Many Worlds in One: The Search for Other Universes

by Vilenkin, Alex

  My model of the universe tunneling out of nothing did not appear from nothing—I had some predecessors. The first suggestion of this sort came from Edward Tryon of Hunter College, City University of New York. He proposed the idea that the universe was created out of vacuum as a result of a quantum fluctuation.

  The thought first occurred to him in 1970, during a physics seminar. Tryon says that it struck him like a flash of light, as if some profound truth had suddenly been revealed to him. When the speaker paused to collect his thoughts, Tryon blurted out, “Maybe the universe is a vacuum fluctuation!” The room roared with laughter.2

  As we discussed earlier, the vacuum is anything but dull or static; it is a site of frantic activity. Electric, magnetic, and other fields are constantly fluctuating on subatomic scales because of unpredictable quantum jerks. The spacetime geometry is also fluctuating, resulting in a frenzy of spacetime foam at the Planck distance scale. In addition, the space is full of virtual particles, which spontaneously pop out here and there and instantly disappear. The virtual particles are very short-lived, because they live on borrowed energy. The energy loan needs to be paid off, and according to Heisenberg’s uncertainty principle, the larger the energy borrowed from the vacuum, the faster it has to be repaid. Virtual electrons and positrons typically disappear in about one-trillionth of a nanosecond. Heavier particles last even less than that, as they require more energy to materialize. Now, what Tryon was suggesting was that our entire universe, with its vast amount of matter, was a huge quantum fluctuation, which somehow failed to disappear for more than 10 billion years. Everybody thought that was a very funny joke.

  But Tryon was not joking. He was devastated by the reaction of his colleagues, to the extent that he forgot his idea and suppressed the memory of the whole incident. But the idea continued brewing at the back of his mind and resurfaced three years later. At that time, Tryon decided to publish it. His paper appeared in 1973 in the British science journal Nature, under the title “Is the Universe a Vacuum Fluctuation?”

  Tryon’s proposal relied upon a well-known mathematical fact—that the energy of a closed universe is always equal to zero. The energy of matter is positive, the gravitational energy is negative, and it turns out that in a closed universe the two contributions exactly cancel each other. Thus, if a closed universe were to arise as a quantum fluctuation, there would be no need to borrow energy from the vacuum and the lifetime of the fluctuation could be arbitrarily long.

  The creation of a closed universe out of the vacuum is illustrated in Figure 17.3. A region of flat space begins to swell, taking the shape of a balloon. At the same time, a colossal number of particles are spontaneously created in that region. The balloon eventually pinches off, and—voilà—we have a closed universe, filled with matter, that is completely disconnected from the original space.3 Tryon suggested that our universe could have originated in this way and emphasized that such a creation event would not require a cause. “In answer to the question of why it happened,” he wrote, “I offer the modest proposal that our universe is simply one of those things which happen from time to time.”4

  Figure 17.3. A closed universe pinches off a large region of space.

  The main problem with Tryon’s idea is that it does not explain why the universe is so large. Closed baby universes are constantly pinched off any large region of space, but all this activity occurs at the Planck distance scale, as in the spacetime foam picture shown in Figure 12.1. Formation of a large closed universe is possible in principle, but the probability for this to happen is much smaller than that for a monkey to randomly type the full text of Shakespeare’s Hamlet.

  In his paper Tryon argued that even if most of the universes are tiny, observers can only evolve in a large universe and therefore we should not be surprised that we live in one. But this falls short of resolving the difficulty, because our universe is much larger than necessary for the evolution of life.

  A more fundamental problem is that Tryon’s scenario does not really explain the origin of the universe. A quantum fluctuation of the vacuum assumes that there was a vacuum of some pre-existing space. And we now know that “vacuum” is very different from “nothing.” Vacuum, or empty space, has energy and tension, it can bend and warp, so it is unquestionably something.5 As Alan Guth wrote, “In this context, a proposal that the universe was created from empty space is 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.”6

  The picture of quantum tunneling from nothing has none of these problems. The universe is tiny right after tunneling, but it is filled with a false vacuum and immediately starts to inflate. In a fraction of a second, it blows up to a gigantic size.

  Prior to the tunneling, no space or time exists, so the question of what happened before is meaningless. Nothing—a state with no matter, no space, and no time—appears to be the only satisfactory starting point for the creation.

  A few years after publishing my tunneling-from-nothing paper, I realized that I had missed an important reference. Normally, one finds out about such things much sooner, by way of pesky e-mails from the omitted authors. But this author did not write to me, and for a good reason: he did his work more than 1,500 years ago. He was Saint Augustine, the bishop of Hippo, one of the major cities in northern Africa.

  Augustine grappled with the question of what God was doing before the creation—a quest he eloquently described in his Confessions. “For if he was idle … and doing nothing, then why did he not continue in that state forever—doing nothing, as he has always done?” Augustine thought that in order to answer his question, he first had to figure out what time is: “What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.” A lucid analysis led him to the realization that time could be defined only through motion and could not, therefore, exist before the universe. Augustine’s final conclusion was that “[t]he world was made not in time, but simultaneously with time. There was no time before the world.” And thus it is meaningless to ask what God was doing then. “If there was no time, there was no ‘then.’”7 This is very close to what I argued in my tunneling-from-nothing scenario.

