- #1

peteb

- 35

- 1

Consider the following scenario:

An inertial reference frame S' moves with respect to another inertial reference frame S in the positive x direction of S. The clocks in S and S' are synchronized at the instant t = t '= 0 when the coordinate origins O and O' of the two frames coincide. At this instant a light wave is emitted from the point O = O'. After time t it is observed in S that the light wave is spherical with a radius r = ct and is described by the equation r^2 = x^2 + y^2 + z^2 which means that the center of the light sphere as determined in S is at O. Consider now the shape of the light wavefront in S' at time t'. Is it also a sphere whose center is at O'? If so, does this lead to a paradox? If not, does this lead to a contradiction with the principle of relativity?

The relativity principle requires all physical phenomena to look the same in all inertial reference frames. Therefore an observer in S' should determine that the wavefront of the propagating light signal is also a sphere whose center is at O'. This conclusion is confirmed by the Lorentz transformations. But our everyday experience tells us that there must be something totally wrong here -- the center of the same light wave cannot be at two different places (at O and O' which may be thousands of kilometers apart). A standard explanation of this apparent paradox is the following: the wavefront of the propagating light sphere constitutes a set of simultaneous events and since according to relativity simultaneity is relative, the observers in S and S' have different sets of simultaneous events and consequently different light spheres. This is a correct explanation, but it certainly does not satisfy me.

The explanation is conceptually incomplete since it merely shifts the paradox from the specific case of light propagation to the relativity of simultaneity itself. What remains unexplained is why the two observers in S and S', who are in relative motion, have different sets of simultaneous events and therefore different light spheres (one centered at O and the other at O') given the fact that the two spheres originated from a single light signal. What physical meaning of relativity of simultaneity can be conceptually explained such that this paradox will be explained as well?

How can we really understand this world we live in?

Pete B