Search Results (53)

We analyze the formal equivalence between the electromagnetic energy conservation law derived from Maxwell’s equations in an optical microcavity and the conservation of a probability fluid associated with the de Broglie–Bohm theory for an effective massive particle describing a photon in this cavity. This work is part of a critical analysis of recent experiments by Sharoglazova et al. carried out with a view to refuting the de Broglie–Bohm theory. Furthermore, the consequences of our analysis for microphotonics go far beyond these experiments. In particular, extensions that take into account photon spin and stochastic aspects associated with radiative or absorption losses are considered. From the point of view of symmetries and probability current, here the effective photon behaves like a spin-1/2 particle. Full article

We show that loophole-free Bell-type no-go theorems cannot be derived in theories involving local hidden fields. At the time of measurement, a contextuality loophole appears because each particle’s electromagnetic field interacts with the field of its respective apparatus, preventing the expression of the probability density as a function independent of the orientation of the measuring devices. Then, we use the dynamical evolution of the probability distribution to show that the spin-correlation integral cannot be expressed in terms of initial Cauchy data restricted to the particles. A measurement independence loophole ensues, which prevents the usage of the non-contextual correlation integrals required to demonstrate the CHSH-Bell inequality. We propose that correlated fields are the missing hidden variable triggering the coupled nonlinear oscillations of the particles, which bring about the synchronicities observed in the Einstein–Podolsky–Rosen–Bohm (EPRB) experiment. Full article

A remarkable feature of manifestly covariant quantum gravity theory (CQG-theory) is represented by its unconstrained Hamiltonian structure expressed in evolution form. This permits the identification of the corresponding dynamical evolution parameter advancing the quantum-wave equation for the $4-$scalar quantum wave function defined on an appropriate Hilbert space. In the framework of CQG-theory, such a temporal parameter is represented by a $4-$scalar proper time s identifying a canonical variable with conjugate quantum operator. The observable character of the evolution parameter is also established through its correspondence with the quantum representation of the cosmological constant originating from non-linear Bohm quantum–vacuum interaction, which is shown to admit an intrinsic functional dependence on s. These conclusions overcome the conceptual limitations about the so-called “problem of time” mentioned in alternative approaches to quantum gravity available in the literature. Hence, the outcome permits one to promote CQG theory as a viable mathematical setting for the establishment of a theory of quantum gravity consistent with the logical and physical principles of both general relativity and canonical quantum mechanics. Full article

In this work celebrating the centenary of quantum mechanics, we review the principles of the de Broglie–Bohm theory (dBB), also known as pilot-wave theory. We assess the most common reading of it (the Nomological interpretation based on the notion of primitive ontology in tridimensional space) and defend instead a more causal and pluralistic approach, drawing on classical analogies with optics and hydrodynamics. Within this framework, we review some of the approaches exploiting mechanical analogies to overcome the limitations of the current dBB theory and perhaps quantum mechanics itself. Full article

In the framework of the quantum theory of many-particle systems, we study the compatibility of approximated non-equilibrium Green’s functions (NEGFs) and of approximated solutions of the Dyson equation with a modified continuity equation of the form ${\partial }_t⟨\rho ⟩+(1-\gamma )\nabla ·⟨\mathbf{J}⟩=0$. A continuity equation of this kind allows the e.m. coupling of the system in the extended Aharonov–Bohm electrodynamics, but not in Maxwell electrodynamics. Focusing on the case of molecular junctions simulated numerically with the Density Functional Theory (DFT), we further discuss the re-definition of local current density proposed by Wang et al., which also turns out to be compatible with the extended Aharonov–Bohm electrodynamics. Full article

In the de Broglie Bohm pilot-wave theory and the many-worlds interpretation, unitary development of the quantum state is universally valid. They differ in that de Broglie and Bohm assumed that there are point particles with positions that evolve in time and that our observations are observations of the particles. The many-worlds interpretation is based on the fact that the quantum state can explain our observations. Both interpretations rely on the decoherence mechanism to explain the disappearance of interference effects at a measurement. From this fact, it is argued that for the pilot-wave theory to work, circumstances must be such that the many-worlds interpretation is a viable alternative. However, if this is the case, the de Broglie–Bohm particles become irrelevant to any observer. They are truly hidden. The violation of locality and the corresponding violation of Lorenz invariance are good reasons to believe that dBB particles do not exist. Full article

