Detection of light from moving objects in six-dimensional special relativity

Abstract

In a six-dimensional space-time involving three space and three time coordinates we investigate how a particle would appear to an observer when it is moving at a speedv and when its time direction lies at an angle θ to that of the observer. It is shown how, unlike the standard four-dimensional case, the world-line of the particle is able to slip off the light surface of the observer so that the particle seems to vanish. Whether or not it does so depends on the value of γ (v) cos θ. The Doppler shift of the radiation emitted by a nonvanishing particle is calculated and it is found that when θ= 0, then a value of the red-shift can be obtained with smaller values of the observed velocity than is the case in the standard theory.