by Brian Greene
Table 7.2 Every whole number is paired with every other even number, leaving an infinite set of even bachelors, suggesting that there are more evens than wholes.
From one perspective, the population of even numbers is less than that of whole numbers. From another, the populations are equal. From another still, the population of even numbers is greater than that of the whole numbers. And it’s not that one conclusion is right and the others wrong. There simply is no absolute answer to the question of which of these kinds of infinite collections are larger. The result you find depends on the manner in which you do the comparison.10
That raises a puzzle for multiverse theories. How do we determine whether galaxies and life are more abundant in one or another type of universe when the number of universes involved is infinite? The very same ambiguity we’ve just encountered will afflict us just as severely, unless physics picks out a precise basis on which to make the comparisons. Theorists have put forward proposals, various analogs of the pairings given in the tables, that emerge from one or another physical consideration—but a definitive procedure has yet to be derived and agreed upon. And, just as in the case of infinite collections of numbers, different approaches yield different results. According to one way of comparing, universes with one array of properties preponderate; according to an alternative way, universes with different properties do.
The ambiguity has a dramatic impact on what we conclude are typical or average properties in a given multiverse. Physicists call this the measure problem, a mathematical term whose meaning is well suggested by its name. We need a means for measuring the sizes of different infinite collections of universes. It is this information that we need in order to make predictions. It is this information that we need in order to work out how likely it is that we reside in one type of universe rather than another. Until we find a fundamental dictum for how we should compare infinite collections of universes, we won’t be able to foretell mathematically what typical multiverse dwellers—us—should see in experiments and observations. Solving the measure problem is imperative.
A Further Contrarian Concern
I’ve called out the measure problem in its own section not only because it is a formidable impediment to prediction, but also because it may entail another, disquieting consequence. In Chapter 3, I explained why the inflationary theory has become the de facto cosmological paradigm. A brief burst of rapid expansion during our universe’s first moments would have allowed today’s distant regions to have communicated early on, which explains the common temperature that measurements have found; rapid expansion also irons out any spatial curvature, rendering the shape of space flat, in line with observations; and finally, such expansion turns quantum jitters into tiny temperature variations across space that are both measurable in the microwave background radiation and essential to galaxy formation. These successes yield a strong case.11 But the eternal version of inflation has the capacity to undermine the conclusion.
Whenever quantum processes are relevant, the best you can do is predict the likelihood of one outcome relative to another. Experimental physicists, taking this to heart, perform experiments over and over again, acquiring reams of data on which statistical analyses can be run. If quantum mechanics predicts that one outcome is ten times as likely as another, then the data should very nearly reflect this ratio. The cosmic microwave background calculations, whose match to observations is the most convincing evidence for the inflationary theory, rely on quantum field jitters, so they are also probabilistic. But, unlike laboratory experiments, they can’t be checked by running the big bang over and over again. So how are they interpreted?
Well, if theoretical considerations conclude, say, that there’s a 99 percent probability that the microwave data should take one form and not another, and if the more probable outcome is what we observers see, the data are taken as strongly supporting the theory. The rationale is that if a collection of universes were all produced by this same underlying physics, the theory predicts that about 99 percent of them should look much like what we observe and about 1 percent to deviate significantly.
Now, if the Inflationary Multiverse had a finite population of universes, we could straightforwardly conclude that the number of oddball universes where quantum processes result in data not matching expectations remains, comparatively speaking, very small. But if, as in the Inflationary Multiverse, the population of universes is not finite, it is far more challenging to interpret the numbers. What’s 99 percent of infinity? Infinity. What’s 1 percent of infinity? Infinity. Which is bigger? The answer requires us to compare two infinite collections. And as we’ve seen, even when it seems plain that one infinite collection is larger than another, the conclusion you reach depends on your method of comparison.
The contrarian concludes that when inflation is eternal, the very predictions that we use to build our confidence in the theory are compromised. Every possible outcome allowed by the quantum calculations, however unlikely—a .1 percent quantum probability, a .0001 percent quantum probability, a .0000000001 percent quantum probability—would be realized in infinitely many universes simply because any of these numbers times infinity equals infinity. Without a fundamental prescription for comparing infinite collections, we can’t possibly say that one collection of universes is larger than the rest and is thus the most likely kind of universe for us to witness, we lose the capacity to make definite predictions.
The optimist concludes that the spectacular agreement between quantum calculations in inflationary cosmology and data, as in Figure 3.5, must reflect a deep truth. With a finite number of universes and observers, the deep truth is that universes in which the data deviate from quantum predictions—those with a .1 percent quantum probability, or a .0001 percent quantum probability, or a .0000000001 percent quantum probability—are indeed rare, and that’s why garden-variety multiverse inhabitants like us don’t find ourselves living inside one of them. With an infinite number of universes, the optimist concludes, the deep truth must be that the rarity of anomalous universes, in some yet to be established manner, still holds. The expectation is that we will one day derive a measure, a definite means for comparing the various infinite collections of universes, and that those universes emerging from rare quantum aberrations will have a tiny measure compared with those emerging from the likely quantum outcomes. To accomplish this remains an immense challenge, but the majority of researchers in the field are convinced that the agreement in Figure 3.5 means that we will one day succeed.12
Mysteries and Multiverses:
Can a multiverse provide explanatory power of which we’d otherwise be deprived?
