The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos - Brian Greene (2011)
Chapter 7. Science and the Multiverse
On Inference, Explanation, and Prediction
When David Gross, co-recipient of the 2004 Nobel Prize in physics, inveighs against string theory’s Landscape Multiverse, there’s a fair chance he’ll quote Winston Churchill’s speech of October 29, 1941: “Never give in.… Never, never, never, never—in nothing, great or small, large or petty—never give in.” When Paul Steinhardt, the Albert Einstein Professor in Science at Princeton University and co-discoverer of the modern form of inflationary cosmology, speaks of his distaste for the Landscape Multiverse, the rhetorical flourishes are more subdued, but you can be pretty sure a comparison to religion, an unfavorable one at that, will at some point appear. Martin Rees, the United Kingdom’s Astronomer Royal, sees the multiverse as the natural next step in our deepening grasp of all there is. Leonard Susskind says those who ignore the possibility that we’re part of a multiverse are merely averting their eyes from a vision they find overwhelming. And these are just a few examples. There are many others on both sides, vehement naysayers and enthusiastic devotees, and they don’t always express their opinions in terms so lofty.
In the quarter century I’ve been working on string theory, I’ve never seen passions run quite so high, or language turn quite so sharp, as in discussions of string theory’s landscape and the multiverse to which it may give rise. And it’s clear why. Many see these developments as a battleground for the very soul of science.
The Soul of Science
While the Landscape Multiverse has been the catalyst, the arguments turn on issues central to any theory in which a multiverse plays a role. Is it scientifically justifiable to speak of a multiverse, an approach that invokes realms inaccessible not just in practice but, in many cases, even in principle? Is the notion of a multiverse testable or falsifiable? Can invoking a multiverse provide explanatory power of which we’d otherwise be deprived?
If the answer to these questions is no, as detractors insist is the case, then multiverse proponents are assuming an unusual stance. Nontestable, nonfalsifiable proposals, invoking hidden realms beyond our capacity to access—these seem a far cry from what most of us would want to call science. And therein lies the spark that makes passions flare. Proponents counter that although the manner in which a given multiverse connects with observation may be different from what we’re used to—it may be more indirect; it may be less explicit; it may require fortune to shine favorably on future experiments—in respectable proposals, such connections are not fundamentally absent. Unapologetically, this line of argument takes an expansive view of what our theories and observations can reveal, and how the insights can be verified.
Where you come down on the multiverse also depends on your view of science’s core mandate. General summaries often emphasize that science is about finding regularities in the workings of the universe, explaining how the regularities both illuminate and reflect underlying laws of nature, and testing the purported laws by making predictions that can be verified or refuted through further experiment and observation. Reasonable though the description may be, it glosses over the fact that the actual process of science is a much messier business, one in which asking the right questions is often as important as finding and testing the proposed answers. And the questions aren’t floating in some preexisting realm in which the role of science is to pick them off, one by one. Instead, today’s questions are very often shaped by yesterday’s insights. Breakthroughs generally answer some questions but then give rise to a host of others that previously could not even be imagined. In judging any development, including multiverse theories, we must take account not only of its capacity for revealing hidden truths but also of its impact on the questions we are led to address. The impact, that is, on the very practice of science. As will become clear, multiverse theories have the capacity to reshape some of the deepest questions scientists have wrestled with for decades. That prospect invigorates some and infuriates others.
Having set the scene, let’s now systematically think through the legitimacy, testability, and utility of frameworks that imagine ours to be one of many universes.
It’s hard to achieve consensus on these issues partly because the multiverse concept isn’t monolithic. We’ve already come upon five versions—Quilted, Inflationary, Brane, Cyclic, and Landscape—and in the chapters that follow we will encounter four more. Understandably, the generic notion of a multiverse has a reputation for lying beyond testability. After all, the typical assessment goes, we’re considering universes other than our own, but since we have access only to this one, we might as well be talking about ghosts or the tooth fairy. Indeed, this is the central problem, with which we’ll shortly grapple, but note first that some multiverses do allow for interactions between member universes. We’ve seen that in the Brane Multiverse untethered string loops can travel from one brane to another. And in the Inflationary Multiverse, bubble universes can find themselves in even more direct contact.
