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May 1985 - present

## Publications

Publications (93)

The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum theory could be, if not resolved, at least mitigated by a proper interpretation of probability. We rather show, th...

Proietti et al. (arXiv:1902.05080) reported on an experiment designed to settle, or at least to throw light upon, the paradox of Wigner's friend. Without questioning the rigor or ingenuity of the experimental protocol, I argue that its relevance to the paradox itself is rather limited.

All investigators working on the foundations of quantum mechanics agree that the theory has profoundly modified our conception of reality. But there ends the consensus. The unproblematic formalism of the theory gives rise to a number of very different interpretations, each of which has consequences on the notion of reality. This paper analyses how...

Kastner (arXiv:1709.09367) and Kastner and Cramer (arXiv:1711.04501) argue that the Relativistic Transactional Interpretation (RTI) of quantum mechanics provides a clear definition of absorbers and a solution to the measurement problem. I briefly examine how RTI stands with respect to unitarity in quantum mechanics. I then argue that a specific pro...

Everett's interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves unitarily. It then claims that whenever an observable is measured, all possible results of the measurement exist. This...

Everett's interpretation of quantum mechanics was proposed to avoid problems
inherent in the prevailing interpretational frame. It assumes that quantum
mechanics can be applied to any system and that the state vector always evolves
unitarily. It then claims that whenever an observable is measured, all possible
results of the measurement exist. This...

Quantum Bayesianism, or QBism, is a recent development of the epistemic view
of quantum states, according to which the state vector represents knowledge
about a quantum system, rather than the true state of the system. QBism
explicitly adopts the subjective view of probability, wherein probability
assignments express an agent's personal degrees of...

The transactional interpretation of quantum mechanics, which uses retarded
and advanced solutions of the Schrodinger equation and its complex conjugate,
offers an original way to visualize and understand quantum processes. After a
brief review, we show how it can be applied to different quantum situations,
emphasizing the importance of specifying a...

The transactional interpretation of quantum mechanics, following the
time-symmetric formulation of electrodynamics, uses retarded and advanced
solutions of the Schrodinger equation and its complex conjugate to understand
quantum phenomena by means of transactions. A transaction occurs between an
emitter and a specific absorber when the emitter has...

Generalizations of the complex number system underlying the mathematical
formulation of quantum mechanics have been known for some time, but the use of
the commutative ring of bicomplex numbers for that purpose is relatively new.
This paper provides an analytical solution of the quantum Coulomb potential
problem formulated in terms of bicomplex num...

Bicomplex numbers are pairs of complex numbers with a multiplication law that makes them a commutative ring. The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers. Starting with the commutator of the bicomplex position and momentum operators, we find eigenvalues and eigenkets of the bicomplex harmonic...

This is the first part of a two-paper series, in which we critically examine the various proposals that have been made for superluminal coordinate transformations. Here we consider the two-dimensional case. Starting from rather general assumptions, we show that the superluminal coordinate transformations in two dimensions are essentially uniquely d...

Bicomplex numbers are pairs of complex numbers with a multiplication law that makes them a commutative ring. The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers. Starting with the commutator of the bicomplex position and momentum operators, we find eigenvalues and eigenkets of the bicomplex harmonic...

This paper begins the study of infinite-dimensional modules defined on
bicomplex numbers. It generalizes a number of results obtained with
finite-dimensional bicomplex modules. The central concept introduced is the one
of a bicomplex Hilbert space. Properties of such spaces are obtained through
properties of several of their subsets which have the...

Bicomplex numbers represent one possible generalization of complex numbers, to entities with four real components. We investigate the quantum harmonic oscillator problem in this framework. Starting with the commutation relation of the bicomplex position and momentum operators, we find the eigenvalues and eigenfunctions of the bicomplex quantum harm...

This paper is a detailed study of finite-dimensional modules defined on
bicomplex numbers. A number of results are proved on bicomplex square matrices,
linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces,
including the spectral decomposition theorem. Applications to concepts relevant
to quantum mechanics, like the evolutio...

Everett's relative states interpretation of quantum mechanics has met with
problems related to probability, the preferred basis, and multiplicity. The
third theme, I argue, is the most important one. It has led to developments of
the original approach into many-worlds, many-minds, and decoherence-based
approaches. The latter especially have been ad...

