by Jim Holt
Of course, showing that a principle is self-subsuming is no proof that the principle in question is valid. Consider the sentence “Every sentence of exactly eight words is true.” Call this sentence S. Since S has exactly eight words, the truth of S is derivable from S itself, making it self-subsuming. But S is clearly false. (I leave this as an exercise for the reader.) Another statement that is self-subsuming yet false is “All generalizations are true.”
When a self-subsuming principle is true, however, it does in a sense explain why it is true. (What is explanation, after all, but subsumption under a law?) “The ultimate principle which is true will, I have suggested, explain itself by subsuming itself,” Nozick wrote. “Being a deep fact, deep enough to subsume itself and to yield itself, the principle will not be left dangling without any explanation.” So as the terminus of an explanatory chain, a self-subsuming principle is certainly preferable to a brute fact.
Still, self-subsumption does not by itself eliminate all explanatory loose ends. Consider again the self-subsuming sentence S: “All sentences of exactly eight words are true.” Although S is false, it is possible to imagine a world that makes it true. Even in this world, however, we would not be satisfied with S as an ultimate explanation. For one thing, it looks arbitrary. Why should S be true and not some rival self-subsuming sentence—say, “All sentences that contain exactly nine words are true”? For another thing, S does not have the look of ultimacy. If it were true, we would seek some deeper explanation of why it was the case—of why the world and language were arranged just that way.
Even though self-subsumption is not a guarantee of ultimacy, it may at least be a mark of ultimacy. Suppose, Nozick said, we were to find “a self-subsuming statement that is deep enough to yield everything else in an area or realm, while repeated efforts fail to find a further truth that yields it.” Then, he contended, it would be “a reasonable conjecture, tentatively held and overturnable, that an ultimate truth has been reached.” In other words, we may have found our superturtle.
Could some self-subsuming principle of the kind envisioned by Nozick furnish the answer to the question Why is there something rather than nothing? David Deutsch thought there could be no such answer, no end to explanation. Richard Swinburne thought the best we could do was to find the right explanatory “stopping point,” a hypothesis of maximum simplicity and power, which for him was the existence of God. Yet Swinburne conceded that God’s own existence had no explanation, “for surely never does anything explain itself.” Nozick, by contrast, saw a way that a principle could explain itself without being blatantly circular. His ideal of self-subsumption would thus seem to mark an explanatory advance over Swinburne’s ideal of simplicity.
But what sort of self-subsuming principle could explain why there is Something rather than Nothing?
Nozick thought he might have the answer. He proposed what he called “the principle of fecundity.” This is the most liberal of all ontological principles. It states that all possible worlds are real. The principle of fecundity was not invented by Nozick. In essence, the idea—which is also known as the “principle of plenitude”—goes back to Plato. Versions of it have been entertained throughout the history of thought. What is novel with Nozick is the claim that the principle of fecundity, being self-subsuming, furnishes its own justification. “If it is a very deep fact that all possibilities obtain,” he wrote, “then that fact, being a possibility, obtains in virtue of the deep fact that all possibilities do.”
A reality governed by the principle of fecundity would be the richest and most expansive reality conceivable. But it would have a rather odd structure. All possible worlds would exist, but they would exist as “parallel universes,” in logical isolation from one another. Some of these worlds would be very large and complicated. The largest of them, which we might call the maximal world, would itself contain every possibility, mirroring the richness of the entire ensemble of possible worlds that made up reality as a whole. At the other end of the range of possibilities would be the minimal or null world, representing the possibility that nothing at all existed. In between would come all possibilities of intermediate size and complexity: worlds containing a single electron and positron orbiting each other, worlds looking much like our own universe, worlds containing the Greek gods, worlds made of cream cheese, and so on.
The principle of fecundity, if true, would mean that reality is infinitely more encompassing than we had imagined. It would make our little universe look provincial in the extreme. And such a reality would have the virtue of eliminating the mystery of existence—so, at any rate, contended Nozick. The minimal world, one of the separate possibilities realized according to the principle of fecundity, is just our old friend nothingness. So why is there something rather than nothing? “There isn’t,” Nozick replied. “There’s both.”
But wait—the logic seems to have gone askew here. There can’t be both something and nothing. If you have a reality that consists of bits of something and you add a bit of nothing to it, you still have something. And the absurdity does not stop there. The principle of fecundity says that all possibilities are realized. Now, one possibility is
R: Everything is red.
Another possibility is:
not-R: There is at least one thing that isn’t red.
So the principle of fecundity implies R and not-R—a contradiction. And anything that implies a contradiction must be false.
Nozick had a response to this objection. Although the two possibilities R and not-R are both realized, he said, “they exist in independent noninteracting realms.” We might think of them as two different planets, “Planet Red” and “Planet not-Red.” That’s one way out of the contradiction. But it’s not a good way. For even if R and not-R prevail on separate planets, there can be no planet where both possibilities are realized together. In other words, there can be no “Planet Fecundity” among the possible planets. Even if all possible planets are realized, there is no planet where all possibilities are realized. So fecundity is not self-subsuming after all. It’s a cruel dilemma for Nozick: either his ultimate explanatory principle leads to contradiction, or it fails to be self-subsuming.
