Zero: The Biography of a Dangerous Idea

by Charles Seife

In the 1850s, however, William Thomson, a British physicist, noticed something odd about Charles’ law: the specter of zero. Lower the temperature and the volume of the balloons gets smaller and smaller. Keep lowering at a steady pace and the balloons keep shrinking at a constant rate, but they cannot go on shrinking forever. There is a point at which gas, in theory, takes up no space at all; Charles’ law says that a balloon of gas must shrink to zero space.

Of course, zero space is the smallest possible volume; when a gas reaches this point, it takes up no space at all. (It certainly can’t take up negative space.) If the volume of a gas is related to its temperature, a minimum volume means that there is a minimum temperature.

A gas cannot keep getting colder and colder indefinitely; when you can’t shrink the balloon any further, you can’t lower the temperature any further. This is absolute zero. It is the lowest temperature possible, a little more...

Absolute zero is the state where a container of gas has been drained of all of its energy. This is, in actuality, an unattainable goal. You can never cool an object to absolute zero. You can get very close; thanks to laser cooling, physicists can chill atoms to a few millionths of a degree above the ultimate coldness. However, everything in the universe is conspiring to stop you from actually reaching absolute zero. This is because any object that has energy is bouncing around—and radiating light.

Say you are trying to cool a banana to absolute zero. To get rid of all of the energy in the banana, you’ve got to stop its atoms from moving around; you have to put it in a box and cool it down. However, the box the banana is in is made of atoms, too. The box’s atoms are wiggling around, and they will bump the banana’s atoms and set them in motion again. Even if you get the banana to float in a perfect vacuum in the center of the box, you can’t stop the wiggling entirely, because dancing particles give off light. Light is constantly coming off of the box and striking the banana, getting the banana’s molecules to move again.

Absolute zero was a discovery that had a very different flavor from Newton’s laws. Newton’s equations gave physicists power. They could predict the orbits of the planets and the motion of objects with great accuracy. On the other hand, Kelvin’s discovery of absolute zero told physicists what they couldn’t do. They couldn’t ever reach absolute zero. This barrier was disappointing news to the physics world, but it was the beginning of a new branch of physics: thermodynamics.

Thermodynamics is the study of the way heat and energy behave. Like Kelvin’s discovery of absolute zero, the laws of thermodynamics erected impenetrable barriers that no scientists can ever cross, no matter how hard they try. For instance, thermodynamics tells you that it is impossible to create a perpetual-motion machine.

(Thermodynamics is worse than a casino; you can’t win, no matter how much you work at it. You can’t even break even.)

The nature of light was a problem that had consumed scientists for centuries. Isaac Newton believed that light was composed of little particles that flowed from every bright object. Over time, though, scientists came to believe that light was not in fact a particle, but a wave. In 1801 a British scientist discovered that light interferes with itself, apparently putting the matter to rest once and for all.

When you drop a stone into a pond, you create circular ripples in the water—waves. The water bobs up and down, and crests and troughs spread outward in a circular pattern. If you drop two stones at the same time, the ripples interfere with one another. You can see this more clearly if you dip two oscillating pistons into a tub of water. When a crest from one piston runs into a trough from the other, the two cancel out; if you look carefully at the pattern of ripples, you can see lines of still, wave-free water (Figure 45).

The same thing is true of light. If light shines through two small slits, there are areas that are dark—wave-free (Figure 46). (You can see a related effect at home. Hold your fingers together; you should have tiny gaps where some light can get through. Gaze through one of those gaps at a lightbulb and you’ll see faint dark lines, especially near the top and bottom of the gap. These lines, too, are due to the wavelike nature of light.) Waves interfere in this way; particles do not. Thus, the phenomenon of interference seemed to settle the ...

With light, the faster the wave bobs up and down—the higher its frequency—the more energy it has. (Also, the higher its frequency, the smaller its wavelength: the distance between two wave crests.) Indeed, one of the most important thermodynamic laws—the so-called Stefan-Boltzmann equation—seems to tie the wiggles of molecules to the wiggles of light. It relates the temperature of an object to the total amount of light energy it radiates. This was the biggest victory for statistical mechanics and the wave theory of light.

(The equation states that the radiated energy is proportional to the temperature raised to the fourth power. It not only tells how much radiation an object gives off, but also how hot an object gets when irradiated with a given amount of energy. This is the law that physicists used—along with a passage in the book of Isaiah—to determine that heaven is more than 500 degrees Kelvin.)

