Bohmian Research Articles

The superfluid vacuum and the neural nature of the Universe

Recent experiments seem to confirm the Bohmian interpretation of quantum mechanics by supporting the hypothesis of the existence of what Bohm called "pilot waves”, but numerous clues coming from the world of scientific research, suggest the existence of what Prigogine identified as the "world behind the scenes" that seems to underlie quantum phenomena; in particular, life related phenomena have anti-entropic behaviors opposite to those typical of classical thermodynamics, showing increases in the degree of order coexisting with the absorption of energy from the environment. If we limited ourselves to the physics of the macroscopic world, except not wanting to admit the existence of "delayed potentials" or "feedbacks" that travel in the opposite direction to that of propagation of the phenomenon, or even through an inversion of the "cause- effect" and of time, as proposed by the "syntropic”mechanism theorized by Luigi Fantappié, it is necessary to look elsewhere for the origin of these behaviors. In this article, starting from recent studies on the superfluid nature of vacuum , taking into account the possibility of a description of polar superfluids through an Ising model, or through a Spin Glass model, and the relative connection of these mathematical models with Hopfield's neural networks, the possibility is suggested that quantum phenomena are connected to an emergent behavior of the void that can be explained through its intrinsic dynamic behavior that can be described with neural mathematical models. In other words, a neural nature of the superfluid vacuum is proposed, and the consequences of this hypothesis are examined.

Complex Quantum Hydrodynamics in Momentum Space with Broken Time-Reversal Symmetry

Shortly after Schrödinger’s wave mechanics in terms of complex wave functions was published, Madelung formulated this theory in terms of two real hydrodynamic-like equations. This version is also the formal basis of Bohmian mechanics, albeit with a different ontological interpretation. A point of criticism raised by Pauli against Bohmian mechanics is its missing symmetry between position and momentum that is present in classical phase space as well as in the quantum mechanical position and momentum representations. Both Madelung’s quantum hydrodynamics formulation and Bohmian mechanics are usually expressed only in position space. Recently, with the use of complex quantities, we were able to provide a hydrodynamic formulation also in momentum space. In this paper, we extend this formalism to include dissipative systems with broken time-reversal symmetry. In classical Hamiltonian mechanics and conventional quantum mechanics, closed systems with reversible time-evolution are usually considered. Extending the discussion to include open systems with dissipation, another form of symmetry is broken, that under time-reversal. There are different ways of describing such systems; for instance, Langevin and Fokker–Planck-type equations are commonly used in classical physics. We now investigate how these aspects can be incorporated into our complex hydrodynamic description and what modifications occur in the corresponding equations, not only in position, but particularly in momentum space.

On the Existence of a Preserved Ontology Posited by a High-Dimensional Bohmian Interpretation

AbstractIt has been argued that in the context of Bohm’s approach to quantum mechanics, the postulation of a three-dimensional ontology (as opposed to a high-dimensional one) is presumed to be the only interpretation that may reliably support object-oriented realism by virtue of the fact that this ontology is approximately preserved through scientific change, at least in the classical–quantum transition. Based on an interpretative analysis of the Bohmian formulation, I shall critically evaluate the tenability of this argument. In so doing, I shall argue that this formulation admits the postulation of an alternative ontology that is properly defined in a high-dimensional space, and is approximately preserved among this transition. As a result, both the three-dimensional and the high-dimensional worldviews shall form the basis of an equally reliable endorsement of object-oriented realism in the context of the Bohmian framework. I shall conclude that this argument becomes a problem of metaphysical underdetermination between a three and a high-dimensional Bohmian interpretation.

On a Reformulation of Bohmian Mechanics Including Open Dissipative Systems

In Bohmian mechanics it is assumed that quantum objects are particles that follow real physical paths. These Bohmian trajectories are obtained by integrating the velocity field that occurs in the continuity equation. However, in the course of deriving these trajectories, the independent position variable x, appearing in the velocity field, is arbtirarily replaced by the time-dependent trajectory q(t). We show under which restrictions such a replacement can be justified, leading to a totally different interpretation of the Bohmian trajectories. They are not real paths of physical particles but borders of regions of constant probability, so-called quantiles, and therefore must be seen in the context of descriptive statistics. Thus they provide a tool complementary to the conventional statistical formulation of quantum mechanics. A possible extension to include open dissipative systems is also discussed, showing that the inclusion of an environment does not change our interpretation of the Bohmian trajectories.