  I learned about Augustine’s ideas accidentally, in a conversation with my Tufts colleague Kathryn McCarthy. I read the Confessions and quoted Saint Augustine in my next paper.8

  MANY WORLDS

  The universe emerging from quantum tunneling does not have to be perfectly spherical. It can have a variety of different shapes, and it can also be filled with different kinds of false vacuum. As usual in quantum theory, we cannot tell which of these possibilities has been realized, but can only calculate their probabilities. Could it be, then, that there is a multitude of other universes that started differently from our own?

  This issue is closely related to the thorny question of how quantum probabilities are to be interpreted. As we discussed in Chapter 11, there are two major alternatives. According to the Copenhagen interpretation, quantum mechanics assigns probabilities to all possible outcomes of an experiment, but only one of these outcomes actually happens. The Everett interpretation, on the other hand, asserts that all possible outcomes are realized in disconnected, “parallel” universes.

  If the Copenhagen interpretation is adopted, then the creation was a one-shot event, with a single universe popping out of nothing. This, however, leads to a problem. The most likely thing to pop out of nothing is a tiny Planck-sized universe, which would not tunnel, but would instantly recollapse and disappear. Tunneling to a larger size has a small probability and therefore requires a large number of trials. It appears to be consistent only with the Everett interpretation.

  In the Everett picture, there is an ensemble of universes with all possible initial states. Most of them are Planck-sized “flicker” universes, which blink in and out of existence. But in addition, there are some universes that tunnel to a larger size and i
nflate. The crucial difference from the Copenhagen interpretation is that all these universes are not merely possible, but real.9 Since observers cannot evolve in the “flickers,” only large universes will be observed.

  All of the universes in the ensemble are completely disconnected from one another. Each has its own space and its own time. Calculations show that the most probable—and thus the most numerous—of the tunneling universes are the ones nucleating with the smallest initial radius and the highest energy density of the false vacuum. Our best guess, then, is that our own universe also nucleated in this way.

  In scalar field models of inflation, the highest vacuum energy density is reached at the top of the energy hill, and thus most of the universes will nucleate having the scalar field in that vicinity. This is the most favorable starting point for inflation. Remember, I promised to explain how the field got to the top of the hill. In the tunneling-from-nothing scenario, this is where it was when the universe came into being.

  The nucleation of the universe is basically a quantum fluctuation, and its probability decreases rapidly with the volume it encompasses. Universes nucleating with a larger initial radius have smaller probability, and in the limit of infinite radius, the probability vanishes. An infinite, open universe has a strictly zero probability of nucleating, and thus all universes in the ensemble must be closed.

  THE HAWKING FACTOR

  In July 1983 several hundred physicists from all over the world gathered in the Italian city of Padova for the tenth International Conference on General Relativity and Gravitation. The conference site was the thirteenth-century Palazzo della Ragione, the old courthouse, located at the very heart of Padova. The ground floor of the Palazzo is taken by the famous food market, which spills outdoors into the adjacent piazza. The upper floor is occupied by a spacious hall, frescoed with signs of the zodiac around its perimeter. That’s where the lectures were held. The highlight of the program was the talk by Stephen Hawking, entitled “The Quantum State of the Universe.” The entrance to the lecture hall was through a long stairway, and it was a nontrivial task to carry Hawking in his wheelchair up the stairs. I was glad I arrived early, since by the time Hawking appeared on stage, the hall was completely packed.

  In his talk Hawking unveiled a new vision for the quantum origin of the universe, based on the work he had done with James Hartle of the University of California at Santa Barbara.10 Instead of focusing on the early moments of creation, he asked a more general question: How can we calculate the quantum probability for the universe to be in a certain state? The universe could follow a large number of possible histories before it got to that state, and the rules of quantum mechanics can be used to determine how much each particular history contributes to the probability.bk The final result for the probability depends on what class of histories is included in the calculation. The proposal of Hartle and Hawking was to include only histories represented by spacetimes that have no boundaries in the past.

  A space without boundaries is easy to understand: it simply means a closed universe. But Hartle and Hawking required that the spacetime should also have no boundary, or edge, in the past direction of time. It should be closed in all four dimensions, except for the boundary corresponding to the present moment (see Figure 17.4).

  Figure 17.4. A two-dimensional spacetime without a past boundary.

  A boundary in space would mean that there is something beyond the universe, so that things can come in and go out through the boundary. A boundary in time would correspond to the beginning of the universe, where some initial conditions would have to be specified. The proposal of Hartle and Hawking asserts that the universe has no such boundary; it is “completely self-contained and not affected by anything outside itself.” That sounded like a very simple and attractive idea. The only problem was that spacetimes closed to the past, of the kind shown in Figure 17.4, do not exist. There should be three spacelike and one timelike direction at every spacetime point, but a closed spacetime necessarily has some pathological points with more than one timelike direction (see Figure 17.5).

