The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos
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In the table below, I’ve summarized the possible shapes, emphasizing that some are finite in extent (the sphere, the video-game screen) while others are infinite (the endless tabletop, the endless Pringles chip). As it stands, Table 2.1 is incomplete. There are additional possibilities, with wonderful names like the binary tetrahedral space and the Poincaré dodecahedral space, that also have uniform curvature, but I’ve not included them because they’re harder to visualize using everyday objects. By judicious slicing and paring they can be sculpted from those that I’ve put in the list, so Table 2.1 provides a good representative sampling. But these details are secondary to the main conclusion: The uniformity of the cosmos articulated by the cosmological principle substantially winnows the possible shapes for the universe. Some of the possible shapes have infinite spatial extent, while others do not.10
Table 2.1 Possible shapes for space consistent with the assumption that every location in the universe is on a par with every other (the cosmological principle).
Our Universe
The expansion of space found mathematically by Friedmann and Lemaître applies verbatim to a universe that has any one of these shapes. For positive curvature, use the two-dimensional mental imagery to think of a balloon’s surface expanding as it is filled with air. For zero curvature, think of a flat sheet of rubber that is being stretched uniformly in all directions. For negative curvature, mold that rubber sheet into the shape of a Pringles chip and then carry on with the stretching. If galaxies are modeled as glitter evenly sprinkled on any of these surfaces, the expansion of space results in the individual specks of glitter—the galaxies—moving apart from one another, just as Hubble’s 1929 observations of distant galaxies revealed.
It’s a compelling cosmological template, but if it is to be definitive and complete, we need to determine which of the uniform shapes describes our universe. We can determine the shape of a familiar object, such as a doughnut, a baseball, or a block of ice, by picking it up and turning it this way and that. The challenge is that we can’t do so with the universe, and so we must determine its shape through indirect means. The equations of general relativity provide a mathematical strategy. They show that the curvature of space reduces to a single observational quantity: the density of matter (more precisely, the density of matter and energy) in space. If there is a lot of matter, gravity will cause space to curve back on itself, yielding the spherical shape. If there is little matter, space is free to flare outward in the Pringles shape. And if there is just the right amount of matter, space will have zero curvature.*
The equations of general relativity also provide a precise numerical demarcation among the three possibilities. The mathematics shows that “just the right amount of matter,” the so-called critical density, weighs in today at about 2 × 10–29 grams per cubic centimeter, which is about six hydrogen atoms per cubic meter or, in more familiar terms, the equivalent of a single raindrop in every earth-sized volume.11 Looking around, it would surely seem that the universe exceeds the critical density, but that would be a hasty conclusion. The mathematical calculation of the critical density assumes that matter is uniformly spread throughout space. So you need to envision taking the earth, the moon, the sun, and everything else and evenly dispersing the atoms they contain across the cosmos. The question then is whether each cubic meter would weigh more or less than six hydrogen atoms.
Because of its important cosmological consequences, astronomers have been trying for decades to measure the average density of matter in the universe. Their method is straightforward. With powerful telescopes, they carefully observe large volumes of space and add up the masses of the stars they can see as well as the mass of other material whose presence they can infer by studying stellar and galactic motion. Until recently, the observations indicated that the average density was on the low side, about 27 percent of the critical density—the equivalent of about two hydrogen atoms in each cubic meter—which would imply a negatively curved universe.
But then, in the late 1990s, something extraordinary happened. Through some magnificent observations and a chain of reasoning we’ll explore in Chapter 6, astronomers realized that they had been leaving out an essential component of the tally: a diffuse energy that appears to be spread uniformly throughout space. The data came as a shock to most everyone. An energy suffusing space? That sounds like the cosmological constant, which, as we’ve seen, Einstein introduced and then famously retracted eight decades earlier. Had modern observations resurrected the cosmological constant?
We still don’t know for sure. Even today, a decade after the initial observations, astronomers have yet to establish if the uniform energy is fixed or if the amount of energy in a given region of space varies over time. A cosmological constant, as its name signifies (and as its mathematical representation by a single fixed number on the general relativity tax form implies), would be unchanging. To account for the more general possibility that the energy evolves, and to also emphasize that the energy does not give off light (explaining why it had for so long evaded detection) astronomers have coined a new term: dark energy. “Dark” also describes well the many gaps in our understanding. No one can explain the dark energy’s origin, fundamental composition, or detailed properties—issues currently under intense investigation to which we shall return in later chapters.
But, even with the numerous open questions, detailed observations using the Hubble Space Telescope and other earth-based observatories have reached consensus on the amount of dark energy that is now permeating space. The result differs from what Einstein long ago proposed (since he posited a value that would yield a static universe, whereas our universe is expanding). That’s not surprising. Instead, what’s remarkable is that the measurements have concluded that the dark energy filling space contributes approximately 73 percent of the critical density. When added to the 27 percent of criticality astronomers had already measured, this brings the total right up to 100 percent of the critical density, just the right amount of matter and energy for a universe with zero spatial curvature.
