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

by Brian Greene

  The fly has raised an important point. In principle, he can occupy an infinite variety of positions and attain an infinite variety of speeds. But in any practical sense, there is a limit to how fine the differences in location and speed can be before they go completely unnoticed. This is true even if the fly employs the best of equipment. There is always a limit on how small an increment in position or speed can be and yet still register. And regardless of how fine those minimal increments are, if they’re not zero, they radically reduce the range of possible experience.

  For instance, if the smallest increments that can be detected are a hundredth of a centimeter, then each centimeter offers not an infinite number of detectably different locations, but only a hundred. Each cubic centimeter would thus provide 1003 = 1,000,000 different locations, and your average bedroom would offer about 100 trillion. Whether the fly would find this array of options sufficiently impressive to keep away from your ear is difficult to say. The conclusion, though, is that anything but measurements with perfect resolution reduces the number of possibilities from infinite to finite.

  You might counter that the inability to distinguish between tiny spatial separations or differences in speed reflects nothing more than a technological limitation. With progress, the precision of equipment always improves, so the number of discernibly distinct positions and speeds available to a well-funded fly will also always increase. Here I must invoke some basic quantum theory. According to quantum mechanics, there’s a precise sense in which there is a fundamental limit on how accurate particular measurements can be, and this limit can’t ever be surpassed, regardless of technological progress—ever. The limit arises from a central feature of quantum mechanics, the uncertainty principle.

  The uncertainty principle establishes that regardless of what equipment you use or what techniques you employ, if you increase the resolution of your measurement of one property, there is an unavoidable cost: you necessarily reduce how accurately you can measure a complementary property. As a prime example, the uncertainty principle shows that the more accurately you measure an object’s position, the less accurately you can measure its speed, and vice versa.

  From the perspective of classical physics, the physics that informs much of our intuition about how the world works, this limitation is completely foreign. But as a rough analogy, think about photographing that impish fly. If your shutter speed is high, you’ll get a sharp image that records the fly’s location at the moment you snapped the picture. But because the photo is crisp, the fly appears motionless; the image gives no information about the fly’s speed. If you set your shutter speed low, the resulting blurry image will convey something of the fly’s motion, but because of that blurriness it also provides an imprecise measurement of the fly’s location. You can’t take a photo that gives sharp information about position and speed simultaneously.

  Using the mathematics of quantum mechanics, Werner Heisenberg provided a precise limit on how imprecise the combined measurements of position and speed necessarily are. This inescapable imprecision is what quantum physicists mean by uncertainty. For our purpose, there’s a particularly useful way of framing his result. Much as a sharper photograph requires that you use a higher shutter speed, Heisenberg’s math shows that a sharper measurement of an object’s position requires that you use a higher energy probe. Turn on your bedside lamp, and the resulting probe—diffuse, low-energy light—allows you to make out the general shape of the fly’s legs and eyes; illuminate him with higher energy photons, like x-rays (keeping the photon bursts short to avoid cooking him), and the finer resolution reveals the minuscule muscles that flap the fly’s wings. But perfect resolution, according to Heisenberg, requires a probe with infinite energy. That’s unattainable.

  And so, the essential conclusion is at hand. Classical physics makes clear that perfect resolution is unattainable in practice. Quantum physics goes further and establishes that perfect resolution is unattainable in principle. If you imagine both the speed and the position of an object—be it a fly or an electron—changing by sufficiently small amounts, then according to quantum mechanics, you are imagining something meaningless. Changes that are too small to be measured, even in principle, are not changes at all.13

  By the same reasoning we used in our pre-quantum analysis of the fly, the limit on resolution reduces from infinite to finite the number of distinct possibilities for an object’s position and speed. And since the limited resolution entailed by quantum mechanics is entwined in the very fibers of physical law, this reduction to finite possibilities is unavoidable and unassailable.

  Cosmic Repetition

  So much for flies in bedrooms. Now consider a larger region of space. Consider a region the size of today’s cosmic horizon, a sphere with a radius of 41 billion light-years. A region, that is, which is the size of a single patch in the cosmic quilt. And consider filling it not with a single fly but with particles of matter and radiation. Here’s the question: How many different arrangements of the particles are possible?

  Well, as with a box of Legos, the more pieces you have—the more matter and radiation you cram into the region—the greater the number of possible arrangements. But you can’t cram pieces in indefinitely. Particles carry energy, so more particles means more energy. If a region of space contains too much energy, it will collapse under its own weight and form a black hole.* And if after a black hole forms you try to cram yet more matter and energy into the region, the black hole’s boundary (its event horizon) will grow larger, encompassing more space. There is thus a limit to how much matter and energy can exist fully within a region of space of a given size. For a region of space as large as today’s cosmic horizon, the limits involved are huge (about 1056 grams). But the size of the limit is not central. What’s central is that there is a limit.

