Figure 57: The expanding universe
As time runs forward, the universe expands and expands. Looking at it another way, if you had a film of the universe’s history and ran the film backward, the universe would shrink and shrink. At some point the balloon would shrivel and wither, getting smaller and smaller, and then eventually disappear as a point—the singularity at the beginning of time and space. This is the primal zero, the birthplace of the universe: the big bang, a furious explosion that created the cosmos. It is from this singularity that all the matter and energy in the universe spewed forth, creating all the galaxies, stars, and planets that have ever—and will ever—exist. The universe had a beginning, about 15 billion years in the past, and space has been expanding ever since. Einstein’s hope for a steady, eternal universe was all but dead.
One glimmer of hope remained, one alternative to the big bang: steady-state theory. Some astronomers proposed that there were fountains that spat out matter, and the galaxies moved away from these founts, aging and dying. Though the individual galaxies zoomed away and died, the entire universe as a whole never changed. It was always in equilibrium, constantly replenishing itself. Aristotle’s eternal universe still survived.
For a time, big bang theory and steady-state theory lived side by side, alternatives that astronomers chose between depending on their philosophy. In the mid-1960s, that all changed. Steady-state theory was killed by what scientists had mistaken for pigeon droppings.
In 1965 several astrophysicists at Princeton University were calculating what would have happened right after the big bang. The entire universe must have been incredibly hot and dense; it would have been glowing with bright light. That light would not have disappeared as the balloon universe expanded; it would instead have gotten stretched out as the rubber fabric of space-time stretched. A few calculations later, the Princeton physicists realized that this light had to be in the microwave region of the spectrum, and had to be coming from all directions. This cosmic background radiation was the afterglow of the big bang. It would give physicists the first direct evidence that the big bang was correct and that steady state was wrong.
The Princeton scientists did not have long to wait before their prediction was confirmed. At Bell Labs in nearby Murray Hill, New Jersey, two engineers had been testing out sensitive microwave-detecting equipment. For all their tinkering, they could not get the equipment to work just right. There was a background hiss of microwave noise—like static on a radio program—that they could not get rid of. At first they thought that pigeons defecating in their antenna were to blame, but after chasing away the birds and cleaning out the droppings, the hiss remained. They tried everything they could think of to get rid of the noise, but nothing worked. Then when the engineers heard of the Princeton group’s work, they realized that they had found the cosmic background radiation. The noise wasn’t pigeon droppings. It was the scream of light from the big bang, stretched and distorted into a whisper’s hiss. (For their discovery the engineers, Arno Penzias and Robert Wilson, got the Nobel Prize. The Princeton physicists, notably Bob Dicke and P. J. E. “Jim” Peebles, got nothing—hardly fair in many scientists’ opinions. The Nobel committee tends to reward painstaking and careful experiments more than important theory.)
The big bang had been spotted; the myth of the static universe was dead. As unappealing as the idea of a finite universe was, physicists gradually accepted the big bang and agreed that the universe had a beginning. However, there were still problems with the theory. For one thing, the universe is somewhat lumpy. Knots of dense galaxies are separated by vast voids. At the same time, the universe is not too lumpy; it looks roughly the same in all directions, so all the matter did not wind up in one huge glob. If the universe had come from a singularity, with all probability the energy from the big bang should have covered the entire balloon fairly evenly or wound up in one big lump; the balloon should be evenly shaded or it should have one giant spot, rather than being polka-dotted. Something had to account for that just-right amount of lumpiness. More troubling still, where did the singularity of the big bang come from? Zero holds the secret.
The zero of the vacuum might explain the lumpiness of the universe. Since the vacuum everywhere in the universe is seething with a quantum foam of virtual particles, the fabric of the universe is filled with infinite zero-point energy. Under the right conditions this energy is able to push objects around; in the early universe it might have pushed objects apart.
In the 1980s physicists suggested that the zero-point energy in the early universe was greater than it is today. That extra energy would try to expand in all directions, pushing the fabric of space and time outward with great speed. It would inflate the balloon with a huge burst of power, smoothing out the lumpiness of the universe in the same way a breath of air smooths out the wrinkles of a balloon. This explains why the universe is relatively smooth. But the vacuum of the first few moments is a false vacuum; its zero-point energy is unnaturally large. The higher energy state of the zero-point energy makes it inherently unstable, and very quickly—in less than a millionth of a millionth of a millionth of a millionth of a second—the false vacuum would collapse, reverting to the true vacuum, with its everyday zero-point energy that we observe in our universe. It was like a pot of water that was instantly flash heated to a huge temperature. Little bubbles of “true” vacuum would have formed and expanded at the speed of light. Our observable universe sits inside one of these bubbles—or several of them that got linked together. The asymmetry of the universe could be explained by the asymmetrical nature of these expanding bubbles that formed and merged. According to this theory of inflation, it is the nonzero zero-point energy that created the stars and galaxies.
