by Brian Greene
This suggests a tack for injecting probabilities into the Many Worlds approach. Before you undertake a given experiment, you are much like your precloned self. You contemplate all outcomes allowed by quantum mechanics and know that there’s a 100 percent certainty that a copy of you will see each. Nothing at all chancy has made an appearance. You then undertake the experiment. At that point, as with the Zaxtarian scenario, a notion of probability presents itself. Each copy of you is an independent sentient being capable of wondering about which world he or she happens to inhabit—the likelihood, that is, that when the experiment’s results are revealed, he or she will see this or that particular outcome. Probability enters through each inhabitant’s subjective experience.
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.
It’s a captivating vision—Einstein and Bohr agreeing on quantum mechanics. But there are pesky details that for more than half a century have convinced many that it’s still too early to sign on. Those who have studied Everett’s thesis generally agree that while his intent was clear—a deterministic theory that to its inhabitants nevertheless appears probabilistic—he didn’t convincingly spell out how to achieve it. For example, much in the spirit of material covered in Chapter 7, Everett sought to determine what a “typical” inhabitant of the many worlds would observe in any given experiment. But (unlike our focus in Chapter 7) in the Many Worlds approach, the inhabitants we need to contend with are all the same person; if you’re the experimenter, they are all you, and collectively they will see a range of different outcomes. So who is the “typical” you?
Inspired by the Zaxtarian scenario, a natural suggestion is to count the number of yous who will see a given result; the outcome seen by the greatest number of yous would then qualify as typical. Or, more quantitatively, define the probability of a result to be proportional to the number of yous who see it. For simple examples, this works: in Figure 8.16, there’s one of you who sees each outcome, and so you peg the odds at 50:50 for seeing one result or the other. That’s good; the usual quantum mechanical prediction is also 50:50, because the probability wave heights at the two locations are equal.
Figure 8.17 The combined probability wave for you and your device encounters a probability wave that has multiple spikes of different magnitudes.
However, consider a more general situation, such as that in Figure 8.17, in which the probability wave heights are unequal. If the wave is a hundred times larger at Strawberry Fields than at Grant’s Tomb, then quantum mechanics predicts that you are a hundred times more likely to find the electron at Strawberry Fields. But in the Many Worlds approach, your measurement still generates one you who sees Strawberry Fields and another you who sees Grant’s Tomb; the odds based on counting the number of yous is thus still 50:50—the wrong result. The origin of the mismatch is clear. The number of yous who see one result or another is determined by the number of spikes in the probability wave. But the quantum mechanical probabilities are determined by something else—not by the number of spikes but by their relative heights. And it’s these predictions, the quantum mechanical predictions, which have been convincingly confirmed by experiments.
Everett developed a mathematical argument that was meant to address this mismatch; many others have since pushed it further.9 In broad strokes, the idea is that in calculating the odds of seeing one or another outcome, we should place ever-less weight on universes whose wave heights are ever smaller, as depicted symbolically in Figure 8.18. But this is perplexing. And controversial. Is the universe in which you find the electron at Strawberry Fields somehow a hundred times as genuine, or a hundred times as likely, or a hundred times as relevant as the one in which you find it at Grant’s Tomb? These suggestions would surely create tension with the belief that every world is just as real as every other.
After more than fifty years, during which distinguished scientists have revisited, revised, and extended Everett’s arguments, many agree that the puzzles persist. Yet it remains seductive to imagine that the mathematically simple, totally bare-bones, profoundly revolutionary Many Worlds approach yields the probabilistic predictions that form the foundation of belief in quantum theory. This has inspired many other ideas, beyond the Zaxtarian-type reasoning, for joining probability and Many Worlds.10
A prominent proprosal comes from a leading group of researchers at Oxford, including, among others, David Deutsch, Simon Saunders, David Wallace, and Hilary Greaves. They’ve developed a sophisticated line of attack that focuses on a seemingly boorish question. If you’re a gambler, and you believe in the Many Worlds approach, what’s the optimum strategy for placing bets on quantum mechanical experiments? Their answer, which they argue for mathematically, is that you’d bet just as Neils Bohr would. When speaking of maximizing your return, these authors have in mind something that would have sent Bohr into a tizzy—they’re considering an average over the many inhabitants of the multiverse who claim to be you. But even so, their conclusion is that the numbers that Bohr and everyone since have been calculating and calling probabilities are the very numbers that should guide how you wager. That is, even though quantum theory is fully deterministic, you should treat the numbers as if they were probabilities.