The problem of the quantum harmonic oscillator is investigated in the
framework of bicomplex numbers, which are pairs of complex numbers making up a
commutative ring with zero divisors. Starting with the commutator of the
bicomplex position and momentum operators, and adapting the algebraic treatment
of the standard quantum harmonic oscillator, we...

Since the beginning, quantum mechanics has raised major foundational and interpretative problems. Foundational research has been an important factor in the development of quantum cryptography, quantum information theory and, perhaps one day, practical quantum computers. Many believe that, in turn, quantum information theory has bearing on foundatio...

Several arguments have been proposed some years ago, attempting to prove the
impossibility of defining Lorentz-invariant elements of reality. Here I revisit
that question, and bring a number of additional considerations to it. I will
first analyze Hardy's argument, which was meant to show that Lorentz-invariant
elements of reality are indeed incons...

Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. I find that a sufficient condition for the existence of elements of reality, introduced in these proofs, seems to be used also as a necessary condition. I argue that Lorentz-invariant elements of reality can...

The interpretation of quantum mechanics (or, for that matter, of any physical
theory) consists in answering the question: How can the world be for the theory
to be true? That question is especially pressing in the case of the
long-distance correlations predicted by Einstein, Podolsky and Rosen, and
rather convincingly established during the past de...

Cramer's transactional interpretation of quantum mechanics is reviewed, and a
number of issues related to advanced interactions and state vector collapse are
analyzed. Where some have suggested that Cramer's predictions may not be
correct or definite, I argue that they are, but I point out that the
classical-quantum distinction problem in the Copen...

The idea that the wave function represents information, or knowledge, rather than the state of a microscopic object has been held to solve foundational problems of quantum mechanics. Realist interpretation schemes, like Bohmian trajectories, have been compared to the ether in pre-relativistic theories. I argue that the comparison is inadequate, and...

Once considered essential to the explanation of electromagnetic phenomena,
the ether was eventually discarded after the advent of special relativity. The
lack of empirical signature of realist interpretative schemes of quantum
mechanics, like Bohmian trajectories, has led some to conclude that, just like
the ether, they can be dispensed with, repla...

In the last few years the hydrodynamic formulation of quantum mechanics, equivalent to the Bohmian equations of motion, has been used to obtain numerical solutions of the Schrodinger equation. Problems, however, have been experienced near wave function nodes (or low probability regions). Here we attempt to compute wave functions and Bohmian traject...

The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this epistemic view of states appears to solve foundational problems of quantum mechanics only at the price of bei...

We investigate Lie symmetries of general Yang-Mills equations. For this
purpose, we first write down the second prolongation of the symmetry generating
vector fields, and compute its action on the Yang-Mills equations. Determining
equations are then obtained, and solved completely. Provided that Yang-Mills
equations are locally solvable, this allow...

The Aharonov-Bergmann-Lebowitz rule assigns probabilities to quantum measurement results at time t on the condition that the system is prepared in a given way at t_1 < t and found in a given state at t_2 > t. The question whether the rule can also be applied counterfactually to the case where no measurement is performed at the intermediate time t h...

A number of assertions have recently been made that in two-particle interference devices, Bohmian trajectories may not reproduce exactly all statistical predictions of quantum mechanics. Specifically, let two identical bosons go through identical slits arranged symmetrically with respect to a plane, with wave functions transforming into each other...

In a recently proposed interpretation of quantum mechanics, U. Mohrhoff
advocates original and thought-provoking views on space and time, the
definition of macroscopic objects, and the meaning of probability statements.
The interpretation also addresses a number of questions about factual events
and the nature of reality. The purpose of this note i...

The compatibility of standard and Bohmian quantum mechanics has recently been challenged in the context of two-particle interference, both from a theoretical and an experimental point of view. We analyze different setups proposed and derive corresponding exact forms for Bohmian equations of motion. The equations are then solved numerically, and sho...

A mathematical formalism, like the one introduced in Chap. 2, is not by itself a physical theory. The latter includes, in addition, interpretation rules that associate, more or less directly, empirical concepts or procedures to objects of the formalism. The purpose of this chapter is twofold: to state the fundamental interpretation rules of quantum...

The search for eigenvalues and eigenfunctions of an atom’s Hamiltonian is a very complex problem. The central-field model simplifies it while remaining fairly close to physical reality. The model assumes each electron moves in a spherically symmetric potential due to the nucleus and all other electrons. Moreover, it introduces in a simple way the n...

