The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos - Brian Greene (2011)

Chapter 11. The Limits of Inquiry

Multiverses and the Future

Isaac Newton cracked the scientific enterprise wide open. He discovered that a few mathematical equations could describe the way things move, both here on earth and up in space. Considering the power and simplicity of his results, one could easily have imagined that Newton’s equations reflected eternal truths etched into the bedrock of the cosmos. But Newton himself didn’t think so. He believed that the universe was far more rich and mysterious than his laws implied; later in life he famously reflected, “I do not know what I may appear to the world, but to myself I seem to have only been a boy playing on the seashore, diverting myself in now and then finding a smoother pebble or prettier shell than ordinary, whilst the great ocean of truth lay before me all undiscovered.” The centuries since have abundantly affirmed this.

I’m glad. Had Newton’s equations enjoyed unlimited reach, accurately describing phenomena in any context however big or small, heavy or light, fast or slow, the subsequent scientific odyssey would have taken on a distinctly different character. Newton’s equations teach us much about the world, but their unlimited validity would have meant that the cosmic flavor was vanilla through and through. Once you understood physics on everyday scales, you’d be done. The same story would have held all the way up and all the way down.

In continuing Newton’s explorations, scientists have ventured into realms far beyond the reach of his equations. What we’ve learned has required sweeping changes in our understanding of the nature of reality. Such changes are not made lightly. They are closely examined by the community of scientists, and they are often sharply resisted; only when the evidence reaches a critical abundance is the new view embraced. Which is just as it should be. There’s no need to rush to judgment. Reality will wait.

The central fact, most forcefully emphasized by the last hundred years of theoretical and experimental progress, is that common experience fails to be a trustworthy guide for excursions that wander beyond everyday circumstances. But for all the radically new physics encountered in extreme conditions—described by general relativity, quantum mechanics, and, should it prove correct, string theory—the fact that radically new ideas would be required is not surprising. The basic assumption of science is that regularities and patterns exist on all scales, but as Newton himself anticipated, there’s no reason to expect the patterns we directly encounter to be recapitulated on all scales.

The surprise would have been to find no surprises.

The same is undoubtedly true regarding what physics will reveal in the future. A given generation of scientists can never know whether the long view of history will judge their work as a diversion, as passing fascination, as a stepping-stone, or as having revealed insights that will stand the test of time. Such local uncertainty is balanced by one of physics’ most gratifying features—global stability—that is, new theories generally do not erase those they supplant. As we’ve discussed, while new theories may require acclimation to new perspectives on the nature of reality, they almost never render past discoveries irrelevant. Instead, they incorporate and extend them. Because of this, the story of physics has maintained an impressive coherence.

In this book we’ve explored a candidate for the next major development in this story: the possibility that our universe is part of a multiverse. The journey has taken us through nine variations on the multiverse theme, which are summarized in Table 11.1. Although the various proposals differ widely in detail, they all suggest that our commonsense picture of reality is only part of a grander whole. And they all bear the indelible mark of human ingenuity and creativity. But determining whether any of these ideas goes beyond mathematical musings of the human mind will require more insight, knowledge, calculation, experiment, and observation than we’ve so far achieved. A final reckoning on whether parallel universes will be written into the next chapter of physics’ story must therefore also await the perspective that only the future can bring.

Table 11.1 Summary of Various Versions of Parallel Universes

PARALLEL UNIVERSE PROPOSAL: Quilted Multiverse

DESCRIPTION: Conditions in an infinite universe necessarily repeat across space, yielding parallel worlds.

PARALLEL UNIVERSE PROPOSAL: Inflationary Multiverse

EXPLANATION: Eternal cosmological inflation yields an enormous network of bubble universes, of which our universe would be one.

PARALLEL UNIVERSE PROPOSAL: Brane Multiverse

EXPLANATION: In string/M-theory’s braneworld scenario, our universe exists on one three-dimensional brane, which floats in a higher-dimensional expanse potentially populated by other branes—other parallel universes.

