L. Marchildon

L. Marchildon
Université du Québec à Trois-Rivières · Département de Physique

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596
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Introduction
Skills and Expertise
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May 1985 - present
Université du Québec à Trois-Rivières
Position
  • Emeritus Professor of Physics

Publications

Publications (93)
Preprint
Full-text available
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...
Preprint
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.
Preprint
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...
Article
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...
Article
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...
Article
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
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...
Article
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...
Article
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...
Article
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...
Conference Paper
Full-text available
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...
Article
Full-text available
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...
Poster
Full-text available
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...
Article
Full-text available
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...
Article
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...
Article
Full-text available
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
Full-text available
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
Full-text available
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...
Chapter
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...
Chapter
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...
Chapter
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.
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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.
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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...
Chapter
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.
Chapter
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...
Article
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.
Article
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.
Article
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
Article
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...
Article
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...
Article
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
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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.
Article
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...
Article
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...
Article
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...
Article
Thèse (M.A.(physique))--Université du Québec à Trois-Rivières, 1973. Bibliographie: feuillets [140]-144. Microfiche du manuscrit dactylographié.

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