Aberration, Continued
In a short paper it is impossible to enumerate those fruitless efforts of three centuries, all trying to establish incontrovertibly the veracity of Galileo's legendary "Eppur Si muove!". Those interested in particulars will find them sprinkled throughout the extensive literature dealing with the issues involved.(15)^{ } For the purpose at hand we may restrict ourselves  as a cursory view of history clearly intimates  to a crucial experiment at the crossroads of classical and relativistic science. To wit, as already mentioned, the test performed in 1871 by Airy, a test more than a century earlier suggested by a forgotten genius, Ruggiero Guiseppe Boscovich (1711 1787).
Since the readers for whom this essay is intended range, professionally grouped, from interested laymen to doctors in astrophysics, I am compelled to be popular without sacrificing correctness and to elaborate where for those "in the know" a single sentence would suffice. Only one mental favour I must ask all of them to grant me. It is that for the sake of argument they suspend or forget for a few minutes a fact they already "know" or are convinced of, i.e. that the Earth is no more than an
De Labore Solis 27
Imagine somewhere on Earth a closed box ABCD with a pinhole P in the top through which a light ray, from a source S stationed in a tower, touches the bottom DC in S. Now suppose that we set our box in motion towards the right. Then the light in a straight line moving ray SS still needs a fraction of time after passing through the pinhole to reach the bottom DC. But during this split second the box has moved to position A_{1}, B_{1, }C_{1}, D_{1}, and "inside" the box S will hence have veered to S_{1} at the left of S. Further: it is not difficult to see that, when we fasten our frame of reference on the box, the path of the light ray will show a slant.
Next we now fill the box with water and repeat our Gedankenexperiment. With light source and box both at rest, relative to us and the Earth, nothing alters, but as soon as we again set the box in motion we observe a change. In water the speed of light is about three fourths of its speed in air. Consequently the "wavicles" emanated by S need more time to traverse the box. As seen by an observer situated at the bottom of that box their trajectory is, it follows, more slanted than it was on our first trial run, and they will reach the bottom at S_{2}.
So far, so good. However, now the action shifts in space and time to a duo of astronomers who became convinced that they had found a phenomenon capable of removing the last lingering doubt whether Copernicus had indeed the right sow by the ear. In December A.D. 1725 we see James Bradley and Samuel Molyneux manipulating a telescope fixed to a chimney stack and directed at the star Gamma Draconis, almost vertically overhead. Neglecting for brevity's sake the finer points of the affair: prolonged observation showed the two stargazers that Gamma Draconis, relative to the
28 De Labore Solis
eartbound chimney of Molineux's house, in the course of a year described a small circle. By the light of the foregoing their conclusion is easy to grasp and crystal clear: the Earth is moving, and in fact revolving relative to Gamma Draconis and hence relative to all fixed stars, the Sun included. More: taking into account the speed of light and the observed angle of aberration, simple trigonometry shows our orbiting home to have exactly the velocity that Bradley already "knew" it had of more than one hundred thousand km/hr. The slightest skepticism remaining about the truth of Copernican astronomical gospel could therefore be laid to rest.
Well, not totally! Logically considered, this conclusion uses that invalid theoretical syllogism, the modus ponendo ponens. If situation P is the case, we agree, then we shall observe the phenomenon Q. Now indeed we observe Q. Does it therefore follow that P is the factual state of affairs? By no means necessarily, for Q may be caused by a variety of other circumstances. As one of my textbooks of logic remarks: "We shall have frequent occasions to call the reader's attention to this fallacy. It is sometimes committed by eminent men of science, who fail to distinguish between necessary and probable inferences, or who disregard the distinction between demonstrating a proposition and verifying it".(17)
"Aberration", to quote van der Waals, "may equally well be squared with the supposition that the stars indeed describe circlets. And though we find the latter explanation improbable and prefer the first, the question may arise: is it in no way possible by means of observations to decide which of the two suppositions is the right one?"(18)
Boscovich, sensibly and objectively not inclined to
De Labore Solis 29
put all his theoretical eggs in Bradley's logically bottomless basket, saw a chance to do just that. And many an astronomically nonconversant reader, having followed the discourse thus far, may already have realized that chance also. Fill a telescope with water and measure the aberration angle for any fixed star. If the angle in this manner obtained is larger than the one measured by Bradley, the Earth indeed orbits, relative to firmament and Sun. If no different value is registered, then the starry sphere swings, with the Sun on which it appears to be centered, around that beautifully blueandwhite marbled "planet" Gea.