Recall that the space between two bubble universes in the Inflationary Multiverse is permeated by an inflaton field whose energy and negative pressure remain high and which therefore undergoes inflationary expansion. This expansion drives the bubble universes apart. Even so, if the rate at which the bubbles themselves expand exceeds the rate at which the swelling space propels them to separate, the bubbles will collide. Bearing in mind that inflationary expansion is cumulative—the more swelling space there is between two bubbles, the faster they’re driven apart—we come to an interesting realization. If two bubbles form really close together, there will be so little intervening space that their rate of separation will be slower than their rate of expansion. That puts the bubbles on a collision course.
This reasoning is borne out by the mathematics. In the Inflationary Multiverse, universes can collide. Moreover, a number of research groups (including Jaume Garriga, Alan Guth, and Alexander Vilenkin; Ben Freivogel, Matthew Kleban, Alberto Nicolis, and Kris Sigurdson; as well as Anthony Aguirre and Matthew Johnson) have established that whereas some collisions may violently disrupt each bubble universe’s internal structure—not good for possible bubble dwellers like us—gentler brush-ups may also occur, avoiding disastrous consequences yet still yielding observable signatures. The calculations show that if we had such a fender-bender with another universe, the impact would send shock waves rippling through space, generating modifications to the pattern of hot and cold regions in the microwave background radiation.1Researchers are now working out the detailed fingerprint such a disruption would leave, laying the groundwork for observations that could one day provide evidence that our universe has collided with others—evidence that other universes are out there.
But, however exciting the prospect may be, what if no test seeking evidence of an interaction or an encounter with another universe proves successful? Taking a hardheaded perspective, where does the concept of a multiverse stand if we never find any experimental or observational signatures of other universes?
Science and the Inaccessible I:
Can it be scientifically justifiable to invoke unobservable universes?
Every theoretical framework comes with an assumed architecture—the theory’s fundamental ingredients, and the mathematical laws that govern them. Besides defining the theory, this architecture also establishes the kinds of questions we can ask within the theory. Isaac Newton’s architecture was tangible. His mathematics dealt with the positions and velocities of objects we directly encounter or can easily see, from rocks and balls to the moon and sun. A great many observations confirmed Newton’s predictions, giving us confidence that his mathematics did indeed describe how familiar objects move. James Clerk Maxwell’s architecture introduced a significant step of abstraction. Vibrating electric and magnetic fields are not the kinds of things for which our senses have evolved a direct affinity. Although we see “light”—electromagnetic undulations whose wavelengths lie in the range our eyes can detect—our visual experiences don’t directly trace the undulating fields the theory posits. Even so, we can build sophisticated equipment that measures these vibrations and that, together with the theory’s abundance of confirmed predictions, builds an overwhelming case that we’re immersed in a pulsating ocean of electromagnetic fields.
In the twentieth century, fundamental science came to increasingly rely on inaccessible features. Space and time, through their melded union, provide the scaffolding for special relativity. When subsequently endowed with Einsteinian malleability, they become the flexible backdrop of the general theory of relativity. Now, I’ve seen watches tick and I’ve used rulers to measure, yet I’ve never grasped spacetime in the same way I grasp the arms of my chair. I feel the effects of gravity, but if you pressed me on whether I can directly affirm that I’m immersed in curved spacetime, I find myself back in the Maxwellian situation. I’m convinced that the theories of special and general relativity are correct not because I have tangible access to their core ingredients but rather because when I accept their assumed frameworks, the mathematics makes predictions about things I can measure. And the predictions turn out to be extraordinarily accurate.
Quantum mechanics takes such inaccessibility still further. The central ingredient of quantum mechanics is the probability wave, governed by an equation discovered in the mid-1920s by Erwin Schrödinger. Even though such waves are its hallmark feature, we will see in Chapter 8 that the architecture of quantum physics ensures that they’re permanently and completely unobservable. Probability waves give rise to predictions for where this or that particle is likely to be found, but the waves themselves slither outside the arena of everyday reality.2 Nevertheless, because the predictions succeed so well, generations of scientists have accepted such an odd situation: a theory introduces a radically new and vital construct that, according to the theory itself, is unobservable.