Some are convinced that this completes Everett’s program. Some are not.
The lack of consensus on the crucial question of how to treat probability in the Many Worlds approach is not all that unexpected. The analyses are highly technical and also deal with a topic—probability—that is notoriously tricky even outside its application to quantum theory. When you roll a die, we all agree that you have a 1 in 6 chance of getting a 3, and so we’d predict that over the course of, say, 1,200 rolls the number 3 will turn up about 200 times. But since it’s possible, in fact likely, that the number of 3s will deviate from 200, what does the prediction mean? We want to say that it’s highly probable that ⅙th of the outcomes will be 3s, but if we do that, then we’ve defined the probability of getting a 3 by invoking the concept of probability. We’ve gone circular. That’s just a small taste of how the issues, beyond their intrinsic mathematical complexity, are conceptually slippery. Throw into the mix the added Many Worlds intricacy of “you” no longer referring to a single person, and it’s no wonder researchers find ample points of contention. I have little doubt that full clarity will one day emerge, but not yet, and perhaps not for some time.
Figure 8.18 (a) A schematic illustration of the evolution, dictated by Schrödinger’s equation, of the combined probability wave for all the particles making up you and the measuring device, when you measure the position of an electron. The electron’s own probability wave is spiked at two locations, but with unequal wave heights.
Figure 8.18 (b) Some proposals suggest that in the Many Worlds approach, unequal wave heights imply that some worlds are less genuine, or less relevant, than others. There is controversy over what, if anything, this mea
ns.
Predictions and Understanding
For all these controversies, quantum mechanics itself remains as successful as any theory in the history of ideas. The reason, as we’ve seen, is that for the kinds of experiments we can do in the laboratory, and for many of the observations we can make of astrophysical processes, we have a “quantum algorithm” that produces testable predictions. Use Schrödinger’s equation to calculate the evolution of the relevant probability waves and use the results—the various wave heights—to predict the probability that you’ll find one outcome or another. As far as predictions are concerned, why this algorithm works—whether the wave collapses upon measurement, whether all possibilities are realized in their own universes, whether some other process is at work—is secondary.
Some physicists argue that even calling the issue secondary accords it more status than it deserves. In their view, physics is only about making predictions, and as long as different approaches don’t affect those predictions, why should we care which is ultimately correct? I offer three thoughts.
First, beyond making predictions, physical theories need to be mathematically coherent. The Copenhagen approach is a valiant effort, but it fails to meet this standard: at the critical moment of observation, it retreats into mathematical silence. That’s a substantial gap. The Many Worlds approach attempts to fill it.11
Second, in some situations, the predictions of the Many Worlds approach would differ from those of the Copenhagen approach. In Copenhagen, the process of collapse would revise Figure 8.16a to have a single spike. So if you could cause the two waves depicted in the figure—representing macroscopically distinct situations—to interfere, generating a pattern similar to that in Figure 8.2c, it would establish that Copenhagen’s hypothesized wave collapse didn’t happen. Because of decoherence, as discussed earlier, it is an extraordinarily formidable task to do this, but, at least theoretically speaking, the Copenhagen and Many Worlds approaches yield different predictions.12 It is an important point of principle. The Copanhagen and Many Worlds approaches are often referred to as different “interpretations” of quantum mechanics. This is an abuse of language. If two approaches can yield different predictions, you can’t call them mere interpretations. Well, you can. And people do. But the terminology is off the mark.
Third, physics is not just about making predictions. If one day we were to find a black box that always and accurately predicted the outcome of our particle physics experiments and our astronomical observations, the existence of the box would not bring inquiry in these fields to a close. There’s a difference between making predictions and understanding them. The beauty of physics, its raison d’être, is that it offers insights into why things in the universe behave the way they do. The ability to predict behavior is a big part of physics’ power, but the heart of physics would be lost if it didn’t give us a deep understanding of the hidden reality underlying what we observe. And should the Many Worlds approach be right, what a spectacular reality our unwavering commitment to understanding predictions will have uncovered.
I don’t expect theoretical or experimental consensus to come in my lifetime concerning which version of reality—a single universe, a multiverse, something else entirely—quantum mechanics embodies. But I have little doubt that future generations will look back upon our work in the twentieth and twenty-first centuries as having nobly laid the basis for whatever picture finally emerges.
