Hyperspace (15 page)

At first, this seemed absurd. This meant that we could never overtake the train (light beam). Worse, no matter how fast we drove our car, the train would always seem to be traveling ahead of us at the
same
velocity. In other words, a light beam is like the “ghost ship” that old sailors love to spin tall tales about. It is a phantom vessel that can never be caught. No matter how fast we sail, the ghost ship always eludes us, taunting us.

In 1905, with plenty of time on his hands at the patent office, Einstein carefully analyzed the field equations of Maxwell and was led to postulate the principle of
special relativity:
The speed of light is the same in all constantly moving frames. This innocent-sounding principle is one of the greatest achievements of the human spirit. Some have said that it ranks with Newton’s law of gravitation as one of the greatest scientific creations of the human mind in the 2 million years our species has been evolving on this planet. From it, we can logically unlock the secret of the vast energies released by the stars and galaxies.

To see how this simple statement can lead to such profound conclusions, let us return to the analogy of the car trying to overtake the train. Let us say that a pedestrian on the sidewalk clocks our car traveling at 99 miles per hour, and the train traveling at 100 miles per hour. Naturally, from our point of view in the car, we see the train moving ahead of us at 1 mile per hour. This is because velocities can be added and subtracted, just like ordinary numbers.

Now let us replace the train by a light beam, but keep the velocity of light at just 100 miles per hour. The pedestrian still clocks our car traveling at 99 miles per hour in hot pursuit of the light beam traveling at 100 miles per hour. According to the pedestrian, we should be closing in on the light beam. However, according to relativity, we in the car actually see the light beam not traveling ahead of us at 1 mile per hour, as expected, but speeding ahead of us at 100 miles per hour. Remarkably, we see the light beam racing ahead of us as though we were at rest. Not believing our own eyes, we slam on the gas pedal until the pedestrian
clocks our car racing ahead at 99.99999 miles per hour. Surely, we think, we must be about to overtake the light beam. However, when we look out the window, we see the light beam still speeding ahead of us at 100 miles per hour.

Uneasily, we reach several bizarre, disturbing conclusions. First, no matter how much we gun the engines of our car, the pedestrian tells us that we can approach but never exceed 100 miles per hour. This seems to be the top velocity of the car. Second, no matter how close we come to 100 miles per hour, we still see the light beam speeding ahead of us at 100 miles per hour, as though we weren’t moving at all.

But this is absurd. How can both people in the speeding car and the stationary person measure the velocity of the light beam to be the same? Ordinarily, this is impossible. It appears to be nature’s colossal joke.

There is only one way out of this paradox. Inexorably, we are led to the astonishing conclusion that shook Einstein to the core when he first conceived of it. The only solution to this puzzle is that
time slows down
for us in the car. If the pedestrian takes a telescope and peers into our car, he sees everyone in the car moving exceptionally slowly. However, we in the car never notice that time is slowing down because our brains, too, have slowed down, and everything seems normal to us. Furthermore, he sees that the car has become flattened in the direction of motion. The car has shrunk like an accordion. However, we never feel this effect because our bodies, too, have shrunk.

Space and time play tricks on us. In actual experiments, scientists have shown that the speed of light is always
c
, no matter how fast we travel. This is because the faster we travel, the slower our clocks tick and the shorter our rulers become. In fact, our clocks slow down and our rulers shrink just enough so that whenever we measure the speed of light, it comes out the same.

But why can’t we see or feel this effect? Since our brains are thinking more slowly, and our bodies are also getting thinner as we approach the speed of light, we are blissfully unaware that we are turning into slow-witted pancakes.

These relativistic effects, of course, are too small to be seen in everyday life because the speed of light is so great. Being a New Yorker, however, I am constantly reminded of these fantastic distortions of space and time whenever I ride the subway. When I am on the subway platform with nothing to do except wait for the next subway train, I sometimes let my imagination drift and wonder what it would be like if the speed of light were only, say, 30 miles per hour, the speed of a subway train. Then when the train finally roars into the station, it appears squashed,
like an accordion. The train, I imagine, would be a flattened slab of metal 1 foot thick, barreling down the tracks. And everyone inside the subway cars would be as thin as paper. They would also be virtually frozen in time, as though they were motionless statues. However, as the train comes to a grinding halt, it suddenly expands, until this slab of metal gradually fills the entire station.

As absurd as these distortions might appear, the passengers inside the train would be totally oblivious to these changes. Their bodies and space itself would be compressed along the direction of motion of the train; everything would appear to have its normal shape. Furthermore, their brains would have slowed down, so that everyone inside the train would act normally. Then when the subway train finally comes to a halt, they are totally unaware that their train, to someone on the platform, appears to miraculously expand until it fills up the entire platform. When the passengers depart from the train, they are totally oblivious to the profound changes demanded by special relativity.
^*

There have been, of course, hundreds of popular accounts of Einstein’s theory, stressing different aspects of his work. However, few accounts capture the essence behind the theory of special relativity, which is that time is the fourth dimension and that the laws of nature are simplified and unified in higher dimensions. Introducing time as the fourth dimension overthrew the concept of time dating all the way back to Aristotle. Space and time would now be forever dialectically linked by special relativity. (Zollner and Hinton had assumed that the next dimension to be discovered would be the fourth spatial dimension. In this respect, they were wrong and H. G. Wells was correct. The next dimension to be discovered would be time, a fourth temporal dimension. Progress in understanding the fourth spatial dimension would have to wait several more decades.)