The common theme running through these examples is that a theory’s success can be used as an after-the-fact justification for its basic architecture, even when that architecture remains beyond our ability to access directly. This is so thoroughly part of the daily experience of theoretical physicists that the language used and the questions formulated regularly refer, without the slightest hesitation, to things that are at the very least far less accessible than tables and chairs and some of which lie permanently outside the bounds of direct experience.*
When we go further and use a theory’s architecture to learn about the phenomena it entails, yet other kinds of inaccessibility present themselves. Black holes emerge from the mathematics of general relativity, and astronomical observations have provided substantial evidence that they’re not only real but commonplace. Even so, the interior of a black hole is an exotic environment. According to Einstein’s equations, the black hole’s edge, its event horizon, is a surface of no return. You can cross in, but you can’t cross out. We committed exterior dwellers will never observe a black hole’s interior, not just because of practical considerations but as a consequence of the very laws of general relativity. Yet, there’s full consensus that the region on the other side of a black hole’s event horizon is real.
The application of general relativity to cosmology provides even more extreme instances of inaccessibility. If you don’t mind a one-way journey, the interior of a black hole is at least a possible destination. But realms lying beyond our cosmic horizon are unreachable, even if we were able to travel at nearly light speed. In an accelerating universe such as ours, this point becomes forcefully evident. Given the measured value of the cosmological speedup (and assuming it will never change), any object more distant from us than about 20 billion light-years lies permanently outside what we can see, visit, measure, or influence. Farther than that distance, space will always be receding from us so quickly that any attempt to breach the separation would be as fruitless as a kayaker navigating against a current flowing faster than she can paddle.
Objects that have always been beyond our cosmic horizon are objects that we have never observed and never will observe; conversely, they have never observed us, and never will. Objects that at some time in the past were within our cosmic horizon but have been dragged beyond it by spatial expansion are objects that we once could see but never will again. Yet I think we can agree that such objects are as real as anything tangible, and so are the realms they inhabit. It would surely be peculiar to argue that a galaxy that we could once see but that has since slipped over our cosmic horizon has entered a realm that’s nonexistent, a realm that because of its permanent inaccessibility needs to be wiped off reality’s map. Even though we can’t observe or influence such realms, nor they us, they are properly included in our picture of what exists.3
These examples make clear that science is no stranger to theories that include elements, from basic ingredients to derived consequences, that are inaccessible. Our confidence in such intangibles relies on our confidence in the theory. When quantum mechanics invokes probability waves, its impressive ability to describe things we can measure, such as the behavior of atoms and subatomic particles, compels us to embrace the ethereal reality it posits. When general relativity predicts the existence of places we can’t observe, its phenomenal successes in describing those things we can observe, such as the motion of planets and the trajectory of light, compels us to take the predictions seriously.
So for confidence in a theory to grow we don’t require that all of its features be verifiable; a robust and varied assortment of confirmed predictions is enough. Scientific work going back well over a century has accepted that a theory may invoke hidden, inaccessible elements—provided it also makes interesting, novel, and testable predictions about an abundance of observable phenomena.
This suggests that it’s possible to mount a convincing argument for a theory involving a multiverse even if we can’t obtain any direct evidence for universes beyond our own. If the experimental and observational evidence supporting a theory compels you to embrace it, and if the theory is founded on such a tight mathematical structure that there’s no room for cherry-picking among its features, then you have to embrace all of it. And if the theory implies the existence of other universes, then that’s the reality the theory requires you to take on board.
In principle, then—and make no mistake, my point here is one of principle—the mere invocation of inaccessible universes does not consign a proposal to stand outside science. To amplify this, imagine that one day we assemble a convincing experimental and observational case for string theory. Perhaps a future accelerator is able to detect sequences of string vibrational patterns and evidence for extra dimensions, while astronomical observations detect stringy features in the microwave background radiation, as well as the signatures of long stretched strings undulating through space. Suppose further that our understanding of string theory has progressed substantially, and we’ve learned that the theory absolutely, positively, incontrovertibly generates the Landscape Multiverse. Notwithstanding calls to the contrary, a theory with strong experimental and observational support, whose internal structure requires a multiverse, would lead us to conclude inexorably that the time for “giving in” had arrived.*
So to address the question heading this section, in the right scientific context it would not merely be respectable to invoke a multiverse; failing to do so would evidence nonscientific prejudice.
Science and the Inaccessible II:
So much for principle; where do we stand in practice?
The skeptic will rightly respond that it’s one thing to make a point of principle about how the case for a given multiverse theory might be fashioned. It’s another to assess whether any of the multiverse proposals we’ve described qualify as experimentally confirmed theories that come equipped with an absolute prediction of other universes. Do they?
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 requireit, 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 same consideration affects the Inflationary Multiverse, which also emerges from eternal inflation. Astronomical observations over the past decade have bolstered the physics community’s confidence in inflationary cosmology but have nothing to say about whether the inflationary expansion is eternal. Theoretical studies show that although many versions are eternal, yielding bubble universe upon bubble universe, some entail but a single ballooning spatial expanse.