*For simplicity, we won’t consider the electron’s position in the vertical direction—we focus solely on its position on a map of Manhattan. Also, let me re-emphasize that while this section will make clear that Schrödinger’s equation doesn’t allow waves to undergo an instantaneous collapse as in Figure 8.6, waves can be carefully prepared by the experimenter in a spiked shape (or, more precisely, very close to a spiked shape).
*For a mathematical depiction, see note 4.
*This non-chancy perspective would argue strongly for abandoning the colloquial terminology that I’ve used, “probability wave,” in favor of the technical name, “wavefunction.”
CHAPTER 9
Black Holes and Holograms
The Holographic Multiverse
Plato likened our view of the world to that of an ancient forebear watching shadows meander across a dimly lit cave wall. He imagined our perceptions to be but a faint inkling of a far richer reality that flickers beyond reach. Two millennia later, it seems that Plato’s cave may be more than a metaphor. To turn his suggestion on its head, reality—not its mere shadow—may take place on a distant boundary surface, while everything we witness in the three common spatial dimensions is a projection of that faraway unfolding. Reality, that is, may be akin to a hologram. Or, really, a holographic movie.
Arguably the strangest parallel world entrant, the holographic principle envisions that all we experience may be fully and equivalently described as the comings and goings that take place at a thin and remote locus. It says that if we could understand the laws that govern physics on that distant surface, and the way phenomena there link to experience here, we would grasp all there is to know about reality. A version of Plato’s shadow world—a parallel but thoroughly unfamiliar encapsulation of everyday phenomena—would be reality.
The journey to this peculiar possibility combines developments deep and far flung—insights from general relativity; from research on black holes; from thermodynamics; quantum mechanics; and, most recently, string theory. The thread linking these diverse areas is the nature of information in a quantum universe.
Information
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.”
I wasn’t surprised. For some time, Wheeler had been advocating a view of physical law quite unlike what a fledgling physicist learns in the standard academic curriculum. Traditionally, physics focuses on things—planets, rocks, atoms, particles, fields—and investigates the forces that affect their behavior and govern their interactions. Wheeler was suggesting that things—matter and radiation—should be viewed as secondary, as carriers of a more abstract and fundamental entity: information. It’s not that Wheeler was claiming that matter and radiation were somehow illusory; rather, he argued that they should be viewed as the material manifestations of something more basic. He believed that information—where a particle is, whether it is spinning one way or another, whether its charge is positive or negative, and so on—forms an irreducible kernel at the heart of reality. That such information is instantiated in real particles, occupying real positions, having definite spins and charges, is something like an architect’s drawings being realized as a skyscraper. The fundamental information is in the blueprints. The skyscraper is but a physical realization of the information contained in the architect’s design.
From this perspective, the universe can be thought of as an information processor. It takes information regarding how things are now and produces information delineating how things will be at the next now, and the now after that. Our senses become aware of such processing by detecting how the physical environment changes over time. But the physical environment itself is emergent; it arises from the fundamental ingredient, information, and evolves according to the fundamental rules, the laws of physics.
I don’t know whether such an information-theoretic stance will reach
the dominance in physics that Wheeler envisioned. But recently, driven largely by the work of physicists Gerard ’t Hooft and Leonard Susskind, a major shift in thinking has resulted from puzzling questions regarding information in one particularly exotic context: black holes.
Black Holes
Within a year of general relativity’s publication, the German astronomer Karl Schwarzschild found the first exact solution to Einstein’s equations, a result that determined the shape of space and time in the vicinity of a massive spherical object such as a star or a planet. Remarkably, not only had Schwarzschild found his solution while calculating artillery trajectories on the Russian front during World War I, but also he had beaten the master at his own game: to that point, Einstein had found only approximate solutions to the equations of general relativity. Impressed, Einstein publicized Schwarzschild’s achievement, presenting the work before the Prussian Academy, but even so he failed to appreciate a point that would become Schwarzschild’s most tantalizing legacy.
Schwarszchild’s solution shows that familiar bodies like the sun and the earth produce a modest curvature, a gentle depression in the otherwise flat spacetime trampoline. This matched well the approximate results Einstein had managed to work out earlier, but by dispensing with approximations, Schwarzschild could go further. 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.