by Brian Greene
In an Inflationary Multiverse, the member universes are sharply divided. Each is a hole in the cosmic cheese, separated from the others by domains in which the inflaton’s value remains high. Since such intervening regions are still undergoing inflationary expansion, the bubble universes are rapidly driven apart, with a speed of recession proportional to the amount of swelling space between them. The farther apart they are, the greater the expansion’s speed; the ultimate result is that distant bubbles move apart faster than the speed of light. Even with unlimited longevity and technology, there’s no way to cross such a divide. There’s no way to even send a signal.
All the same, we can still imagine a voyage to one or more of the other bubble universes. On such a journey, what would you find? Well, because each bubble universe results from the same process—the inflaton is knocked from its perch, yielding a region that drops out of the inflationary expansion—they are all governed by the same physical theory and so are all subject to the same set of physical laws. But, much as the behavior of identical twins can differ profoundly as a result of environmental differences, identical laws can manifest themselves in profoundly different ways in different environments.
Imagine, for example, that one of the other bubble universes looks much like ours, dotted by galaxies containing stars and planets, but with one essential difference. Permeating the universe is a magnetic field, thousands of times stronger than that created in our most advanced MRI machines, and one that can’t be switched off by a technician. Such a powerful field would affect the way a great many things behave. Not only would objects containing iron have a nasty habit of flying off in the direction of the field, but even basic properties of particles, atoms, and molecules would shift. A sufficiently strong magnetic field would so disrupt cellular function that life as we know it couldn’t take hold.
Yet just as the physical laws operating inside an MRI are the very same laws that operate outside, so the fundamental physical laws operating in this magnetic universe would be the same as ours. The discrepancies in experimental results and observable features would be due solely to an aspect of the environment: the strong magnetic field. Talented scientists in the magnetic universe would in time tease out this environmental factor and home in on the same mathematical laws we’ve discovered.
Over the past forty years, researchers have built a case for a similar scenario right here in our own universe. The most lauded theory of fundamental physics, the Standard Model of particle physics, posits that we are immersed in an exotic mist called the Higgs field (named after the English physicist Peter Higgs, who with important contributions from Robert Brout, François Englert, Gerald Guralnik, Carl Hagen, and Tom Kibble pioneered this idea in the 1960s). Both Higgs fields and magnetic fields are invisible and hence can fill space without directly revealing their presence. However, according to modern particle theory, a Higgs field camouflages itself far more fully. As particles move through a uniform, space-filling Higgs field, they don’t speed up, they don’t slow down, they are not coaxed to follow particular trajectories, as some would in the presence of a strong magnetic field. Instead, the theory claims, they’re influenced in ways more subtle and profound.
As fundamental particles burrow through a Higgs field, they acquire and maintain the mass that experiments have revealed them to possess. According to this idea, when you push against an electron or quark in an effort to change its speed, the resistance you feel comes from the particle’s “rubbing” against the molasses-like Higgs field. It’s this resistance that we call the particle’s mass. Were you to remove the Higgs field from some region, particles passing through would suddenly become massless. Were you to double the value of the Higgs field in another region, particles passing through would suddenly have twice their usual mass.*
Such human-induced changes are hypothetical, because the energy required to substantially modify a Higgs field’s value in even a small region of space is enormously beyond what we can muster. (The changes are also hypothetical because the existence of the Higgs fields is still up in the air. Theorists eagerly anticipate highly energetic collisions between protons at the Large Hadron Collider chipping off small chunks of the Higgs field—Higgs particles—that may be detected in the coming years.) But in many versions of inflationary cosmology, a Higgs field would naturally have different values in different bubble universes.
A Higgs field, much like an inflaton field, has a curve that records the amount of energy it contains for various values it can assume. An essential difference from the inflaton field’s energy curve, though, is that the Higgs typically settles not at the value 0 (as in Figure 3.1), but rather rolls to one of the troughs illustrated in Figure 3.6a. Picture, then, an early stage in each of two bubble universes, ours and another. In both, the hot, tempestuous frenzy causes the value of the Higgs field to undulate wildly. As each universe expands and cools, the Higgs field calms and its value rolls toward one of the troughs in Figure 3.6a. In our universe, the Higgs field’s value settles down in, say, the left trough, giving rise to the particle properties familiar from experimental observation. But in the other universe, the Higgs’ motion may result in its value settling down in the right trough. If it did, that universe would have properties substantially different from ours. Although the underlying laws in both universes would be the same, the masses and various other properties of particles would not.
Even a modest difference in particle properties would have weighty consequences. If the electron mass in another bubble universe were a few times larger than it is here, electrons and protons would tend to merge, forming neutrons and thus preventing the widespread production of hydrogen. The fundamental forces—the electromagnetic force, the nuclear forces, and (we believe) gravity—are also communicated by particles. Change the particle properties and you drastically change the properties of the forces. The heavier a particle, for example, the more sluggish its motion and so the shorter the distance over which the corresponding force is transmitted. The formation and stability of atoms in our bubble universe rely on the properties of the electromagnetic and nuclear forces. If you substantially modify those forces, atoms will fall apart or, more likely, not coalesce in the first place. An appreciable change to the properties of particles would thus disrupt the very processes that give our universe its familiar features.
