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

by Brian Greene

The Quilted Multiverse arises from an infinite spatial expanse, a possibility that fits squarely within general relativity. The snag is that general relativity allows for an infinite spatial expanse but doesn’t require it, which in turn explains why, even though general relativity is an accepted framework, the Quilted Multiverse remains tentative. An infinite spatial expanse does emerge directly from eternal inflation—recall that each bubble universe when viewed from the inside appears infinitely large—but in this setting the Quilted Multiverse is rendered uncertain because the underlying proposal, eternal inflation, remains hypothetical.

The Brane, Cyclic, and Landscape Multiverses are based on string theory, so they suffer multiple uncertainties. Remarkable as string theory may be, rich as its mathematical structure may have become, the dearth of testable predictions, and the concomitant absence of contact with observations or experiments, relegates it to the realm of scientific speculation. Moreover, with the theory still very much a work in progress,

Can we? Can a theory’s invocation of other universes yield testable predictions even if those universes lie beyond the reach of experiments and observations? Let’s address this key question through a number of steps. We’ll follow the pattern above, progressing from an “in principle” to an “in practice” perspective.

Anthropic reasoning thus focuses our attention on the portion of the multiverse in which the cosmological constant lies in a narrow window; as discussed in Chapter 6, the calculations show that for a given universe to contain galaxies, its cosmological constant needs to be less than about 200 times the critical density (a mass equivalent of about 10–27 grams in each cubic centimeter of space, or about 10–121 in Planck units).7

So the way to think about the problem is this. You and I and computers and bacteria and viruses and everything else material are made of molecules and atoms, which are themselves composed of particles like electrons and quarks. Schrödinger’s equation works for electrons and quarks, and all evidence points to its working for things made of these constituents, regardless of the number of particles involved. This means that Schrödinger’s equation should continue to apply during a measurement. After all, a measurement is just one collection of particles (the person, the equipment, the computer …) coming into contact with another (the particle or particles being measured). But if that’s the case, if Schrödinger’s math refuses to bow down, then Bohr is in trouble. Schrödinger’s equation doesn’t allow waves to collapse. An essential element of the Copenhagen approach would therefore be undermined.

Let’s now consider a slightly more complicated wave shape, as in Figure 8.10. This probability wave indicates that, at the given moment, there are two places the electron might be found—Strawberry Fields, the John Lennon memorial in Central Park, and Grant’s Tomb in Riverside Park.

In describing how quantum mechanics may generate many realities, I used the word “split.” Everett used it. So did DeWitt. Nevertheless, in this context it’s a loaded verb with the potential to grossly mislead, and I’d intended not to invoke it. But I gave in to temptation. In my defense, it’s sometimes more effective to use a sledgehammer to break down a barrier separating us from an unfamiliar proposal about the workings of reality, and to subsequently repair the damage, than it is to delicately carve a pristine window that directly reveals the new vista. I’ve been using that sledgehammer; in this and the next section I’ll undertake the necessary repairs. Some of the ideas are a touch more difficult than those we’ve so far encountered, and the explanatory chains are a bit longer as well, but I encourage you to stay with me. I’ve found that all too often, people who learn about, or are even somewhat familiar with, the Many Worlds idea have the impression that it emerged from speculation of the most extravagant sort. But nothing could be further from the truth. As I will explain, the Many Worlds approach is, in some ways, the most conservative framework for defining quantum physics, and it’s important to understand why.

My undergraduate students, many of whom are quite able, often struggle to solve Schrödinger’s equation for even a single particle. Between you and the device, there are something like 1027 particles.

Physically, each spike in Figure 8.16a represents a configuration of an enormous number of particles that results in a device having a particular reading and your mind acquiring that information. In the left spike, the reading is Strawberry Fields; in the right, it’s Grant’s Tomb. Besides that difference, nothing distinguishes one spike from the other. I emphasize this because it’s essential to realize that neither is somehow more real than the other. Nothing but the device’s particular reading, and your reading of that reading, distinguishes the two multiparticle wave spikes.

One quick answer is that for a single isolated electron, we don’t tell a type-two story because without a measurement or an observation there’s no link to human experience that’s in need of articulation. The type-one story of a probability wave evolving via Schrödinger’s math is all that’s needed. And without a type-two story, there’s no opportunity to invoke multiple realities. Although this explanation is adequate, it proves worthwhile to delve a little deeper, revealing a special feature of quantum waves that comes into play when many particles are involved.

A frequent criticism of the Many Worlds approach is that it’s just too baroque to be true. The history of physics teaches us that successful theories are simple and elegant; they explain data with a minimum of assumptions and provide an understanding that’s precise and economical. A theory that introduces an ever-growing cornucopia of universes falls way short of this ideal.

