanta. He made himself at that time a concrete physical picture of the coexistence of waves and particles and, in 1927, attempted to give them precise form in his “theory of the double solution.” As other ideas prevailed at the time, he abandoned the development of his conception. But for the past twenty years, (...) once again convinced, like Einstein, that present-day quantum mechanics is only a statistical theory and does not give a true picture of physical reality, he has again taken up his old ideas and developed them considerably. He has in particular introduced an element of randomness into the theory and has thus attained to a “hidden thermodynamics of particles,” the results of which appear to be very interesting. (shrink)

Now, this is precisely the experimental law of the photo-electric effect in the form which has been verified in succession for all the radiations from the ultra ...

In this paper an attempt is made to interpret inertial mass as a consequence of the invariant periodicity associated with physical de Broglie waves. In the case of a free particle, such waves, observed from an arbitrary reference frame, would exhibit the velocity-dependent wavelength given by de Broglie's relation; and it is conjectured that the inertial and additive properties of mass (or, more precisely, the conservation of momentum and energy) can be related to nonlinear interference effects occurring between (...) the de Broglie waves for different particles. This picture could throw light on the physical meaning of quantization and suggests the possibility of reformulating classical and quantum mechanics in terms of a “quasi-classical” nonlinear field theory in which both inertial and quantization effects result essentially from the periodicity of de Broglie waves. (shrink)

MATTER AND LIGHT The New Physics By LOUIS DE BROGLIE. Originally published in 1937. TRANSLATORS NOTE: THE Author has in certain places modified the original French text for the English translation, for the sake of greater cohesion, and has also revised some passages, in order to bring them into accord with the results of later research. Occasional Translators Notes are shown in square brackets. The chapter on The Undulatory Aspects of the Electron has the special historical interest of having (...) been delivered as a Lecture on the occasion of the Authors receipt of the Nobel Award, while that on Wave Mechanics and its Interpretations was given as an Address at the Glasgow meeting of the British Association in 1928. I am indebted to Dr. J. E. Turner, of the University of Liver pool, for assistance with the translation and the proofs, and to Dr. C. Strachan, of the same University, I am indebted for valuable assistance in dealing with the equations and the more technical passages, as well as for reading the proofs. W. H. J. PREFACE: THE amiable insistence of my friend Andr George has induced me to collect in the present Volume a number of Studies on con temporary Physics written from both the general and the more metaphysical point of view. Each of these Studies forms an inde pendent whole, and can be read by itself. A slight degree of repeti tion which the reader is asked to overlook has been the inevi table result for on more than one occasion I have been compelled to duplicate a summary of the great fundamental stages of con temporary Physics, such as the classification of simple substances, the investigation of the photo-electric effect and the origin of the Theory of Light Quanta and of Wave Mechanics the subjects are somewhat technical, and I cannot well assume that they are common knowledge. But though the same subject is outlined in several of these Studies, I have tried to take up a different point of view in each, and have endeavoured to throw light on different aspects of the essential problems of Quantum Physics in order to facilitate a grasp of their importance. On comparing the different chapters the reader will observe that, while overlapping, they also complement one another and he will feel the fascination and greatness inherent in the vast structure of modern Physics. And while admiring the vast number and the extreme delicacy of experimental facts which laboratory physicists have succeeded in revealing, and the strange and brilliant concepts devised by theorists to explain them, he will appreciate to what a degree the methods and ideas of physicists have grown in subtlety during recent years, and how great has been the progress from the somewhat ingenuous Realism and the over-simplified Mechanics of earlier thinkers. The more deeply we descend into the minutest structures of Matter, the more clearly we see that the concepts evolved by the mind in the course of everyday experience especially those of Time and Space must fail us in an endeavour to describe the new worlds which we are entering. One feels tempted to say that the outlines of our concepts must undergo a progressive blurring, in order that they may retain some semblance of relevance to the realities of the subatomic scales. Time and Space, in other words, are too loose a dress for the elementary entities individuality becomes attenuated in the mysterious pro cesses of interaction, and even Determinism, the darling of an older generation of physicists, is forced to yield... (shrink)