  To resolve this difficulty, Hartle and Hawking suggested that we switch from real time to Euclidean time. As we discussed earlier in this chapter, Euclidean time is no different from another spatial direction; so the spacetime simply becomes a four-dimensional space, and there is no problem making it closed. Thus, the proposal was that we calculate probabilities by adding up contributions from all Euclidean spacetimes without boundaries. Hawking emphasized that this was only a proposal. He had no proof that it was correct, and the only way to find out was to check whether or not it makes reasonable predictions.

  Figure 17.5. Same as in Figure 17.4, with timelike and spacelike directions indicated by solid and dashed lines, respectively. The point P is pathological, since all directions are timelike at that point.

  The Hartle-Hawking proposal has a certain mathematical beauty about it, but I thought that after switching to Euclidean time it lost much of its intuitive appeal. Instead of summing over possible histories of the universe, it instructs us to sum over histories that are certainly impossible, because we do not live in Euclidean time. So, after the scaffolding of the original motivation is dropped, we are left with a rather formal prescription for calculating probabilities.11

  In the conclusion of his talk, Hawking discussed the implications of the new proposal for the inflationary universe. He argued that the main contribution to the sum over histories is given by the Euclidean spacetime having the form of a hemisphere—the same as appeared in my tunneling calculation—and that the following evolution is represented by the inflationary expansion in ordinary time. (Switching back to ordinary time from the Euclidean formalism was a tricky procedure, which I will not try to describe here.) The result was the same spacetime history as in my Figure 17.3, but obtained from a very different starting point.

  I expected that Hawking would mention my work on quantum tunneling from nothing and was disappointed when he didn’t. But I was sure that with Hawking now in the field, the whole subject of quantum cosmology, and my work in particular, would receive a lot more attention than before.

  MUCH ADO ABOUT NOTHING

  An important difference between the “tunneling from nothing” and “no boundary” proposals is that they give very different, and in some sense opposite, predictions for the probabilities. The tunneling proposal favors nucleation with the highest vacuum energy and the smallest size of the universe. The no-boundary prescription, on the contrary, suggests that the most likely starting point is a universe of the smallest vacuum energy and largest possible size. The most probable thing to pop out of nothing is then an infinite, empty, flat space. I find this very hard to believe!

  The conflict between the two approaches became apparent only after some initial confusion. The result in my 1982 paper was that larger universes had a higher probability of nucleating, so it looked as though the two proposals were in agreement. I kept returning to my calculation, because the result was so counter-intuitive. In 1984 I found an error, which reversed the probability trend. At the time, Hawking was visiting Harvard, and I rushed to talk to him and share my new insight. But Stephen was unconvinced and thought that I had gotten it right the first time around.bl

  Hawking is a legend among physicists and far beyond. I admire both his science and his spirit and treasure the opportunities to talk to him. Since it takes him so much effort to communicate, people are often reluctant to approach him. It took me a while to realize that Stephen actually enjoys conversation and does not even mind some joking around. We have very different views on eternal inflation and on quantum cosmology, but this only makes the discussion more interesting.

  In 1988 I took the battle to Hawking’s turf and gave a talk to his group at Cambridge University, highlighting the advantages of my approach. After the talk, Hawking rolled up to me in his wheelchair. I expected some critical remarks, but instead he invited me over for dinner. After a meal of duck with potatoes and a plum pie, cooked by S
tephen’s mother, we talked about the use of wormholes—shortcut tunnels through spacetime—for intergalactic travel. This is the physicist’s notion of a light after-dinner conversation. As for the no-boundary proposal, Stephen did not change his mind.

  The dispute between proponents of the two approaches is still going on. There was even an “official” debate at the Cosmo-98 conference in Monterey, California, with Hawking defending the no-boundary proposal and Andrei Linde and me arguing for the tunneling one.bm It was not actually much of a debate. It takes a long time for Hawking to compose sentences with his speech synthesizer, so we did not progress much beyond the prepared statements.

  We could resolve the dispute if we devised some observational test to distinguish between the two proposals. This, however, appears rather unlikely, and the reason is eternal inflation. Quantum cosmology makes predictions about the initial state of the universe, but in the course of eternal inflation any effect of the initial conditions is completely erased. Take, for example, the string theory landscape that we discussed before. We can start in one inflating vacuum or another, but inevitably bubbles of other vacua will be formed, and the entire landscape will be explored. The properties of the resulting multiverse will be independent of how inflation started.12

  Figure 17.6. Discussing quantum cosmology with Hawking. From left to right: the author, Bill Unruh of the University of British Columbia, and Stephen Hawking (drinking tea with the help of his nurse). (Courtesy of Anna Zytkow)

  Thus, quantum cosmology is not about to become an observational science. The dispute between different approaches will probably be resolved by theoretical considerations, not by observational data. For example, the quantum state of the universe may be determined by some new, yet to be discovered, principle of string theory. It may, of course, differ from either of the present proposals. This issue is not likely to be settled any time soon.