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, it’s unclear which features will continue to play a primary role in future refinements. Will branes, the basis of the Brane and Cyclic Multiverses, remain central? Will the copious choices for the extra dimensions, the basis for the Landscape Multiverse, persist, or will we eventually find a mathematical principle that picks out one particular shape? We just don’t know.
So, although it’s conceivable that we could fashion a convincing argument for a multiverse theory that made little or no reference to its prediction of other universes, for the multiverse scenarios we’ve encountered that approach won’t fly. At least not yet. To assess any of them, we will need to tackle their prediction of a multiverse head-on.
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.
Predictions in a Multiverse I:
If the universes constituting a multiverse are inaccessible, can they nevertheless meaningfully contribute to making predictions?
Some scientists who resist multiverse theories see the enterprise as an admission of failure, a full-fledged retreat from the long-sought goal of understanding why the universe we see has the properties it does. I empathize, being one of many who have worked for decades to realize string theory’s tantalizing promise of calculating every fundamental observable feature of the universe, including the values of nature’s constants. If we accept that we’re part of a multiverse in which some or perhaps even all of the constants vary from one universe to another, then we accept that this goal is misguided. If the fundamental laws allow, say, the strength of the electromagnetic force to have many different values across the multiverse, then the very notion of calculating the strength is meaningless, like asking a pianist to pick out the note.
But here’s the question: Does variation in features mean that we lose all power to predict (or postdict) those intrinsic to our own universe? Not necessarily. Even though a multiverse precludes uniqueness, it’s possible that a degree of predictive capability can be retained. It comes down to statistics.
Consider dogs. They don’t have a unique weight. There are very light dogs, such as Chihuahuas, that can weigh under two pounds; there are very heavy dogs, such as Old English mastiffs, that can tip the scales at over two hundred pounds. Were I to challenge you to predict the weight of the next dog you pass in the street, it might seem that the best you could do would be to pick a random number within the range I’ve given. Yet, with a little information, you can make a more refined guess. If you get ahold of the dog population data in your neighborhood, such as the number of people who have this or that breed, the distribution of weights within each breed, and perhaps even information on the number of times per day different breeds typically need to be taken for a walk, you can figure out the weight of the dog you are most likely to encounter.
This wouldn’t be a sharp prediction; statistical insights often aren’t. But depending on the distribution of dogs, you may be able to do much better than just pulling a number out of a hat. If your neighborhood has a highly skewed distribution, with 80 percent of the dogs being Labrador retrievers whose average weight is sixty pounds, and the other 20 percent composed of a range of breeds from Scottish terriers to poodles whose average weight is thirty pounds, then something in the fifty-five- to sixty-five-pound range would be a good bet. The dog you next encounter may be a fluffy shih tzu, but odds are it won’t be. For distributions that are even more skewed, your predictions can be more precise. If 95 percent of the dogs in your area were sixty-two-pound Labrador retrievers, then you’d be on firmer ground in predicting that the next dog you pass will be one of these.
A similar statistical approach can be applied to a multiverse. Imagine we are investigating a multiverse theory that allows for a wide range of different universes—different values of force strengths, particle properties, cosmological constant values, and so on. Imagine further that the cosmological process by which these universes form (such as the creation of bubble universes in the Landscape Multiverse) is sufficiently well understood that we can determine the distribution of universes, with various properties, across the multiverse. This information has the capacity to yield significant insights.
To illustrate the possibilities, suppose our calculations yield a particularly simple distribution: some physical features vary widely from universe to universe, but others are unchanging. For example, imagine the math reveals that there’s a collection of particles, common to all the universes in the multiverse, whose masses and charges have the same values in each universe. A distribution like this generates absolutely firm predictions. If experiments undertaken in our single lone universe don’t find the predicted collection of particles, we’d rule out the theory, multiverse and all. Knowledge of the distribution thus makes this multiverse proposal falsifiable. Conversely, if our experiments were to find the predicted particles, that would increase our confidence that the theory is right.4
For another example, imagine a multiverse in which the cosmological constant varies across a huge range of values, but it does so in a highly nonuniform manner, as illustrated schematically in Figure 7.1. The graph denotes the fraction of universes within the multiverse (vertical axis) that have a given value of the cosmological constant (horizontal axis). If we were part of such a multiverse, the mystery of the cosmological constant would take on a decidedly different character. Most universes in this scenario have a cosmological constant close to what we’ve measured in our universe, so while the range of possiblevalues would be huge, the skewed distribution implies that the value we’ve observed is nothing special. For such a multiverse, you should be no more mystified by our universe’s having a cosmological constant value 10–123 than you should be surprised by encountering a sixty-two-pound Labrador retriever during your next stroll around the neighborhood. Given the relevant distributions, each is the most likely thing that could happen.