In this work, we present a new theoretical approach to interpreting and reproducing quantum mechanics using trajectory-guided wavelets. Inspired by the 1925 work of Louis de Broglie, we demonstrate that pulses composed of a difference between a delayed wave and an advanced wave (known as antisymmetric waves) are capable of following quantum trajectories predicted by the de Broglie–Bohm theory (also known as Bohmian mechanics). Our theory reproduces the main results of orthodox quantum mechanics and unlike Bohmian theory, is local in the Bell sense. We show that this is linked to the superdeterminism and past–future (anti)symmetry of our theory. Full article

Einstein’s 1919 distinction between “principle theories” and ”constructive theories” has been applied by Jeffrey Bub to classify the Copenhagen interpretation of quantum mechanics (QM) as a principle theory agree with this classification. Additionally, I argue that Bohm’s interpretation of QM fits Einstein’s concept of a constructive theory. Principle theories include empirically established laws or principles, such as the first and second laws of thermodynamics or the principles of special relativity, including the Born Rule of QM. According to Einstein, principle theories offer ”security in their foundations and logical perfection”. However, ultimate understanding requires constructive theories, which build complex phenomena from simpler models. Constructive theories provide intelligible models of physical phenomena. Bohm’s QM, with its added microstructure, presents such a model. In this framework, quantum phenomena appear from statistical ensembles of microparticles in motion, with deterministic particle trajectories guided by the wave function. This reveals how Bohm’s account offers a constructive model for understanding quantum phenomena. Full article

In this work, we analyze recent proposals by Das and Dürr (DD) to measure the arrival time distributions of quantum particles within the framework of de Broglie Bohm theory (or Bohmian mechanics). We also analyze the criticisms made by Goldstein Tumulka and Zanghì (GTZ) of these same proposals, and show that each protagonist is both right and wrong. In detail, we show that DD’s predictions are indeed measurable in principle, but that they will not lead to violations of the no-signalling theorem used in Bell’s theorem, in contradiction with some of Das and Maudlin’s hopes. Full article

We consider the local value of an operator for a given position or momentum and, more generally on the value of another arbitrary observable. We develop a general approach that is based on breaking up $\mathbf{A}\psi \left(x\right)$ as ${\displaystyle \frac{\mathbf{A}\psi \left(x\right)}{\psi \left(x\right)}}={\left({\displaystyle \frac{\mathbf{A}\psi \left(x\right)}{\psi \left(x\right)}}\right)}_R+i{\left({\displaystyle \frac{\mathbf{A}\psi \left(x\right)}{\psi \left(x\right)}}\right)}_I$ where $\mathbf{A}$ is the operator whose local value we seek and $\psi \left(x\right)$ is the position wave function. We show that the real part is related to the conditional value for a given position and the imaginary part is related to the standard deviation of the conditional value. We show that the uncertainty of an operator can be expressed in two parts that depend on the real and imaginary parts. In the case of the position representation, the expression for the uncertainty of an operator shows that there are two fundamental contributions, one due to the amplitude of the wave function and the other due to the phase. We obtain the equation of motion for the conditional values, and in particular, we generalize the Ehrenfest theorem by deriving a local version of the theorem. We give a number of examples, including the local value of momentum, kinetic energy, and Hamiltonian. We also discuss other approaches for obtaining a conditional value in quantum mechanics including using quasi-probability distributions and the characteristic function approach, among others. Full article