Unlike the conclusion of Bradley's invalid ponendo ponens argument, which by affirming affirms, this reasoning in the modus tollendo tollens, the mood which by denying denies, cannot logically be faulted. If P, then also Q, and hence if no Q, then no P. The outcome of the experiment will settle the case unless, of course, we may not like the verdict and therefore refuse to accept it!
For more than a century after Boscovich suggested this verification of the heliocentric theory nobody of any astronomical consequence thought an effort to execute it worth the trouble. Bradley, after all, had only and somewhat superfluously confirmed what on the authority of Copernicus, Kepler and Galileo  with Newton standing on the shoulders of those giants everybody knew to be true. Why bother to lay bare the glaring untruth of Tycho Brahe's nonsensical scheme? As far as this is concerned we may for the ruling consensus from 1726 until today well quote the late (from relativist to antirelativist converted) Herbert Dingle that "surely no one in his senses would now maintain that the Earth
30 De Labore Solis
provided a standard of rest for all the light in the Universe.(19)
Yet progress of the sciences during the nineteenth century evoked such a welter of conflicting theories about aethers, spaces, and motions(15) that in 1871 Airy, taking his clue from Boscovich, decided for once and for all to measure that supposed alteration in the amount of stellar aberration by means of a waterfilled telescope. He had no great expectations about a decisive result, since trials conducted by the German Klinkerfuesz and the Dutchman Hoek  more about the latter later!  had already presaged a failure to find any alteration in Bradley's 20".47 angle.(20) And indeed that failure turned out to be the case, wherefore the only remaining difficulty was how to explain such a seemingly Ptolemaic result in Newtonian terms. Happily the means to do this were available readymade, for half a century earlier, after considering an experiment by Francis Arago (17861853),(21) the French physicist Augustin Fresnel (17881827) had devised a theory that offered the needed solace.(22) Taking his clue from the fact that the square of the speed of sound in gases is in inverse ratio to their specific gravity, and assuming an elasticsolid aether, Fresnel had obtained a formula for the velocity of light in moving transparent media involving a factor 1(1/n^{2}). This socalled "dragging coefficient" was in 1859 tested by Fizeau (18191896), whose affirmative results, after much travail, were in 1886 by Michelson and Morley found to be "essentially correct".(23)
De Labore Solis 33
kilometers  we cannot demonstrate that speed! Sparing the reader the mathematics and neglecting miniscule higherorder terms: if we work it out we find Fresnel's dragging coefficient adequate to explain Hoek's negative result. "If the aether carrying the light moves with a velocity w... then we find w = v(n^{2}^{1}/n^{2}), which is exactly the aether velocity according to Fresnel."(26) After all, convinced as we are that his laboratory was not at rest in the omnipresent aether, but was in any case with the Earth orbiting the Sun at V = 30 km/sec, this must be true. If the drag coefficient were not this 1(^{1}/n^{2}), Hoek would have observed some effect! Was this conclusion truly inescapable? Unblushingly to overlook the not yet ruled out most plausible inference  that of the apparatus at rest in space  bears testimony to a willful, prejudiced, unscientific shortsightedness. What if v=0 and consequently w=0? To get ahead of the argument: only if here on Earth his hexagon moving at high speed also will stubbornly show no interference shall we have to affirm Hoek's explanation. As yet, and without such a control experiment, it seems logically a too hastily accepted conclusion.
Dutifully to follow the storyline taken in the standard textbooks: "An entirely different piece of experimental evidence shows that Fresnel's equation must be very nearly correct. In 1871 Airy remeasured the angle of aberration of light using a telescope filled with water", and "it will be seen that if the velocity of the light with respect to the solar system be made less by entering the water, one would expect the angle of aberration to be increased... Actually the most careful measurements gave the same angle of aberration for a telescope filled with water as for one filled with air."(27)
34 De Labore Solis
It was, as said, feasible to explain this strange phenomenon with Fresnel's dragging coefficient, but "a different explanation is now accepted, based on the theory of relativity".(28) Or to quote van der Waals: "It is possible generally to prove how Fresnel's theory entails that not a single optical observation will enable us to decide whether the direction in which one sees a star has been changed by aberration. By means of aberration we can hence not decide whether the Earth is moving or rather the star: only that one of the two must be moving with respect to the other can be established. Fresnel's theory is hence a step in the direction of the theory of relativity."(29)
