Anticipatory Effects in Relativistic Electromagnetism

摘要

This paper is a continuation of our preceding paper dealing with the foundation of anticipation in electromagnetism: the distance r(t′) at time t′ from a moving charge to an observer is viewed by the observer as the anticipated distance r_a(t). At the future time t = t′ + r(t′)/c. Where c is the light velocity of the propagation of the electrical potential. The anticipated distance r_a(t) is equal to the distance r(t′) extrapolated by the velocity dr(t′)dt′ during (t ― t′). For particle at rest or moving at small constant velocity, the anticipated distance is exactly the actual distance at time t. With acceleration and deceleration, the anticipated distance is no more equal to the actual distance: advanced or retarded distances occur depending on the trajectory properties. Numerical simulations were performed to show these anticipatory effects in the cases of different movements: at rest, at constant velocity, with acceleration and deceleration, and in oscillatory particles. In three dimensions space, the anticipated direction of the electrical field is exactly the actual direction for a particle moving at constant velocity. These anticipatory effects permit to understand the relativistic Lorentz transform in a new way.