Monday, July 28, 2014

About the sign of advanced magnetic forces

In time-symmetric electrodynamics, it is always assumed that the sign of the electric force is the same for the advanced force as for the retarded force.  This must be so (one would think) because in the inertial reference frame where an infinitely heavy charge is at rest, a test charge held initially at rest and then released would experience no net Coulomb force if it were otherwise.

It follows from this seemingly necessary choice that the sign of the magnetic force in a different inertial reference frame, where the heavy charge is in motion, will invert for advanced compared to retarded magnetic forces.  So, in time symmetric electrodynamics, magnetic forces tend to cancel out.  This appears at least at first glance to keep the magnetic force that seems to correspond to my predicted anti-centrifugal force from being able to overcome Coulomb repulsion.

On account of the considerations above, I have recently been going carefully over how to get the time-advanced and time-retarded fields and forces by Lorentz transforming from the reference frame where the field-source charge is stationary.  (The retarded case is already analyzed quite a bit in the appendices of my arxiv paper.)  There haven't been any surprises there, but a few days ago I began to realize that the derivation of the magnetic force as the anti-Coriolis force of the Thomas precession doesn't care whether the field or force is retarded or advanced.  It can't change sign from retardation to advancement because neither has entered into the derivation in any way.  Thus, if the anti-Coriolis force is a real force, then either time-advanced electromagnetic forces cannot exist, or the sign of the Coulomb force must flip between retardation and advancement.  Consistency of the force law with relativistic kinematics demands this, if I am correct.