Cet ouvrage offre aux lecteurs une série de monographies consacrées presque toutes à diverses questions de Physique quantique et de Mécanique ondulatoire. Cet ensemble d'essais étudie l'aspect vraiment nouveau que prennent dans la Physique de l'époque le traditionnel dilemme « continu ou discontinu », la classique opposition de l'élément simple et indivisible avec le continu étendu et divisible. Ces réflexions, révolutionnaires à l'époque, restent aujourd'hui encore d'une étonnante modernité. Dans la science moderne, l'élément simple et indivisible, c'est le grain, grain (...) de matière ou grain de lumière, neutron, électron ou photon. Par contre, dans les théories nouvelles comme dans les anciennes, l'étendue continue et divisible, c'est essentiellement le champ, c'est-à-dire l'ensemble des propriétés physiques qui caractérisent à chaque instant les divers points de l'espace et qui s'expriment par des fonctions généralement continues des coordonnées d'espace et de temps. Mais les conceptions antinomiques de grain et de champ doivent nécessairement en fin de compte venir à la rencontre l'une de l'autre puisqu'elles doivent trouver leur place côte à côte dans le cadre de la Physique totale. Comment les concilier? (shrink)

The general properties of measurements in microphysics are studied and the three types of probabilities that, according to the authors, appear in wave mechanics are set up. Such a distinction, together with the principle of the localization of the corpuscle as was laid down at the very introduction of the theory of the double solution, provides a good grasp of certain phenomena whose explanation according to the usual theory (which makes no use of permanent localization and where the three (...) types of probabilities are intermingled) leads to paradoxical or self-contradictory situations. (shrink)

A simple stationary state is set up by combining the two de Broglie waves from two particles traveling in one direction with equal and opposite velocities. By considering the waves forming this state from the point of view of all possible observers moving in the same direction, it is shown that the basic standing wave pattern does not alter, but that the particle will be confined to a small region stationary relative to this pattern. This region is similar (...) in extent to that confining a free particle, the natural internal frequency of the particle being raised. This agrees with previous suggestions that a particle in a stationary state without angular momentum is stationary. (shrink)

La physique moderne et l'oeuvre de Fresnel.--Ondes et corpuscules dans la physique actuelle.--La crise récente le l'optique ondulatoire.--Comme la lumière les électrons peuvent interférer.--Déterminisme et causalité dans la physique contemporaine.

It is assumed that the motion of a particle in spacetime does not depend on the motion relative to it of any observer or of any frame of reference. Thus if the particle has an internal vibration of the type hypothesized by de Broglie, the phase of that vibration at any point in spacetime must appear to be the same to all observers, i.e., the same in all frames of reference. Each observer or reference frame will have its own (...) de Broglie wave for the particle. The phase of the particle's vibration must, by definition, be the same as that of all possible de Broglie waves at the point where the particle is. By superimposing all these possible de Broglie waves, a wave packet is formed centered in space on the particle. The formation of such a packet is discussed with the help of spacetime diagrams; the packet does not spread with time. The relevance of this packet to the wave mechanics of Schrödinger is discussed; it is also pointed out that any vibration can lead to such a packet. (shrink)

Relative motion of particles is examined in the context of relational space-time. It is shown that de Broglie waves may be derived as a representation of the coordinate maps between the rest-frames of these particles. Energy and momentum are not absolute characteristics of these particles, they are understood as parameters of the coordinate maps between their rest-frames. It is also demonstrated the position of a particle is not an absolute, it is contingent on the frame of reference used to (...) observe the particle. (shrink)

The geometrical structures implicit in the de Broglie waves associated with a relativistic charged scalar quantum mechanical particle in an external field are analyzed by employing the ray concept of the causal interpretation. It is shown how an osculating Finslerian metric tensor, a torsion tensor, and a tetrad field define respectively the strain, the dislocation density, and the Burgers vector in the “natural state” of the wave, which is a non-Riemannian space of distant parallelism. A quantum torque determined (...) by the quantum potential is introduced and the example of a screw dislocated wave is discussed. (shrink)

