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162 Dr. L. Silberstein on the recent Eclipse Results
given up * and replaced by the assumption that the aether is condensed round the Earth, and other celestial bodies, as if it were subjected to the force of gravitation and behaved more or less like a perfect gas. Lorentz, in spite of his personal preference for a fixed rather, took up Planck's idea and worked out the problem under the special (but by no means the only possible) assumption that the aether density p and pressure p obey Boyle’s law, p = ap, where a = const. If M be the Earth’s mass, in astronomical units, this gives
where is the density at infinity and r the distance of any external point from the Earth’s centre. The maximum velocity of slip at the Earth's surface (r=H), in the direction opposite to that of its motion becomes t
where a = otM/R, and is the velocity of the aether, relative to the Earth, at infinity.
To account for the astronomical aberration within the limits of experimental error it is necessary and sufficient to make This gives, by (2), with sufficient approxi
mation (since the required a is manifestly so large as to make the second term of the denominator negligible],
so that the said requirement is amply satisfied by
This means, according to (1), a condensation J, of the aether amounting at the Earth’s surface to little less than
and gives at the same time for the (lower limit of the) coefficient a the value 10"2R/M, to which we may return
* Of. H. A. Lorentz’s paper on Stokes’s theory of aberration in A mster-dam Proc. for 1898-99, p. 443, reprinted in vol. i. of his Abhandlungen.
t A short deduction of this formula will be found in Lorentz’s 1 Theory of Electrons,’ 1909, p. 314.
J What is commonly called “condensation” would in our case be
--1. But it will be convenient to use this as a short name for p/p .
which will henceforth be denoted by s.
and Stokes-Planclcs SEtlier.
later on. In order to reduce the slip to ^ per cent, of a •condensation of about 60000 would be required *.
In view of this considerable condensation, required by the theory of Stokes-Planck, Lorentz made in 1909 (‘ Theory of Electrons/ pp. 173-4) the following characteristic remark:—
“In this department of physics, in which we can make no progress without some hypothesis that looks somewhat startling at first sight, we must be careful not rashly to reject a new idea, and in making his suggestion Planck has certainly done a good thing. Yet I dare say that this assumption of an enormously condensed ether, combined, as it must be, ivith the hypothesis that the velocity of Jiglit is not in the least altered by it, is not very satisfactory/’ [The last words are italicised for our present purpose.]
In fact, such a condensation, introduced ad hoc and serving only the negative purpose of not upsetting the theory of aberration, did not seem very satisfactory, and the present writer has as recently as 1914 expressed the same opinion in his book on Relativity (p. 63), not so much to defend Fresnel's and Lorentz’s fixed aether, as to prepare the reader’s mind for the complete abolition of the a?tber and thus to introduce him to Einstein’s “special” relativity of 1905. Such has been the position of things until recently.
3. Now, it so happens that, stimulated by the desire to test Einstein’s generalized relativity and theory of gravitation, the astronomers participating in the last Eclipse Expedition have found an undoubtedly positive effect, the bending of rays passing near the Sun. As I have pointed out on previous occasions, it seems premature to interpret this result us a verification of Einstein’s theory, not merely in view of the small outstanding discrepancies, but chiefly in view of the failure of detecting the spectrum shift predicted by the theory, with which the whole theory stands or falls. But the Eclipse result proves at any rate that there is an
alteration,99 a change of light-velocitv all around the Sun, which thus invalidates the words of Lorentz italicized in the quotation above. The condensation claimed by Planck's modification of Stokes’s theory, for the Sun as well as for the Earth and for all other material bodies, is no longer devoid of influence on observable phenomena. It suddenly acquires physical life, so to speak.
* Notice that the aberration is a first order effect, while such phenomena as that expected by Michelson-Morley are second order effects (v2/c2), so that the above condensation suiting the aberration up to 1 per cent, will reduce the Michelson-Morley effect to one ten-thousandth of its value, and thus practically annihilate it. There is thus no need for making <r larger than 10*2.