PARALLEL UNIVERSE PROPOSAL: Cyclic Multiverse

EXPLANATION: Collisions between braneworlds can manifest as big bang-like beginnings, yielding universes that are parallel in time.

PARALLEL UNIVERSE PROPOSAL: Landscape Multiverse

EXPLANATION: By combing inflationary cosmology and string theory, the many different shapes for string theory’s extra dimensions give rise to many different bubble universes.

PARALLEL UNIVERSE PROPOSAL: Quantum Multiverse

EXPLANATION: Quantum mechanics suggests that every possibility embodied in its probability waves is realized in one of a vast ensemble of parallel universes.

PARALLEL UNIVERSE PROPOSAL: Holographic Multiverse

EXPLANATION: The holographic principle asserts that our universe is exactly mirrored by phenomena taking place on a distant bounding surface, a physically equivalent parallel universe.

PARALLEL UNIVERSE PROPOSAL: Simulated Multiverse

EXPLANATION: Technological leaps suggest that simulated universes may one day be possible.

PARALLEL UNIVERSE PROPOSAL: Ultimate Multiverse

EXPLANATION: The principle of fecundity asserts that every possible universe is a real universe, thereby obviating the question of why one possibility—ours—is special. These universes instantiate all possible mathematical equations.

As with the metaphorical book of nature, so with the book you’re reading. In this last chapter, I’d be delighted to pull all the pieces together and answer the subject’s most essential question: Universe or multiverse? But I can’t. That’s the nature of explorations that brush the edge of knowledge. Instead, to catch a glimpse of where the multiverse concept might be headed, as well as to emphasize the essential highlights of where it now stands, here are five central questions with which physicists will continue to grapple in the years ahead.

Is the Copernican Pattern Fundamental?

Regularities and patterns, evident in observations and in mathematics, are essential to formulating physical laws. Patterns of a different sort, in the nature of the physical laws accepted by each successive generation, are also revealing. Such patterns reflect how scientific discovery has shifted humankind’s perspective on its place in the cosmic order. Over the course of nearly five centuries, the Copernican progression has been a dominant theme. From the rising and setting of the sun to the motion of constellations across the night sky to the leading role we each play in our mind’s inner world, experience abounds with clues suggesting that we’re a central hub around which the cosmos revolves. But the objective methods of scientific discovery have steadily corrected this perspective. At nearly every turn, we’ve found that were we not here, the cosmic order would hardly differ. We’ve had to give up our belief in earth’s centrality among our cosmic neighbors, the sun’s centrality in the galaxy, the Milky Way’s centrality among the galaxies, and even the centrality of protons, neutrons, and electrons—the stuff of which we’re made—in the cosmic recipe. There was a time when evidence contrary to long-held collective delusions of grandeur was viewed as a frontal assault on human worth. With practice, we’ve gotten better at valuing enlightenment.

The trek in this book has been toward what may be the capstone Copernican correction. Our universe itself may not be central to any cosmic order. Much as with our planet, star, and galaxy, our universe may merely be one among a great many. The idea that reality based on a multiverse extends the Copernican pattern and perhaps completes it is cause for curiosity. But what elevates the multiverse concept above idle speculation is a key fact that we’ve now repeatedly encountered. Scientists have not been on a hunt for ways to extend the Copernican revolution. They’ve not been plotting in darkened laboratories for ways to complete the Copernican pattern. Instead, scientists have been doing what they always do: using data and observations as a guide, they’ve been formulating mathematical theories to describe the fundamental constituents of matter and the forces that govern how those constituents behave, interact, and evolve. Remarkably, when diligently following the trail these theories blaze, scientists have run smack into one potential multiverse after another. Take a trip along a great many of the most traveled scientific highways, stay moderately attentive, and you’ll encounter a diverse assortment of multiverse candidates. They’re harder to avoid than they are to find.

