Stephen Hawking (5 page)

Even within the established framework of religious belief in seventeenth-century Europe, these were disturbing questions, since although it might seem reasonable to say that the clockwork could have been wound up and set in motion by God, the traditional Christian view sees human beings as having free will, so that they can choose to follow the teachings of Christ or not, as they wish. The notion that sinners might actually have no freedom of choice concerning their actions, but were sinning in obedience to inflexible laws, following a path to eternal damnation actually laid out by God in the beginning, simply could not be fit into the established Christian world view.

Strangely, though, in Newton's day, and down into the twentieth century, science did not really contemplate the notion of a beginning to the Universe at all. The Universe at large was perceived as eternal and unchanging, with “fixed” stars hanging in space. The biblical story of the Creation, still widely accepted in the seventeenth century by scientists as well as ordinary people, was thought of as applying only to our planet, Earth, or perhaps to the Sun's family, the Solar System, but not to the whole Universe.

Newton believed (incorrectly, as it turns out) that the fixed stars could stay as they were in space forever if the Universe were infinitely big, because the force of gravity tugging on each individual star would then be the same in all directions. In fact, we now know that such a situation would be highly unstable. The slightest deviation from a perfectly uniform distribution of stars would produce an overall pull in one
direction or another, making the stars start to move. As soon as a star moves toward any source of gravitational force, the distance to the source decreases, so the force gets stronger, in line with Newton's inverse-square law. So once the stars have started to move, the force causing the nonuniformity gets bigger, and they keep on moving at an accelerating rate. A static universe would soon start to collapse under the pull of gravity. But that became clear only after Einstein had developed a new theory of gravity—a theory, moreover, that contained within itself a prediction that the Universe would certainly not be static and might actually be not collapsing, but expanding.

Like Newton, Albert Einstein made many contributions to science. Also like Newton, his masterwork was his theory of gravity, the general theory of relativity. It is some measure of just how important this theory is to the modern understanding of the Universe that even Einstein's special theory of relativity, the one that leads to the famous equation
E = mc
²
, is by comparison a relatively minor piece of work. Nevertheless, the special theory, which was published in 1905, contributed a key ingredient to the new understanding of the Universe. Before we move on to this, though, we should at least give a brief outline of the main features of the special theory.

Einstein developed the special theory of relativity in response to a puzzle that had emerged from nineteenth-century science. The great Scottish physicist, James Clerk Maxwell, had found the equations that describe the behavior
of electromagnetic waves. Maxwell's equations were soon developed to explain the behavior of radio waves, which were discovered in 1888. But Maxwell had found that the equations automatically gave him a particular speed,
^*
which is identified as the speed at which electromagnetic waves travel. The unique speed that came out of Maxwell's equations turned out to be exactly the speed of light, which physicists had already measured by that time. This revealed that light must be a form of electromagnetic wave, like radio waves but with shorter wavelength (that is, higher frequency). And it also meant, according to those equations, that light (as well as other forms of electromagnetic radiation, including radio waves) always travels at the same speed.

This is not what we expect from our everyday experience of how things move. If I stand still and toss a ball to you gently, it is easy for you to catch the ball. If I am driven toward you at 60 miles an hour in a car and toss the ball equally gently out the window, it hurtles toward you at 60 miles an hour plus the speed of the toss. You would, rightly, be dumbfounded if the ball tossed gently out the car window reached you traveling only at the gentle speed of the toss, without the speed of the car being added in, yet that is exactly what happens with light pulses. Equally, if one vehicle traveling at 50 miles an hour along a straight road is overtaken by another traveling at 60 miles an hour, the second vehicle is moving at 10 miles an hour relative to the first one. Speed, in other words, is relative. And yet, if you are overtaken by a light pulse, and measure its
speed as it goes past, you will find it has the same speed you would measure for a light pulse going past you when you are standing still.

Nobody knew this until the end of the nineteenth century. Scientists had assumed that light behaved in the same way, as far as adding and subtracting velocities is concerned, as objects like balls being thrown from one person to another. And they explained the “constancy” of the speed of light in Maxwell's equations by saying that the equations applied to some “absolute space,” a fundamental reference frame for the entire Universe.

According to this view, space itself defined the framework against which things should be measured—absolute space, through which the Earth, the Sun, light, and everything else moved. This absolute space was also sometimes called the “aether” (or “ether”) and was conceived of as a substance through which electromagnetic waves moved, like water waves moving over the sea. The snag was, when experimenters tried to measure changes in the velocity of light caused by the motion of the Earth through absolute space (or “relative to the aether”), none could be found.

Because the Earth moves around the Sun in a roughly circular orbit, it should be moving at different speeds relative to absolute space at different times of the year. It's like swimming in a circle in a fast-flowing river. Sometimes the Earth will be “swimming with the aether,” sometimes across the aether, and sometimes against the flow. If light always travels at the same speed relative to absolute space, common sense tells us this ought to show up in the form of seasonal changes in the speed of light measured from the Earth. It does not.