Figure 7.1 A possible distribution of cosmological constant values across a hypothetical multiverse, illustrating that highly skewed distributions can make otherwise puzzling observations understandable.
Here’s a variation on the theme. Imagine that, in a given multiverse proposal, the cosmological constant’s value varies widely, but unlike in the previous example, it varies uniformly; the number of universes that have a given value of the cosmological constant is on a par with the number of universes that have any other value of the cosmological constant. But imagine further that a close mathematical study of the proposed multiverse theory reveals an unexpected feature in the distribution. For those universes in which the cosmological constant is in the range we’ve observed, the math shows there’s always a species of particle whose mass is, say, five thousand times that of the proton—too heavy to have been observed in accelerators built in the twentieth century, but right within the range of those built in the twenty-first. Because of the tight correlation between these two physical features, this multiverse theory is also falsifiable. If we fail to find the predicted heavy species of particle we would disprove this proposed multiverse; discovery of the particle would strengthen our confidence that the proposal is correct.
Let me underscore that these scenarios are hypothetical. I invoke them because they illuminate a possible profile for scientific insight and verification in the context of a multiverse. I suggested earlier that if a multiverse theory gives rise to testable features beyond the prediction of other universes, it’s possible—in principle—to assemble a supporting case even if the other universes are inaccessible. The examples just given make this suggestion explicit. For these kinds of multiverse proposals, the answer to the question heading this section would unequivocally be yes.
The essential feature of such “predictive multiverses” is that they’re not composed from a grab-bag of constituent universes. Instead, the capacity to make predictions emerges from the multiverse evincing an underlying mathematical pattern: physical properties are distributed across the constituent universes in a sharply skewed or highly correlated manner.
How might this happen? And, leaving the realm of “in principle,” does it happen in the multiverse theories we’ve encountered?
Predictions in a Multiverse II:
So much for principle; where do we stand in practice?
The distribution of dogs in a given area depends on a range of influences, among them cultural and financial factors and plain old happenstance. Because of this complexity, if you were intent on making statistical predictions your best bet would be to bypass considerations of how a given dog distribution came to be and simply use the relevant data from the local dog licensing authority. Unfortunately, multiverse scenarios don’t have comparable census bureaus, so the analogous option isn’t available. We’re forced to rely on our theoretical understanding of how a given multiverse might arise to determine the distribution of the universes it would contain.
The Landscape Multiverse, relying on eternal inflation and string theory, provides a good case study. In this scenario, the twin engines driving the production of new universes are inflationary expansion and quantum tunneling. Remember how this goes: An inflating universe, corresponding to one or another valley in the string landscape, quantum-tunnels through one of the surrounding mountains and settles down in another valley. The first universe—with definite features such as force strengths, particle properties, value of the cosmological constant, and so forth—acquires an expanding bubble of the new universe (see Figure 6.7), with a new set of physical features, and the process continues.
Now, being a quantum process, such tunneling events have a probabilistic character. You can’t predict when or where they will happen. But you can predict the probability that a tunneling event will happen in any given interval of time and burrow in any given direction—probabilities that depend on detailed features of the string landscape, such as the altitude of the various mountain peaks and valleys (the value, that is, of their respective cosmological constants). The more probable tunneling events will happen more often, and the resulting distribution of universes will reflect this. The strategy, then, is to use the mathematics of inflationary cosmology and string theory to calculate the distribution of universes, with various physical features, across the Landscape Multiverse.
The rub is that so far no one has been able to do so. Our current understanding suggests a lush string landscape with a gargantuan number of mountains and valleys, which makes it a ferociously difficult mathematical challenge to work out the details of the resulting multiverse. Pioneering work by cosmologists and string theorists have contributed significantly to our understanding, but the investigations are still rudimentary.5
To go further, multiverse proponents advocate introducing one more important element into the mix. Consideration of the selection effects introduced in the previous chapter: anthropic reasoning.
