What is so special about special relativity?

So far, I have
asked you to imagine higher dimensions, expected you to accept
that gravity can warp space and time and to takemyword for what
we think it would be like to fall into a black hole. However, I have
not covered them in sufficient depth for you to fully appreciate
the logical reasoning that led to them, as that would have been
beyond the scope of this book. This chapter is different. I cannot
brush aside the reasoning that led us to the view of space and time
that Einstein has shown us. Here is where you will see his true
genius and, I hope, appreciate the unavoidable, yet astonishing,
conclusions he was forced to reach.
Ten years before his general theory of relativity of 1915
Einstein showed, through logical necessity, how time and space
are related. This, as we shall see, is where the idea of time as the
fourth dimension comes in. It became known as his special theory
of relativity, and it was only after he had understood the structure
of this ‘spacetime’ that he could turn his attention to his general
theory in which he showed how gravity could curve it. Einstein announced his special theory of relativity (now
known simply as special relativity) to the world in 1905 while still
in his mid-twenties. But he had been struggling with the concepts
leading up to it since his mid-teens. Special relativity is the reason
Einstein is famous today, despite the fact that it was superseded
by the much grander general relativity a few years later, and that
it was, in fact, the experimental confirmation of general relativity
that turned him into a household name. Einstein’s paper on special
relativity was not even deemed to be his most important piece
of work in the year it was published. Its impact took time to
sink in. Remember he received the recognition of the Nobel prize
committee for his work proving that light consists of particles. So
what is it about the special theory that makes it so special?
Popular accounts of special relativity will often try and fob
you off with the explanation that it was the theory that gave us the
famous equation
E = mc2.
This is true, and it was this simple formula which led us, for better
or worse, into the nuclear age. However, special relativity goes
much deeper than that. It is a bit like describing the industrial
revolution as having given us the steam engine. In reality, the
industrial revolution meant much more than a single invention.
Not only did political power shift from the landowner to the
industrial capitalist, but with the later development of the internal
combustion engine and electricity came a complete change in
ordinary people’s lives. In a similar way, special relativity is about
much more than E = mc2. It heralded a revolution in physics.
It showed how and why the old notions of space and time had
to be ditched and replaced with such a new and unfamiliar set
of concepts that, to this day, we still have not been able to shake
off the ‘old notions’. The space and time that most people still
take for granted as ‘common sense’ were shown to be wrong
by Einstein. Since then every experiment ever devised has only
served to confirm, with ever-increasing accuracy, that he was right.
We will see in this chapter why it has been so hard for many people
to accept his ideas, even almost a hundred years later.Newton is rightly acknowledged as having sewn up the whole
of classical mechanics with his laws of motion. These describe
how objects move and how forces such as gravity affect them by
making them speed up, slow down or change direction. The most
familiar of these laws is probably the third one. You probably
remember it as the one about every action having an equal and
opposite reaction. However, it is the second law which is the most
important and fundamental—it is pure coincidence that the most
important law in the field of thermodynamics is also the second
one—and describes how a body will behave when pushed.
All moving objects can be divided into two categories: those
that do not feel any force, and are therefore either stationary or
coasting along in a straight line at a constant speed, and those
which are under the influence of some force that is causing them
to change either their speed or direction. Examples of the second
category include falling objects, an accelerating or braking car, a car
going round a corner, even a ball rolling along a flat surface since
wind resistance and friction are both forces that act to slow the ball
down. Newton’s laws of motion cover all the above cases with an
accuracy that in most everyday situations is very impressive.
Einstein’s theories of relativity go far deeper than merely
stating laws of motion. The reason he needed two theories was
because he had to distinguish between the above two categories
of motion. Bodies moving freely at constant velocities and in the
absence of gravity are described by special relativity. Once the
force of gravity is switched on we must turn to general relativity.
You have already seen how Newton’s law of gravity is only
an approximation to the more exact general relativity, but it
nevertheless works very well in weak gravitational fields, such
as the Earth’s. In the same way, Newton’s laws of motion are
only approximations to special relativity, but the differences now
only show up when objects move at very high speeds. For most
purposes in everyday life the accuracy of Newtonian mechanics is
as much as we need. Even NASAuses Newton’s laws to calculate
the path a rocket should take to reach the Moon, and rockets
are probably the fastest moving objects most people can think of.
Clearly the high speeds I am referring to, at which Newton’s laws break down, are much higher than the speeds attained by today’s
rockets. In fact, it is only for bodies moving at a substantial fraction
of the speed of light (which stands at three hundred thousand
kilometres per second) that special relativity is required. In the
following discussion I will often use examples of objects moving
at close to the speed of light. This is just to highlight the effects
of relativity more clearly and you should not take these examples
too literally.
There are several ways that special relativity is traditionally
explained. The usual way is by deriving a set of algebraic equations
called the Lorentz transformation equations. Don’t worry,we
will not follow that route here. The second way is by using special
kinds of graph called spacetime diagrams. Many authors of nontechnical
books on relativity use such diagrams because they feel
that they are simpler to interpret than abstract equations. In a way
this is true. Most people are used to seeing graphs of one sort or
another. Newspapers and television show the varying fortunes of
political parties in opinion polls or the fluctuations of share prices
on the stock market. Most companies present data in their annual
reports using bar charts, pie charts and histograms. Such graphical
methods may well be informative and simple to interpret. But
spacetime diagrams are another matter. If you are mathematically
inclined you will most likely find them very helpful. If you are not
then they will be almost as impenetrable as algebraic formulae. I
will therefore adopt the third route for explaining Einstein’s ideas:
I will restrict myself to words only.
So what is all the fuss about? You might be wondering why
I don’t just get on and explain it instead of this tedious fanfare.
But special relativity deserves respect. Its conclusions provide the
stock-in-trade for so much of science fiction, and are synonymous
with the name of Einstein. As an example I will quote two of the
most frequently asked questions in the whole of modern physics.
Both are direct results of special relativity. They are:
• Why can nothing travel faster than the speed of light?
• Why do clocks tick more slowly when they are moving very
fast? (This has nothing to do with alarm clocks being hurled
across bedrooms.)When I am asked these questions my usual reply is that the
questioner really needs to take a course in special relativity if
they wish to get to the bottom of things. For there are a number
of logical steps that you will need to work through before you
can feel convinced. In this chapter I will lead you through those
steps. If you are not interested in the answers to these questions
and are happy to accept them, for it is quite true that nothing
could ever go faster than light and we really do see fast moving
clocks slow down, then you can skip the next few pages, but since
you have reached this far I have every faith in your continued
perseverance.