A SWAN AND A STAR

Consider a great big pool of water with no wind to make waves. S is the swan Sylvester swimming for his pleasure and making waves on the water. E is the ship Ebenezer steaming with velocity v (with respect to the water) commanded by Captain Ezekiel. The Captain can't see the swan because it is too far away, but he can measure where the waves are coming from. If he does so with respect to his own boat, clearly the velocity of the boat will cause them to arrive at a tilted angle because the boat is driving into the waves, just as if they had come not from S, but from S*. The difference in direction between the true position of S and the seeming position S* is called the aberration (angle) e of S.

For swans and ships Einstein and everybody else is agreed on how to calculate the aberration e. But now let S represent a star and E the Earth. Then the old classics, who believed in an ether carrying light not very differently from water carrying waves, calculated the aberration the same way. This instantaneous" aberration turned out to be e = (v/c) sina where c is the velocity of light and if sina really intimidates you, choose a star with a = 90 deg. and sina, will disappear... In any case, it did not do them much good, because there was no way to measure it directly. Indeed, what would they compare the aberration to? There are no "non-aberrant" stars. What you see is what you get, and you do not know where the real source of light is. So what has been done since the 18^th century (actually since 1690 by the great Danish astronomer Roemer) was to measure the angle of passage of a star through the meridian in summer and winter, when the orbital velocity of the Earth (30 km/s) was reversed and take the difference. The velocity of the star canceled out and left the result (2vorb/c) sina which agreed nicely with experiment.

But then came Einstein who said there is no ether, only moving systems (star at rest in one, Earth in the other) and relative velocity. He got the same formulas except that the v was the relative velocity of star and Earth. And that is where he was wrong.