  Finite energy within a cosmic horizon entails a finite number of particles, be they electrons, protons, neutrons, neutrinos, muons, photons, or any of the other known or as yet unidentified species in the particle bestiary. Finite energy within a cosmic horizon also entails that each of these particles, like the annoying fly in your bedroom, has a finite number of distinct possible locations and speeds. Collectively, a finite number of particles, each of which can have finitely many distinct positions and velocities, means that within any cosmic horizon only a finite number of different particle arrangements are available. (In the more refined language of quantum theory proper, which we’ll encounter in Chapter 8, we don’t speak of particle positions and velocities per se, but rather of the quantum state of these particles. From this perspective, we would say there are only a finite number of observably distinct quantum states for the particles in the cosmic patch.) Indeed, a short calculation—described in the notes, if you’re curious about the details—reveals that the number of distinct possible particle configurations within a cosmic horizon is about 1010122 (a 1 followed by 10122 zeros). This is a huge but decidedly finite number.14

  The limited number of different clothes combinations ensures that with enough outings, Imelda’s attire will necessarily repeat. The limited number of different card orderings ensures that with enough decks, Randy’s shuffles will necessarily repeat. By the same reasoning, the limited number of particle arrangements ensures that with enough patches in the cosmic quilt—enough independent cosmic horizons—the particle arrangements, when compared from patch to patch, must somewhere repeat. Even if you were able to play cosmic designer and tried to arrange each patch to be different from the ones you’d examined before, with a big enough expanse you’d eventually run out of distinct designs and would be forced to repeat a previous arrangement.

  In an infinitely big universe, the repetition is yet more extreme. There are infinitely many patches in an infinite expanse of space; so, with only finitely many different particle arrangements, the arrangements of particles within patches must be duplicated an infinite number of times.

  That’s the result we’ve been after.

  Nothing but Physics
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br />   In interpreting the implications of this statement, I should declare my bias. I believe that a physical system is completely determined by the arrangement of its particles. Tell me how the particles making up the earth, the sun, the galaxy, and everything else are arranged, and you’ve fully articulated reality. This reductionist view is common among physicists, but there are certainly people who think otherwise. Especially when it comes to life, some believe that an essential nonphysical aspect (spirit, soul, life force, chi, and so on) is required to animate the physical. Although I remain open to this possibility, I’ve never encountered any evidence to support it. The position that makes the most sense to me is that one’s physical and mental characteristics are nothing but a manifestation of how the particles in one’s body are arranged. Specify the particle arrangement and you’ve specified everything.15

  Adhering to this perspective, we conclude that if the particle arrangement with which we’re familiar were duplicated in another patch—another cosmic horizon—that patch would look and feel like ours in every way. This means that if the universe is infinite in extent, you are not alone in whatever reaction you are now having to this view of reality. There are many perfect copies of you out there in the cosmos, feeling exactly the same way. And there’s no way to say which is really you. All versions are physically and hence mentally identical.

  We can even estimate the distance to the nearest copy. If the particle arrangements are randomly distributed from patch to patch (an assumption that’s compatible with the refined cosmological theory we will encounter in the next chapter), then we can expect that the conditions in our patch will be duplicated as frequently as those in any other. In every collection of 1010122 cosmic patches, we thus expect there to be, on average, one patch that looks just like ours. That is, in every region of space that’s roughly 1010122 meters across, there should be a cosmic patch that replicates ours—one that contains you, the earth, the galaxy, and everything else that inhabits our cosmic horizon.

  If you lower your sights and don’t seek an exact replica of our entire cosmic horizon, but would be satisfied with an exact copy of a region a few light-years in radius and centered on our sun, the order is more easily filled: on average, in every region that’s about 1010100 meters across, you should find one such copy. Still easier to find are approximate copies. After all, there is only one way to duplicate a region exactly, but many ways to almost duplicate it. Were you to visit these inexact copies, you’d find some that are barely distinguishable from ours, while in others the differences would range from obvious to exhilarating to shocking. Every decision you’ve ever made is tantamount to a particular particle arrangement. If you turned left, your particles went one way; if you turned right, your particles went the other. If you said yes, the particles in your brain, lips, and vocal cords proceeded through one pattern; if you said no, they proceeded through a different pattern. And so every possible action, every choice you’ve made and every option you’ve discarded, will be played out in one patch or another. In some, your worst fears about yourself, your family, and life on earth have been realized. In others, your wildest dreams have come to pass. In others still, the differences arising from the close but distinct particle arrangements have combined to yield an unrecognizable environment. And in most patches, the particle complexion would not include the highly specialized arrangements we recognize as living organisms, so the patches would be lifeless, or at least devoid of life as we know it.