To see how higher dimensions simplify the laws of nature, we recall that any object has length, width, and depth. Since we have the freedom
to rotate an object by 90 degrees, we can turn its length into width and its width into depth. By a simple rotation, we can interchange any of the three spatial dimensions. Now if time is the fourth dimension, then it is possible to make “rotations” that convert space into time and vice versa. These four-dimensional “rotations” are precisely the distortions of space and time demanded by special relativity. In other words, space and time have mixed in an essential way, governed by relativity. The meaning of time as being the fourth dimension is that time and space can rotate into each other in a mathematically precise way. From now on, they must be treated as two aspects of the same quantity: space-time. Thus adding a higher dimension helped to unify the laws of nature.

Newton, writing 300 years ago, thought that time beat at the same rate everywhere in the universe. Whether we sat on the earth, on Mars, or on a distant star, clocks were expected to tick at the same rate. There was thought to be an absolute, uniform rhythm to the passage of time throughout the entire universe. Rotations between time and space were inconceivable. Time and space were two distinct quantities with no relationship between them. Unifying them into a single quantity was unthinkable. However, according to special relativity, time can beat at different rates, depending on how fast one is moving. Time being the fourth dimension means that time is intrinsically linked with movement in space. How fast a clock ticks depends on how fast it is moving in space. Elaborate experiments done with atomic clocks sent into orbit around the earth have confirmed that a clock on the earth and a clock rocketing in outer space tick at different rates.

I was graphically reminded of the relativity principle when I was invited to my twentieth high-school reunion. Although I hadn’t seen most of my classmates since graduation, I assumed that all of them would show the same telltale signs of aging. As expected, most of us at the reunion were relieved to find that the aging process was universal: It seemed that all of us sported graying temples, expanding waistlines, and a few wrinkles. Although we were separated across space and time by several thousand miles and 20 years, each of us had assumed that time had beat uniformly for all. We automatically assumed that each of us would age at the same rate.

Then my mind wandered, and I imagined what would happen if a classmate walked into the reunion hall looking
exactly
as he had on graduation day. At first, he would probably draw stares from his classmates. Was this the same person we knew 20 years ago? When people realized that he was, a panic would surge through the hall.

We would be jolted by this encounter because we tacitly assume that clocks beat the same everywhere, even if they are separated by vast distances. However, if time is the fourth dimension, then space and time can rotate into each other and clocks can beat at different rates, depending on how fast they move. This classmate, for example, may have entered a rocket traveling at near-light speeds. For us, the rocket trip may have lasted for 20 years. However, for him, because time slowed down in the speeding rocket, he aged only a few moments from graduation day. To him, he just entered the rocket, sped into outer space for a few minutes, and then landed back on earth in time for his twentieth high-school reunion after a short, pleasant journey, still looking youthful amid a field of graying hair.

I am also reminded that the fourth dimension simplifies the laws of nature whenever I think back to my first encounter with Maxwell’s field equations. Every undergraduate student learning the theory of electricity and magnetism toils for several years to master these eight abstract equations, which are exceptionally ugly and very opaque. Maxwell’s eight equations are clumsy and difficult to memorize because time and space are treated separately, (To this day, I have to look them up in a book to make sure that I get all the signs and symbols correct.) I still remember the relief I felt when I learned that these equations collapse into one trivial-looking equation when time is treated as the fourth dimension. In one masterful stroke, the fourth dimension simplifies these equations in a beautiful, transparent fashion.
⁴
Written in this way, the equations possess a higher
symmetry;
that is, space and time can turn into each other. Like a beautiful snowflake that remains the same when we rotate it around its axis, Maxwell’s field equations, written in relativistic form, remain the same when we rotate space into time.

Remarkably, this one simple equation, written in a relativistic fashion, contains the same physical content as the eight equations originally written down by Maxwell over 100 years ago. This one equation, in turn, governs the properties of dynamos, radar, radio, television, lasers, household appliances, and the cornucopia of consumer electronics that appear in everyone’s living room. This was one of my first exposures to the concept of
beauty
in physics—that is, that the symmetry of four-dimensional space can explain a vast ocean of physical knowledge that would fill an engineering library.

Once again, this demonstrates one of the main themes of this book, that the addition of higher dimensions helps to simplify and unify the laws of nature.

This discussion of unifying the laws of nature, so far, has been rather abstract, and would have remained so had Einstein not taken the next fateful step. He realized that if space and time can be unified into a single entity, called space-time, then perhaps matter and energy can also be united into a dialectical relationship. If rulers can shrink and clocks slow down, he reasoned, then everything that we measure with rulers and clocks must also change. However, almost everything in a physicist’s laboratory is measured by rulers and clocks. This meant that physicists had to recalibrate all the laboratory quantities they once took for granted to be constant.

Specifically, energy is a quantity that depends on how we measure distances and time intervals. A speeding test car slamming into a brick wall obviously has energy. If the speeding car approaches the speed of light, however, its properties become distorted. It shrinks like an accordion and clocks in it slow down.

More important, Einstein found that the mass of the car also increases as it speeds up. But where did this excess mass come from? Einstein concluded that it came from the energy.

This had disturbing consequences. Two of the great discoveries of nineteenth-century physics were the conservation of mass and the conservation of energy; that is, the total mass and total energy of a closed system, taken separately, do not change. For example, if the speeding car hits the brick wall, the energy of the car does not vanish, but is converted into the sound energy of the crash, the kinetic energy of the flying brick fragments, heat energy, and so on. The total energy (and total mass) before and after the crash is the same.

However, Einstein now said that the energy of the car could be converted into mass—a new conservation principle that said that the sum total of the mass added to energy must always remain the same. Matter does not suddenly disappear, nor does energy spring out of nothing. In this regard, the God-builders were wrong and Lenin was right. Matter disappears only to unleash enormous quantities of energy, or vice versa.