Determinism in hidden variable interpretation and Turings halting problem

Heisenberg deduced the famous uncertainty principle which shows that there exist several conjugated quantities that can never be measured precisely at the same time. Further, Copenhagen interpretation gives a new perspective about quantum mechanics, which claims that particles do not have properties like position or momentum until people measure it. Hence, the famous EPR paradox was proposed to question the realism and locality of Quantum mechanics, which leads to the Hidden Variable explanation. However, this theorem was proved wrong by John Bell in 1964 with Bell Inequality. In addition, Hidden Variable Interpretation was developed by De Broglie and Bohm, they came up with the Bohmian Mechanics, which can be considered as Non-local Hidden Variable theorem. This interpretation gives physical meaning to waves. Unlike Copenhagen Interpretation, this theorem claims that particles do have a determined position. Some people may argue that it can be proved contradicted by using the Turing method (self-reference). Because if the algorithm represented by physics law described Hidden Mechanics to determine particles state, then the future is determined and predictable. Therefore, another algorithm can be established based on that, which will lead to Liar Paradox. This article will briefly introduce the uncertainty principle and some interpretations about quantum mechanics. Furthermore, this article will combine some ideas in Alan Turings Halting Problem to the universe of non-local hidden variables as a thought experiment, which involve self-reference, to give an interesting result of locality and determinism.

Neo-Aristotelian Metaphysics and the Theology of Nature edited by William M.R. Simpson, Robert C. Koons, and James Orr, Routledge, 2022, pp. 446, £118.82, hbk

Neo-Aristotelian Metaphysics and the Theology of Nature edited by William M.R. Simpson, Robert C. Koons, and James Orr, Routledge, 2022, pp. 446, £118.82, hbk

Reconstructing the multiphoton spatial wave function with coincidence wave-front sensing

The quantum wave function of multiple particles provides additional information which is inaccessible to detectors working alone. Here, we introduce the coincidence wavefront sensing (CWS) method to reconstruct the phase of the multiphoton transverse spatial wave function. The spatially resolved coincidence photon counting is involved. Numerical simulations of two-photon cases using the weak measurement wavefront sensor are performed to test its correctness, and the phase information hidden in the correlation are revealed. Our work provides a direct spatial way to characterize multipartite quantum systems, and leads to fundamental studies like experimental Bohmian mechanics and applications in quantum optical technologies.

Dynamic core-electron-polarization effect on the high-order harmonic generation process from a quantum-trajectory perspective

It is argued that the dynamic core-electron polarization (DCEP) in polar molecules primarily affects harmonic processes at the ionization step only. This manifestation can also be understood in view of the strong-field assumption that the parent ion's potential becomes irrelevant when the electron is accelerated in the continuum-energy region. However, the scenario becomes vastly different, especially in the case of long-wavelength lasers as shown in this paper, where we demonstrate a complete physical picture of the DCEP on the harmonic process from asymmetric carbon monoxide (CO) molecules comprising the propagation step. To do so, we develop a visualization method for the harmonic process with and without DCEP based on Bohmian mechanics. As tracer particles evolving along quantum trajectories, Bohmian trajectories provide an intuitive picture of the ``harmonic process from the CO molecules. Remarkably, when the change of the harmonic intensity with respect to the DCEP inclusion cannot be explained by the instantaneous ionization rate, the Bohmian trajectories can attribute this change to the difference in the number of returning events and returning time of the electron after the propagation stage. By analyzing the dynamics of individual Bohmian trajectories (the acceleration and the time-frequency profile), we show that the DCEP alters nonlocally the innermost trajectories, which encode all the dynamics of the harmonic process. This insight into the DCEP effect necessitates a careful reinvestigation into other strong-field physics theories on the role of the target over the propagation stage.

Countering a fundamental law of attraction with quantum wave-packet engineering

Bohmian mechanics was designed to give rise to predictions identical to those derived by standard quantum mechanics, while invoking a specific interpretation of it - one which allows the classical notion of a particle to be maintained alongside a guiding wave. For this, the Bohmian model makes use of a unique quantum potential which governs the trajectory of the particle. In this work we show that this interpretation of quantum theory naturally leads to the derivation of interesting new phenomena. Specifically, we demonstrate how the fundamental Casimir-Polder force, by which atoms are attracted to a surface, may be temporarily suppressed by utilizing a specially designed quantum potential. We show that when harnessing the quantum potential via a suitable atomic wavepacket engineering, the absorption by the surface can be dramatically reduced. This is proven both analytically and numerically. Finally, an experimental scheme is proposed for achieving the required shape for the atomic wavepacket. All these may enable new insights into Bohmian mechanics as well as new applications to metrology and sensing.

A Compact Derivation of Quantum Potential in de Broglie–Bohm Theory

In the stochastic electrodynamics, various quantum effects on particles are supposed to emerge from the interactions of the particles with the fluctuating background field. We have adopted the same supposition and further supposed that the quantum potential arises from the velocity fluctuations of particles around their local averages. Based on these suppositions we have derived the expression of the quantum potential in the framework of de Broglie–Bohm theory, which is a reformulation of Schrödinger’s. Thus we are allowed to use the wave functions and Schrödinger operators explicitly so that we have been able to derive the quantum potential in simpler and more compact manner as compared with the stochastic electrodynamics’s. A new hydrodynamical version of Schrödinger equation is also presented, which has been found in the course of our study.

Can a Bohmian be a Rovellian for all practical purposes?