Figure 3.6 (a) A potential energy curve for a Higgs field that has two troughs. The familiar features of our universe are associated with the field settling down in the left trough; in another universe, however, the field can settle down in the right trough, yielding different physical features. (b) A sample potential energy curve for a theory with two Higgs fields.
Figure 3.6a illustrates only the simplest case, in which there is a single species of Higgs field. But theoretical physicists have explored more complicated scenarios involving multiple Higgs fields (we will shortly see that such possibilities naturally emerge from string theory), which translate into an even richer set of distinct bubble universes. An example with two Higgs fields is illustrated in Figure 3.6b. As before, the various troughs represent Higgs field values that one or another bubble universe could settle into.
Permeated by such unfamiliar values of various Higgs fields, these universes would differ from ours considerably, as schematically illustrated in Figure 3.7. This would make a journey through the Inflationary Multiverse a perilous undertaking. Many of the other universes would not be places you’d want high on your itinerary, because the conditions would be incompatible with the biological processes essential to survival, giving new meaning to the saying that there’s no place like home. In the Inflationary Multiverse, our universe could well be an island oasis in a gigantic but largely inhospitable cosmic archipelago.
Figure 3.7 Because fields can settle down to different values in different bubbles, the universes in the Inflationary Multiverse can have different physical features, even though the universes are all governed by the same fundamental physical laws.
Universes in
a Nutshell
Because of their fundamental differences, the Quilted and Inflationary Multiverses might appear unrelated. The quilted variety emerges if the extent of space is infinite; the inflationary variety emerges from eternal inflationary expansion. Yet, there is a deep and wonderfully satisfying connection between them, one that brings the discussion in the previous two chapters full circle. The parallel universes arising from inflation generate their quilted cousins. The process has to do with time.
Of the many strange things Einstein’s work revealed, the fluidity of time is the hardest to grasp. Whereas everyday experience convinces us that there is an objective concept of time’s passage, relativity shows this to be an artifact of life at slow speeds and weak gravity. Move near light speed, or immerse yourself in a powerful gravitational field, and the familiar, universal conception of time will evaporate. If you’re rushing past me, things I insist happened at the same moment will appear to you to have occurred at different moments. If you’re hanging out near the edge of a black hole, an hour’s passage on your watch will be monumentally longer on mine. This isn’t evidence of a magician’s trickery or a hypnotist’s deception. The passage of time depends on the particulars—trajectory followed and gravity experienced—of the measurer.12
When applied to the entire universe, or to our bubble in an inflationary setting, this immediately raises a question: How does such malleable, custom-made time comport with the notion of an absolute cosmological time? We freely speak of the “age” of our universe, but given that galaxies are moving rapidly relative to one another, at speeds dictated by their various separations, doesn’t the relativity of time’s passage create a nightmarish accounting problem for any would-be cosmic timekeeper? More pointedly, when we speak of our universe being “14 billion years old,” are we using a particular clock to measure that duration?
We are. And a careful consideration of such cosmic time reveals a direct link between parallel universes of the inflationary and quilted varieties.
Every method we use to measure time’s passage involves an examination of change that occurs to some particular physical system. Using a common wall clock, we examine the change in position of its hands. Using the sun, we examine the change in its position in the sky. Using carbon 14, we examine the percentage of an original sample that’s undergone radioactive decay to nitrogen. Historical precedent and general convenience have led us to use the rotation and revolution of the earth as physical referents, giving rise to our standard notions of “day” and “year.” But when we’re thinking on cosmic scales, there is another, more useful, method for keeping time.
We’ve seen that inflationary expansion yields vast regions whose properties on average are homogeneous. Measure the temperature, pressure, and average density of matter in two large but separate regions within a bubble universe, and the results will agree. The results can change over time, but the large-scale uniformity ensures that, on average, the change here is the same as the change there. As an important case in point, the mass density in our bubble universe has steadily decreased over our multibillion-year history, thanks to the relentless expansion of space, but because the change has occurred uniformly, our bubble’s large-scale homogeneity has not been disrupted.
This proves important because just as the steadily decreasing amount of carbon 14 in organic matter provides a means of measuring time’s passage on earth, so the steadily decreasing mass density provides a means of measuring time’s passage across space. And because the change has happened uniformly, mass density as a marker of time’s passage provides our bubble universe with a global standard. If everyone diligently calibrates their watches to the average mass density (and recalibrates after trips to black holes, or periods of travel at near light speed), the synchronicity of our timepieces across our bubble universe will be maintained. When we speak of the age of the universe—the age of our bubble, that is—it is on such cosmically calibrated watches that we imagine time’s passage being measured; it is only with respect to them that cosmic time is a sensible concept.
