  We study the case of two rockets which meet at a point O of an inertial
co-ordinate system S, and are scheduled to move at constant speed, in opposite
directions, toward two targets placed at equal distances from point O. At the
instant they meet, the clocks inside the rockets are set to zero. When they
reach the targets the rockets meet two clocks A and B whose reading is
identical. This question which was tackled in ref [1] is studied here in depth.
Assuming the existence of a preferred aether frame So in which the one-way
speed of light is isotropic, and the anisotropy of this speed in the other
frames, we show that, if the equal reading of the clocks A and B results from
an exact synchronization, the clocks inside the rockets will display different
readings when they reach A and B in contradiction with the relativity
principle. Conversely, if the clocks A and B, which display an equal reading,
have been synchronized by means of the Einstein-Poincare procedure, the inboard
clocks will also display the same reading, a fact which seems in agreement with
the relativity principle. But this synchronization method presupposes the
invariance of the one-way speed of light, in contradiction with the assumptions
made, and, therefore, introduces a measurement error. This demonstrates that if
we assume the existence of an aether frame, the apparent relativity principle
is not a fundamental principle; it depends on an arbitrary synchronization. In
any case, this is an example of an experimental measurement which can be
explained by aether theory without the assumption of the invariance of the
one-way speed of light in all inertial frames.
