Shrinking distances

Not content with overthrowing the old notions of absolute time,
Einstein still had a few more surprises up his sleeve. Consider how things would look to you if you were sitting on a muon as it
travelled down to Earth. You would agree with someone standing
on the ground watching you that you were approaching each other
at 99% of the speed of light. How is it that he would see you
covering the distance of one mile, say, in a time of five millionths
of a second (fivemuonlifetimes) according to his Earth clock, while
you claim to cover the same distance in just one tenth of that time.
There are no light beams involved here and you would think that
the only maths required is the relation: speed equals distance over
time. Howis it that both of you agree on the speed you are moving
and yet cannot agree on the time it takes you to cover the same
distance?
Something else has to give, and now it is distance. In order
to obtain the same value for the muon’s speed in both cases (by
dividing distance over time) the distance travelled as seen by the
muon must also be one tenth of its value as seen from Earth. That
is, the muons will see the distance squashed up to much less than
a mile. This explains how it is able to survive the journey; it does
not think it has had so far to travel.
This property of high speed travel is known as length
contraction. It states that fast moving objects look shorter than
they do when standing still. In the example of the muons the object
in question is the thickness of the atmosphere. An Irishman and
a Dutchman first suggested this effect soon after Michelson and
Morley’s experiment, and several years before special relativity.
George Fitzgerald and Hendrik Lorentz pointed out that the
result of the ether experiment could be explained if there was a
contraction of lengths with high speed motion. This would have
rescued the idea of the ether. Lorentz even went so far as to derive
a set of equations that now bear his name. Unfortunately for him,
he did not make that final leap of intuition that was the second
postulate of relativity. In a way, therefore, a lot of the groundwork
had already been done before Einstein and it is often claimed that,
had he not discovered special relativity, someone else would have.
As with the slowing down of time, the shortening of lengths
is something which shows up more the closer a moving object
gets to the speed of light. So what sort of effect would we observe in the real world? To give you a solid example, imagine
taking a high precision photograph of a jet that is flying at twice
the speed of sound (over two thousand kilometres per hour).
You would observe it to be ever so slightly shorter than it was
when on the ground. But for a typical aircraft this shortening
of length would be less than the width of a single atom! This is
certainly not measurable from a photograph of the aircraft. But
you have to remember that although twice the speed of sound
seems impressively fast to us, it is nothing compared with the
speed of light. If the jet had been travelling several hundred
thousand times faster, say over three-quarters the speed of light,
then we would see a difference. The jet would look only half its
original length. If it were to travel as fast as the cosmic ray muons,
it would look squashed to just one tenth of its length.
How uncomfortable for the poor pilot, you must be thinking.
Presumably this is one of the hazards of such high speed travel.
The truth is that the pilot will feel nothing unusual. To him the
dimensions of the plane (and himself) have not changed at all. In
fact, due to the first principle of relativity, he sees the world around
him squashed up, in the same way that the muons would (if they
could see that is!)