Abstract
In the context of Stueckelberg's covariant symplectic mechanics, Horwitz and Aharonovich [1] have proposed a simple mechanism by which a particle traveling below light speed almost everywhere may exhibit a transit time that suggests superluminal motion. This mechanism, which requires precise measurement of the particle velocity, involves a subtle perturbation affecting the particle's recorded time coordinate caused by virtual pair processes. The Stueckelberg framework is particularly well suited to such problems, because it permits pair creation/annihilation at the classical level. In this paper, we study a trajectory of the type proposed by Horwitz and Aharonovich, and derive the Maxwell 4-vector potential associated with the motion. We show that the resulting fields carry a signature associated with the apparent superluminal motion, providing an independent test for the mechanism that does not require direct observation of the trajectory, except at the detector.
Highlights
The interpretation of antiparticles as negative energy particles propagating backward in time was proposed by Stueckelberg [2] in the context of his covariant Hamiltonian theory of interacting spacetime events xμ(τ) evolving as functions of a Poincareinvariant parameter τ. His goal was to represent a particle/antiparticle process by a single worldline whose time coordinate advances and retreats with respect to the laboratory clock as its instantaneous energy changes sign under interaction with gauge fields
In the context of Stueckelberg electrodynamics, Horwitz and Aharonovich [1] have proposed a simple mechanism by which a particle traveling below light speed almost everywhere may exhibit a transit time that suggests superluminal motion
In the previous section we derived the Maxwell potential associated with a particle trajectory that includes a “pull-back” in time
Summary
The interpretation of antiparticles as negative energy particles propagating backward in time was proposed by Stueckelberg [2] in the context of his covariant Hamiltonian theory of interacting spacetime events xμ(τ) evolving as functions of a Poincareinvariant parameter τ His goal was to represent a particle/antiparticle process by a single worldline whose time coordinate advances and retreats with respect to the laboratory clock as its instantaneous energy changes sign under interaction with gauge fields. Exchanging time and space, an event may briefly reverse its time direction without affecting its space motion In this case, the particle will continue its progress in space coordinates from the source to the detector, but the laboratory clock will report a difference between time-of-start and time-of-arrival that is less than expected. We study the Coulomb field expected from motion of this type and indicate a small deviation from the field expected for continuous linear motion
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
