Thought experiments and brain teasers

Einstein was only a child when Michelson and Morley carried out
their experiment. Even during his youth he pondered the unusual
properties of light by devising thought experiments (his famous
gedanken). He tried to imagine himself flying at the speed of light
while holding a mirror in front of him. Would he see his own
reflection? How could the light from his face ever reach the mirror
if the mirror itself was movingawayat the speed of light? His years
of contemplation culminated in two simple statements known as
the principles of relativity. They can be put in the following way:
1. There are no experiments you could perform that would tell
you whether you were standing still or moving at constant speed. All motion is relative so nothing can be said to be truly
stationary.
2. Light behaves like a wave in that its speed does not depend
on the speed of its source. At the same time it does not require
a medium to travel through like other waves.
So far, so good. You would think that there is nothing in the above
innocuous statements that you might have difficulty subscribing
to. They certainly look too lightweight to be able to answer the two
questions posed earlier in the chapter about nothing going faster
than light and time slowing down. They may look harmless but
believe me, by accepting them you will be selling your soul to the
devil.
First let me assure you that they are both quite true and can
be demonstrated easily. The first postulate suggests that if you
perform a simple experiment like dropping a ball while on board
an aircraft travelling at a constant speed, the ball will, according to
you, fall vertically in the same way that it would if you performed
the experiment on the ground. You therefore have just as much
right in claiming that the aircraft is stationary while the Earth is
moving beneath you at several hundred kilometres an hour in
the opposite direction. A clearer example is that of two rockets
travelling at constant speeds towards each other in space. If both
the rockets’ engines are off and they are just ‘cruising’ they could
never decide whether they were both moving towards each other
or whether one was stationary and the other approaching it. It is
no good appealing to a nearby star as a reference point since who
is to say that it is really stationary?
The second postulate was confirmed by the Michleson and
Morley experiment and on its own seems harmless. It is when
the two postulates are combined that the trouble starts. I know I
sound a bit like a doctor, but I want you to be brave as this might
hurt a little.
We have established that the light reaching us from a source
will travel at the same speed regardless of how fast the source is
moving. But because it doesn’t have a medium to travel through
and with respect to which we can measure its speed, then we
can equally well say that it is not the source moving towards us but us moving towards the source since all motion is relative. This
is just a statement that light obeys the first principle of relativity.
Consider the two rockets approaching each other again. An
astronaut aboard one of them shines a light beam towards the other
and measures the speed of the light as it leaves her rocket. Since
she can quite legitimately claim to be stationary, with the other
rocket is doing all the moving, she sees the light moving away from
her at the usual three hundred thousand kilometres per second.
At the same time, the astronaut aboard the other rocket can also
legitimately claim to be stationary. He will measure the speed of
the light reaching him to be three hundred thousand kilometres per
second and states that this is not at all surprising since the beam’s
speed does not depend on how fast its source is approaching.
Both measure the light to have the same speed. This is
amazing, and goes quite against common sense. Both astronauts
measure the same light beam to be travelling at the same speed,
despite moving relative to each other!
We can now answer Einstein’s question involving the mirror.
It does not matter how close he gets to the speed of light—and I
will explain later why he could never travel at the speed of light—
he will always see his reflection. This is because regardless of his
speed he still sees light travelling at the same speed from his face
to the mirror and back again.
A better way of formulating this is to imagine shining a
torch, then travelling alongside the torch beam at three quarters
of the speed of light according to someone left holding the torch.
Your common sense tells you that you should see the light still
overtaking you but at a much reduced speed of one quarter its
original speed. Right?
Wrong! You still see it moving at the same speed that the
person holding the torch measures it to be moving.