The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos

by Brian Greene

  That string theory embraces the holographic principle, and provides concrete examples of holographic parallel worlds, is a testament to how cutting-edge developments are coming together in a powerful synthesis. That these examples have provided the basis for explicit calculations, some of whose results can be compared with results from real-world experiments, is a gratifying step toward making contact with observable reality. But within string theory itself, there’s a broader frame within which these developments should be seen.

  For nearly thirty years after the initial discovery of string theory, physicists lacked a full mathematical definition of the theory. Early string theorists laid out the essential ideas of vibrating strings and extra dimensions, but even after decades of further work, the mathematical foundations of the theory remained approximate and thus incomplete. Maldacena’s insight represents major progress. The species of quantum field theory Maldacena identified as living on the boundary is among the mathematically best understood of those particle physicists have studied since the middle of the twentieth century. It does not include gravity, and that’s a big plus since, as we’ve seen, trying to bring general relativity directly into quantum field theory is like setting a campfire in a gunpowder factory. We’ve now learned that this mathematically friendly, nongravitational quantum field theory generates string theory—a theory that contains gravity—holographically. Operating way out on the boundary of a universe with the specific shape schematically illustrated in Figure 9.5, this quantum field theory embodies all physical features, processes, and interactions of strings that move within the interior, a link made explicit through the dictionary translating phenomena between the two. And since we have a sure-footed mathematical definition of the boundary quantum field theory, we can use it as a mathematical definition of string theory, at least for strings moving within this spacetime shape. The holographic parallel universes may thus be more than a potential outgrowth of fundamental laws; they may be part of the very definition of the fundamental laws.18

  When I introduced string theory in Chapter 4, I noted that it fit the venerable pattern of providing a new approach to nature’s laws that, nevertheless, did not erase past theories. The results we’ve now described take this observation to a whole different level. String theory doesn’t just reduce to quantum field theory in certain circumstances. Maldacena’s result suggests that string theory and quantum field theory are equivalent approaches expressed in different languages. The translation between them is complicated, which is why it took more than forty years for this connection to come to light. But if Maldacena’s insights are fully valid, as all available evidence attests, string theory and quantum field theory may very well be two sides of the same coin.

  Physicists are working hard to generalize the methods so they might apply to a universe with any shape; if string theory is right, that would include ours. But even with the current limitations, finally having a firm formulation of a theory we’ve worked on for many years is an essential foundation for future progress. It is surely enough to make many a physicist sing and dance.

  *This loose definition will suffice for now; in a moment, I’ll be more precise.

  *In Chapter 3, we discussed how the energy embodied by a gravitational field can be negative; this energy, however, is potential energy. The energy we’re discussing here, kinetic energy, comes from the electron’s mass and its motion. In classical physics this has to be positive.

  *Besides flipping the coins, you could also swap around their locations, but for the purpose of illustrating the main ideas, we can safely ignore this complication.

  *If you’re interested in the full story, I highly recommend Leonard Susskind’s excellent book The Black Hole Wars.

  *The reader familiar with black holes will note that even without the quantum considerations that lead to Hawking radiation, the two perspectives would differ with regards to the rate of time’s passage. Hawking radiation makes the perspectives yet more distinct.

  *There is a related story that I’ve not told in this chapter, to do with a long-standing debate regarding whether black holes require a modification of quantum mechanics—whether, by swallowing information, they upend the ability to fully evolve probability waves forward in time. A one-sentence summary is that Witten’s result, by establishing an equivalence between a black hole and a physical situation that does not destroy information (a hot quantum field theory), supplied conclusive evidence that all information that falls into a black hole is ultimately available to the outside world. Quantum mechanics needs no modification. This application of Maldacena’s discovery also establishes that the boundary theory provides a full description of the information (entropy) stored on a black hole’s surface.

  CHAPTER 10

  Universes, Computers, and Mathematical Reality

  The Simulated and the Ultimate Multiverses

  The parallel universe theories we considered in previous chapters emerged from mathematical laws developed by physicists in their pursuit of nature’s deepest workings. The credence accorded one set of laws or another varies widely—quantum mechanics is viewed as established fact; inflationary cosmology has observational support; string theory is thoroughly speculative—as does the type and logical necessity of the parallel worlds associated with each. But the pattern is clear. When we hand over the steering wheel to the mathematical underpinnings of the major proposed physical laws, we’re driven time and again to some version of parallel worlds.

  Let’s now change tack. What happens if we seize the wheel? Can we humans manipulate the cosmic unfolding to volitionally create universes parallel to our own? If you believe, as I do, that the behavior of living beings is dictated by nature’s laws, then you may see this as no change of tack at all but simply as a narrowing of perspective, to the impact of physical law when funneled through human activity. This line of thought quickly engages thorny issues such as the age-old debate about determinism and free will, but that’s not a direction in which I want to head. Rather, my question is this: With the same sense of intent and control you feel when you choose a movie or a meal, might you create a universe?