A self-subsuming ultimate principle is like a barber who shaves all the men in the village and himself too. There’s nothing logically wrong with that. It’s the principle of fecundity that’s the problem. It countenances too many possibilities—including the paradoxical one of a barber who shaves all and only those men who don’t shave themselves. Given this fatal logical defect, the principle of fecundity is clearly not fit to serve as the ultimate explanation.
Is the search for a self-subsuming principle of reality then hopeless? Unhappily, Nozick himself had nothing else to offer. (He died in 2002, of stomach cancer, at the age of sixty-three.) Perhaps his ontological speculations, wild as they seemed to many of his fellow philosophers, were not quite wild enough. If philosophy, like theology before it, had so far failed to come up with the goods, maybe it was time for me to look elsewhere, in the still-wilder reaches of contemporary physics. I might not find the sought-for explanatory “superturtle” there. But I had heard theoretical physicists talking about the universe as a “free lunch,” and that sounded almost as good.
8
THE ULTIMATE FREE LUNCH?
Science cannot answer the deepest questions. As soon as you ask why there is something instead of nothing, you have gone beyond science.
—ALLAN SANDAGE, the father of modern astronomy
Science is impotent to address the mystery of existence—so, at least, it is often claimed. The point was put forcefully by the secular humanist (and evolutionary biologist) Julian Huxley. “The clear light of science, we are often told, has abolished mystery, leaving only logic and reason,” Huxley wrote. “This is quite untrue. Science has removed the obscuring veil of mystery from many phenomena, much to the benefit of the human race: but it confronts us with a basic and universal mystery—the mystery of existence. . . . Why does the world
exist? Why is the world-stuff what it is? Why does it have mental or subjective aspects as well as material or objective ones? We do not know. . . . But we must learn to accept it, and to accept its and our existence as the one basic mystery.”
The question Why is there something rather than nothing? is supposed to be “too big” for science to explain. Scientists can account for the organization of the physical universe. They can trace how the individual things and forces within it causally interact. They can shed light on how the universe as a whole has, in the course of its history, evolved from one state into another. But when it comes to the ultimate origin of reality, they have nothing to say. That is an enigma best left to metaphysics, or to theology, or to poetic wonderment, or to silence.
As long as the universe was thought to be eternal, its existence did not greatly vex scientists anyway. Einstein in this theorizing simply assumed the eternity of the universe, and he fudged his relativity equations accordingly. With the discovery of the Big Bang, however, everything changed. We are evidently living in the dilute, expanding, cooled-down remnants of a great cosmic explosion that occurred some 14 billion years ago. What could have caused this primal explosion? And what, if anything, preceded it? These certainly sound like scientific questions. But any attempt by science to answer them faces a seemingly insuperable obstacle, known as the singularity.
Suppose we take the laws of general relativity, which govern cosmic evolution on the largest scale, and extrapolate them backward in time toward the beginning of the universe. As we watch the evolution of our expanding and cooling cosmos in reverse, we would see its contents contracting and growing hotter. At t = 0—the moment of the Big Bang—the temperature, density, and curvature of the universe all go to infinity. Here the equations of relativity break down, become meaningless. We have reached a singularity, a boundary or edge to spacetime itself, a point at which all causal lines converge. If there is a cause for this event, it must transcend spacetime and hence escape the reach of science.
The conceptual breakdown of science at the Big Bang was disturbing to cosmologists, so disturbing that they searched for scenarios in which the initial singularity was somehow avoided. But in 1970, the physicists Stephen Hawking and Roger Penrose showed that these efforts were futile. Hawking and Penrose began by assuming, quite reasonably, that gravity is always attractive, and that the density of matter in the universe is roughly what it has been measured to be. Given this pair of assumptions, they proceeded to prove, with mathematical certainty, that there must have been a singularity at the beginning of the universe.
Did this mean that the ultimate origin of the universe is forever shrouded in unknowability? Not necessarily. It merely means that the Big Bang cannot be completely understood by “classical” cosmology—that is, the kind of cosmology that is based on Einstein’s general relativity alone. Other theoretical resources would be needed.
As a clue to what kind of resources, consider that, a fraction of a second after its birth, the entire observable universe was no bigger than an atom. At that size scale, classical physics no longer applies. It is quantum theory that governs the realm of the very tiny. So cosmologists—Stephen Hawking prominently among them—began to ask, What if quantum theory, previously used to describe subatomic phenomena, were applied to the universe as a whole? Thus was born the field of quantum cosmology, which has been described (by the physicist John Gribbin) as “the most profound development in science since Isaac Newton.”
Quantum cosmology seemed to offer a way around the singularity problem. Classical cosmologists had supposed that the singularity lurking behind the Big Bang was a pointlike thing, with zero volume. But quantum theory forbids such a sharply defined state of affairs. It decrees that nature, at the most fundamental level, is irredeemably fuzzy. It rules out the possibility of a precise temporal origin to the universe, a time t = 0.