Predictions in a Multiverse III:
Many of the universes in a given multiverse are bound to be lifeless. The reason, as we’ve seen, is that changes to nature’s fundamental parameters from their known values tend to disrupt the conditions favorable for life to emerge.6 Our very existence implies that we could never find ourselves in any of the lifeless domains, and so there’s nothing further to explain about why we don’t see their particular combination of properties. If a given multiverse proposal implied a unique life-supporting universe, we’d be golden. We would work out that special universe’s properties mathematically; if they differed from what we’ve measured in our own universe, we could rule out that multiverse proposal. If the properties agreed with ours, we’d have an impressive vindication of anthropic multiverse theorizing—and reason to vastly expand our picture of reality.
In the more plausible case that there is not a unique life-supporting universe, a number of theorists (they include Steven Weinberg, Andrei Linde, Alex Vilenkin, George Efstathiou, and many others) have advocated an enhanced statistical approach. Rather than calculate the relative preponderance, within the multiverse, of various kinds of universes, they propose that we calculate the number of inhabitants—physicists usually call them observers—who would find themselves in various kinds of universes. In some universes, conditions might barely be compatible with life, so observers would be rare, like the occasional cactus in a harsh desert; other universes, with more hospitable conditions, would teem with observers. The idea is that, just as canine census data let us predict what kinds of dogs we can expect to encounter, so observer census data let us predict the properties that a typical inhabitant living somewhere in the multiverse—you and I, according to the reasoning of this approach—should expect to see.
A concrete example was worked out in 1997 by Weinberg and his collaborators Hugo Martel and Paul Shapiro. For a multiverse in which the cosmological constant varies from universe to universe, they calculated how abundant life would be in each. This difficult task was made feasible by invoking the Weinberg proxy (Chapter 6): instead of life proper, they considered the formation of galaxies. More galaxies means more planetary systems and hence, the underlying assumption goes, a greater likelihood of life, intelligent life in particular. Now, as Weinberg had found in 1987, even a modest cosmological constant generates enough repulsive gravity to disrupt galaxy formation so only domains of the multiverse that have sufficiently small cosmological constants need be considered. A cosmological constant that’s negative results in a universe that collapses well before galaxies form, so these realms of the multiverse can be omitted from the analysis, too. 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
For universes whose cosmological constant is in this range, Weinberg, Martel, and Shapiro then undertook a more refined calculation. They determined the fraction of matter in each such universe that would clump together over the course of cosmological evolution, a pivotal step on the road to galaxy formation. They found that if the cosmological constant is very near the window’s upper limit, relatively few clumps would form, because the outward push of the cosmological constant acts like a strong wind, blowing most dust accumulations apart. If the cosmological constant’s value is near the window’s lower limit, zero, they found that many clumps form, because the disrupting influence of the cosmological constant is minimized. Which means there’s a large chance you’ll be in a universe whose cosmological constant is near zero, since such universes have an abundance of galaxies and, by the reasoning of this approach, life. There’s a small chance you’ll be in a universe whose cosmological constant is near the window’s upper limit, about 10–121, because such universes are endowed with far fewer galaxies. And there’s a modest chance you’ll be in a universe whose cosmological constant lies at a value between these extremes.
Using the quantitative version of these results, Weinberg and his collaborators calculated the cosmic analog of encountering a sixty-two-pound Labrador on an average walk around the neighborhood—the cosmological constant value, that is, witnessed by an average observer in the multiverse. The answer? Somewhat larger than what the subsequent supernova measurements revealed, but definitely in the same ballpark. They found that roughly 1 in 10 to 1 in 20 inhabitants of the multiverse would have an experience comparable to ours, measuring the cosmological constant’s value in their universe to be about 10–123.
While a higher percentage would be more satisfying, the result is impressive, nonetheless. Prior to this calculation, physics faced a mismatch between theory and observation of more than 120 orders of magnitude, suggesting strongly that something was profoundly amiss with our understanding. The multiverse approach of Weinberg and his collaborators, however, showed that finding yourself in a universe whose cosmological constant is on a par with the value we’ve measured is roughly as surprising as running into that shih tzu in a neighborhood dominated by Labs. Which is to say, not that surprising at all. Certainly, when viewed from this multiverse perspective, the observed value of the cosmological constant doesn’t suggest a profound lack of understanding, and that’s an encouraging step forward.