Perhaps future discoveries will cast a different light on the series of Copernican corrections. But from our current vantage point, the more we understand, the less central we appear. Should the scientific considerations we’ve discussed in earlier chapters continue to push us toward multiverse-based explanations, it would be the natural step toward completing the Copernican revolution, five hundred years in the making.

Can Scientific Theories that Invoke a Multiverse Be Tested?

Although the multiverse concept fits snugly within the Copernican template, it differs qualitatively from our earlier migrations from center stage. By invoking realms that may be forever beyond our ability to examine—either with any degree of precision or, in some cases, even at all—multiverses seemingly erect substantial barriers to scientific knowledge. Regardless of one’s view of humanity’s place in the cosmic arrangement, a widely held assumption has been that through conscientious experimentation, observation, and mathematical calculation, the capacity for gaining deeper understanding is boundless. But if we’re part of a multiverse, a reasonable expectation is that at best we can learn about our universe, our little corner of the cosmos. More distressing is the worry that by invoking a multiverse, we enter the domain of theories that can’t be tested—theories that rely on “just so” stories, relegating everything we observe to “the way things just happen to be here.”

As I’ve argued, however, the multiverse concept is more nuanced. We’ve seen various ways in which a theory that involves a multiverse might offer testable predictions. For instance, while the particular universes constituting a given multiverse may differ considerably, because they emerge from a common theory there may be features they all share. Failure to find those features, through measurements we undertake here in the one universe to which we have access, would prove that multiverse proposal wrong. Confirmation of those features, especially if they’re novel, would build confidence that the proposal was right.

Or, if there aren’t features common to all universes, correlations between physical features can provide another class of testable predictions. For example, we’ve seen that if all universes whose particle roster includes an electron also include an as-yet-undetected particle species, failure to find the particle through experiments undertaken here in our universe would rule out the multiverse proposal. Confirmation would build confidence. More complicated correlations—such as, those universes whose particle roster includes, say, all the known particles (electrons, muons, up-quarks, down-quarks, etc.) necessarily contain a new particle species—would similarly yield testable, falsifiable predictions.

In the absence of such tight correlations, the manner in which physical features vary from universe to universe can also provide predictions. Across a given multiverse, for example, the cosmological constant might take on a wide range of values. But if the vast majority of universes have a cosmological constant whose value agrees with what measurements have found here (as illustrated in Figure 7.1), confidence in that multiverse would deservedly grow.

Finally, even if most universes in a given multiverse have properties that differ from ours, there’s one more diagnostic we can bring into play. We can invoke anthropic reasoning by considering only those universes in the multiverse hospitable to our form of life. If the vast majority of this subclass of universes has properties that agree with ours—if our universe is typical among those in which the conditions allow us to live—confidence in the multiverse would build. If we’re atypical, we can’t rule the theory out, but that’s a familiar limitation of statistical reasoning. Unlikely outcomes can and sometimes do happen. Even so, the less typical we are, the less compelling the given multiverse proposal would be. If among all life-supporting universes in a given multiverse our universe would stick out like a sore thumb, that would provide a strong argument to deem that multiverse proposal irrelevant.

To probe a multiverse proposal quantitatively, therefore, we must determine the demographics of the universes that populate it. It’s not enough to know the possible universes the multiverse proposal allows; we must determine the detailed features of the actual universes to which the proposal gives rise. This requires understanding the cosmological processes that bring the various universes of a given multiverse proposal into existence. Testable predictions can then emerge from the way physical features vary from universe to universe across the multiverse.

Whether this sequence of evaluations yields sharp results is something that can only be assessed multiverse by multiverse. But the conclusion is that theories that involve other universes—realms we can’t access now or perhaps ever—can still provide testable, and hence falsifiable, predictions.

Can We Test the Multiverse Theories We’ve Encountered?