  The question sounds outlandish. And it is. I’ll tip you off now that in addressing it we will find ourselves in territory even more speculative than what we’ve already covered, and considering where we’ve been, that says a lot. But let’s have a little fun and see where it takes us. Let me lay out the perspective I’ll take. In contemplating universe creation, I’m less interested in practical constraints than in the possibilities made available by the laws of physics. So, when I speak of “you” creating a universe, what I really mean is you, or a distant descendant, or an army of such descendants possibly millennia down the road. These present or future humans will still be subject to the laws of physics, but I will imagine that they’re in possession of arbitrarily advanced technologies. I will also consider the creation of two distinct types of universes. The first type comprises the usual universes, ones that encompass an expanse of space and are filled with various forms of matter and energy. The second kind is less tangible: virtual computer-generated universes. The discussion will also naturally forge a link to a third multiverse proposal. This variety does not originate from thinking about universe creation, per se, but instead addresses the question of whether mathematics is “real” or is instead created by the mind.

  To Create a Universe

  Despite uncertainties in delineating the composition of the universe—What is the dark energy? What is the full list of fundamental particulate ingredients?—scientists are confident that were you to weigh everything that’s within our cosmic horizon, the tally would come in at about 10 billion billion billion billion billion billion grams. If the contents weighed significantly more or less than this, their gravitational influence on the cosmic microwave background radiation would cause the splotches in Figure 3.4 to be much larger or smaller, and that would conflict with refined measurements of their angular size. But the precise weight of the observable un
iverse is secondary; my point is that it’s huge. So huge that the notion of us humans creating another such realm seems utterly fatuous.

  Using big bang cosmology as our blueprint for universe formation, we find no guidance on how to clear this hurdle. In the standard big bang theory, the observable universe was ever-smaller at ever-earlier times, but the stupendous quantities of matter and energy we now measure were always present; they were just squeezed into an ever-smaller volume. If you want a universe like the one we see today, you have to start with raw material whose mass and energy are those we see today. The big bang theory takes such raw material as an unexplained given.1

  In broad strokes, then, the big bang’s instructions for creating a universe like ours require that we gather a gargantuan amount of mass and compress it to a fantastically small size. But having achieved that, however improbable, we would face another challenge. How do we ignite the bang? It’s an obstacle that becomes only more daunting when we recall that the big bang is not an explosion that takes place within a static region of space; the big bang propels the expansion of space itself.

  If the big bang theory were the pinnacle of cosmological thought, the scientific pursuit of universe creation would stop here. But it’s not. We’ve seen that the big bang theory has given way to the more robust inflationary cosmology, and inflation offers a strategy for going forward. With a powerful outward burst of spatial expansion being its trademark, the inflationary theory puts a bang in the big bang, and a big one at that; according to inflation, an anti-gravity blast is what set the outward expansion of space in motion. Of equal importance, as we’ll now see, inflation establishes that vast amounts of matter can be created from the most modest of seeds.

  Recall from Chapter 3 that in the inflationary approach, a universe like ours—a hole in the cosmic Swiss cheese—formed when the inflaton’s value rolled down its potential energy curve, bringing to a close the phenomenal outward surge in our vicinity. As the inflaton’s value dropped, the energy it contained was transformed into a bath of particles uniformly filling our bubble. That’s where the matter we see originated. Progress, for sure, but the insight raises the next question: What’s the source of the inflaton’s energy?

  It comes from gravity. Remember that inflationary expansion is much like viral replication: a high-valued inflaton field drives the region it inhabits to rapidly grow, and in doing so creates an increasingly large spatial volume that is itself infused with a high-valued inflaton field. And because a uniform inflaton field contributes a constant energy per unit volume, the larger the volume it fills, the more energy it embodies. The driving force behind the expansion is gravity—in its repulsive guise—and so gravity is the source of the ever-larger energy the region contains.

  Inflationary cosmology can thus be thought of as creating a sustained energy flow from the gravitational field to the inflaton field. This might seem like one more passing of the energy buck—where does gravity get its energy?—but the situation is a good deal better than that. Gravity is different from the other forces because where there’s gravity, there’s a virtually unlimited reservoir of energy. It’s a familiar idea expressed in unfamiliar language. When you jump off a cliff, your kinetic energy—the energy of your motion—gets ever larger. Gravity, the force driving your motion, is the energy’s source. In any realistic situation, you will hit the ground, but in principle you could fall arbitrarily far, tumbling down an increasingly long rabbit hole, while your kinetic energy grows ever larger. The reason gravity can supply such unlimited quantities of energy is that, much like the U.S. Treasury, it has no fear of debt. As you fall and your energy gets ever more positive, gravity compensates by its energy becoming ever more negative. You know intuitively that the gravitational energy is negative because to climb out of the rabbit hole, you need to exert positive energy—pushing with your legs, pulling with your arms; that’s how you repay the energy debt gravity incurred on your behalf.2

  The essential conclusion is that as an inflaton-filled region rapidly grows, the inflaton extracts energy from the gravitational field’s inexhaustible resources, resulting in the region’s energy rapidly growing too. And because the inflaton field supplies the energy that’s converted into ordinary matter, inflationary cosmology—unlike the big bang model—does not need to posit the raw material for generating planets, stars, and galaxies. Gravity is matter’s sugar daddy.