The concept of the de Broglie wave as an electromagnetic wave of a special kind is examined. Natural and ensemble coherence lengths are defined. Using these concepts, two experiments with neutrons are considered. The first experiment(22) is concerned with interferences of the neutron de Broglie waves for neutrons propagating in moving matter. The second experiment(23) is a diffraction experiment on neutron optical test of nonlinear wave mechanics. Finally, a short description of a proposed Young's experiment (...) with ultra cold neutrons is given. (shrink)

Based on de Broglie’s wave hypothesis and the covariant ether, the Three Wave Hypothesis (TWH) has been proposed and developed in the last century. In 2007, the author found that the TWH may be attributed to a kinematical classical system of two perpendicular rolling circles. In 2012, the author showed that the position vector of a point in a model of two rolling circles in plane can be transformed to a complex vector under a proposed effect of (...) partial observation. In the present project, this concept of transformation is developed to be a lab observation concept. Under this transformation of the lab observer, it is found that velocity equation of the motion of the point is transformed to an equation analogising the relativistic quantum mechanics equation (Dirac equation). Many other analogies has been found, and are listed in a comparison table. The analogy tries to explain the entanglement within the scope of the transformation. These analogies may suggest that both quantum mechanics and special relativity are emergent, both of them are unified, and of the same origin. The similarities suggest analogies and propose questions of interpretation for the standard quantum theory, without any possible causal claims. (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.

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.

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)

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)

In the early 1960s of the 20th century de Broglie was able to explain the cosmological observable red shift, without ad hoc assumptions. Starting from basic quantum considerations he developed his tired light model for the photon. This model explains in a single and beautiful causal way the cosmological redshift without need of assuming the Big Bang and consequently a beginning for the universe. Evidence coming from Earth sciences seems also to confirm these ideas and furthermore concrete proposal of (...) laboratorial scale experiments that can test the model are reviewed. (shrink)

Mandel and Pfleegor have shown the existence of interference effects produced by the superposition of two independent single-mode lasers even under conditions in which one photon is absorbed before the next is emitted by one or the other source. We propose here a modification of their experiment which would establish (if the interferences persist) the simultaneous existence of waves and particles (photons), a result which is assumed as basis by the stochastic interpretation of quantum mechanics.

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)

Recent double-slit type neutron experiments (1) and their theoretical implications (2) suggest that, since one can tell through which slit the individual neutrons travel, coherent wave packets remain nonlocally coupled (with particles one by one), even in the case of wide spatial separation. Following de Broglie's initial proposal, (3) this property can be derived from the existence of the persisting action of real superluminal physical phase waves considered as building blocks of the real subluminal wave field packets (...) which surround individual particle paths in the Einstein-de Broglie-Bohm interpretation of quantum mechanics. (shrink)

We present here solutions of a non-linear Schrödinger equation in presence of an arbitrary linear external potential. The non-linearity expresses a self-focusing interaction. These solutions are the product of the pilot wave with peaked solitons the velocity of which obeys the guidance equation derived by Louis de Broglie in 1926. The degree of validity of our approximations increases when the size of the soliton decreases and becomes negligible compared to the typical size over which the pilot wave (...) varies. We discuss the possibility to reveal their existence by implementing a humpty-dumpty Stern-Gerlach interferometer in the mesoscopic regime. (shrink)

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)

We provide the construction of a de Broglie–Bohm model of the N-body system within the framework of Pure Shape Dynamics. The equation of state of the curve in shape space is worked out, with the instantaneous shape being guided by a wave function. In order to get a better understanding of the dynamical system, we also give some numerical analysis of the 3-body case. Remarkably enough, our simulations typically show the attractor-driven behaviour of complexity, well known in the (...) classical case, thereby providing further evidence for the claim that the arrow of complexity is the ultimate cause of the experienced arrow of time. (shrink)

This article discusses the historical similarities and differences between Schroedinger's and de Broglie's ideas on wave mechanics and gives a biographical account of their scientific relationship. Their arguments over questions such as quantum jumps, the viability of particles within wave mechanics theory, and the inclusion of space, time, and relativity in quantum mechanics are analyzed. The final section of the paper considers the overall role of Schroedinger's ideas in modern quantum mechanics.