In the course of theoretical research, physical intuition is vital. Theorists need to navigate a bewildering array of possibilities. Should I try this equation or that, invoke that pattern or this? The best physicists have sharp and wonderfully accurate hunches or gut feelings about which directions are promising and which are likely to be fruitless. But that happens behind the scenes. When scientific proposals are brought forward, they are not judged by hunches or gut feelings. Only one standard is relevant: a proposal’s ability to explain or predict experimental data and astronomical observations.

Therein lies the singular beauty of science. As we struggle toward deeper understanding, we must give our creative imagination ample room to explore. We must be willing to step outside conventional ideas and established frameworks. But unlike the wealth of other human activities through which the creative impulse is channeled, science supplies a final reckoning, a built-in assessment of what’s right and what’s not.

A complication of scientific life in the late twentieth and early twenty-first centuries is that some of our theoretical ideas have soared past our ability to test or observe. String theory has for some time been the poster child for this situation; the possibility that we’re part of a multiverse provides an even more sprawling example. I’ve laid out a general prescription for how a multiverse proposal might be testable, but at our current level of understanding none of the multiverse theories we’ve encountered yet meet the criteria. With ongoing research, this situation could greatly improve.

Our investigations of the Landscape Multiverse, for example, are in their earliest stages. The collection of possible string theory universes—the string landscape—is schematically illustrated in Figure 6.4, but detailed maps of this mountainous terrain have yet to be drawn. Like ancient seafarers, we have a rough sense of what’s out there, but it will require extensive mathematical explorations to map the lay of the land. With such knowledge in hand, the next step will be to determine how these potential universes are distributed across the corresponding Landscape Multiverse. The essential physical process, the creation of bubble universes through quantum tunneling (illustrated in Figure 6.6 and Figure 6.7), is well understood in principle but has yet to be examined with quantitative depth in string theory. Various research groups (including my own) have undertaken initial reconnaissance, but there is vast terrain yet to scout. As we’ve seen in earlier chapters, a variety of similar uncertainties afflict the other multiverse proposals too.

No one knows whether it will take years, decades, or even longer for observational and theoretical progress to extract detailed predictions from any given multiverse. Should the current situation persist, we’ll face a choice. Do we define science—“respectable science”—as including only those ideas, realms, and possibilities that fall within the capacity of contemporary human beings on Planet Earth to test or observe? Or do we take a more expansive view and consider as “scientific” ideas that might be testable with technological advances we can imagine achieving in the next hundred years? The next two hundred years? Longer? Or do we take a still more expansive view? Do we allow science to follow any and all paths it reveals, to travel in directions that radiate from experimentally confirmed concepts but that may lead our theorizing into hidden realms that lie, perhaps permanently, beyond human reach?

There’s no clear-cut answer. It is here that personal scientific taste comes to the fore. I understand well the impulse to tether scientific investigations to those propositions that can be tested now, or in the near future; this is, after all, how we built the scientific edifice. But I find it parochial to bound our thinking by the arbitrary limits imposed by where we are, when we are, and who we are. Reality transcends these limits, so it’s to be expected that sooner or later the search for deep truths will too.

