Environmental Engineering Reference
In-Depth Information
c
u
u
Figure
5.3
The
addition
of
velocities
relevant
to
path
1
of
the
Michelson-Morley
experiment.
speed and so the total time take for the round trip is
2
L
t
1
=
v
2
/c
2
.
(5.5)
c
1
−
Path 2 is easier since the light is either parallel or antiparallel to the direction of
the ether. On the outward path the light is travelling into the ether at speed
c
−
v
whilst on the return path it is swept along by the ether at speed
c
+
v
. The time
for each leg is thus different and the total time taken is
L
L
2
L
t
2
=
v
+
v
=
v
2
/c
2
)
.
(5.6)
c
−
c
+
c(
1
−
The time taken by the light which travels along path 1 is therefore slightly shorter
than for the light which travels along path 2.
The experiment of Michelson and Morley was designed to be sufficiently sensi-
tive to this time difference that it could detect a speed through the ether comparable
to the speed with which the Earth rotates around the Sun (which is about 30 km/s).
In this way they hoped to be sure of seeing an effect at some time during the
year since if at one instant the Earth just happened to be at rest relative to the
ether, it would be unlikely to be at rest some time later and six months later one
might reasonably expect it to be travelling at twice the orbital speed, i.e. 60 km/s.
Of course we know that the Sun is moving at vast speeds relative to the centre
of the galaxy and that the galaxy moves relative to other galaxies so one really
ought to expect that the speed of the Earth through the ether is at the very least
equal to its orbital speed around the Sun. However, Michelson and Morley did not
measure any time difference. There was no error in their experiment, they were
simply forced to conclude that the Earth does not move relative to an ether.
5.2.2 Stellar aberration
The simplest way out of this null observation might seem to be to suppose that
the ether is being dragged along by the Earth, i.e. it is as if the Earth has an
atmosphere of ether. However, since 1727 it was well known that this could not
be so. James Bradley's observations of stellar aberration seemed to require that
observers on Earth should be moving through the ether at relative speeds which
differ over the course of a year by an amount equal to twice the Earth's rotational
speed about the Sun. Let's go into a little more detail.