The aim of this article is to discuss the preferred basis problem in relational quantum mechanics (RQM). The issue is at the heart of quantum mechanics and we first show that the mathematical formalism of RQM is immune to recent critics concerning consistency. Moreover, we also analyse the notion of interaction in RQM and provide a for all practical purposes reading of RQM comparing it with Bohmian mechanics.

Quantum Solitodynamics: Non-linear Wave Mechanics and Pilot-Wave Theory

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.

Chaos In 2D Bohmian Trajectories of Commensurate Harmonics Oscillators

Particle trajectories guided by the wave function are well-defined through Bohmian mechanics, which is a causal interpretation of quantum mechanics. Periodic and chaotic behaviours could be exhibited from the certain classical integrable systems that have been shown within this framework. In this study, we developed Mathematica programs to plot the Bohmian trajectories and Lyapunov exponents. These programs serve as computer experiments for numerical generation and illustration of the results. We show that the behaviours of commensurate two-dimensional harmonic oscillator systems are dependent on ratios of frequency.

An extension of many-interacting-worlds method on non-Guassian model

Discussions about whether quantum theory is determinism or indeterminism has lasted for a century. A new approach to standard quantum mechanics called many-interacting-worlds method based on many-worlds interpretation and de Broglie–Bohm mechanics provided the possibility to demonstrate probability from deterministic universe. The many-interacting-worlds method has been proved successful in the ground state of harmonic oscillator. In this article we extend this method to one dimensional Coulomb potential and construct a corresponding empirical density function. We also provide a theoretical proof of the convergence of density function. Our numerical simulation of one dimensional Coulomb potential in the first excited state obtains the consistent result with standard quantum mechanics and shows the applicability of many-interacting-worlds method. This research provides the possibility to extend many-interacting-worlds method to non-Gaussian quantum systems.

Semiclassical trajectories in the double-slit experiment

We provide a semiclassical description of the double-slit experiment given by the momentous quantum mechanics. This formulation allows the study of quantum systems by an effective augmented Hamiltonian. The use of canonical variables enables us to comprise all the quantum information into a finite system of equations. We show the evolution of individual particles and their semiclassical trajectories, and how their collective behavior seems to reproduce the well-known quantum interference pattern. We are able to follow the individual evolution of each particle and its interaction with the effective quantum potential, showing that, contrary to the non-crossing rule present in Bohmian mechanics, particle trajectories actually cross each other in our description. By discussing the quantum-effective potential obtained, we mention possible extensions and applications to other areas.

Perspectives on determinism in quantum mechanics: Born, Bohm, and the "Quantal Newtonian" laws.

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen-Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a "probability amplitude." A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or "Quantal Newtonian" Laws obeyed by each electron. These Laws, derived from the temporal and stationary-state Schrödinger equation, are interpreted in terms of "classical" fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. According to the Second Law, each electron experiences an external field-the quantal Coulomb-Lorentz law. It also experiences an internal field representative of properties of the system: correlations due to Coulomb repulsion and Pauli principle; the density; kinetic effects; and an internal magnetic field component. There is a response field. The First Law states that the sum of the external and internal fields experienced by each electron vanishes. These fields are akin to those of classical physics: They pervade all space; their structure is descriptive of the quantum system; the energy of the system is stored in these fields. It is in the classical behavior of these fields, which arise from quantal sources that one may then speak of determinism in quantum mechanics.

Do(es the Influence of) Empty Waves Survive in Configuration Space?

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).

The Point of Primitive Ontology

Bohmian mechanics grounds the predictions of quantum mechanics in precise dynamical laws for a primitive ontology of point particles. In an appraisal of the de-Broglie-Bohm theory, the paper discusses the crucial epistemological and conceptual role that a primitive ontology plays within a physical theory. It argues that quantum theories without primitive ontology fail to make contact with observable reality in a clear and consistent manner. Finally, it discusses Einstein's epistemological model and why it supports the primitive ontology approach.

The Identification of Mean Quantum Potential with Fisher Information Leads to a Strong Uncertainty Relation

The Cramer-Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show that the identification of the mean quantum potential, an important notion in Bohmian mechanics, with the Fisher information, leads, through the Cramer-Rao bound, to an uncertainty principle which is stronger, in general, than both Heisenberg and Robertson-Schrodinger uncertainty relations, allowing to experimentally test the validity of such an identification.

A Proposed Interpretation of the Wave-Particle Duality.

Within the framework of quantum mechanics, the wave function squared describes the probability density of particles. In this article, another description of the wave function is given which embeds quantum mechanics into the traditional fields of physics, thus making new interpretations dispensable. The new concept is based on the idea that each microscopic particle with non-vanishing rest mass is accompanied by a matter wave, which is formed by adjusting the phases of the vacuum fluctuations in the vicinity of the vibrating particle. The vibrations of the particle and wave are phase-coupled. Particles move on continuous approximately classical trajectories. By the phase coupling mechanism, the particle transfers the information on its kinematics and thus also on the external potential to the wave. The space dependence of the escorting wave turns out to be equal to the wave function. The new concept fundamentally differs from the pilot wave concept of Bohmian mechanics.