  Over time, the size of the cosmic patches laid out in Figure 2.1b will increase; with more time, light can travel farther and so each of the cosmic horizons will grow larger. Ultimately, the cosmic horizons will overlap. And when they do, the regions can no longer be considered as separate and isolated; the parallel universes will no longer be parallel—they will have merged. Nevertheless, the result we’ve found will continue to hold. Just lay out a new grid of cosmic patches with patch size set by the distance light can have traveled since the big bang through this later moment. The patches will be bigger, so to fill out a pattern like that in Figure 2.1b their centers will need to be farther apart, but with infinite space at our disposal, there’s ample room to accommodate this adjustment.16

  And so we’ve come to a conclusion that’s both general and provocative. Reality in an infinite cosmos is not what most of us would expect. At any moment in time, the expanse of space contains an infinite number of separate realms—constituents of what I’ll call the Quilted Multiverse—with our observable universe, all we see in the vast night sky, being but one member. Canvassing this infinite collection of separate realms, we find that particle arrangements necessarily repeat infinitely many times. The reality that holds in any given universe, including ours, is thus replicated in an infinite number of other universes across the Quilted Multiverse.17

  What to Make of This?

  It’s possible that the conclusion we’ve reached strikes you as so outlandish that you’re inclined to turn the discussion on its head. You might argue that the bizarre nature of where we’ve gotten—infinite copies of you and everyone and everything—is evidence of the faulty nature of one or more of the assumptions that led us here.

  Might the assumption that the entire cosmos is inhabited by particles be wrong? Perhaps beyond our cosmic horizon is a vast realm containing nothing but empty space. It’s possible, but the theoretical contortions required to accommodate such a picture render it thoroughly unconvincing. The most refined cosmological theories, to be encountered shortly, don’t lead us anywhere near this possibility.

  Might the very laws of physics change beyond our cosmic horizon, corrupting our ability to perform any reliable theoretical analyses of those distant realms? Again, it’s possible. But as we will see in the next chapter, recent developments yield a compelling argument that although the laws can vary, that variation doesn’t invalidate our conclusions regarding the Quilted Multiverse.

  Might the universe’s spatial expanse be finite? Sure. Definitely possible. If space were finite yet large enough, there could still be some interesting patches way out there. But a smallish finite universe could easily fail to have adequate space to accommodate substantial numbers of distinct patches, let alone any that are duplicates of our own. A finite universe poses the most convincing way to upend the Quilted Multiverse.

  But in the last few decades, physicists working to push the big bang theory back to time zero—in search of a deeper understanding of the origin and nature of Lemaître’s primeval atom—have developed an approach called inflationary cosmology. In the inflationary framework, the argument in support of an infinitely large cosmos, not only garners strong observational and theoretical support but, as we will see in the next chapter, becomes an almost inevitable conclusion.

  What’s more, inflation brings to the fore another, even more exotic, variety of parallel worlds.

  *It’s easier to envision curved space than curved time, and that’s why many popularizations of Einsteinian gravity focus solely on the former. However, for the gravity generated by familiar objects like the earth and sun, it is actually the curvature of time—not space—that exerts the dominant impact. For an illustration, think of two clocks, one on the ground, the other on top of the Empire State Building. Because the ground clock is closer to the earth’s center, it experiences slightly stronger gravity than the clock that’s high above Manhattan. General relativity shows that because of this, the rate at which time passes on each will be slightly different: the ground clock will run a tiny bit slow (billionths of a second per year) compared to the elevated clock. The temporal mismatch is an example of what we mean by time being curved or warped. General relativity then establishes that objects move toward regions where time elapses more slowly; in a sense, all objects “want” to age as slowly as possible. From an Einsteinian perspective, that explains why an object falls when you let go of it.

  *Given our earlier discussion of how matter curves the region in which it is immersed, you might wonder how there can be no c
urvature even though there’s matter. The explanation is that a uniform presence of matter generally curves spacetime; in this particular case, there is zero space curvature but nonzero spacetime curvature.

  *I will discuss black holes more fully in later chapters. Here we’ll stick to the familiar notion, by now well ingrained in popular culture, of a spatial region—think of it as a ball in space—whose gravitational pull is so strong that nothing crossing its edge can escape. The bigger the black hole’s mass, the larger its size, so when anything falls in, not only does the black hole’s mass increase but its size does too.

  CHAPTER 3

  Eternity and Infinity

  The Inflationary Multiverse

  A pioneering group of physicists in the mid-1900s realized that if you were to shut off the sun, remove the other stars from the Milky Way, and even sweep away the more distant galaxies, space would not be black. To the human eye it would appear black, but if you could see radiation in the microwave part of the spectrum, then every which way you turned you’d see a uniform glow. Its origin? The origin. Remarkably, these physicists discovered a pervasive sea of microwave radiation filling space that is a present-day relic of the universe’s creation. The story of this breakthrough recounts a phenomenal achievement of the big bang theory, but in time it also revealed one of the theory’s fundamental shortcomings and thus set the stage for the next major breakthrough in cosmology after the pioneering works of Friedmann and Lemaître: the inflationary theory.