our universe. Yet if there really is a complete unified theory, it would also presumably determine our actions.
And so the theory itself would determine the outcome of our search for it! And why should it determine that we
come to the right conclusions from the evidence? Might it not equally well determine that we draw the wrong
conclusion.? Or no conclusion at all?
The only answer that I can give to this problem is based on Darwin’s principle of natural selection. The idea is
that in any population of self-reproducing organisms, there will be variations in the genetic material and
upbringing that different individuals have. These differences will mean that some individuals are better able
than others to draw the right conclusions about the world around them and to act accordingly. These individuals
will be more likely to survive and reproduce and so their pattern of behavior and thought will come to dominate.
It has certainly been true in the past that what we call intelligence and scientific discovery have conveyed a
survival advantage. It is not so clear that this is still the case: our scientific discoveries may well destroy us all,
and even if they don’t, a complete unified theory may not make much difference to our chances of survival.
However, provided the universe has evolved in a regular way, we might expect that the reasoning abilities that
natural selection has given us would be valid also in our search for a complete unified theory, and so would not
lead us to the wrong conclusions.
Because the partial theories that we already have are sufficient to make accurate predictions in all but the most
extreme situations, the search for the ultimate theory of the universe seems difficult to justify on practical
grounds. (It is worth noting, though, that similar arguments could have been used against both relativity and
quantum mechanics, and these theories have given us both nuclear energy and the microelectronics
revolution!) The discovery of a complete unified theory, therefore, may not aid the survival of our species. It
may not even affect our lifestyle. But ever since the dawn of civilization, people have not been content to see
events as unconnected and inexplicable. They have craved an understanding of the underlying order in the
world. Today we still yearn to know why we are here and where we came from. Humanity’s deepest desire for
knowledge is justification enough for our continuing quest. And our goal is nothing less than a complete
description of the universe we live in.
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PREVIOUS NEXT
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CHAPTER 2
SPACE AND TIME
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Our present ideas about the motion of bodies date back to Galileo and Newton. Before them people believed
Aristotle, who said that the natural state of a body was to be at rest and that it moved only if driven by a force or
impulse. It followed that a heavy body should fall faster than a light one, because it would have a greater pull
toward the earth.
The Aristotelian tradition also held that one could work out all the laws that govern the universe by pure
thought: it was not necessary to check by observation. So no one until Galileo bothered to see whether bodies
of different weight did in fact fall at different speeds. It is said that Galileo demonstrated that Aristotle’s belief
was false by dropping weights from the leaning tower of Pisa. The story is almost certainly untrue, but Galileo
did do something equivalent: he rolled balls of different weights down a smooth slope. The situation is similar to
that of heavy bodies falling vertically, but it is easier to observe because the Speeds are smaller. Galileo’s
measurements indicated that each body increased its speed at the same rate, no matter what its weight. For
example, if you let go of a ball on a slope that drops by one meter for every ten meters you go along, the ball
will be traveling down the slope at a speed of about one meter per second after one second, two meters per
second after two seconds, and so on, however heavy the ball. Of course a lead weight would fall faster than a
feather, but that is only because a feather is slowed down by air resistance. If one drops two bodies that don’t
have much air resistance, such as two different lead weights, they fall at the same rate. On the moon, where
there is no air to slow things down, the astronaut David R. Scott performed the feather and lead weight
experiment and found that indeed they did hit the ground at the same time.
Galileo’s measurements were used by Newton as the basis of his laws of motion. In Galileo’s experiments, as a
body rolled down the slope it was always acted on by the same force (its weight), and the effect was to make it
constantly speed up. This showed that the real effect of a force is always to change the speed of a body, rather
than just to set it moving, as was previously thought. It also meant that whenever a body is not acted on by any
force, it will keep on moving in a straight line at the same speed. This idea was first stated explicitly in Newton’s
Principia Mathematica, published in 1687, and is known as Newton’s first law. What happens to a body when a
force does act on it is given by Newton’s second law. This states that the body will accelerate, or change its
speed, at a rate that is proportional to the force. (For example, the acceleration is twice as great if the force is
twice as great.) The acceleration is also smaller the greater the mass (or quantity of matter) of the body. (The
same force acting on a body of twice the mass will produce half the acceleration.) A familiar example is
provided by a car: the more powerful the engine, the greater the acceleration, but the heavier the car, the
smaller the acceleration for the same engine. In addition to his laws of motion, Newton discovered a law to
describe the force of gravity, which states that every body attracts every other body with a force that is
proportional to the mass of each body. Thus the force between two bodies would be twice as strong if one of
the bodies (say, body A) had its mass doubled. This is what you might expect because one could think of the
new body A as being made of two bodies with the original mass. Each would attract body B with the original
force. Thus the total force between A and B would be twice the original force. And if, say, one of the bodies had
twice the mass, and the other had three times the mass, then the force would be six times as strong. One can
now see why all bodies fall at the same rate: a body of twice the weight will have twice the force of gravity
pulling it down, but it will also have twice the mass. According to Newton’s second law, these two effects will
exactly cancel each other, so the acceleration will be the same in all cases.