Zero wavelength equals infinite energy; zero and infinity conspired to break a nice, neat system of laws. Solving this paradox quickly became the leading puzzle in physics.

To physicists, vacuum has all particles and forces latent in it. It’s a far richer substance than the philosopher’s nothing. —SIR MARTIN REES

Quantum mechanics got rid of the zero in the classical theory of light—removing the infinite energy that supposedly came from every bit of matter in the universe. However, this was not much of a victory. A zero in quantum mechanics means that the entire universe—including the vacuum—is filled with an infinite amount of energy: the zero-point energy. This, in turn, leads to the most bizarre zero in the universe: the phantom force of nothing.

According to quantum theory, everything—light, electrons, protons, small dogs—have both wavelike and particle-like properties. But if objects are particles and waves at the same time, what on earth could they be? Mathematicians know how to describe them: they are wave functions, solutions to a differential equation called the Schrödinger equation.

Unfortunately, this mathematical description has no intuitive meaning; it is all but impossible to visualize what these wave functions are.* Worse yet, as physicists discovered the intricacies of quantum mechanics, stranger and stranger things began to appear. Perhaps the weirdest of all is caused by a zero in the equations of quantum mechanics: the zero-point energy.

This strange force is woven into the mathematical equations of the quantum universe. In the mid-1920s a German physicist, Werner Heisenberg, saw that these equations had a shocking consequence: uncertainty. The force of...

Heisenberg’s uncertainty principle applies to more than just measurements performed by humans. Like the laws of thermodynamics, the principle applies to nature itself. Uncertainty makes the universe seethe with infinite energy.

Einstein realized that there is one way around this: the flow of time changes, depending on an observer’s speed. The clock on the train must tick more slowly than the stationary clock.

Not only does time change with speed, so do length and mass. As objects speed up, they get shorter and heavier. At nine-tenths of the speed of light, for instance, a yardstick would only be 0.44 yards long, and a one-pound bag of sugar would weigh nearly 2.3 pounds—from a stationary observer’s point of view. (Of course, this doesn’t mean that you would be able to bake more cookies with the same bag of sugar. From the bag’s point of view, its weight stays the same.)

This variability in the flow of time might be hard to believe, but it has been observed. When a subatomic particle travels very fast, it survives longer than expected before it decays, because its clock is slow. Also, a very precise clock has been observed to slow down ever so slightly when flown in an airplane at great speed. Einstein’s theory works.

When a spaceship approaches the speed of light, time slows down more and more and more. If the ship were to travel at the speed of light, every tick of the clock on board would equal infinite seconds on the ground. In less than a fraction of a second, billions and billions of years would pass; the universe would have already met its ultimate fate and burned itself...

Luckily, it is not so easy to stop time. As the spaceship goes ever faster, time slows down more and more, but at the same time, the spaceship’s mass gets greater and greater. It is like pushing a baby carriage where the baby grows and grows. Pretty soon you are pushing a sumo wrestler—not so easy. If you manage to push the carriage even faster, the baby becomes as massive as a ca...

Einstein’s equations also predicted something much more sinister: the black hole, a star so dense that nothing can escape its grasp, not even light.

When an extremely massive star collapses, it disappears. The gravitational attraction is so great that physicists know of no force in the universe that can stop its collapse—not the repulsion of its electrons, not the pressure of neutron against neutron or quark against quark—nothing. The dying star gets smaller and smaller and smaller. Then . . . zero. The star crams itself into zero space. This is a black hole, an object so paradoxical that some scientists believe that black holes can be used to travel faster than light—and backward in time.

If you toss a rock upward, it will curve back down, pulled back by the earth’s gravity. But if you throw a rock fast enough, it won’t curve back down to earth; it will zoom out of the earth’s atmosphere and escape the earth’s gravitational pull. This is roughly what NASA does when it sends a spacecraft to Mars. The minimum speed you need to throw the rock to enable it to escape is called, naturally enough, the escape velocity. Black holes are so dense that if you get too close—past the so-called event horizon—the escape velocity is faster than the speed of light. Past the event horizon the pull of a black hole’s gravity is so strong—and space is so curved—that nothing can escape, not even light.

Even though nature tries to shield the singularities of black holes, scientists know that black holes exist. In the direction of the constellation Sagittarius, at the very center of our galaxy, sits a supermassive black hole that weighs as much as two-and-a-half million suns. Astronomers have watched stars dance around an invisible partner; the stars’ motions reveal the presence of the black hole even if the black hole is not visible.