Current data thus favor an ever-expanding universe shaped like the three-dimensional version of the infinite tabletop or of the finite video-game screen.
Reality in an Infinite Universe
At the beginning of this chapter, I noted that we don’t know whether the universe is finite or infinite. The previous sections have laid out the case that both possibilities naturally emerge from our theoretical studies, and that both possibilities are consistent with the most refined astrophysical measurements and observations. How might we one day determine observationally which possibility is right?
It’s a tough question. If space is finite, then some of the light emitted by stars and galaxies might cycle around the entire cosmos multiple times before entering our telescopes. Like the repeated images generated when light bounces between parallel mirrors, cycling light would give rise to repeated images of stars or galaxies. Astronomers have looked for such multiple images but as yet haven’t found any. This, in itself, doesn’t prove that space is infinite, but it does suggest that if space is finite it may be so large that light hasn’t had time to complete multiple laps around the cosmic racetrack. And that reveals the observational challenge. Even if the universe is finite, the larger it is the better it can masquerade as infinite.
For some cosmological questions, such as the age of the universe, the distinction between the two possibilities plays no role. Whether the cosmos is finite or infinite, at ever-earlier times, the galaxies would have been squeezed ever closer together, making the universe denser, hotter, and more extreme. We can use today’s observations of the rate of expansion, together with theoretical analysis of how that rate has changed over time, to tell us how long it’s been since everything we see would have been compressed into a single fantastically dense nugget, what we can call the beginning. And for either a finite or an infinite universe, state-of-the-art analyses now peg that moment at about 13.7 billion years ago.
But for
other considerations, the finite-infinite distinction matters. In the finite case, for example, as we consider the cosmos at ever-earlier times, it’s accurate to picture the entirety of space continually shrinking. Although the mathematics breaks down at time zero itself, it’s correct to envision that at moments ever closer to time zero, the universe is an ever-smaller speck. For the infinite case, however, this description is wrong. If space is truly infinite in size, then it always has been and always will be. When it shrinks, its contents are squeezed ever closer together, making the density of matter ever larger. But its overall extent remains infinite. After all, shrink an infinite tabletop by a factor of 2 and what do you get? Half of infinity, which is still infinite. Shrink by a factor of 1 million and what do you get? Infinity still. The closer to time zero you consider an infinite universe, the denser it becomes at every location, but its spatial extent remains unending.
Although observations leave the finite-versus-infinite issue undecided, I’ve found that when pressed, physicists and cosmologists tend to favor the proposition that the universe is infinite. Partly, I think this view is rooted in the historical happenstance that for many decades researchers paid little heed to the finite video-game shape, mostly because it is more mathematically complex to analyze. Perhaps the view also reflects a common misconception that the difference between an infinite and a huge-but-finite universe is a cosmological distinction that’s only of academic interest. After all, if space is so large that you will only ever have access to a small portion of its entirety, should you care whether it extends for a finite or for an infinite distance beyond what you can see?
You should. The issue of whether space is finite or infinite has a profound impact on the very nature of reality. Which takes us to the heart of this chapter. Let’s now consider the possibility of an infinitely big cosmos and explore its implications. With minimal effort, we’ll find ourselves inhabiting one of an infinite collection of parallel worlds.
Infinite Space and the Patchwork Quilt
Let’s start simply, back here on earth, far from the vast reaches of an infinite cosmic expanse. Imagine that your friend Imelda, to satisfy her penchant for variety in personal attire, has acquired five hundred richly embroidered dresses and a thousand pairs of designer shoes. If each day she wears one dress with one pair of shoes, at some point she will exhaust all possible combinations and duplicate an earlier outfit. It’s easy to figure out when. Five hundred dresses and a thousand pairs of shoes yield 500,000 different combinations. Five hundred thousand days is about 1,400 years, so if she lived long enough Imelda would be seen in an outfit she’d already worn. If Imelda, blessed with infinite longevity, continued to cycle through every possible combination, she’d necessarily don each of her outfits an infinite number of times. An infinite number of appearances with a finite number of outfits ensures infinite repetition.
Pursuing the same theme, imagine that Randy, an expert card dealer, has shuffled a gargantuan number of decks, one by one, and neatly stacked each next to the others. Can the order of cards in every shuffled deck be different, or must they repeat? The answer depends on the number of decks. Fifty-two cards can be arranged in different ways (52 possibilities for which card will be the first, times 51 remaining possibilities for which will be the second, times 50 remaining possibilities for the next card, and so on). If the number of decks Randy shuffles exceeds the number of different possible card orderings, then some of the shuffled decks would match. If Randy were to shuffle an infinite number of decks, the orderings of the cards would necessarily repeat an infinite number of times. As with Imelda and her outfits, an infinite number of occurrences with a finite number of possible configurations ensures that outcomes are infinitely repeated.