But what is more interesting than what it forbids is what quantum theory permits. It permits particles to pop into existence spontaneously, if briefly, out of a vacuum. This scenario of creation ex nihilo led quantum cosmologists to entertain an arresting possibility: that the universe itself, through the laws of quantum mechanics, bounded into existence out of nothing. The reason there is Something rather than Nothing is, as they fancifully put it, that nothingness is unstable.
The physicist’s statement “nothingness is unstable” is sometimes mocked by philosophers as an abuse of language. “Nothingness” does not name an object, they say; therefore, it is meaningless to ascribe a property, like instability, to it. But there is another way of thinking of nothingness: not as a thing, but as a description of a state of affairs. For a physicist, “nothingness” describes a state of affairs where there are no particles and where all the mathematical fields have the value zero.
Now we can ask, Is such a state of nothingness possible? That is, is it logically consistent with physical principles? One of the deepest of these principles, lying at the very basis of our quantum understanding of nature, is Heisenberg’s uncertainty principle. This principle says that certain pairs of properties—called “canonically conjugate variables”—are linked in such a way that they cannot both be measured precisely. One such pair is position and momentum: the more precisely you locate the position of a particle, the less you know about its momentum, and vice versa. Another pair of conjugate properties is time and energy: the more precisely you know the time span in which something occurred, the less you know about the energy involved, and vice versa.
Quantum uncertainty also forbids the precise determination of the value of a field and the rate at which that field value changes. (That’s like saying you can’t know the exact price of a stock and how quickly that price is changing.) And, when you think about it, this pretty much rules out nothingness. Nothingness is, by definition, a state in which all field values are timelessly equal to zero. But Heisenberg’s principle tells us that if the value of a field is precisely known, its rate of change is completely random. In other words, that rate of change can’t be precisely zero. So a mathematical description of changeless emptiness is incompatible with quantum mechanics. To put the point more pithily, nothingness is unstable.
Could this have something to do with cosmogenesis? The thought that it might seems first to have occurred back in 1969 to a New York City physicist named Ed Tryon. Doing a bit of wool-gathering during a talk by a visiting celebrity physicist at Columbia University, Tryon suddenly blurted out, “Maybe the universe is a quantum fluctuation!” The remark was reportedly greeted by the several Nobel laureates present with derisive laughter.
But Tryon was on to something. It may seem implausible that a universe containing so much sheer stuff—there are a hundred billion galaxies just in the little region of it we can observe, each with a hundred billion stars—could have arisen from nothing. As we know from Einstein, all of this mass is frozen energy. But against the vast amount of positive energy locked up in the stars and galaxies must be set the negative energy of the gravitational attraction among them. In fact, in a “closed” universe—one that will eventually collapse back on itself—these positive and negative energies precisely cancel each other. In other words, the net energy of such a universe is zero.
The possibility that the entire universe could be made out of no energy at all is an astonishing one. It certainly astonished Einstein: when the idea was explained to him by a fellow physicist, George Gamow, while the two were walking in Princeton, a stunned Einstein “stopped in his tracks,” Gamow recalled, “and, since we were crossing a street, several cars had to stop to avoid running us down.”
From the quantum point of view, a zero-energy universe presents an interesting possibility, which Tryon seized upon. Suppose the total energy of the universe is indeed exactly zero. Then, owing to the trade-off in uncertainty between energy and time (as decreed by the Heisenberg principle), the indeterminacy in its time span becomes infinite. In other words, such a universe, once it popped into existence out of the void, could r
un away with itself and last forever. It would be like a loan of pure being that need never be repaid. As for what “caused” such a universe to pop into existence, that is simply a matter of quantum chance. “In answer to the question of why it happened,” Tryon later commented, “I offer the modest proposal that our universe is simply one of those things which happen from time to time.”
Is this creatio ex nihilo? Not quite. It is true that Tryon’s genesis scenario has a zero cost in terms of energy and matter; in that sense, it does seem to get “something from nothing.” But the state out of which Tryon’s cosmos spontaneously materializes, called the “quantum vacuum,” is very far from the philosopher’s conception of nothingness. For one thing, it is a kind of empty space, and space is not nothing. Nor is the space of the quantum vacuum really empty. It has a complicated mathematical structure; it bends and flexes like rubber; it is saturated with energy fields and seethes with virtual-particle activity. The quantum vacuum is a physical object; indeed, it is a little proto-cosmos unto itself. Why should such a thing as a quantum vacuum ever have existed? As the physicist Alan Guth has observed, “A proposal that the universe was created from empty space seems no more fundamental than a proposal that the universe was spawned by a piece of rubber. It might be true, but one would still want to ask where the piece of rubber came from.”
The man who seems to have come the closest to solving the “rubber problem” is Alex Vilenkin. Vilenkin was born in Ukraine, in the former Soviet Union, where, after obtaining an undergraduate degree in physics, he held a job as a night watchman in a zoo. In 1976 he immigrated to the United States, and in little more than a year he managed to earn a Ph.D. in physics. Vilenkin now teaches at Tufts University near Boston, where he is also director of the Tufts Institute of Cosmology. He is known for wearing dark glasses during seminars, Anna Wintour–like, supposedly because of the sensitivity of his eyes to light.