Zero might also hold the secret of what created the cosmos. Just as the nothingness of the vacuum and the zero-point energy spawn particles, they might spawn universes. The froth of quantum foam, the spontaneous birth and death of particles, might explain the origin of the cosmos. Perhaps the universe is just a quantum fluctuation on a grand scale—an enormous singular particle that came into existence out of the ultimate vacuum. This cosmic egg would explode, inflate, and create the space-time of our universe. It may be that our universe is simply one of many fluctuations. Some physicists believe that the singularities at the center of black holes are windows into the primordial quantum foam before the big bang—and the froth of foam at the center of a black hole, where time and space have no meaning, is constantly creating countless numbers of new universes that bubble off, inflate, and create their own stars and galaxies. Zero might hold the secret to our existence—and the existence of an infinite number of other universes.
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, zero cannot be ignored. Not only does zero hold the secret to our existence, it will also be responsible for the end of the universe.
Chapter 9
Zero’s Final Victory
[END TIME]
This is the way the world ends
Not with a bang but a whimper.
—T. S. ELIOT, “THE HOLLOW MEN”
While some physicists are trying to eliminate zero from their equations, others are showing that zero may have the last laugh. Even though scientists might never unlock the secrets of the universe’s birth, they are on the brink of understanding its death. The ultimate fate of the cosmos lies with zero.
Einstein’s gravitational equations didn’t allow for a static, unchanging universe. They did, however, allow for several other fates, which depend on the amount of mass in the cosmos. In the case of a light universe, the balloon of space-time could expand forever, getting bigger and bigger. The stars and galaxies would wink out, one by one. The universe grows cold and dies a heat death. However, if there is enough mass—galaxies, galaxy clusters, and unseen dark matter—the initial push given by the big bang would
n’t be enough to allow the balloon to inflate forever. The galaxies would tug on one another, eventually pulling the fabric of space-time together; the balloon would begin to deflate. The deflation would get faster and faster, the universe would get hotter and hotter, and it would eventually end in a backward big bang: the big crunch. Which will be our fate: big crunch or heat death? The answer is at hand.
When astronomers peer at a distant galaxy, they are looking backward in time. A nearby galaxy might be a million light-years away. A light beam leaving that galaxy now will take a million years to make its trip to Earth; the light reaching our eyes now left that galaxy a million years ago. The more distant the objects that astronomers look at, the farther back they are looking in time.
The universe’s fate hinges on how well our space-time balloon is expanding. If the expansion is slowing down rapidly, then it’s a good sign that the energy from the big bang is nearly spent; our universe would be heading for a big crunch. On the other hand, if the universe’s expansion isn’t slowing down very much, the energy of the big bang might have given the fabric of space-time enough of a kick to let it expand for eternity.
Astronomers have begun to measure the change in the universe’s expansion. A certain type of supernova (exploding star), called a type Ia, is a standard candle like Hubble’s Cepheid stars. The Ia supernovas explode in roughly the same way and with the same brightness. But unlike Hubble’s dim Cepheids, supernovas are visible halfway across the universe.
In late 1997 astronomers announced that they had used these supernovas to measure the distance to some very dim and ancient galaxies. The distance of the galaxy yields its age—and its Doppler shift yields its velocity. By comparing how fast galaxies were receding at different eras in the past, the astronomers were able to track how fast space-time was expanding. The answer they got was an odd one.
The expansion of the universe isn’t slowing down. It might even be speeding up. The supernova data imply that the universe is getting bigger and bigger, faster and faster. If this is the case, there is little chance of a big crunch, because something is opposing the force of gravity. Once again physicists are talking about the cosmological constant—the mysterious term that Einstein added to his equations to balance the push of gravity. Einstein’s biggest blunder might not have been a blunder after all.
The mysterious force, once again, might be the force of the vacuum. The tiny particles that seethe through space-time exert a gentle outward push, stretching the fabric of space-time imperceptibly. Over billions of years, that stretch adds up, and the universe inflates faster and faster. The fate of our universe will not be a big crunch but an eternal expansion, cooling, and heat death, thanks to the zero-point energy, a zero in the equations of quantum mechanics that imbues the vacuum with an infinity of particles.
Astronomers are still cautious. These supernova results are preliminary, but they are getting more solid with each observation. Other studies, which analyze plumes of gas or the number of gravitational lenses in a given field of view, also support the supernova results, implying that the cosmos will expand forever. The universe will die a cold death, not a hot one.