This basic notion is of the essence for cosmology in an infinite universe. Two key steps show why.
In an infinite universe, most regions lie beyond our ability to see, even using the most powerful telescopes possible. Although light travels enormously quickly, if an object is sufficiently distant, then the light it emits—even light that may have been emitted shortly after the big bang—will simply not have had sufficient time to reach us. Since the universe is about 13.7 billion years old, you might think that anything farther away than 13.7 billion light-years would fall into this category. The reasoning behind this intuition is right on target, but the expansion of space increases the distance to objects whose light has long been traveling and has only just been received; so the maximum distance we can see is actually longer—about 41 billion light-years.12 But the exact numbers hardly matter. The important point is that regions of the universe beyond a certain distance are regions currently beyond our observational reach. Much as ships that have sailed beyond the horizon are not visible to someone standing on shore, astronomers say that objects in space that are too far away to be seen lie beyond our cosmic horizon.
Similarly, the light we’ve been emitting can’t yet have reached those distant regions, so we are beyond their cosmic horizon. And it’s not that cosmic horizons solely delineate what someone can and cannot see. From Einstein’s special relativity, we know that no signal, no disturbance, no information, no anything can travel faster than light—which means that regions of the universe so far apart that light hasn’t had time to travel between them are regions that have never exchanged any influence of any kind, and so have evolved completely independently.
Using a two-dimensional analogy, we can compare the expanse of space, at a given moment of time, to a giant patchwork quilt (with circular patches) in which each patch represents a single cosmic horizon. Someone located in the center of a patch can have interacted with anything that lies in the same patch, but has had no contact with anything lying in a different patch (see Figure 2.1a), because they’re too far away. Points lying near the border between two patches are closer together than their respective centers and so can have interacted, but if we consider, say, patches in every other row and every other column of the cosmic quilt, all points residing in different patches are now so far from one another that no cross-patch interactions of any kind could have taken place (see Figure 2.1b). The same idea applies in three dimensions, where the cosmic horizons—the patches in the cosmic quilt—are spherical, and the same conclusion holds: sufficiently distant patches lie beyond one another’s spheres of influence and so are independent realms.
If space is large but finite, we can divide it into a large but finite number of such independent patches. If space is infinite, then there are an infinite number of independent patches. It’s this latter possibility that’s of particular allure, and the second part of the argument tells why. As we will now see, in any given patch the particles of matter (more precisely, matter and all forms of energy) can be arranged in only a finite number of different configurations. Using the reasoning rehearsed with Imelda and Randy, this means that conditions in the infinity of far-flung patches—in regions of space like the one we inhabit but distributed through a limitless cosmos—necessarily repeat.
Figure 2.1 (a) Because of light’s finite speed, an observer at the center of any patch (called the observer’s cosmic horizon) can have interacted only with things lying in that same patch. (b) Sufficiently distant cosmic horizons are too far apart to have had any interactions, and so have evolved completely independently of one another.
Finite Possibilities
Imagine it’s a hot summer night and there’s an annoying fly buzzing around your bedroom. You’ve tried the swatter, you’ve tried the nasty spray. Nothing’s worked. In desperation, you try reason. “This is a big bedroom,” you tell the fly. “There are so many other places you could be. There’s no reason to keep buzzing around my ear.” “Really?” the fly slyly counters. “How many places are there?”
In a classical universe, the answer is “Infinitely many.” As you tell the fly, he (or, more precisely, his center of mass) could move 3 meters to the left, or 2.5 meters to the right, or 2.236 meters up, or 1.195829 meters down, or … you get the idea. Si
nce the fly’s position can vary continuously, there are infinitely many places it can be. In fact, as you explain all this to the fly, you realize that not only does position present the fly with infinite variety, but so does velocity. At one moment the fly can be here, heading to the right at a kilometer per hour. Or it might be heading to the left at half a kilometer per hour, or heading up at a quarter of a kilometer per hour, or heading down at .349283 kilometers per hour, and so on. Although the fly’s speed is constrained by a number of factors (including the limited energy it possesses, since the faster it flies, the more energy it needs to expend), it can vary continuously and hence provides another source of infinite variety.
The fly isn’t convinced. “I’m with you when you talk about moving a centimeter, or half a centimeter, or even a quarter of a centimeter,” the fly responds. “But when you speak of locations that differ by a ten-thousandth or a hundred-thousandth of a centimeter, or even less, you’ve lost me. To an egghead, those might be different locations, but it flies in the face of experience to say that here and a billionth of a centimeter to the left of here are really different. I can’t sense such a tiny change in location and so I don’t count them as different places. Same goes for speed. I can tell the difference between going a kilometer per hour and going at half that rate. But the difference between .25 kilometers per hour and .249999999 kilometers per hour? Please. Only a wise fly would claim to be able to tell the difference. Fact is, none of us can. So as far as I’m concerned, those are the same speeds. There’s far less variety available than you’re describing.”