Proponents of the Many Worlds approach argue, credibly, that in assessing the complexity of a scientific proposal, you shouldn’t focus on its implications. What matters is the fundamental features of the proposal itself. The Many Worlds approach assumes that a single equation—Schrödinger’s—governs all probability waves all the time, so for simplicity of formulation and economy of assumptions, it’s hard to beat. The Copenhagen approach is surely no simpler. It, too, invokes Schrödinger’s equation, but it also includes a vague, ill-defined prescription for when Schrödinger’s equation should be turned off, and then an even less detailed prescription regarding the process of wave collapse that is meant to take its place. That the Many Worlds approach leads to an exceptionally rich picture of reality is no more a black mark against it than the rich diversity of life on earth is a black mark against Darwinian natural selection. Mechanisms that are fundamentally simple can give rise to complicated consequences.

Everett’s approach, which he described as “objectively deterministic” with probability “reappearing at the subjective level,” resonated with this strategy. And he was thrilled by the direction. As he noted in the 1956 draft of his dissertation, the framework offered to bridge the position of Einstein (who famously believed that a fundamental theory of physics should not involve probability) and the position of Bohr (who

was perfectly happy with a fundamental theory that did). According to Everett, the Many Worlds approach accommodated both positions, the difference between them merely being one of perspective. Einstein’s perspective is the mathematical one in which the grand probability wave of all particles relentlessly evolves by the Schrödinger equation, with chance playing absolutely no role.* I like to picture Einstein soaring high above the many worlds of Many Worlds, watching as Schrödinger’s equation fully dictates how the entire panorama unfolds, and happily concluding that even though quantum mechanics is correct, God doesn’t play dice. Bohr’s perspective is that of an inhabitant in one of the worlds, also happy, using probabilities to explain, with stupendous precision, those observations to which his limited perspective gives him access.

Beyond John Wheeler’s knack for finding and mentoring the world’s most gifted young scientists (besides Hugh Everett, Wheeler’s students included Richard Feynman, Kip Thorne, and, as we will shortly see, Jacob Bekenstein), he had an uncanny ability to identify issues whose exploration could change our fundamental paradigm of nature’s workings. During a lunch we had at Princeton in 1998, I asked him what he thought the dominant theme in physics would be in the decades going forward. As he had already done frequently that day, he put his head down, as if his aging frame had grown weary of supporting such a massive intellect. But now the length of his silence left me wondering, briefly, whether he didn’t want to answer or whether, perhaps, he had forgotten the question. He then slowly looked up and said a single word: “Information.”

His exact solution revealed something startling: if enough mass were crammed into a small enough ball, a gravitational abyss would form. The spacetime curvature would become so extreme that anything venturing too close would be trapped. And because “anything” includes light, such regions would fade to black, a characteristic that inspired the early term “dark stars.” The extreme warping would also bring time to a grinding halt at the star’s edge; hence another early label, “frozen stars.” Half a century later, Wheeler, who was nearly as adept at marketing as he was at physics, popularized such stars both within and beyond the scientific community with a new and more memorable name: black holes. It stuck.

The idea is general. Glass shattering, a candle burning, ink spilling, perfume pervading: these are different processes, but the statistical considerations are the same. In each, order degrades to disorder and does so because there are so many ways to be disordered. The beauty of this kind of analysis—the insight provided one of the most potent “Aha!” moments in my physics education—is that, without getting lost in the microscopic details, we have a guiding principle to explain why a great many phenomena unfold the way they do.

Bekenstein was wrong. Black holes do not have a temperature. Black holes do not harbor entropy. Black holes are entropy sinkholes. In their presence, the Second Law of Thermodynamics fails. Despite

A huge black hole, like the one at the center of our galaxy, has a temperature that’s less than a trillionth of a degree above absolute zero.

And the answer he found is proportional to the surface area of the black hole, just as Bekenstein had proposed. So by the end of 1974, the Second Law was law once again. The insights of Bekenstein and Hawking established that in any situation, total entropy increases, as long as you account for not only the entropy of ordinary matter and radiation but also that contained within black holes, as measured by their total surface area. Rather than being entropy sinks that subvert the Second Law, black holes play an active part in upholding the law’s pronouncement of a universe with ever-increasing disorder. The conclusion provided a welcome relief. To many physicists, the Second Law, emerging from seemingly unassailable statistical considerations, came as close to sacred as just about anything in science. Its restoration meant that, once again, all was right with the world. But, in time, a vital little detail in the entropy accounting made it clear that the Second Law’s balance sheet was not the deepest issue in play. That honor went to identifying where entropy is stored, a matter whose importance becomes clear when we recognize the deep link between entropy and the central theme of this chapter: information.