No doubt you’ve noticed that even the most sanguine projections suggest that predictions emerging from a multiverse framework will have a different character from those we traditionally expect from physics. The precession of the perihelion of Mercury, the magnetic dipole moment of the electron, the energy released when a nucleus of uranium splits into barium and krypton: these are predictions. They result from detailed mathematical calculations based on solid physical theory and produce precise, testable numbers. And the numbers have been verified experimentally. For example, calculations establish that the electron’s magnetic moment is 2.0023193043628; measurements reveal it to be 2.0023193043622. Within the tiny margins of error inherent to each, experiment thus confirms theory to better than 1 part in 10 billion.
From where we now stand, it seems that multiverse predictions will never reach this standard of precision. In the most refined scenarios, we might be able to predict that it’s “highly likely” that the cosmological constant, or the strength of the electromagnetic force, or the mass of the up-quark lies within some range of values. But to do better, we’ll need extraordinarily good fortune. In addition to solving the measure problem, we’ll need to discover a convincing multiverse theory with profoundly skewed probabilities (such as a 99.9999 percent probability that an observer will find himself in a universe with a cosmological constant equal to the val
ue we measure) or astonishingly tight correlations (such as that electrons exist only in universes with a cosmological constant equal to 10–123). If a multiverse proposal doesn’t have such favorable features, it will lack the precision that for so long has distinguished physics from other disciplines. To some researchers, that’s an unacceptable price to pay.
For quite a while, I took that position too, but my view has gradually shifted. Like every other physicist, I prefer sharp, precise, and unequivocal predictions. But I and many others have come to realize that although some fundamental features of the universe are suited for such precise mathematical predictions, others are not—or, at the very least, it’s logically possible that there may be features that stand beyond precise prediction. From the mid-1980s, when I was a young graduate student working on string theory, there was broad expectation that the theory would one day explain the values of particle masses, force strengths, the number of spatial dimensions, and just about every other fundamental physical feature. I remain hopeful that this is a goal we will one day reach. But I also recognize that it is a tall order for a theory’s equations to churn away and produce a number like the electron’s mass (.000000000000000000000091095 in units of the Planck mass) or the top quark’s mass (.0000000000000000632, in units of the Planck mass). And when it comes to the cosmological constant, the challenge appears herculean. A calculation that after pages of manipulations and megawatts of computer-crunching results in the very number that highlights the first paragraph of Chapter 6—well, it’s not impossible but it does strain even the optimist’s optimism. Certainly, string theory seems no closer to calculating any of these numbers today than it did when I first started working on it. This doesn’t mean that it, or some future theory, won’t one day succeed. Maybe the optimist needs to be yet more imaginative. But given the physics of today, it makes sense to consider new approaches. That’s what the multiverse does.
In a well-developed multiverse proposal, there’s a clear delineation of the physical features that need to be approached differently from standard practice: those that vary from universe to universe. And that’s the power of the approach. What you can absolutely count on from a multiverse theory is a sharp vetting of which single-universe mysteries persist in the many-universe setting, and which do not.
The cosmological constant is a prime example. If the cosmological constant’s value varies across a given multiverse, and does so in sufficiently fine increments, what was once mysterious—its value—would now be prosaic. Just as a well-stocked shoe store surely has your shoe size, an expansive multiverse surely has universes with the value of the cosmological constant we’ve measured. What generations of scientists might have struggled valiantly to explain, the multiverse would have explained away. The multiverse would have shown that a seemingly deep and perplexing issue emerged from the misguided assumption that the cosmological constant has a unique value. It is in this sense that a multiverse theory has the capacity to offer significant explanatory power, and it has the potential to profoundly influence the course of scientific inquiry.
Such reasoning must be wielded with care. What if Newton, after the apple fell, reasoned that we’re part of a multiverse in which apples fall down in some universes, up in others, and so the falling apple simply tells us which kind of universe we inhabit, with no need for further investigation? Or, what if he’d concluded that in each universe some apples fall down while others fall up, and the reason we see the falling-down variety is simply the environmental fact that, in our universe, apples that fall up have already done so and have thus long since departed for deep space? This is a fatuous example, of course—there’s never been any reason, theoretical or otherwise, for such thinking—but the point is serious. By invoking a multiverse, science could weaken the impetus to clarify particular mysteries, even though some of those mysteries might be ripe for standard, nonmultiverse explanations. When all that was really called for was harder work and deeper thinking, we might instead fail to resist the lure of multiverse temptation and prematurely abandon conventional approaches.
This potential danger explains why some scientists shudder at multiverse reasoning. It’s why a multiverse proposal that’s taken seriously needs to be strongly motivated from theoretical results, and it must articulate with precision the universes of which it’s composed. We must tread carefully and systematically. But to turn away from a multiverse because it could lead us down a blind alley is equally dangerous. In doing so, we might well be turning a blind eye to reality.