In this work, the two-dimensional fluid models for two types of inductively coupled plasma, Ar/O₂ and Ar/SF₆, are numerically solved by the finite element method. Four interesting phenomena revealed by the simulations are reported: (1) comet-shaped and semi-circle-shaped structures in Ar/O₂ and Ar/SF₆ plasmas, respectively; (2) blue sheaths that surround the two structures; (3) the collapse and dispersion of semi-circle-shaped structures of certain Ar/SF₆ plasma cations and anions when they are observed separately; and (4) the rebuilding of coagulated structures by minor cations in the Ar/SF₆ plasma at the discharge center. From the simulation detail, it was found that the cooperation of free diffusion and negative chemical sources creates the coagulated structure of anions, and the self-coagulation theory is therefore built. The advective and ambipolar types of self-coagulation are put forth to explain the co-existence of blue sheath and internal neutral plasma, among which the advective type of self-coagulation extends the Bohm’s sheath theory of cations to anions, and the ambipolar type of self-coagulation originates from the idea of the ambipolar diffusion process, and it updates the recognition of people about the plasma collective interaction. During the ambipolar self-coagulation, each type of Ar/SF₆ plasma cations and anions is self-coagulated, and the coagulated plasma species are then modeled as mass-point type (or point-charge type, more precisely). When the charge amounts of two point-charge models of plasma species with the same charge type are equal, the expelling effect caused by the Coulomb’s force of them leads to the collapse or dispersal of heavily coagulated species. The simulation shows that the lighter the species is, the easier it self-coagulates and the more difficult its coagulation is broken, which implies the inertia effect of density quantity. Moreover, the collapse of cation coagulation creates the spatially dispersed charge cloud that is not shielded into the Debye’s length, which indicates the anti-collective behavior of electronegative plasmas when they are self-coagulated. The rebuilt coagulated structure of minor Ar/SF₆ plasma species at the discharge center and the weak coagulation of electrons in the periphery of the main coagulated structure that is under the coil are caused by the monopolar and spontaneous (non-advective) type of self-coagulation. The analysis predicts an intensity order of physically driven coagulation force, chemical self-coagulation force, and ambipolar self-coagulation force. The popular coagulated structure of the electronegative ICP sources is urgently needed to validate the experiment. Full article

The theoretical connections between quantum trajectories and quantum dwell times, previously explored in the context of 1D time-independent stationary scattering applications, are here generalized for multidimensional time-dependent wavepacket applications for particles with spin 1/2. In addition to dwell times, trajectory-based dwell time distributions are also developed, and compared with previous distributions based on the dwell time operator and the flux–flux correlation function. Dwell time distributions are of interest, in part because they may be of experimental relevance. In addition to standard unipolar quantum trajectories, bipolar quantum trajectories are also considered, and found to relate more directly to the dwell time (and other quantum time) quantities of greatest relevance for scattering applications. Detailed calculations are performed for a benchmark 3D spin-1/2 particle application, considered previously in the context of computing quantum arrival times. Full article

In this work, we review and extend a version of the old attempt made by Louis de Broglie for interpreting quantum mechanics in realistic terms, namely, the double solution. In this theory, quantum particles are localized waves, i.e., solitons, that are solutions of relativistic nonlinear field equations. The theory that we present here is the natural extension of this old work and relies on a strong time-symmetry requiring the presence of advanced and retarded waves converging on particles. Using this method, we are able to justify wave–particle duality and to explain the violations of Bell’s inequalities. Moreover, the theory recovers the predictions of the pilot-wave theory of de Broglie and Bohm, often known as Bohmian mechanics. As a direct consequence, we reinterpret the nonlocal action-at-a-distance in the pilot-wave theory. In the double solution developed here, there is fundamentally no action-at-a-distance but the theory requires a form of superdeterminism driven by time-symmetry. Full article

The introduction of branes immersed in the space-times of higher dimensions revealed itself to be a useful instrument for the study of high-dimensional models in quantum field theory. Moreover, low-dimensional quantum field theories represent an especially interesting class of models in physics due to their unique properties and renormalizability when interactions are treated perturbatively. The advantages of both approaches can be combined in a model for a low-dimensional brane immersed in the usual tetradimensional Minkowski space-time, the properties of which are relatively well known. This approach can be used for the study of systems like graphene and carbon nanotubes. In the present work, we present an effective model for nanotubes based on the Lagrangian obtained from a tight-binding model for graphene. The induced current, appearing azimuthally in the presence of a magnetic flux through the tube section (Aharonov–Bohm effect), will be derived. A reduced Lagragian for photons confined on the tube surface, obtained from the literature, is included in the last part of the work to threat perturbative corrections to the induced current. Full article

Everett’s many-worlds or multiverse theory is an attempt to find an alternative to the standard Copenhagen interpretation of quantum mechanics. Everett’s theory is often claimed to be local in the Bell sense. Here, we show that this is not the case and debunk the contradictions by analyzing in detail the Greenberger–Horne–Zeilinger (GHZ) nonlocality theorem. We discuss and compare different notions of locality often mixed in the Everettian literature and try to explain the nature of the confusion. We conclude with a discussion of probability and statistics in the many-worlds theory and stress that the strong symmetry existing between branches in the theory prohibits the definition of probability and that the theory cannot recover statistics. The only way out from this contradiction is to modify the theory by adding hidden variables à la Bohm and, as a consequence, the new theory is explicitly Bell-nonlocal. Full article