Entropy measures the additional information hidden within the microscopic details of the system, which, should you have access to it, would distinguish the configuration at a micro level from all the macro look-alikes.

So, you start to ponder. What actually is information, and what does it do? Your response is simple and direct. Information answers questions. Years of research by mathematicians, physicists, and computer scientists have made this precise. Their investigations have established that the most useful measure of information content is the number of distinct yes-no questions the information can answer.

As with the dropped dollars, a system’s entropy is the number of yes-no questions that its microscopic details have the capacity to answer, and so the entropy is a measure of the system’s hidden information content.6

black holes may be, these developments suggested that, when it comes to entropy, black holes behave much like everything else. But the results also raised puzzles. Although Bekenstein and Hawking tell us how much information is hidden within a black hole, they don’t tell us what that information is. They don’t tell us the specific

Which perspective is right? The claim advanced by Susskind and others is that both are. Granted, this is hard to square with ordinary logic—the logic by which you are either alive or not alive. But this is

no ordinary situation. Most saliently, the wildly different perspectives can never confront each other. You can’t climb out of the black hole and prove to the distant observer that you are alive. And, as it turns out, the distant observer can’t jump into the black hole and confront you with evidence that you’re not. When I said that the distant observer “sees” you immolated by the black hole’s Hawking radiation, that was a simplification. The distant observer, by closely examining the tired radiation that reaches her, can piece together the story of your fiery demise. But for the information to reach her takes time. And the math shows that by the time she can conclude you’ve burned, she won’t have enough time left to then hop into the black hole and catch up with you before you’re destroyed by the singularity. Perspectives can differ, but physics has a built-in fail-safe against paradoxes.

The conclusion is that the distant observer—us—infers that a black hole’s entropy is determined by the area of its horizon because the horizon is where the entropy is stored. Said that way, it seems utterly sensible. But don’t lose sight of how unexpected it is that the storage capacity isn’t set by the black hole’s volume. And, as we will now see, this result doesn’t merely highlight a peculiar feature of black holes. Black holes don’t just tell us about how black holes store information. Black holes inform us about information storage in any context. This paves a direct path to the holographic perspective.

We thus learn an important lesson. The amount of information contained within a region of space, stored in any objects of any design, is always less than the area of the surface that surrounds the region (measured in square Planck units).

This is the conclusion we’ve been chasing. Notice that although black holes are central to the reasoning, the analysis applies to any region of space, whether or not a black hole is actually present. If you max out a region’s storage capacity, you’ll create a black hole, but as long as you stay under the limit, no black hole will form.

I hasten to add that in any practical sense, the information storage limit is of no concern. Compared with today’s rudimentary storage devices, the potential storage capacity on the surface of a spatial region is humongous. A stack of five off-the-shelf terabyte hard drives fits comfortably within a sphere of radius 50 centimeters, whose surface is covered by about 1070 Planck cells. The surface’s storage capacity is thus about 1070 bits, which is about a billion, trillion, trillion, trillion, trillion ...

Take a Wheelerian perspective and imagine that whatever happens in the region amounts to information processing—information regarding how things are right now is transformed by the laws of physics into information regarding how they will be in a second or a minute or an hour.

Since the physical processes we witness, as well as those by which we’re governed, seemingly take place within the region, it’s natural to expect that the information those processes carry is also found within the region. But the results just derived suggest an alternative view. For black holes, we found that the link between information and surface area goes beyond mere numerical accounting; there’s a concrete sense in which information is stored on their surfaces. Susskind and ’t Hooft stressed that the lesson should be general: since the information required to describe physical phenomena within any given region of space can be fully encoded by data on a surface that surrounds the region, then there’s reason to think that the surface is where the fundamental physical processes actually happen. Our familiar three-dimensional reality, these bold thinkers suggested, would then be likened to a holographic projection of those distant two-dimensional physical processes.

Incredible,

If this line of reasoning is correct, then there are physical processes taking place on some distant surface that, much like a puppeteer pulls strings, are fully linked to the processes taking place in my fingers, arms, and brain as I type these words at my desk. Our experiences here, and that distant reality there, would form the most interlocked of

parallel worlds. Phenomena in the two—I’ll call them Holographic Parallel Universes—would be so fully joined that their respective evolutions wo...

Another important point is that throughout the discussion, we’ve spoken of a region of space, of a surface that surrounds it, and of the information content of each. But since our focus has been on entropy and the Second Law—both of which concern themselves primarily with the quantity of information in a given context—we’ve not elaborated on the details of how that information is physically realized or stored. When we talk about information residing on a sphere surrounding a

region of space, what does that really mean? How does the information manifest itself? What form does it take? To what extent can we develop an explicit dictionary that translates from phenomena taking place on the boundary to those taking place in the interior?

