Slowing down time

We have reached the above strange state of affairs by following a
number of logical steps coupled with firm experimental findings.So where are we going wrong? After all, it is the same light
beam; the same electromagnetic waves or photons or whatever
you choose the light to consist of, that is leaving the torch. How
can you, while travelling alongside it at some healthy fraction of
the speed of light, still see it moving past you at the same speed
as that seen by the guy holding the torch? The only way this
could happen is if your time is running at a slower rate than his. Ifhe
could see a stopwatch you are holding he would see it counting by
the seconds more slowly than his. If he could somehow remotely
measure your heartbeat he would find it slower. Everything about
you is, according to him, running slower. That’s not all; if you
forget about the light beam for a moment, the first principle of
relativity implies that you could equally well consider your friend
who is standing on the ground to be the one who is moving at three
quarters the speed of light, in the opposite direction. You would
see his time running slower than yours!
This is not some crackpot theory devised to make sense of
the ridiculous notion that light would travel at the same speed
for everyone. The notion about the speed of light is far from
ridiculous and is confirmed all the time these days in experiments
in particle accelerators. These are huge laboratories with circular
underground tunnels, several miles long, that send subatomic
particles round at close to the speed of light, such as the famous
CERN facility in Switzerland. The slowing down (called dilation)
of time is an unavoidable consequence of the behaviour of high
speed particles.
Let me first quickly mention these particle experiments. It
is known that a certain type of subatomic particle, called pions
(pronounced ‘pie-on’), emit photons of light. When a pion is
stationary the photon will, of course, emerge at the speed of light
(it is a particle of light after all). But at CERN, pions can be made
to move round in a large circular underground tunnel at very close
to the speed of light. They still emit their photons however, and
those photons emerging in the direction that the pions are moving
can be detected and their speed measured. They are found to be
still travelling at the same speed that they travel when emitted
from a stationary pion. Thus the same photon emerging from the moving pion is seen
to travel at the speed of light from our point of view standing in
the laboratory and from the point of view of the pion itself.
As for the slowing down of time, we can see how this comes
about by considering the following thought experiment. Figure 6.1
shows a box containing a light source with a detector at the bottom
and a mirror at the top. The source, which is pointing straight up,
emits a flash of light (called a light pulse) which bounces off the
mirror at the top and backdowninto a detector which signalswhen
it has received it. According to someone inside the box the light
will take a certain time to go fromthe source to the mirror and back
to the detector. Now imagine that the whole box is itself moving
sideways at close to the speed of light. To an observer watching
it zoom by (it has a glass front), the light pulse traces a path that
is longer than the straight-up-and-down path seen by the person
inside the box. To the observer watching from outside, the pulse
must cover the longer distance shown in the figure, but he still sees
the light travelling at the same speed. However, since it must now
cover a longer distance (the dashed line), a longer time will have
elapsed before it gets back to the detector3. Therefore more time
goes by according to a clock on the ground than according to a
clock inside the box. Since both clocks are measuring the duration
of the same process (the time taken for the light to move up and
down the box) time inside the box must be running slower for its
clock to record a shorter duration! Aficionados of special relativity
will be aware that this explanation is not strictly the whole story
since to say that someone ‘sees’ something implies that light must
reach that person’s eyes from the object, and it will take a finite
time to reach them.
So moving clocks run slow and the above example shows how
that happens. Often, when people encounter this effect for the first
time, they have the impression that the rapid motion affects the
mechanics of the clock; that the clock is somehow responding to
the speed at which it is moving. This is quite wrong. In fact, since all motion is relative, the person inside the box in the last example
can rightly claim not to be moving at all and that it is the outside
observer who is travelling at close to light speed. This is borne out
by the fact that he will indeed see the clock on the ground running
slower than the one inside the box! This often gives rise to what
appears to be a logical contradiction. How can both clocks be
running slower than each other? People who do not understand
relativity surmise that the clocks only seem to run slow according
to each other because it takes light a certain time to travel from the
clocks to the other observers. As James ASmith states in his book
Introduction to Special Relativity “nothing could malign the theory
of relativity more thoroughly”. We will see in the discussion of
the paradox of the twins later on how we can slow time down
permanently by making a clock speed up and slow down again.
I am sure you must be thinking that this is, after all, just
a theory. It may be fine for science fiction writers but surely it
can have no place in the ‘real world’. If the rate at which clocks
tick can be so dependent on their relative motion, why would we
bother about such things as high precision timekeepers like atomic
clocks? The reason is that the effect only shows up when clocks
are travelling at extremely high speeds relative to each other. The
closer to the speed of light that a clock moves, the slower it will
tick. If it were to travel at the speed of light relative to us then we
would see its time stand completely still.
Here is another example. Consider a sprinter who runs the
hundred metres in exactly ten seconds, according to the reliable
and highly accurate timekeeping of the judges. If he had carried his
own very accurate stopwatch with him then, due to time slowing
down very slightly for him while he was running, his watch would
show a time of 9.999999999999995 seconds. Of course, this is so
close to ten seconds that we would never know the difference.
However, scientists routinely need to measure times with this
sort of accuracy. The difference between the runner’s and the
judges’ watches is just five ‘femtoseconds’. The reason it is such a
small time difference is because the athlete is moving much more
slowly than light. Even the fastest rockets are too slow to show an
appreciable effect. Can we therefore ever see real time dilation in action? Well,
this is something I can vouch for personally because, like many
physics students, I performed a laboratory experiment while I was
a student at university. The experiment involves another type of
subatomic particle called a muon (‘mew-on’) which is produced
by cosmic rays. These are high energy particles from space that
are continually bombarding the Earth’s atmosphere. In the upper
atmosphere many new types of particle, mostly muons, are created
in this way, and travel down to the surface of the Earth. Physicists
have studied the properties of muons and know that they have an
extremely short lifetime of one millionth of a second. This lifetime
is, of course, only statistical in that some muons might live for a
little longer, some for a little less. But if a thousand muons are
created at once then after a millionth of a second there will be
roughly five hundred left.
The muons created in the upper atmosphere are so energetic
that they travel towards the Earth at an incredible 99% of the speed
of light. However, even at this speed it should still take them
several lifetimes to cover the distance to the surface of the Earth
(and, more importantly, into the muon detector in the laboratory).
We should therefore observe only those few with unusually long
lifetimes that were able to complete the journey. Instead we find
nearly all the muons are comfortably able to complete the journey.
The reason this is possible is that the muons’ time (their internal
clocks that measure their lifetime) is running much slower than
ours. So from the muons’ point of view only a fraction of their
lifetime has elapsed.
An alternative argument that fast moving muons must for
some reason live longer than stationary ones does not hold water.
On closer scrutiny we see that this cannot be correct since it would
be violating the first principle of relativity: a moving muon is only
‘moving’ relative to us.