I. Simple First-Order Test of Special Relativity
Since the improved version of my experiment, used when in April 1982 we performed it, is copyrighted by the American Journal of Physics (Jan. 1985, Vol. 53, pp. 43-45) I can only reproduce my original proposal of 1968 here in its 1972 form.
For the benefit of math-phobes I add a Gedankenexperiment that will, I suppose, convey the basic idea behind this outline. Imagine two airplanes, A and B, flying past us on a windless day, first north-south and after that east-west. We measure their speeds relative to us and both times find these to be 300 and 225 km/hr. The ratio between those two velocities is therefore 4/3. And this confirms what we know already: we are at rest. Next we station ourselves on a flat car of a slowly moving east-west train, and ask the pilots of the planes to repeat those two performances. That during their north-south flight they must pass us slightly off course we may neglect. However, when the planes roar past parallel to the railroad tracks we find the ratio between their velocities to be 296/221. Question: what is the speed of our train? Remembering that for the first two fly-pasts the ratio was 4/3, we easily find the answer: 4/3 = 300//225 = 296+4/221+4 Hence our train rolls at 4 km/hr.
In the real experiment the air becomes space, the planes two ray rays of light, the one travelling through an empty tube, the other through a tube filled with water, the flat-car a space satellite or fast airplane.
The first earth-bound test we have performed and it showed an Earth absolutely at rest in space. The second we would like to see performed. If then the ratio between the velocities of the two rays (observable by a change of the light fringes) still turns out to be the same, the STR will have been vindicated. If the fringe pattern agrees with the speed of the satellite, that theory has been falsified, and the geocentric theory strongly favoured.
To be sure: Hoek’s 1868 experiment will serve too. But it observes, as in the Michelson and Morley trial, two returning rays, and that will evoke (viz. the enormous literature on the particular of that M. and M. probe) endless theoretical considerations and evaluations.