There is nothing that annoys people more about relativity when
they first encounter it than the claim that nothing can travel faster
than light. They are prepared to accept clocks slowing down,
lengths shrinking, even that light travels at the same speed for
all observers, but why in heaven’s name can we not conceive
of anything moving at a speed of over three hundred thousand
kilometres per second? Granted, this is a stupendously high speed
to which nothing that we know of (apart from subatomic particles)
can get close, but special relativity seems to be saying that the laws
of nature forbid anything from going faster. Imagine building a
rocket that could keep accelerating faster and faster. Of course,
such a machine is way beyond our current technological ability, so what if an alien civilization were to build it? What will happen
as it reaches the speed of light? Does some cosmic speed ramp
become activated? Does the rocket blow up, fall into a black hole
or enter a time warp? Nope, nothing so dramatic.
There are a number of ways to explainwhythe speed of light is
the upper speed possible in our Universe. One method is by using
algebra. (Oh great, you’re thinking, that will really convince me.)
However, I will not go into the gory details. Suffice it to say that,
in special relativity, speeds get added up in a very strange way. If
you are on a train moving along at 100 kilometres per hour and you
throw a ball out of the window at ten kilometres per hour in the
direction the train is moving then, to someone standing outside
watching you go by, the ball will initially (before the wind has
slowed it down) be moving at a combined speed of 110 kilometres
per hour. This is known as the law of addition of velocities. What
if we now restate the same example but with much higher speeds?
Consider what the outside observer sees in figure 6.2. The rocket is
moving at three-quarters the speed of light when it fires a missile
that flies off at half the speed of light as seen by the man in the
rocket. Does the observer see the missile moving at one and a
quarter times the speed of light? He would if the usual rule about
adding velocities were correct. But like so much of physics that is
valid for everyday use, this law breaks down at relativistic speeds.
The correct formula to use would say that the observer sees the
missile moving at nine tenths of the speed of light. It does not
matter how close to the speed of light the rocket and missile were
moving, their combined speed according to the stationary observer
would always be greater than their individual speeds but below
the speed of light.
The easiest way of explaining the speed of light barrier also
happens to be a way to explain where Einstein’s most famous
equation (E = mc2) comes from. Once Einstein understood how
space and time were affected close to the speed of light, he went
on to consider what else had to be corrected. Some of the most
important and basic laws in the whole of physics are known
as conservation laws, which state that certain quantities should
remain constant even when other quantities are changing. One of these is the law of conservation of momentum. Remember the
momentum of a body is given by its mass multiplied by its velocity,
so a cannon ball slowly rolling along the ground can be stopped
in its tracks by a bullet hitting it head-on. This will happen when the two have equal but opposite momentum which cancel each
other out. The cannon ball has a large mass but low velocity,
whereas the bullet has a small mass and high velocity. In both
cases the product of mass and velocity can give the same number
(the momentum). When any two objects collide, we expect their
combined momentum before and after the collision to be the same.
They don’t have to cancel each other—that is a special case—
but usually one will transfer some of its momentum to the other.
Einstein found that when bodies travel at close to the speed of light
the total momentum is not conserved, as it should be, according
to some observers if they just use the simple ‘mass times velocity’
rule. Again, something had to give. This time it was the definition
of a fast moving body’s mass.
It turns out that the faster an object moves, the heavier it
becomes, and the harder it gets to make it go even faster. The closer
it gets to the speed of light, the larger its momentum becomes, but
this is by virtue of its increasing mass, not its velocity.
Consider what happens to an object’s mass when it moves
very fast. Oneof the most important consequences of the equations
of special relativity is how mass and energy are related. Einstein
showed that mass can be converted into energy and vice versa.
The two are related through the equation E = mc2, which tells us
how much energy is locked up in any given mass. The c stands for
the speed of light, and thus the quantity c2 (the speed of light times
itself) is a very large number indeed and explains how we can get
so much energy out of a small amount of mass. This equation
suggests that we can think of mass as frozen energy.
Since a moving object also has energy due its motion (called
its kinetic energy), its total energy will be the sum of the energy
frozen as mass when it is not moving plus its kinetic energy. The
faster it moves the more energy it has. This means that the real
mass of an object will be due to its frozen energy plus the energy
due to its motion. Most of the time the frozen energy of an object
(its mass) is so much more than the energy of its motion that we
can ignore the latter and take the mass to be the same as it was
when not moving. But as the speed approaches that of light the
kinetic energy becomes so great it can exceed the frozen energy. Thus the mass of a fast moving object is much greater than its mass
when stationary. Of course, as far as the object itself is concerned,
it can claim to be stationary (since all motion is relative) and is thus
unaware of any change in its mass.
You can now see the problem of trying to attain light speed.
Imagine an accelerating train engine pulling a single carriage.
What if, for every ten kilometres per hour faster that it goes,
another carriage is added. It would therefore have to work harder
just to maintain its speed. The faster it goes the more carriages
it has to pull, and the more power it needs. In the same way,
the faster a body moves, relative to some observer, the heavier
it will appear, and the harder it will be to make it go any faster.
To accelerate it up to the speed of light would require an infinite
amount of energy, which is impossible.
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