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 anti-relativist converted) Herbert Dingle that “surely no one in his senses would now maintain that the Earth 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 water-filled 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 ready-made, for half a century earlier, after considering an experiment by Francis Arago (1786-1853),(21) the French physicist Augustin Fresnel (1788-1827) 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 elastic-solid aether, Fresnel had obtained a formula for the velocity of light in moving transparent media involving a factor 1-(1/n2). This so-called “dragging coefficient” was in 1859 tested by Fizeau (1819-1896), whose affirmative results, after much travail, were in 1886 by Michelson and Morley found to be “essentially correct”.(23)
In Fizeau’s experiment (see figure 2) two parallel light rays are sent through an U-form tube of glass containing fast-flowing water, the one ray clockwise, the other counter-clockwise. And both are after their return via a semi-transparent mirror M observed in O. Now: “if one moves relative to the aether (assuming that it exists) then the speed of light must be increased by the speed of the relative motion. Thus the speed of light in a material which moves with a speed u against the direction of motion of the light becomes (v+u), if the speed in the material at rest was equal to v… The outcome of the experiment was, however, quite different from that expected. Instead of the speed iv=v+u, Fizeau’s experiment gave a result which proved to be dependent on the refractive index of the liquid used: w=v+u (1-1/n2) The only reason that one could think of to explain this result was that the aether was swept with the liquid, although not completely but with a ‘drag coefficienf 1-1/n2.” 24)
Fresnel’s suggestion hence seems to hit the mark, and another experiment, in 1868 performed by the Dutchman Hoek had already ostensibly provided further confirmation. He directed light rays clockwise and counterclockwise around a hexagonal circuit ABCDEF of which the segment FE was a water-filled tube, (see figure 3). “If this apparatus would stand still, then a difference in their time of revolution is certainly not to be expected. For every segment of the circuit a fixed amount of time will be required, it being a matter of indifference in which way it is passed through. But imagine the apparatus to move from left to right. Then the light rays meet different conditions.” That is, as in the case of Fizeau, Fresnel’s dragging coefficient will shove in its oar. “Hoek performed the test, and it turned out that between the two times of revolution a difference does not exist. To perform the test he did not have to take great pains to give the whole apparatus a sufficient speed…. The Earth, by means of her rotation and her annual orbit around the Sun, provided a speed that was vastly greater than could have been obtained in any other manner. The result of the experiment only needed to be compared with that obtained when the apparatus was not moving in the direction of the segments CB and EF. This was done by rotating the apparatus 90°, so that those segments of the circuit, which first coincided with the direction of the Earth’s motion, after that were perpendicular to it.”25)
It is not difficult to see the conclusion that Hoek thought he could draw from this null result. Whatever speed v of the aether relative to the Earth we have decided to believe in, be it a few centimeters or many kilometers – we cannot demonstrate that speed! Sparing the reader the mathematics and neglecting miniscule higher-order 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(n2–1/n2), 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/n2), 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 short-sightedness. 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.
- The Fancy Foundations in the Beyond
- The 1887 Cleveland Disenchantment