In the first few chapters, we have introduced the formal objects and laws at the heart of quantum mechanics: state vector, Hermitian operators, eigenvalues, Schrödinger’s equation, etc. In simple cases we have shown how to use them to account for situations which, although idealized, are not unlike the ones studied in the laboratory.

The importance of the evolution operator in quantum mechanics has been emphasized several times. We now obtain an explicit formula for its matrix elements in terms of a path integral. Next we evaluate that integral in the semiclassical case, that is, when the action associated with the classical trajectory is much larger than Planck’s constant. Thi...

Ever since its formulation in 1925–26, quantum mechanics has explained a very large number of phenomena. Examples have been given throughout this book. Properties of atoms, molecules, nuclei, solids, superconductors and superfluids, among others, cannot be understood without the systematic use of quantum mechanics. No major discrepancies are known...

Spatial rotations have been encountered repeatedly and in different contexts. Spin spaces, brought to light by the Stern—Gerlach experiment, were treated in Chap. 4. Orbital angular momentum operators were introduced in Chap. 7. In Chap. 13 the rotation group was defined. In the present chapter we will first show that group-theoretical concepts aff...

With a particle restricted to one space dimension, we begin the study of quantum systems with infinite-dimensional state spaces. The state space of a particle in one dimension is first introduced intuitively. We then carefully examine the dynamical variables position, momentum and energy, which leads to a precise definition of the state space. The...

The formalism of quantum mechanics was proposed in 1925 and 1926, chiefly by W. Heisenberg, E. Schrdinger and P. A. M. Dirac. The key to its interpretation was given by M. Born in 1926. At the outset, creators of quantum mechanics presented it as a fundamental theory of atoms and molecules.

The state of an isolated quantum system has hitherto been represented by a vector in the state space. We shall see that it can also be represented by a Hermitian operator called the density operator. The usefulness of that operator comes from the fact that it can represent not only the state of an isolated system, but also the state of a system tha...

Scattering is one of the two most important methods for the experimental investigation of atomic and molecular properties (the other being spectroscopy) . We will treat scattering by means of the Hamiltonian’s eigenvalue equation, focussing on the continuous spectrum associated with a given potential. After defining the scattering cross section, we...

Many concepts introduced in the study of a particle in one dimension can be adapted directly to the particle in three dimensions. Angular momentum operators, however, are new. Closely linked with the particle in three dimensions, they are much like the spin operators we examined in Chap. 4. Angular momentun operators are particularly useful where t...

Stationary perturbation theory is one of the main approximation methods in quantum mechanics. It applies to quantum systems with a Hamiltonian which, in a sense that will be made clear, is close to a Hamiltonian whose eigenvalues and eigenvectors are known. We will develop the formalism and use it to investigate the effect of the spatial extension...

The behavior of electrons, in atoms and molecules in particular, is normally described by the Schrödinger equation. For several reasons, however, this is not entirely satisfactory. The Schrödinger equation is not invariant under the coordinate transformations of the special theory of relativity. This means that it cannot correctly account for relat...

The investigation of molecular properties by quantum-mechanical methods is a huge field.1 Only the most elementary results can be presented here. First we will see that the quantum problem of a molecule approximately separates into an electronic problem and one for the motion of nuclei. Next we will examine electronic wave functions of diatomic mol...

For a particle either in one or in three dimensions, there are few situations where the eigenvalue equation for the Hamiltonian has closed-form solutions. In most cases one must turn to approximate methods. These, we will see, are very different from one another. Not all methods are adapted to any specific problem, each method having its own domain...

Of all dynamical variables defined in a finite-dimensional state space, spin is no doubt the most important. Spin is associated with particles, atoms and molecules. It is connected with angular momentum and magnetic moment. Historically, atomic magnetic moments were revealed in the Stern—Gerlach experiment, which we will describe schematically. Ana...

In previous chapters we have shown how to obtain atomic energies and wave functions. Here we examine the interaction of a quantum system with an electromagnetic wave. Indeed the experimental investigation of atoms is carried out largely by spectroscopy, i.e. by recording the properties of radiation that they emit or absorb. In most cases electromag...

The stationary energies and wave functions of an atom are obtained by diagonalizing its Hamiltonian. This diagonalization is carried out here in the state space associated with an electronic configuration. Insofar as the Hamiltonian only involves kinetic and potential energy terms, it commutes with the atom’s orbital and spin angular momentum opera...