The answer is ice, not fire, thanks to the power of zero.
To Infinity and Beyond
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.
In Pythagoras’s day, before the age of zero, pure logic reigned supreme. The universe was predictable and orderly. It was built upon rational numbers and implied the existence of God. Zeno’s troubling paradox was explained away by banishing infinity and zero from the realm of numbers.
With the scientific revolution, the purely logical world gave way to an empirical one, based upon observation rather than philosophy. For Newton to explain the laws of the universe, he had to ignore the illogic within his calculus—an illogic caused by a division by zero.
Just as mathematicians and physicists managed to overcome the divison-by-zero problem in the calculus and set it once more upon a logical framework, zero returned in the equations of quantum mechanics and general relativity and, once again, tainted science with the infinite. At the zeros of the universe, logic fails. Quantum theory and relativity fall apart. To solve the problem, scientists set out to banish zero yet once more and unify the rules that govern the cosmos.
If scientists succeed, they will understand the laws of the universe. We would know the physical laws that dictate everything to the edges of space and time, from the beginning of the cosmos to its end. Humans would understand the cosmic whim that created the big bang. We would know the mind of God. But this time, zero might not be so easy to defeat.
The theories that unify quantum mechanics and general relativity, that describe the centers of black holes and explain the singularity of the big bang, are so far removed from experiment that it might be impossible to determine which are correct and which are not. The arguments of string theorists and cosmologists might be mathematically precise and at the same time be as useless as the philosophy of Pythagoras. Their mathematical theories might be beautiful and consistent and might seem to explain the nature of the universe—and be utterly wrong.
All that scientists know is the cosmos was spawned from nothing, and will return to the nothing from whence it came.
The universe begins and ends with zero.
Appendix A
Animal, Vegetable, or Minister?
Let a and b each be equal to 1. Since a and b are equal,
b2 = ab (eq. 1)
Since a equals itself, it is obvious that
a2 = a2 (eq. 2)
Subtract equation 1 from equation 2. This yields
a2 - b2 = a2 - ab (eq. 3)
We can factor both sides of the equation; a2 - ab equals a(a - b). Likewise, a2 - b2 equals (a + b)(a - b). (Nothing fishy is going on here. This statement is perfectly true. Plug in numbers and see for yourself!) Substituting into equation 3, we get
(a + b)(a - b) = a(a - b) (eq. 4)
So far, so good. Now divide both sides of the equation by (a - b) and we get
a + b = a (eq. 5)
Subtract a from both sides and we get
b = 0 (eq. 6)
But we set b to 1 at the very beginning of this proof, so this means that
1 = 0 (eq. 7)
This is an important result. Going further, we know that Winston Churchill has one head. But one equals zero by equation 7, so that means that Winston has no head. Likewise, Churchill has zero leafy tops, therefore he has one leafy top. Multiplying both sides of equation 7 by 2, we see that
2 = 0 (eq. 8)
Churchill has two legs, therefore he has no legs. Churchill has two arms, therefore he has no arms. Now multiply equation 7 by Winston Churchill’s waist size in inches. This means that
(Winston’s waist size) = 0 (eq. 9)
This means that Winston Churchill tapers to a point. Now, what color is Winston Churchill? Take any beam of light that comes from him and select a photon. Multiply equation 7 by the wavelength, and we see that
(Winston’s photon’s wavelength) = 0 (eq. 10)
But multiplying equation 7 by 640 nanometers, we see that
640 = 0 (eq. 11)
Combining equations 10 and 11, we see that
(Winston’s photon’s wavelength) = 640 nanometers
To sum up, we have proved, mathematically, that Winston Churchill has no arms and no legs; instead of a head, he has a leafy top; he tapers to a point; and he is bright orange. Clearly, Winston Churchill is a carrot. (There is a simpler way to prove this. Adding 1 to both sides of equation 7 gives the equation
2 = 1
Winston Churchill and a carrot are two different things, therefore they are one thing. But that’s not nearly as satisfying.)
What is wrong with this proof? There is only one step that is flawed, and that is the one where we go from equation 4 to equation 5. 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.
Used unwisely, zero has the power to destroy logic.
Appendix B
The Golden Ratio
Divide a line in two, such that the ratio of the small part to the large part is equal to the ratio of the large part to the whole line. For the sake of simplicity, let’s say that the small part is 1 foot long.
If the small part is 1 foot long, and the large part is x feet long, then the length of the whole line is obviously 1 + x feet long. Putting our relationship into algebra, we find that the ratio of the small part to the large part is
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