In the earliest era of our bubble universe, the same reasoning would have applied with one change of detail. Ordinary matter had yet to form, so we can’t speak of the average mass density in space. Instead, the inflaton field carried our universe’s storehouse of energy—energy that would shortly be converted into familiar particles—so we need to envisage setting our clocks by the density of the inflaton field’s energy.
Now, the inflaton’s energy is determined by its value, as summarized by its energy curve. To determine what time it is at a given location in our bubble, we therefore need to determine the value of the inflaton at that location. Then, just as two trees are the same age if they have the same number of tree rings, and just as two samples of glacial sediment are the same age if they have the same percentage of radioactive carbon, two locations in space are passing through the same moment in time when they have the same value of the inflaton field. That’s how we set and synchronize clocks in our bubble universe.
The reason I’ve brought all this up is that when applied to the cosmic Swiss cheese of the Inflationary Multiverse, these observations yield a strikingly counterintuitive implication. Much as Hamlet famously declares, “I could be bounded in a nutshell, and count myself a king of infinite space,” each of the bubble universes appears to have finite spatial extent when examined from the outside, but infinite spatial extent when examined from the inside. And that’s a marvelous realization. Infinite spatial extent is just what we need for quilted parallel universes. So we can meld the Quilted Multiverse into the inflationary story.
The extreme disparity between the outsider’s and insider’s perspectives arises because they have vastly different conceptions of time. Although the point is far from obvious, we’ll now see that what appears as endless time to an outsider appears as endless space, at each moment of time, to an insider.13
Space in a Bubble Universe
To grasp how this comes about, imagine that Trixie, floating within a rapidly expanding inflaton-filled region of space, is observing the formation of a nearby bubble universe. Focusing her inflaton-meter on the growing bubble, she is able to directly track its changing inflaton field value. Although the region—the hole in the cosmic cheese—is three-dimensional, it’s simpler to examine the field along a one-dimensional cross section across its diameter, and as Trixie does so she records the data in Figure 3.8a. Each higher row shows the inflaton’s value at a successive moment in time, from Trixie’s perspective. And as is apparent from the figure, Trixie sees the bubble universe—represented in the figure by the lighter locations where the inflaton’s value has dropped—grow ever larger.
Now imagine that Norton is also examining this very same bubble universe, but from the inside; he’s hard at work making detailed astronomical observations with his own inflaton-meter. Norton, unlike Trixie, adheres to a notion of time that’s calibrated by the value of the inflaton. This is key to the conclusion we’re chasing, so I need you to buy into it fully. Imagine, if you will, that everyone in the bubble universe wears a watch that measures and displays the inflaton’s value. When Norton throws a dinner party, he instructs the guests to show up at his house when the inflaton’s value is 60. Since everyone’s watch is calibrated to the same, uniform standard—the inflaton field’s value—the party goes off without a hitch. Everyone shows up at the same moment because everyone is attuned to the same concept of synchronicity.
Figure 3.8a Each row chronicles the inflaton’s value at one moment of time from an outsider’s perspective. Higher rows correspond to later moments. The columns denote positions across space. A bubble is a region of space that stops inflating because of a drop in the inflaton’s value. The lighter entries denote the value of the inflaton field within the bubble. From the perspective of the outside observer, the bubble grows ever larger.
With this understanding, it’s a simple matter for Norton to work out the size of the bubble universe at any given moment of hi
s time. In fact, it’s child’s play: all Norton has to do is paint by numbers. By connecting all points that have the same numerical value for the inflaton field, Norton can delineate all locations within the bubble at a single moment of time. His time. Insider’s time.
Norton’s drawing in Figure 3.8b says it all. Each curve, connecting points with the same inflaton-field value, represents all of space at a given moment of time. As the figure makes clear, each curve extends indefinitely far, which means that the size of the bubble universe, according to its inhabitants, is infinite. This reflects that endless outsider time, experienced by Trixie as the endless number of rows in Figure 3.8, appears as endless space, at each moment of time, according to an insider like Norton.
That’s a powerful insight. In Chapter 2, we found that the Quilted Multiverse was contingent upon space being infinitely large, something that, as we discussed there, might or might not be the case. Now we see that each bubble within the Inflationary Multiverse is spatially finite from the outside but spatially infinite from the inside. If the Inflationary Multiverse is real, then the inhabitants of a bubble—us—would thus be members not only of the Inflationary Multiverse but of the Quilted Multiverse, too.14
Figure 3.8b The same information as in Figure 3.8a is organized differently by someone within the bubble. Inflaton values that agree correspond to identical moments, so the curves drawn sweep through all those points in space that exist at the same moment in time. Smaller inflaton values correspond to later moments. Note that the curves could be extended infinitely far, so from an insider’s perspective, space is infinite.