Page 12 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 2
coming toward them at different speeds, but light's speed relative to the ether would remain fixed. In particular,
as the earth was moving through the ether on its orbit round the sun, the speed of light measured in the
direction of the earth's motion through the ether (when we were moving toward the source of the light) should
be higher than the speed of light at right angles to that motion (when we are not moving toward the source). In
1887Albert Michelson (who later became the first American to receive the Nobel Prize for physics) and Edward
Morley carried out a very careful experiment at the Case School of Applied Science in Cleveland. They
compared the speed of light in the direction of the earth's motion with that at right angles to the earth's motion.
To their great surprise, they found they were exactly the same!

Between 1887 and 1905 there were several attempts, most notably by the Dutch physicist Hendrik Lorentz, to
explain the result of the Michelson-Morley experiment in terms of objects contracting and clocks slowing down
when they moved through the ether. However, in a famous paper in 1905, a hitherto unknown clerk in the
Swiss patent office, Albert Einstein, pointed out that the whole idea of an ether was unnecessary, providing one
was willing to abandon the idea of absolute time. A similar point was made a few weeks later by a leading
French mathematician, Henri Poincare. Einstein’s arguments were closer to physics than those of Poincare,
who regarded this problem as mathematical. Einstein is usually given the credit for the new theory, but
Poincare is remembered by having his name attached to an important part of it.

The fundamental postulate of the theory of relativity, as it was called, was that the laws of science should be
the same for all freely moving observers, no matter what their speed. This was true for Newton’s laws of
motion, but now the idea was extended to include Maxwell’s theory and the speed of light: all observers should
measure the same speed of light, no matter how fast they are moving. This simple idea has some remarkable
consequences. Perhaps the best known are the equivalence of mass and energy, summed up in Einstein’s
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famous equation E=mc (where E is energy, m is mass, and c is the speed of light), and the law that nothing
may travel faster than the speed of light. Because of the equivalence of energy and mass, the energy which an
object has due to its motion will add to its mass. In other words, it will make it harder to increase its speed. This
effect is only really significant for objects moving at speeds close to the speed of light. For example, at 10
percent of the speed of light an object’s mass is only 0.5 percent more than normal, while at 90 percent of the
speed of light it would be more than twice its normal mass. As an object approaches the speed of light, its mass
rises ever more quickly, so it takes more and more energy to speed it up further. It can in fact never reach the
speed of light, because by then its mass would have become infinite, and by the equivalence of mass and
energy, it would have taken an infinite amount of energy to get it there. For this reason, any normal object is
forever confined by relativity to move at speeds slower than the speed of light. Only light, or other waves that
have no intrinsic mass, can move at the speed of light.

An equally remarkable consequence of relativity is the way it has revolutionized our ideas of space and time. In
Newton’s theory, if a pulse of light is sent from one place to another, different observers would agree on the
time that the journey took (since time is absolute), but will not always agree on how far the light traveled (since
space is not absolute). Since the speed of the light is just the distance it has traveled divided by the time it has
taken, different observers would measure different speeds for the light. In relativity, on the other hand, all
observers must agree on how fast light travels. They still, however, do not agree on the distance the light has
traveled, so they must therefore now also disagree over the time it has taken. (The time taken is the distance
the light has traveled – which the observers do not agree on – divided by the light’s speed – which they do
agree on.) In other words, the theory of relativity put an end to the idea of absolute time! It appeared that each
observer must have his own measure of time, as recorded by a clock carried with him, and that identical clocks
carried by different observers would not necessarily agree.

Each observer could use radar to say where and when an event took place by sending out a pulse of light or
radio waves. Part of the pulse is reflected back at the event and the observer measures the time at which he
receives the echo. The time of the event is then said to be the time halfway between when the pulse was sent
and the time when the reflection was received back: the distance of the event is half the time taken for this
round trip, multiplied by the speed of light. (An event, in this sense, is something that takes place at a single
point in space, at a specified point in time.) This idea is shown here, which is an example of a space-time
diagram...

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