Subsequent analyses, though, emphasized an interesting facet that some interpret as weakening the result. For simplicity’s sake, Weinberg and his collaborators imagined that across their multiverse only the cosmological constant’s value varied from universe to universe; other physical parameters were assumed fixed. Max Tegmark and Martin Rees noted that if both the cosmological constant’s value and, say, the size of the early universe quantum jitters were imagined to vary from universe to universe, the conclusion would change. Recall that the jitters are the primordial seeds of galaxy formation: tiny quantum fluctuations, stretched by inflationary expansion, yield a random assortment of regions where the density of matter is a little higher or a little lower than average. The higher-density regions exert a greater gravitational pull on nearby matter and so grow yet larger, ultimately coalescing into galaxies. Tegmark and Rees pointed out that much as bigger piles of leaves can better withstand a brisk breeze, so larger primordial seeds can better withstand the disruptive outward push of a cosmological constant. A multiverse in which both the seed size and the value of the cosmological constant vary would therefore contain universes where larger cosmological constants were offset by larger seeds; that combination would be compatible with galaxy formation—and hence with life. A multiverse of this sort increases the cosmological constant value that a typical observer would see and so results in a decrease—potentially a sharp one—of the fraction of observers who would find their cosmological constant to have as small a value as we’ve measured.
Staunch multiverse proponents are fond of pointing to the analysis of Weinberg and his collaborators as a success of anthropic reasoning. Detractors are fond of pointing to the issues raised by Tegmark and Rees as making the anthropic result less convincing. In reality, the debate is premature. These are all highly exploratory, first-pass calculations, best viewed as providing insight into the general domain of anthropic reasoning. Under certain restrictive assumptions, they show that the anthropic framework can take us within the ballpark of the measured cosmological constant; relax those assumptions somewhat, and the calculations show that the size of the ballpark grows substantially. Such sensitivity implies that a refined multiverse calculation will require a precise understanding of the detailed properties that characterize the constituent universes, and how they vary, thus replacing arbitrary assumptions with theoretical directives. This is essential if a multiverse is to stand a chance of yielding definitive conclusions.
Researchers are working hard to achieve this goal, but as of today, they have yet to reach it.8
Prediction in a Multiverse IV:
What will it take?
What hurdles, then, will we need to clear before we can extract predictions from a given multiverse? There are three that figure most prominently.
First, as pointedly illustrated by the example just discussed, a multiverse proposal must allow us to determine which physical features vary from universe to universe, and for those features that do vary, we must be able to calculate their statistical distribution across the multiverse. Essential for doing so is an understanding of the cosmological mechanism by which the proposed multiverse is populated by universes (such as the creation of bubble universes in the Landscape Multiverse). It is this mechanism that determines how prevalent one kind of universe is relative to another, and so it is this mechanism that determines the statistical distribution of physical features. If we’re fortunate, the resulting distributions, either across the entire multiverse or across those universes supporting life, will be sufficiently skewed to yield definitive predictions.
A second challenge, if we do need to invoke anthropic reasoning, comes from the central assumption that we humans are garden-variety average. Life might be rare in the multiverse; intelligent life might be rarer still. But among all intelligent beings, the anthropic assumption goes, we are so thoroughly typical that our observations should be the average of what intelligent beings inhabiting the multiverse would see. (Alexander Vilenkin has called this the principle of mediocrity). If we know the distribution of physical features across life-supporting universes, we can calculate such averages. But typicality is a thorny assumption. If future work shows that our observations fall into the range of calculated averages in a particular multiverse, confidence in our typicality—and in the multiverse proposal—would grow. That would be exciting. But if our observations fall outside the averages that could be evidence that the multiverse proposal is wrong, or it could mean that we are just not typical. Even in a neighborhood that has 99 percent Labs, you can still run into Dobermans, an atypical dog. Distinguishing between a failed multiverse proposal and a successful one in which our universe is atypical may prove difficult.9
Progress on this issue will likely require a better understanding of how intelligent life arises in a given multiverse; with that knowledge, we could at least clarify how typical our own evolutionary history has so far been. This, of course, is a major challenge. To date, most anthropic reasoning has completely skirted the issue by invoking Weinberg’s assumption—that the number of intelligent life-forms in a given universe is proportional to the number of galaxies it contains. As far as we know, intelligent life needs a warm planet, which requires a star, which is generally part of a galaxy, and so there’s reason to believe Weinberg’s approach holds water. But since we have only the most rudimentary understanding of even our own genesis, the assumption remains tentative. To refine our calculations, the development of intelligent life needs to be far better understood.