The central-field model and Hartree’s self-consistent equations provide a first approximation of atomic orbitals and corresponding energies. In that context atomic wave functions are taken as products of one-electron wave functions. But this representation is not really adequate. The half-integral spin and the identity of all electrons bring import...

The theory of vector spaces and of operators defined in them is the fundamental mathematical tool of quantum mechanics. This chapter summarizes, usually without proofs, the properties of finite-dimensional vector spaces.1 Readers familiar with these results can skip to Chap. 3, after a glance at the notations we introduce.

The notion of symmetry is familiar from daily experience. We say that an object displays a symmetry if it is invariant under a transformation. This means that after the transformation, the object’s configuration is identical with the one it had before the transformation. Thus a sphere is symmetric because it is invariant under rotations. In quantum...

Claims have been made that, in two-particle interference experiments involving bosons, Bohmian trajectories may entail observable consequences incompatible with standard quantum mechanics. By general arguments and by an examination of specific instances, we show that this is not the case.

Two recent claims by A. Neumaier (quant-ph/0001011) and P. Ghose (quant-ph/0001024) that Bohmian mechanics is incompatible with quantum mechanics for correlations involving time are shown to be unfounded.

La théorie quantique et le schisme en physique. Post-scriptum à la Logique de la découverte scientifique, IIIPopperKarl Édition établie et annotée par W. W. Bartley, traduction et présentation d'Emmanuel Malolo Dissaké Paris, Hermann, 1996, XLIV, 228 p. - Volume 37 Issue 1 - Louis Marchildon

We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on Einstein's equations. Instead of setting to zero the coefficients of all independent partial derivatives (which invo...

We investigate Lie symmetries of the self-dual Yang-Mills equations in
four-dimensional Euclidean space (SDYM). The first prolongation of the symmetry
generating vector fields is written down, and its action on SDYM computed.
Determining equations are then obtained and solved completely. Lie symmetries
of SDYM in Euclidean space are in exact corres...

Einstein philosophe. La physique comme pratique philosophiquePatyMichel Collection «Philosophie d'aujourd'hui» Paris, Presses Universitaires de France, 1993, viii, 584 p. - Volume 34 Issue 1 - Louis Marchildon

Hereman, Marchildon and Grundland have earlier reported on an investigation of Lie point symmetries of two systems of nonlinear partial differential equations, both representing classical field theories. Determining equations (more than 200 of them) associated with the first system (coupled electromagnetic and complex scalar fields) were solved com...

A novel numerical procedure for analysing discontinuities in MMIC
and hybrid planar circuits is proposed. It is based on a combination of
boundary elements and a planar waveguide model. Shunt posts are taken
into account in the model by explicit modal field expansion. This
approach employs fewer nodal points than either the finite-element or
bounda...

A new way to determine the complex permittivity of liquid or solid dielectric material samples is proposed. The method makes use of a discontinuity in a rectangular waveguide. The discontinuity is either a rectangular post or a cylinder containing a dielectric sample. A mode mode-matching method is first used to find the reflection and transmission...

We propose a method to calculate field distribution and
S-parameters in a planar n-port junction with rectangular waveguides. We
use boundary elements on metallic walls, combined with modal expansion
in waveguides and analytic representations for the field in dielectric
samples or ferrites. Our approach uses fewer nodal points than either
the finit...

A method for the computation of S-parameters associated with a
rectangular waveguide with a rectangular or cylindrical obstacle of
arbitrary complex scalar permittivity is presented. The method uses
modal analysis and integral relationships to connect appropriate
components of the field. In this way, convergence is achieved faster
than by point-mat...

The synchronization of clocks at distant spatial points is a question of convention. If a synchronization not involving electromagnetic
radiation is agreed upon, the one-way velocity of light becomes meaningful. We develop the prediction of general relativity
and other metric theories of gravity for the one-way speed of light near the surface of th...

An analysis of the relationship between complex permittivity and complex resonance frequency is proposed for a cylindrical cavity oscillating in a TM0mp mode. Effects of wall conductivity, coupling loops, and holes for the insertion of dielectric samples are fully taken into account. With dielectric samples of small radii, insertion holes produce t...