Newton’s law of gravity also tells us that the farther apart the bodies, the smaller the force. Newton’s law of
gravity says that the gravitational attraction of a star is exactly one quarter that of a similar star at half the
distance. This law predicts the orbits of the earth, the moon, and the planets with great accuracy. If the law
were that the gravitational attraction of a star went down faster or increased more rapidly with distance, the
orbits of the planets would not be elliptical, they would either spiral in to the sun or escape from the sun.
The big difference between the ideas of Aristotle and those of Galileo and Newton is that Aristotle believed in a
preferred state of rest, which any body would take up if it were not driven by some force Or impulse. In
particular, he thought that the earth was at rest. But it follows from Newton’s laws that there is no unique
standard of rest. One could equally well say that body A was at rest and body B was moving at constant speed
with respect to body A, or that body B was at rest and body A was moving. For example, if one sets aside for a
moment the rotation of the earth and its orbit round the sun, one could say that the earth was at rest and that a
train on it was traveling north at ninety miles per hour or that the train was at rest and the earth was moving
south at ninety miles per hour. If one carried out experiments with moving bodies on the train, all Newton’s laws
would still hold. For instance, playing Ping-Pong on the train, one would find that the ball obeyed Newton’s laws
just like a ball on a table by the track. So there is no way to tell whether it is the train or the earth that is moving.
The lack of an absolute standard of rest meant that one could not determine whether two events that took place
at different times occurred in the same position in space. For example, suppose our Ping-Pong ball on the train
bounces straight up and down, hitting the table twice on the same spot one second apart. To someone on the
track, the two bounces would seem to take place about forty meters apart, because the train would have
traveled that far down the track between the bounces. The nonexistence of absolute rest therefore meant that
one could not give an event an absolute position in space, as Aristotle had believed. The positions of events
and the distances between them would be different for a person on the train and one on the track, and there
would be no reason to prefer one person’s position to the other’s.
Newton was very worried by this lack of absolute position, or absolute space, as it was called, because it did
not accord with his idea of an absolute God. In fact, he refused to accept lack of absolute space, even though it
was implied by his laws. He was severely criticized for this irrational belief by many people, most notably by
Bishop Berkeley, a philosopher who believed that all material objects and space and time are an illusion. When
the famous Dr. Johnson was told of Berkeley’s opinion, he cried, “I refute it thus!” and stubbed his toe on a
large stone.
Both Aristotle and Newton believed in absolute time. That is, they believed that one could unambiguously
measure the interval of time between two events, and that this time would be the same whoever measured it,
provided they used a good clock. Time was completely separate from and independent of space. This is what
most people would take to be the commonsense view. However, we have had to change our ideas about space
and time. Although our apparently commonsense notions work well when dealing with things like apples, or
planets that travel comparatively slowly, they don’t work at all for things moving at or near the speed of light.
The fact that light travels at a finite, but very high, speed was first discovered in 1676 by the Danish astronomer
Ole Christensen Roemer. He observed that the times at which the moons of Jupiter appeared to pass behind
Jupiter were not evenly spaced, as one would expect if the moons went round Jupiter at a constant rate. As the
earth and Jupiter orbit around the sun, the distance between them varies. Roemer noticed that eclipses of
Jupiter’s moons appeared later the farther we were from Jupiter. He argued that this was because the light from
the moons took longer to reach us when we were farther away. His measurements of the variations in the
distance of the earth from Jupiter were, however, not very accurate, and so his value for the speed of light was
140,000 miles per second, compared to the modern value of 186,000 miles per second. Nevertheless,
Roemer’s achievement, in not only proving that light travels at a finite speed, but also in measuring that speed,
was remarkable – coming as it did eleven years before Newton’s publication of Principia Mathematica. A proper
theory of the propagation of light didn’t come until 1865, when the British physicist James Clerk Maxwell
succeeded in unifying the partial theories that up to then had been used to describe the forces of electricity and
magnetism. Maxwell’s equations predicted that there could be wavelike disturbances in the combined
electromagnetic field, and that these would travel at a fixed speed, like ripples on a pond. If the wavelength of
these waves (the distance between one wave crest and the next) is a meter or more, they are what we now call
radio waves. Shorter wavelengths are known as microwaves (a few centimeters) or infrared (more than a
ten-thousandth of a centimeter). Visible light has a wavelength of between only forty and eighty millionths of a
centimeter. Even shorter wavelengths are known as ultraviolet, X rays, and gamma rays.
Maxwell’s theory predicted that radio or light waves should travel at a certain fixed speed. But Newton’s theory
had got rid of the idea of absolute rest, so if light was supposed to travel at a fixed speed, one would have to
say what that fixed speed was to be measured relative to.
It was therefore suggested that there was a substance called the "ether" that was present everywhere, even in
"empty" space. Light waves should travel through the ether as sound waves travel through air, and their speed
should therefore be relative to the ether. Different observers, moving relative to the ether, would see light
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