This paper is devoted to an analysis of the intellectual itinerary of Louis de Broglie, from the discovery of wave mechanics, until today. Essential attention is paid to the fact that this itinerary is far from being linear, since after a first attempt to develop his own views on wave mechanics through the theory of singular waves, Louis de Broglie abandoned it for twenty five years, under the influence of the Copenhagen School (even embracing the conceptions (...) of the latter), until the beginning of the fifties, when he definitively came back to his primary theory. This evolution of the Louis de Broglie's views on wave mechanics is told here and explained through an analysis of the evolution of all of quantum mechanics and, more generally, the dominating conceptions of theoretical physics in our century.This paper is written in a quite personal form, which is not exactly one to which the readers of scientific journals are accustomed, because it reproduces, in fact, the preface of a book (to be published) of Louis de Broglie, which is precisely devoted to the fundamental problems of quantum mechanics and closely linked to the second turnabout of the author. (shrink)

The purpose of this contribution is to examine the current state of the de Broglie-Bohm theory (dBB) in light of Bohm’s vision as he explicitly set it out in his book Quantum theory [In Bohm, D., Quantum theory, Courier corporation, (1961b)]. In particular, two programmes that differ in many crucial respects are currently being pursued. On the one hand, the Bohmian mechanics school, founded by Dürr Goldstein and Zanghì, considers the theory to be Galilean invariant, regards particles’ motion as (...) determined by a nomological entity, the universal wave function, upholds the quantum equilibrium hypothesis and explains probabilities in terms of typicality. On the other hand, the Pilot-wave school advocated by Valentini considers the theory to be based on Aristotelian dynamics, regards the wave function as a physical field displaying a contingent nature, and explains quantum equilibrium as the result of a process of relaxation from quantum non-equilibrium. Looking at Bohm’s work [In Bohm, D., Quantum theory, Courier corporation, (1961b)], it is clear that his intention was to construct a theory that was empirically different from standard quantum mechanics, so that it would be testable and falsifiable. Only this way could he defend dBB from the criticism that accused the theory of being 'metaphysical'. These methodological concerns about the falsifiability of the theory constitute, in my opinion, a strong reason for regarding Valentini's programme as methodologically valuable, even if it might turn out to be wrong. Indeed, the programme of the Pilot-wave school aims to be falsifiable with respect to standard quantum mechanics and can in principle defend the empirical status of particle trajectories. (shrink)

We investigate the validity of the field explanation of the wave function by analyzing the mass and charge density distributions of a quantum system. It is argued that a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. This is also a consequence of protective measurement. If the wave function is a physical field, then the mass and charge density will be distributed (...) in space simultaneously for a charged quantum system, and thus there will exist a remarkable electrostatic self-interaction of its wave function, though the gravitational self-interaction is too weak to be detected presently. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus we conclude that the wave function cannot be a description of a physical field. In the second part of this paper, we further analyze the implications of these results for the main realistic interpretations of quantum mechanics, especially for de Broglie-Bohm theory. It has been argued that de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wave function, regarded as a Ψ-field, has no mass and charge density distributions, which turns out to be wrong according to the above results. For a charged quantum system, both Ψ-field and Bohmian particle have charge density distribution. This then results in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which contradicts both the predictions of quantum mechanics and experimental observations. Therefore, de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is probably wrong. Lastly, we suggest that the wave function is a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles, and we also briefly analyze the implications of this suggestion for other realistic interpretations of quantum mechanics including many-worlds interpretation and dynamical collapse theories. (shrink)

There are three possible interpretations of the wave function in the de Broglie-Bohm theory: taking the wave function as corresponding to a physical entity or a property of the Bohmian particles or a law. In this paper, we argue that the first interpretation is favored by an analysis of protective measurements.