NASA hopes that zero might hold the secret to traveling to distant stars. In 1998, NASA held a symposium entitled Physics for the Third Millennium, where scientists debated the merits of wormholes, warp drives, vacuum-energy engines, and other far-out ideas.

According to quantum mechanics and general relativity, the power of zero is infinite, so it’s no surprise that people are hoping to tap its potential. But for the time being, it appears that nothing will come of nothing.

Unfortunately, there are objects that lie in both realms. Black holes are very, very massive, so they are subject to the laws of relativity; at the same time, black holes are very, very tiny, so they are in the domain of quantum mechanics. And far from agreeing, the two sets of laws clash at the center of a black hole.

Zero dwells at the juxtaposition of quantum mechanics and relativity; zero lives where the two theories meet, and zero causes the two theories to clash. A black hole is a zero in the equations of general relativity; the energy of the vacuum is a zero in the mathematics of quantum theory.

The big bang, the most puzzling event in the history of the universe, is a zero in both theories. The universe came from nothing—and both theories break down when ...

The Theory of Everything is, in truth, a theory of nothing.

The problem is, when we try to calculate all the way down to zero distance, the equation blows up in our face and gives us meaningless answers—things like infinity. This caused a lot of trouble when the theory of quantum electrodynamics first came out. People were getting infinity for every problem they tried to calculate! —RICHARD FEYNMAN

It is not obvious how to get rid of zero, as zero appears and reappears throughout time and space. Black holes are zero-dimensional, as are particles such as the electron. Electrons and black holes are real things; physicists can’t simply will them away. But scientists can give black holes and electrons an extra dimension.

This is the reason for string theory, which was created in the 1970s when physicists began to see the advantages of treating every particle as a vibrating string rather than as a dot. If electrons (and black holes) are treated as one-dimensional, like a loop of string, instead of as zero-dimensional, like a point, the infinities in general relativity and quantum mechanics miraculously disappear.

Removing zero from the universe might seem like a drastic step, but strings are much more tractable than dots; by eliminating zero, string theory smooths out the discontinuous, particle-like nature of quantum mechanics and mends the gashes torn in general relativity by black holes.

Strings (or their more general counterparts, branes, a term for multidimensional membranes) are so tiny that no instrument can hope to spot them—at least until our civilization becomes much more advanced.

Particle physicists look at the subatomic realm with particle accelerators: they use magnetic fields or other means to get tiny particles moving very fast; when these particles collide with one another, they spit off fragments. Particle accelerators are the microscopes of the subatomic world, and the more energy you put into those particles—the more powerful the microscope—the smaller the objects you can see.

No instrument currently imaginable will give scientists the power to observe strings directly; nobody can think of an experiment that will give physicists evidence about whether black holes and particles are, indeed, strings. This is the chief objection to string theory.

Because science is based upon observation and experiment, some critics argue that string theory is not science but philosophy. (A recent set of theories proposes that some of these rolled-up dimensions might be 10−19 centimeters or even larger, which would put them within the realm of experimentation. But at the moment, these theories are considered rogues—interesting ideas, but very long shots at best.)

String theory, on the other hand, ties together a number of existing theories in a very pretty way, and makes a number of predictions about the way black holes and particles behave, but none of those predictions are testable or observable. While string theory might be mathematically consistent, and even beautiful, it is not yet science.

For the foreseeable future, banishing zero from the universe with string theory is a philosophical idea rather than a scientific one. String theory might well be correct, but we may never have the means to find out. Zero has not yet been banished; indeed, zero seems to be what created the cosmos.

Zero is so powerful because it unhinges the laws of physics. It is at the zero hour of the big bang and the ground zero of the black hole that the mathematical equations that describe our world stop making sense.

However, if we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason—for we would know the mind of God. —STEPHEN HAWKING

Zero is behind all of the big puzzles in physics. The infinite density of the black hole is a division by zero. The big bang creation from the void is a division by zero. The infinite energy of the vacuum is a division by zero. Yet dividing by zero destroys the fabric of mathematics and the framework of logic—and threatens to undermine the very basis of science.

came. The

We divide by a – b. But look out. Since a and b are both equal to 1, a – b=1 – 1=0. We have divided by zero, and we get the ridiculous statement that 1=0. From there we can prove any statement in the universe, whether it is true or false. The whole framework of mathematics has exploded in our faces.