arXiv subjects
Publications and source records attributed to Louis Marchildon.
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 that the epistemic view of quantum states begs the question of interpretation.
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, replaced by the corresponding emergence of the concept of information. Although devices like Bohmian trajectories and the ether do present important analogies, I argue that there is also a crucial difference, related to distinct explanatory functions of quantum mechanics.
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 has recently been the subject of controversy. I argue that the counterfactual meaning may be understood in terms of the true value of an observable at t. Such a value cannot be empirically determined for, by stipulation, the measurement that would yield it is not performed. Nevertheless, it may or may not be well-defined depending on one's proposed interpretation of quantum mechanics. Various examples are discussed illustrating what can be asserted at the intermediate time without running into contradictions.
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 being essentially incomplete.
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 allows for a complete classification of their Lie symmetries. Symmetries of Yang-Mills equations in the Lorentz gauge are also investigated.
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 is to examine several issues raised by Mohrhoff's interpretation, and to assess whether it helps providing solutions to the long-standing problems of quantum mechanics.
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.
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 correspondence with symmetries of the full Yang-Mills equations in Minkowski space.
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 involves a very complicated substitution of Einstein's equations), we set to zero the coefficients of derivatives that do not appear in Einstein's equations. This considerably constrains the coefficients of symmetry generating vector fields. Using the Lie algebra property of generators of symmetries and the fact that general coordinate transformations are symmetries of Einstein's equations, we are then able to obtain all the Lie symmetries. The method we have used can likely be applied to other types of equations.