The third hurdle is simple to explain but in the long run may well be the one that’s last standing. It has to do with dividing up infinity.
Dividing Up Infinity
To understand the problem, return to dogs. If you live in a neighborhood populated with three Labs and one dachshund, then, ignoring complications such as how often the dogs are walked, you’re three times more likely to run into a Lab. The same would apply if there were 300 Labs and 100 dachshunds; 3,000 Labs and 1,000 dachshunds; 3 million Labs and 1 million dachshunds, and so on. But what if these numbers were infinitely large? How do you compare an infinity of dachshunds to three times infinity of Labradors? Although this sounds like the tortured math of one-upping seven-year-olds, there’s a real question here. Is three times infinity larger than plain old infinity? If so, is it three times as large?
Comparisons involving infinitely large numbers are notoriously tricky. For dogs on earth, of course, the difficulty doesn’t arise, because the populations are finite. But for universes constituting particular multiverses, the problem can be very real. Take the Inflationary Multiverse. Looking at the entire block of Swiss cheese from an imaginary outsider’s perspective, we would see it continue to grow and produce new universes endlessly. That’s what the “eternal” in “eternal inflation” means. Moreover, taking an insider’s perspective, we’ve seen that each bubble universe itself harbors an infinite number of separate domains, filling out a Quilted Multiverse. In making predictions we necessarily confront an infinity of universes.
To grasp the mathematical challenge, imagine that you’re a contestant on Let’s Make a Deal and you’ve won an unusual prize: an infinite collection of envelopes, the first containing $1, the second $2, the third $3, and so on. As the crowd cheers, Monty chimes in to make you an offer. Either keep your prize as is, or elect to have him double the contents of each envelope. At first it seems obvious that you should take the deal. “Each envelope will contain more money than it previously did,” you think, “so this has to be the right move.” And if you had only a finite number of envelopes, it would be the right move. To exchange five envelopes containing $1, $2, $3, $4, and $5 for envelopes with $2, $4, $6, $8, and $10 makes unassailable sense. But after another moment’s thought, you start to waver, because you realize that the infinite case is less clear-cut. “If I take the deal,” you think, “I’ll wind up with envelopes containing $2, $4, $6, and so on, running through all the even numbers. But as things currently stand, my envelopes run through all whole numbers, the evens as well as the odds. So it seems that by taking the deal I’ll be removing the odd dollar amounts from my total tally. That doesn’t sound like a smart thing to do.” Your head starts to spin. Compared envelope by envelope, the deal looks good. Compared collection to collection, the deal looks bad.
Your dilemma illustrates the kind of mathematical pitfall that makes it so hard to compare infinite collections. The crowd is growing antsy, you have to make a decision, but your assessment of the deal depends on the way you compare the two outcomes.
A similar ambiguity afflicts comparisons of a yet more basic characteristic of such collections: the number of members each contains. The Let’s Make a Deal example illustrates this, too. Which are more plentiful, whole numbers or even numbers? Most people would say whole numbers, since only half of the whole numbers are even. But your experience with Monty gives you sharper insight. Imagine that you take Monty’s deal and wind up with all even dollar amounts. In doing so, you wouldn’t return any envelopes nor would you require any new ones, since Monty would simply double the amount of money in each. You conclude, therefore, that the number of envelopes required to accommodate all whole numbers is the same as the number of envelopes required to accommodate all even numbers—which suggests that the populations of each category are equal (Table 7.1). And that’s weird. By one method of comparison—considering the even numbers as a subset of the whole numbers—you conclude that there are more whole numbers. By a different method of comparison—considering how many envelopes are needed to contain the members of each group—you conclude that the set of whole numbers and the set of even numbers have equal populations.
Table 7.1 Every whole number is paired with an even number, and vice versa, suggesting that the quantity of each is the same.
You can even convince yourself that there are more even numbers than there are whole numbers. Imagine that Monty offered to quadruple the money in each of the envelopes you initially had, so there would be $4 in the first, $8 in the second, $12 in the third, and so on. Since, again, the number of envelopes involved in the deal stays the same, this suggests that the quantity of whole numbers, where the deal began, is equal to that of numbers divisible by four (Table 7.2), where the deal wound up. But such a pairing, marrying off each whole number to a number that’s divisible by 4, leaves an infinite set of even bachelors—the numbers 2, 6, 10, and so on—and thus seems to imply that the evens are more plentiful than the wholes.
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 value 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.