arXiv subjects

Avshalom Elitzur

Publications and source records attributed to Avshalom Elitzur.

4 recordsLinked to original sources

arXiv2024

Covariant field lines: a geometrical approach to electrodynamics

This paper revisits the geometric foundations of electromagnetic theory, by studying Faraday's concept of field lines. We introduce "covariant electromagnetic field lines," a novel construct that extends traditional field line concepts to a covariant framework. Our work includes the derivation of a closed-form formula for the field line curvature in proximity to a moving electric charge, showcasing the curvature is always non-singular, including nearby a point charge. Our geometric framework leads to a geometric derivation of the Lorentz force equation and its first-order corrections, circumventing the challenges of self-force singularities and providing insights into the problem of radiation-reaction. This study not only provides a fresh geometric perspective on electromagnetic field lines but also opens avenues for future research in fields like quantum electrodynamics, gravitational field theory, and beyond.

physics.class-ph↗

arXiv2022

Quantum reality with negative-mass particles

Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric formulation to assign eigenvalues to unmeasured observables of a system, which results in logical paradoxes, and no clear physical picture. A top-down ontological model is introduced that treats the weak values of observables as physically real during the time between pre- and post-selection (PPS), which avoids these paradoxes. The generally delocalized rank-1 projectors of a quantum system describe its fundamental ontological elements, and the highest-rank projectors corresponding to individual localized objects describe an emergent particle model, with unusual particles whose masses and energies may be negative or imaginary. This retrocausal top-down model leads to an intuitive particle-based ontological picture, wherein weak measurements directly probe the properties of these exotic particles, which exist whether or not they are actually measured

quant-ph↗

arXiv2019

A relational time-symmetric framework for analyzing the quantum computational speedup

The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the problem solver, unitarily computes the corresponding solution and reads it by the final measurement. This simple extension creates a new perspective from which to see the quantum algorithm. First, it highlights the relevance of time-symmetric quantum mechanics to quantum computation: the problem-setting and problem solution, in their quantum version, constitute pre- and post-selection, hence the process as a whole is bound to be affected by both boundary conditions. Second, it forces us to enter into relational quantum mechanics. There must be a representation of the quantum algorithm with respect to Bob, and another one with respect to Alice, from whom the outcome of the initial measurement, specifying the setting and thus the solution of the problem, must be concealed. Time-symmetrizing the quantum algorithm to take into account both boundary conditions leaves the representation to Bob unaltered. It shows that the representation to Alice is a sum over histories in each of which she remains shielded from the information coming to her from the initial measurement, not from that coming to her backwards in time from the final measurement. In retrospect, all is as if she knew in advance, before performing her problem-solving action, half of the information that specifies the solution of the problem she will read in the future and could use this information to reach the solution with fewer computation steps (oracle queries). This elucidates the quantum computational speedup in all the quantum algorithms examined.

quant-ph↗

arXiv2004

Quantum Brain: A Recurrent Quantum Neural Network Model to Describe Eye Tracking of Moving Targets

A theoretical quantum brain model is proposed using a nonlinear Schroedinger wave equation. The model proposes that there exists a quantum process that mediates the collective response of a neural lattice (classical brain). The model is used to explain eye movements when tracking moving targets. Using a Recurrent Quantum Neural Network(RQNN) while simulating the quantum brain model, two very interesting phenomena are observed. First, as eye sensor data is processed in a classical brain, a wave packet is triggered in the quantum brain. This wave packet moves like a particle. Second, when the eye tracks a fixed target, this wave packet moves not in a continuous but rather in a discrete mode. This result reminds one of the saccadic movements of the eye consisting of 'jumps' and 'rests'. However, such a saccadic movement is intertwined with smooth pursuit movements when the eye has to track a dynamic trajectory. In a sense, this is the first theoretical model explaining the experimental observation reported concerning eye movements in a static scene situation. The resulting prediction is found to be very precise and efficient in comparison to classical objective modeling schemes such as the Kalman filter.

q-bio.NC↗