CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 387
The foregoing formula is derived on the assumption that the dielectric substance may be regarded as a continuum. The structure of e has not been taken into account; but the difference would not be appreciable. Both Tomaschek and Chase used not a single condenser, but a great number of plates in order to obtain a large capacity and thus have a large value for the electric energy.
The torque is practically the same for both the classical theory and the theory of relativity, the difference arising only in some terms of the fourth order, which are of no practical importance. In spite of the existence of a torque, relativity contends that no effect can be observed at all. This follows because the torque is compensated in some way. The explanation of this peculiar fact is to be found in the tensor character of the mass in relativity. In this theory mass has a different value for accelerations in direction of the motion (mi) and at right angles (mtr) to it. The ratio of the masses is given by the expression
mi _ i
mtr i — (v/c)2 '
In order to analyze the effect of the torque found above, we must divide the acting forces into two components, one in direction of the motion and one at right angles to it. The first component acts against the heavier mass mi and causes a relatively smaller acceleration than the second component. It thus happens that the two accelerations (as vectors) point to the center of gravity of the system (condenser) although the two forces do not. In this way the torque appears to be compensated in the end effect. Thus we see that the tensor character of mass is responsible for the lack of an effect. The Lorentz contraction has not to be taken into account at all. Even in case there were no Lorentz contraction, we should not obtain an effect on our condenser. If, however, an effect should really be observed it would be a contradiction of relativity, because the ratio mi/mtr is a direct consequence of this theory. Tomaschek and Chase both claim to be able to detect an uncompensated torque corresponding to a velocity of the earth of 4 km/sec. For lower velocities no deflection could be observed with their apparatus. This limit of precision is obtained by assuming the whole torque to be in action.
388
PAUL S. EPSTEIN
Now this assumption is not quite correct even from the standpoint of the classical theory. As the nuclei are of electrical constitution, we must in the classical theory also take into account a definite relation between the mass and the velocity of the nuclei. Considering the nuclei as rigid spheres, for instance (Abraham), we should find
m = 1/(1 —ft2)
mtr l/(l-fft2) ■
If we use this formula, the torque will be compensated in part, but not completely as in relativity. It can easily be seen from the formula that 20 per cent of the calculated torque would manifest itself as deflection. The minimum velocity which could be observed by Chase would then be 4V5 km/sec., which brings us near to Miller’s value of 10 km/sec. Although interesting, these experiments cannot therefore decide either for or against Miller’s results. On this account it would be of great value if they could be carried out with increased precision.
Now some remarks about the experiment of Mr. A. Piccard at Brussels: Piccard thought that the height above the earth’s surface should be of influence on the effect Mr. Miller has found. (This is, in fact, a misunderstanding, because Mr. Miller does not claim any such effect.) If the ether drift may be supposed to be larger on Mount Wilson than at sea-level, it should be still larger in the free atmosphere. So Piccard tried the experiment in a balloon. His inter-
• _
ferometer had branches with an optical path 2.8 m long. The steady temperature was controlled by a thermostat. The balloon was rotated about a vertical axis by means of a propeller. A self-recording device was used, and ninety-six rotations were registered. The curves were analyzed harmonically, but it appeared that the thermostat had not functioned as expected. For this reason the accidental errors were too large (the probable error corresponded to a velocity of 7 km/sec.). All that Piccard claims, then, is that the drift in the free atmosphere at 2300 m altitude is not larger than on Mount Wilson. No further conclusions can be drawn from this experiment.
[Note added April, IÇ28.—Both C. T. Chase and A. Piccard have continued their work during the year intervening since the foregoing