The hypothesis demanded detailed and exhaustive examination. It was for the mathematician to test whether it was in opposition to known and established laws of physics, and to this task Ein stein, Lorentz and others set themselves. If the hypothesis proved to be in opposition to a single firmly established law, then of course it must be abandoned. It was unlikely that such an event would occur among the well-established laws, for if it did, the phenomena governed by that law would enable direct measurement to be made of the earth's velocity through the ether, a measure ment which had so far eluded all attempts of experimenters. It was among the more obscure and less well-established laws, if any where, that discrepancies were to be looked for.
It is impossible here to give a complete account of the many tests to which the relativity hypothesis has been subjected. The result of all can be summed up in one concise and quite general statement :—Wherever the hypothesis of relativity has appeared to be in conflict with known or suspected natural laws, further experiment, where possible, has without a single exception shown the laws to be erroneous, and has moreover shown the alternative laws suggested by the hypothesis of relativity to be accurate. It is only in somewhat exceptional cases that the hypothesis of rela tivity suffices of itself to determine fully the form of a natural law; these cases constitute the most striking triumphs of the theory. As instances may be mentioned the determination of the law connecting the mass of an electron with its velocity; of the law expressing the velocity of light through a transparent medium in motion (Fizeau's water-tube experiment) ; and of the formu lae for the magnetic forces on moving dielectric media (experi ments of Eichenwald and H. A. Wilson)).
Before leaving this general statement, particular mention must be made of one special case. A natural law which, at an early stage, was seen to be in conflict with the hypothesis of relativity was Newton's famous law of gravitation—namely, that every particle of matter attracts every other particle with a force pro portional to the product of the two masses, and to the inverse square of their distance apart. Either, then, Newton's great law had to be abandoned, or else the hypothesis of relativity had to be discarded, in which case it would immediately become possible, in theory at least, to determine the earth's velocity through space by gravitational means. It is the choice between these two alterna tives that has led to the most surprising developments of the theory of, relativity ; and to these we shall return later.
The hypothesis of relativity, as has already been explained in this section, postulates that the phenomena of nature will be the same to two trained observers moving relative to one another with any uniform velocity whatever. The hypothesis has been so amply
tested as regards all optical and electromagnetic phenomena that no doubt is felt, or can rationally be felt, as to its truth with re spect to these phenomena. The hypothesis can be examined and developed in two opposite directions. We may, on the one hand, Tor references to the original papers dealing with these and other tests of the hypothesis of relativity see Cunningham, The Principle of Relativity, or J. H. Jeans, Mathematical Theory of Electricity and Magnetism (4th or 5th ed.).
proceed from the general hypothesis to the detailed laws implied in it ; this has already been done, with completely satisfactory results as regards confirmation of the hypothesis. Or regarding the hypothesis of relativity as being itself a detailed law, we may attempt to generalize upward to something still wider. It is this possibility which must for the moment claim our attention.
In 1905 Einstein examined in full the consequences of the hy pothesis that one simple optical phenomenon—namely, the trans mission of a ray of light in free space—was, in accordance with the hypothesis of relativity, independent of the velocity of the observer. If an ether existed, and provided a fixed framework of reference, then light set free at any instant would obviously travel with a velocity which would appear to an observer at rest in this ether to be the same in all directions, and the wave front at any instant would be a sphere having the observer as centre. On the hypothesis of relativity the phenomenon of light trans mission must remain unaffected by the motion of the observer, so that the light must appear, to a moving observer also, to travd with a uniform velocity in all directions, and thus to the moving observer also the wave front must appear to be a sphere of which he is the centre. It is, however, quite obvious that the same spherical wave front cannot appear, to each of two observers who have moved some distance apart, to be centred round himself, unless the use either of the common conceptions of science or of the ordinary words of language is greatly changed. In fig. 2 it is not possible, in ordinary language, that both 0 and P should at the same instant be at the centre of the sphere ABC. The change to which Einstein was forced is one which has an intimate bearing upon our fundamental conceptions of the nature of space and time; this change it will be necessary to explain in some detail.