  The only independent energy budget required by inflationary cosmology is what’s needed to create an initial inflationary seed, a small spherical nugget of space filled with a high-valued inflaton field that gets the inflationary expansion rolling in the first place. When you put in numbers, the equations show that the nugget need be only about 10–26 centimeters across and filled with an inflaton field whose energy, when converted to mass, would weigh less than ten grams.3 Such a tiny seed would, faster than a flash, undergo spectacular expansion, growing far larger than the observable universe while harboring ever-increasing energy. The inflaton’s total energy would quickly soar beyond what’s necessary to generate all the stars in all the galaxies we observe. And so, with inflation in the cosmological driver’s seat, the impossible starting point of the big bang’s recipe—gather more than 1055 grams and squeeze the whole lot into an infinitesimally small speck—is radically transformed. Gather ten grams of inflaton field and squeeze it into a lump that’s about 10–26 centimeters across. That’s a lump you could put in your wallet.

  This approach, nevertheless, presents daunting challenges. For one thing, the inflaton remains a purely hypothetical field. Cosmologists freely incorporate the inflaton field into their equations, but unlike with electron and quark fields, there is as yet no evidence that the inflaton field exists. For another, even if the inflaton proves real, and even if we one day develop the means to manipulate it much as we do the electromagnetic field, still the density of the requisite inflaton seed would be enormous: about 1067 times that of an atomic nucleus. Although the seed would weigh less than a handful of popcorn, the compressive force we would need to apply is trillions and trillions of times beyond what we can now muster.

  But this is just the kind of technological hurdle that we’re imagining an arbitrarily advanced civilization might one day overcome. So, if our distant descendants one day harness the inflaton field and develop extraordinary compressors capable of producing such dense nuggets, will we have attained the status of universe creators? And, as we contemplate such a step toward Olympus, should we worry that if we artificially set off new inflationary realms, our own corner of space may be swallowed by the ballooning expanse? Alan Guth and a number of collaborators investigated these questions in a series of papers, and found both good news and bad. Start with the last question, as that’s where we’ll find the good news.

  Guth, together with Steven Blau and Eduardo Guendelman, showed that there’s no need to be concerned about an artificial phase of inflationary expansion ripping through our existing environment. The reason has to do with pressure. If an inflationary seed were created in the laboratory, it would harbor the inflaton field’s characteristic positive energy and negative pressure, but it would be surrounded by ordinary space in which the inflaton field’s value, and its pressure, would be zero (or nearly so).

  We usually don’t ascribe much power to zero, but in this case zero makes all the difference. Zero pressure is larger than negative pressure, and so the pressure outside the seed would be larger than the pressure inside. This would subject the seed to a net external force pressing upon it, much like what your eardrums experience when deep-sea diving. It is the pressure differential is powerful enough to prevent the seed from expanding into the surrounding environment.

  But this does not prevent the inflaton’s drive to expand. If you blow air into a balloon while tightly clasping its surface, the balloon will bubble out from between your hands. The inflaton seed can behave similarly. The seed can generate a new expanding spatial realm that sprouts from the original spatial environment, as illustra
ted by the little growing sphere in Figure 10.1. The calculations show that once the new expanding realm reaches a critical size, its umbilical cord to the parent space severs, as in the final image of Figure 10.1, and an independent inflating universe is born.

  As enticing as the process might be—the artificial creation of a new universe—the view from the laboratory wouldn’t live up to the advance billing. It’s a relief that the inflationary bubble would not gobble up the surrounding environment, but the flip side is that there would be little evidence of the creation itself. A universe that expands by generating new space, which then detaches from ours, is a universe we can’t see. Indeed, as the new universe pinches off, its sole residue would be a deep gravitational well—you can see this in the last image of Figure 10.1—which would appear to us as a black hole. And since we have no capacity to see beyond a black hole’s edge, we wouldn’t even be assured that our experiment had been a success; without access to the new universe, we would have no means of establishing observationally that the universe had been created at all.

  Figure 10.1 Because of the greater pressure in the ambient environment, an inflationary seed is forced to expand into newly formed space. As the bubble universe grows, it detaches from the parent environment, yielding a separate, expanding spatial domain. To someone in the ambient environment, the process looks like the formation of a black hole.