Physicists have yet to articulate a general framework for addressing these questions. Given that gravity and quantum mechanics are both central to the reasoning, you might expect that string theory would provide a potent context for theoretical explorations. But when ’t Hooft first formulated the holographic concept, he doubted that string theory would be able to advance the subject, noting, “Nature is much more crazy at the Planck scale than even string theorists could have imagined.”13 Less than a decade later, string theory proved ’t Hooft wrong by p...

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.

Our grip on reality is more tenuous than day-today life can lead us to believe.

The bottom line is that you can’t know for sure. You engage the world through your senses, which stimulate your brain in ways your neural circuitry has evolved to interpret. If someone artificially stimulates your brain so as to elicit electrical crackles exactly like those produced by eating pizza, reading this sentence, or skydiving, the experience will be indistinguishable from the real thing. Experience is dictated by brain processes, not by what activates those processes.

Once you can’t trust your knowledge base, reality quickly sails to sea.

We’ll return to these concerns, but I don’t want them to sink us—at least, not yet. So, for the time being, let’s drop anchor. Imagine that you are real flesh and blood, and so am I, and that everything you and I take to be real, in the everyday sense of the term, is real. With all that assumed, let’s take up the question of computers and brainpower. What, roughly, is the processing speed of the human brain, and how does it compare with the capacity of computers?

Very interesting

The possibility of artificial sentience clearly relies on a functionalist viewpoint. A central assumption of this perspective is that conscious thought is not overlaid on a brain but rather is the very sensation generated by a particular kind of information processing. Whether that processing happens within a three-pound biological mass or within the circuits of a computer is irrelevant. The assumption could be wrong. Maybe a bundle of connections needs a substrate of wrinkled wet matter if it’s to gain self-awareness. Maybe you need the actual physical molecules that constitute a brain, not just the processes and

connections those molecules facilitate, if conscious thought is to animate the inanimate. Maybe the kinds of information processing that computers carry out will always differ in some essential way from brain functioning, preventing the leap to sentience. Maybe conscious thought is fundamentally nonphysical, as claimed by various traditions, and so lies permanently beyond the reach of technological innovation.

This is far from the 100 billion neurons firing away in a typical human head, but the project’s leader, the neuroscientist Henry Markram, anticipates that before 2020 the Blue Brain Project, leveraging processing speeds that are projected to increase by a factor of more than a million, will achieve a full simulated model of the human brain. Blue Brain’s goal is not

to produce artificial sentience, but rather to have a new investigative tool for developing treatments for various forms of mental illness; still, Markram has gone out on a limb to speculate that, when completed, Blue Brain may very well have the capacity to speak and to feel.

If we ever create computer-based sentience, some would likely implant the thinking machines in artificial human bodies, creating a mechanical species—robots—that would be integrated into conventional reality. But my interest here is in those who would be drawn by the purity of electrical impulses to program simulated environments populated by simulated beings that would exist within a computer’s hardware; instead of C-3PO or Data, think Sims or Second Life, but with inhabitants who have self-aware and responsive minds. The history of technological innovation suggests that iteration by iteration, the simulations would gain verisimilitude, allowing the physical and experiential characteristics of the artificial worlds to reach convincing levels of

nuance and realism. Whoever was running a given simulation would decide whether the simulated beings knew that they existed within a computer; simulated humans who surmised that their world was an elaborate computer program might find themselves taken away by simulated technicians in white coats and confined to simulated locked wards. But probably the vast majority of simulated beings would consider the possibility that they’re in a computer simulation too silly to warrant attention. You may well be having that very reaction right now. Even if you accept the possibility of artificial sentience, you may be persuaded that the overwhelming complexity of simulating an entire civilization, or just a smaller community, renders such feats beyond computational reach. On this point, it’s worth looking at some more numbers. Our distant descendants will likely fashion ever-larger quantities of matter into vast computing networks. So allow imagination free rein. Think big. Scientists have estimated that a present-day high-speed computer the size of the earth could perform anywhere from 1033 to 1042 operations per second. By comparison, if we assume that our earlier estimate of 1017 operations per second for a human brain is on target, then an average brain performs about 1024 total operations in a single hundred-year life span. Multiply that by the roughly 100 billion people who have ever walked the planet, and the total number of operations performed by every human brain since Lucy (...

And that’s with today’s technology. Quantum computing—harnessing all the distinct possibilities represented in a quantum probability wave so as to do many different calculations simultaneously—has the capacity to increase processing speeds by spectacular factors. Although we are still very far from mastering this applicati...

than a laptop has the potential to perform the equivalent of all human thought since the dawn of our species ...