Einstein resolved the dilemma with his special theory. This says that all frames of reference are equally valid and that there is no absolute reference frame. Anybody who moves at a constant velocity through space is entitled to regard himself or herself as stationary. They will find that moving objects in their frame of reference obey Newton's laws, while electromagnetic radiation obeys Maxwell's equations and the speed of light is always measured to be the value that comes out of those equations, denoted by the letter
c
(for “constant” or the Latin
celeritas
, meaning “swiftness, celerity”). Furthermore, anybody who is moving at a constant speed relative to the first person (the first observer, in physicists' jargon) will also be entitled to say that they are at rest and will find that objects in their laboratory obey Newton's laws, while measurements always give the speed of light as
c
. Even if one observer is moving toward the other observer at half the speed of light and sends a torch beam out ahead, the second observer will not measure the speed of the light from the torch as 1.5
c
: it will still be
c
!

Starting out from the observed fact that the speed of light is a constant, the same whichever way the Earth is moving through space, Einstein found a mathematical package to describe the behavior of material objects in reference frames that move with constant velocities relative to one another—so-called “inertial” frames of reference. Provided the velocities are small compared with the speed of light, these equations give exactly the same “answers” as Newtonian mechanics. But when the velocities begin to become an appreciable fraction of the speed of light, strange things happen.

Two velocities, for example, can
never
add up to give a relative velocity greater than
c
. An observer may see two other
observers approaching each other on a head-on collision course, each traveling at a speed of 0.9
c
in the first observer's reference frame, but measurements carried out by either of those two fast-moving observers will always show that the other one is traveling at a speed less than
c
but bigger (in this case) than 0.9
c
.

The reason why velocities add up in this strange way has to do with the way both space and time are warped at high velocities. In order to account for the constancy of the speed of light, Einstein had to accept that moving clocks run more slowly than stationary clocks and that moving objects shrink in the direction of their motion. The equations also tell us that moving objects increase in mass the faster they go.

Strange and wonderful though all these things are, they are only peripheral to the story of modern cosmology and to the search for links between quantum physics and gravity. We stress, however, that they are not wild ideas in the sense that we sometimes dismiss crazy notions as “just a theory” in everyday language. To scientists, a theory is an idea that has been tried and tested by experiments and has passed every test. The special theory of relativity is no exception to this rule. All the strange notions implicit in the theory—the constancy of the speed of light, the stretching of time and shrinking of length for moving objects, the increase in mass of a moving object—have been measured and confirmed to great precision in very many experiments. Particle accelerators—“atom-smashing” machines like those at CERN, the European Center for Nuclear Research in Geneva—simply would not work if the theory were not a good one, since they have been designed and built around Einstein's equations. The special
theory of relativity as a description of the high-speed world is as securely founded in solid experimental facts as is Newtonian mechanics as a description of the everyday world; the only reason it conflicts with our common sense is that in everyday life we are not used to the kind of high-speed travel required for the effects to show up. After all, the speed of light,
c
, is ≈186,000 miles a second (≈300,000 kilometers a second), and the relativistic effects can be safely ignored for any speeds less than about 10 percent of this—that is, for speeds less than a mere 30,000 kilometers a second.

In essence, the special theory is the result of a marriage of Newton's equations of motion with Maxwell's equations describing radiation. It was very much a child of its time, and if Einstein hadn't come up with the theory in 1905, one of his contemporaries would surely have done so within the next few years. Without Einstein's special genius, though, it might have been a generation or more before anyone realized the importance of a far deeper insight buried within the special theory.

This key ingredient, to which we have already alluded, was the fruit of another marriage—the union of space and time. In everyday life, space and time seem to be quite different things. Space extends around us in three dimensions (up and down, left and right, forward and backward). We can see where things are located in space, and travel through it, more or less at will. Time, although we all know what it is, is almost impossible to describe. In a sense, it does have a direction (from past to future), but we can look neither into the future
nor into the past, and we certainly cannot move through time at will. Yet the great universal constant,
c
, is a speed, and speed is a measure that relates space and time. Speeds are always in the form of miles per hour, or centimeters per second, or any other unit of length per unit of time. You cannot have one without the other when you are talking about speed. So the fact that the fundamental constant is a velocity must be telling us something significant about the Universe. But what?

If you multiply a speed by a time, you get a length. And if you do this in the right way (by multiplying intervals of time by the speed of light,
c
), you can combine measures of length (space) with measures of time in the same set of equations. The set of equations that combine space and time in this way consists of the equations of the special theory of relativity that describe time dilation and length contraction
^†
and lead to the prediction that a mass
m
is equivalent to an energy
E
as described by the formula
E = mc
²
. Instead of thinking about space and time as two separate entities, as long ago as 1905 Einstein was telling physicists that they should be thinking about them as different aspects of a single, unified whole—spacetime. But this spacetime, the special theory also said, was not fixed and permanent like the absolute space or absolute time of Newtonian physics—it could be stretched or squeezed. And therein lay the clue to the next great step forward.