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the rod at an instant in time. We are told that x 2
1 m and asked to find the
corresponding length as measured by an observer at rest in S .
Our second observer makes their measurement of the length of the rod. Let's
suppose they do it at a time t (the two observers don't have to measure the length
at the same time so t does not have to equal t). Again there are two events, the
measurement of one end of the rod at (x 1 , 0 , 0 ) and the measurement of the other end
of the rod at (x 2 , 0 , 0 ). Now using the Galilean transformations it follows that x 1 =
x 1
x 1 =
vt and x 2 =
vt from which it follows that x 2
x 1 =
x 2
x 2
x 1 =
1 m,i.e.
both observers agree on the length of the rod.
The relationships between measurements of events in different inertial frames
under the assumption of absolute time is called 'Galilean relativity'. According to
Galiliean relativity, all observers will agree on things like the length of a rod or
whether or not two events are simultaneous. It is now time to question the validity
of this simple and intuitive relativity theory.
5.2 EXPERIMENTAL EVIDENCE
We are going to need some pretty compelling reason to give up the Galilean view
of space and time. In this section we'll motivate the need for something different
and we start with the 1887 experiment of Michelson and Morley.
5.2.1 The Michelson-Morley experiment
Is it possible to chase after a beam of light? In classical physics the answer
seems to be a resounding 'yes'. We can even imagine running at close to the speed
of light whilst shining a torch ahead of us. If we run fast enough then we might
expect to see the light travelling slowly out of the front of the torch and when we
reach light speed the torch is finally rendered useless. Thinking like this we are
imagining that the light travels in a medium, just as every other wave we know
of in Nature, and that its speed of propagation is fixed relative to the medium.
The uselessness of our torch as we reach the speed of light is in this way entirely
analogous to the phenomenon whereby a jet aircraft travelling at the speed of sound
cannot be heard until it has passed by. This is a natural way to think, i.e. light
needs a medium to support its vibrations, but it is wrong and the experiment that
proves 2 it is the Michelson-Morley experiment.
If light is a wave travelling through some medium, which is historically referred
to as the 'ether', then it should travel at a fixed speed c relative to the ether. This
means that different observers in different inertial frames will all measure different
speeds for a beam of light. Similarly an observer can tell if they are moving
relative to the ether by sending out two (or more) beams of light in non-parallel
directions. Only if the two beams travel at the same speed is the observer entitled
to say they are at rest relative to the ether and from any difference in speeds the
observer will be able to determine their speed relative to the ether. As an aside,
2 Actually it does not strictly prove the absence of a medium. Rather it provides some very compelling
evidence.
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