In an attempt to explore further the Madelung fluid-like representation of quantum mechanics, we derive the small perturbation equations of the fluid with respect to its basic states. The latter are obtained from the Madelung transform of the Schrödinger equation eigenstates. The fundamental eigenstates of de Broglie monochromatic matter waves are then shown to be mapped into the simple basic states of a fluid with constant density and velocity, where the latter is the de Broglie group velocity. The (...) normal modes with respect to these basic states are derived and found to also satisfy the de Broglie dispersion relation. Despite being dispersive waves, their propagation mechanism is equivalent to that of sound waves in a classical ideal adiabatic gas. We discuss the physical interpretation of these results. (shrink)

A salient feature of de Broglie-Bohm quantum theory is that particles have determinate positions at all times and in all physical contexts. Hence, the trajectory of a particle is a well-defined concept. One then may expect that the closely related notion of inertial trajectory is also unproblematically defined. I show that this expectation is not met. I provide a framework that deploys six different ways in which dBB theory can be interpreted, and I state that only in the canonical (...) interpretation the concept of inertial trajectory is the customary one. However, in this interpretation the description of the dynamical interaction between the pilot-wave and the particles, which is crucial to distinguish inertial from non-inertial trajectories, is affected by serious difficulties, so other readings of the theory intend to avoid them. I show that in the alternative interpretations the concept at issue gets either drastically altered, or plainly undefined. I also spell out further conceptual difficulties that are associated to the redefinitions of inertial trajectories, or to the absence of the concept. (shrink)

An experimental apparatus based on neutron interferometry is is presented which can in principle decide the question whether the empty waves of de Broglie really exist or not.

Pure shape dynamics (PSD) is a novel implementation of the relational framework originally proposed by Julian Barbour and Bruno Bertotti. PSD represents a Leibnizian/Machian approach to physics in that it completely describes the dynamical evolution of a physical system without resorting to any structure external to the system itself. The chapter discusses how PSD effectively describes a de Broglie-Bohm N-body system and the conceptual benefits of such a relational description. The analysis will highlight the new directions in the quest (...) for an understanding of the nature of the wave function that are opened up by a modern relationalist elaboration on de Broglie's and Bohm's original insights. (shrink)

We investigate the implications of protective measurement for de Broglie-Bohm theory, mainly focusing on the interpretation of the wave function. It has been argued that the de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wave function, regarded as a Ψ-field, has no mass and charge density distributions. But this premise turns out to be wrong according to protective measurement; (...) a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. Then in the de Broglie-Bohm theory both Ψ-field and Bohmian particle will have charge density distribution for a charged quantum system. This will result in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Therefore, the de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is problematic according to protective measurement. Lastly, we briefly discuss the possibility that the wave function is not a physical field but a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles. (shrink)

This paper investigates dynamical relaxation to quantum equilibrium in the stochastic de Broglie–Bohm–Bell formulation of quantum mechanics. The time-dependent probability distributions are computed as in a Markov process with slowly varying transition matrices. Numerical simulations, supported by exact results for the large-time behavior of sequences of (slowly varying) transition matrices, confirm previous findings that indicate that de Broglie–Bohm–Bell dynamics allows an arbitrary initial probability distribution to relax to quantum equilibrium; i.e., there is no need to make the ad-hoc (...) assumption that the initial distribution of particle locations has to be identical to the initial probability distribution prescribed by the system’s initial wave function. The results presented in this paper moreover suggest that the intrinsically stochastic nature of Bell’s formulation, which is arguable most naturally formulated on an underlying discrete space-time, is sufficient to ensure dynamical relaxation to quantum equilibrium for a large class of quantum systems without the need to introduce coarse-graining or any other modification in the formulation. (shrink)

We show that the de Broglie-Bohm theory is inconsistent with the established parts of quantum mechanics concerning its physical content. According to the de Broglie-Bohm theory, the mass and charge of an electron are localized in a position where its Bohmian particle is. However, protective measurement implies that they are not localized in one position but distributed throughout space, and the mass and charge density of the electron in each position is proportional to the modulus square of its (...) wave function there. (shrink)

It is shown that the fact that an electron diffraction or interference pattern is not dependent on observer movement may be explained by de Broglie's phase waves, but cannot be explained by Schrödinger waves.