The presence of small sample insertion holes in a cylindrical
cavity produces a shift in the complex resonance frequency of the
cavity. A mathematical model is proposed to compute the shift when the
cavity oscillates in an axially symmetric TM<sub>0mp</sub> mode The
treatment applies to samples with arbitrary complex permittivity. The
model is comp...

A new method for the measurement of gas adsorption at high pressure is described in detail. The method is based on dielectric virial coefficients and it takes advantage of the dielectric technique for the accurate measurement of the compressibility factor of gases at high pressure. The method is simple, self‐sufficient, easy to use, and permits pre...

We investigate a priori possible extensions of the Lorentz group to
nonlinear coordinate transformations between equivalent frames. We
consider nonlinear transformations preserving uniform rectilinear
motion, or mapping the world lines of points at rest to uniform
rectilinear motion with a fixed velocity. In each case, we implement the
requirement...

The effective interaction energy of two test particles immersed in a molecular fluid of finite volume is defined and expressed in terms of the molecular pair correlation function. The specific problem of electric multipoles immersed in a fluid of polar nonpolarizable molecules filling a spherical volume is then analyzed in detail. The long-range pa...

Tolman's paradox arises in Lorentz-invariant theories of superluminal particles. In this paper we first try to clarify the nature of the paradox and what it means to solve it. We then analyze the various attempts made to either solve or eliminate it. We show that general consequences can be drawn which hold in essentially all paradox-free schemes p...

An exact formula for the effective interaction energy of two test multipoles of arbitrary order immersed in a fluid of polar nonpolarizable molecules is derived. Coordinate space as well as Fourier space techniques are used. This allows for a careful specification of the range of validity of the results, which turn out to be rather general. The exp...

We investigate, from a group-theoretical point of view, the possibility of implementing the so-called extended principle of relativity. This consists in postulating that the set of all equivalent reference frames contains frames whose relative velocities are larger than c, in addition to those whose coordinates are related by proper orthochronous L...

Negi et al. have recently obtained field equations for the superluminal electromagnetic field, in theories based on real superluminal transformations along a ``tachyon corridor''. Their results differ from equations obtained some time ago by the present authors. We trace the source of the discrepancy to the failure of Negi et al. to consistently tr...

We investigate how to incorporate the tachyon corridor, that is a preferred spatial direction, in space-time described by
a Robertson-Walker metric. We also look at the effects of local gravitational fields on the corridor. The requirement of avoiding
causal loops allows us to reach conclusions rather independent of any specific model of the corrid...

Several laws governing the electromagnetic interactions of tachyons are derived, under the hypothesis that tachyons are bradyons as seen by a superluminal observer. The postulate of the existence of the tachyon corridor, which solves the causality problems, is assumed. It is shown that the electromagnetic field produced by tachyonic matter obeys di...

We construct a nonlinear representaion of the superconformal group on its coset space with respect to the Lorentz group times the group of dilatations times U(1). Fields and derivatives covariant with respect to group transformations are given up to quadratic terms. From these, group invariants are obtained which contain the Lagrangian of conformal...

We study the graded Lie groups corresponding to the graded Lie algebras SU(2,2/1) and OSp(1/4). General finite group transformations are parametrized, and nonlinear representations are obtained on coset spaces. Jordan and traceless algebras are constructed which admit these groups as automorphism groups.

This article is about resettled Afghan Hazaras in Australia, many of whom are currently undergoing a complex process of transition (from transience into a more stable position) for the first time in their lives. Despite their permanent residency status, we show how resettlement can
be a challenging transitional experience. For these new migrants, w...

The formalism of spontaneous symmetry breaking in gauge theories and the theory of nonlinear invariant Lagrangians are reviewed, with an emphasis on the relationships between the two. The graded conformal group SU(2,2/1) is introduced as a set of transformations leaving a given bilinear form invariant, and it is shown that a general element of SU(2...

We obtain a complete analytical solution of the quantum-mechanical Coulomb potential problem formulated in terms of bicomplex num-bers. We do so by solving the bicomplex three-dimensionnal eigen-value equation associated with a hydrogen-like hamiltonian and ob-taining explicit expressions for its eigenvalues and eigenfunctions. The same eigenvalues...

Thèse (M.A.(physique))--Université du Québec à Trois-Rivières, 1973. Bibliographie: feuillets [140]-144. Microfiche du manuscrit dactylographié.

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