116 The Poetry of Physics and The Physics of Poetry
Light propagating in the opposite direction to the Earth’s motion would
have the relative velocity c+v. On the other hand, light traveling in the
direction perpendicular to the Earth’s velocity would have a relative
velocity of c 1 −v^2 /c^2.
Michelson set out to measure the differences in these relative
velocities with the help of a physicist named Morley. In 1887, they
designed an apparatus, called the Michelson–Morley interferometer
illustrated in Fig. 13.2, which could detect the differences of these
velocities. Using a series of mirrors, one of which was half-silvered, light
from a single source was divided into two paths and then brought back
together again. The light travels along identical paths except for one
segment in which the light traveled back and forth perpendicular to the
Earth’s velocity on one path and parallel to the Earth’s velocity on the
other path. Because the relative velocity of the light is different along
these two paths, as outlined above, it takes longer for the light to travel
along the path in which it moves only parallel to the Earth’s motion.
Because of this time delay, one expects to the two beams of light to
interfere with each other. The arrangement of light source, mirror and
telescopic detector were all mounted on a huge piece of sandstone, which
was floating in mercury. This enabled the apparatus to be easily rotated
so as to align one of its axes with the Earth’s velocity. After carefully
and slowly rotating their interferometer, Michelson and Morley were
unable to measure any interference.
The inability of Michelson and Morley to observe the effects of
the aether was very disturbing to the physicists of their time. Their
experiment was repeated and refined a number of times, always with the
same result. One of the preoccupations of physicists during this period
was an attempt to explain away the results of the Michelson–Morley
experiments.
One of the first attempts in this direction was to claim that the aether
was dragged along by the Earth’s motion and hence, the detection of the
relative motion of the aether and the Earth was impossible. This
explanation was easily dismissed, however, since the phenomenon of
aberration of starlight would not have been detected if the aether were
dragged by the Earth. One observes a star at an angle α = v/c because of
the velocity v of the Earth perpendicular to the direction in which the
starlight is propagating. If the aether was dragged along with the Earth,
then, the starlight would also move with the velocity v in the direction of
the Earth’s motion and hence, it would no longer be necessary to tilt the
telescope through the angle of aberration to capture the starlight.