*Because there are differing perspectives regarding the role of scientific theory in the quest to understand nature, the points I’m making are subject to a range of interpretations. Two prominent positions are realists, who hold that mathematical theories can provide direct insight into the nature of reality, and instrumentalists, who believe that theory provides a means for predicting what our measuring devices should register but tells us nothing about an underlying reality. Over decades of exacting argument, philosophers of science have developed numerous refinements of these and related positions. As no doubt is clear, my perspective, and the approach I take in this book, is decidedly in the realist camp. This chapter in particular, examining the scientific validity of certain types of theories, and assessing what those theories might imply for the nature of reality, is one in which various philosophical orientations would approach the topic with considerable differences.
*In a multiverse containing an enormous number of different universes, a reasonable concern is that regardless of what experiments and observations reveal, there is some universe in the theory’s gargantuan collection that’s compatible with the results. If so, there’d be no experimental evidence that could prove the theory wrong; in turn, no data could be properly interpreted as evidence supporting the theory. I will consider this issue shortly.
CHAPTER 8
The Many Worlds of Quantum Measurement
The Quantum Multiverse
The most reasonable assessment of the parallel universe theories we’ve so far encountered is that the jury is out. An infinite spatial expanse, eternal inflation, braneworlds, cyclical cosmology, string theory’s landscape—these intriguing ideas have emerged from a range of scientific developments. But each remains tentative, as do the multiverse proposals each has spawned. While many physicists are willing to offer their opinions, pro and con, regarding these multiverse schemes, most recognize that future insights—theoretical, experimental, and observational—will determine whether any become part of the scientific canon.
The multiverse we’ll now take up, emerging from quantum mechanics, is viewed very differently. Many physicists have already reached a final verdict on this particular multiverse. The thing is, they haven’t all reached the same verdict. The differences come down to the deep and as yet unresolved problem of navigating from the probabilistic framework of quantum mechanics to the definite reality of common experience.
Quantum Reality
In 1954, nearly thirty years after the foundations of quantum theory had been set down by luminaries like Niels Bohr, Werner Heisenberg, and Erwin Schrödinger, an unknown graduate student from Princeton University named Hugh Everett III came to a startling realization. His analysis, which focused on a gaping hole that Bohr, the grand master of quantum mechanics, had danced around but failed to fill, revealed that a proper understanding of the theory might require a vast network of parallel universes. Everett’s was one of the earliest mathematically motivated insights suggesting that we might be part of a multiverse.
Everett’s approach, which in time would be called the Many Worlds interpretation of quantum mechanics, has had a checkered history. In January 1956, having worked out the mathematical consequences of his new proposal, Everett submitted a draft of his thesis to John Wheeler, his doctoral adviser. Wheeler, one of twentieth-century physics’ most celebrated thinkers, was thoroughly impressed. But that May, when Wheeler visited Bohr in Copenhagen and discussed Everett’s ideas, the reception was icy. Bohr
and his followers had spent decades refining their view of quantum mechanics. To them, the questions Everett raised, and the outlandish ways in which he thought they should be addressed, were of little merit.
Wheeler held Bohr in the highest regard, and so placed particular value on appeasing his elder colleague. In response to the criticisms, Wheeler delayed granting Everett his Ph.D. and compelled him to modify the thesis substantially. Everett was to cut out those parts blatantly critical of Bohr’s methodology and emphasize that his results were meant to clarify and extend the conventional formulation of quantum theory. Everett resisted, but he had already accepted a job in the Defense Department (where he would soon play an important behind-the-scenes role in the Eisenhower and Kennedy administrations’ nuclear-weapons policy) that required a doctorate, so he reluctantly acquiesced. In March of 1957, Everett submitted a substantially trimmed-down version of his original thesis; by April it was accepted by Princeton as fulfilling his remaining requirements, and in July it was published in the Reviews of Modern Physics.1 But with Everett’s approach to quantum theory having already been dismissed by Bohr and his entourage, and with the muting of the grander vision articulated in the original thesis, the paper was ignored.2
Ten years later, the renowned physicist Bryce DeWitt plucked Everett’s work from obscurity. DeWitt, who was inspired by the results of his graduate student Neill Graham that further developed Everett’s mathematics, became a vocal proponent of the Everettian rethinking of quantum theory. Besides publishing a number of technical papers that brought Everett’s insights to a small but influential community of specialists, in 1970 DeWitt wrote a general level summary for Physics Today that reached a much broader scientific audience. And unlike Everett’s 1957 paper, which shied away from talk of other worlds, DeWitt underscored this feature, highlighting it with an unusually candid reflection regarding his “shock” on learning Everett’s conclusion that we are part of an enormous “multiworld.” The article generated a significant response in a physics community that had become more receptive to tampering with orthodox quantum ideology and ignited a debate, still going on, that concerns the nature of reality when, as we believe they do, quantum laws hold sway.