My taste is for the expansive. But I draw the line at ideas that have no possibility of being confronted meaningfully by experiment or observation, not because of human frailty or technological hurdles, but because of the proposals’ inherent nature. Of the multiverses we’ve considered, only the full-blown version of the Ultimate Multiverse falls into this netherland. If absolutely every possible universe is included, then no matter what we measure or observe, the Ultimate Multiverse will nod and embrace our result. The other eight multiverses, as summarized in Table 11.1, aviod this pitfall. Each emerges from a well-motivated, logical chain of reasoning, and each is open to judgment. Should observations provide convincing evidence that the spatial expanse is finite, the Quilted Multiverse would drop from consideration. Should confidence in inflationary cosmology erode, perhaps because more precise cosmic microwave background data can be explained only by assuming contorted (and hence unconvincing) inflaton potential energy curves, the prominence of the Inflationary Multiverse would diminish too.* Should string theory suffer a theoretical setback, perhaps through the discovery of a subtle mathematical flaw showing that the theory is inconsistent (as early researchers initially thought was the case), the motivation for its various multiverses would evaporate. Conversely, observations of patterns in the microwave background radiation expected from bubble collisions could provide direct supporting evidence for the Inflationary Multiverse. Accelerator experiments searching for supersymmetric particles, missing energy signatures, and mini black holes could bolster the case for string theory and the Brane Multiverse, while evidence for bubble collisions could also provide support for the Landscape variety. Detection of gravitational wave imprints from the early universe, or lack thereof, could distinguish between cosmology based on the inflationary paradigm and that of the Cyclic Multiverse.

Quantum mechanics, in its Many Worlds guise, gives rise to the Quantum Multiverse. Should future research show that the equations of quantum mechanics, however reliable they’ve been so far, require small modifications to match more refined data, this type of multiverse could be ruled out. A modification of quantum theory that compromises the property of linearity (on which we relied extensively in Chapter 8) would do just that. We’ve noted as well that there are in-principle tests of the Quantum Multiverse, experiments whose results depend on whether or not Everett’s Many Worlds picture is correct. The experiments are beyond what we can carry out now and perhaps always, but that’s because they’re fantastically difficult, not because some inherent feature of the Quantum Multiverse itself renders them fundamentally undoable.

The Holographic Multiverse emerges from considerations of established theories—general relativity and quantum mechanics—and receives its strongest theoretical support from string theory. Calculations based on holography are already making tentative contact with experimental results at the Relativistic Heavy Ion Collider, and all indications are that such experimental links will grow more robust in the future. Whether one views the Holographic Multiverse merely as a useful mathematical device or as evidence for holographic reality is a matter of opinion. We must await future work, theoretical and experimental, in order to build a stronger case for the physical interpretation.

The Simulated Multiverse rests not on any one theoretical structure but rather on the relentless rise of computational power. The linchpin assumption is that sentience is not fundamentally tied to a particular substrate—the brain—but is an emergent characteristic of a certain variety of information processing. It’s a highly debatable proposition, with passionate arguments advanced on both sides. Maybe future research on the brain and on the nature of consciousness will undermine the idea of self-aware thinking machines. And maybe not. One means for judging this multiverse proposal, though, is clear. Should our descendants one day observe, or interact with, or virtually visit, or become part of a convincing simulated world, the issue would for all practical purposes be settled.

The Simulated Multiverse, at least in theory, might also be linked to a pared-down version of the Ultimate Multiverse that includes only universes based on computable mathematical structures. Unlike the full-blown version of the Ultimate Multiverse, this more limited incarnation has a genesis story that lifts it beyond mere assertion. The users, real and simulated, who are behind the Simulated Multiverse will, by definition, be simulating computable mathematical structures and thus will have the capacity to generate this part of the Ultimate Multiverse.

Gaining experimental or observational insight into the validity of any of the multiverse proposals is surely a long shot. But it’s not an impossibility. And with the immensity of the potential payoff, if the exploration of multiverses is where the natural course of theoretical research takes us, we must follow the trail to see where it leads.

How Does a Multiverse Affect the Nature of Scientific Explanation?

Sometimes science focuses on details. It tells us why planets travel in elliptical orbits, why the sky is blue, why water is transparent, why my desk is solid. However familiar these facts may be, it is wondrous that we’ve been able to explain them. Sometimes science takes a larger view. It reveals that we live within a galaxy containing a few hundred billion stars, it establishes that ours is but one of hundreds of billions of galaxies, and it provides evidence for unseen dark energy permeating every nook and cranny of this vast arena. Looking back just a hundred years, to a time when the universe was thought to be static and populated solely by the Milky Way galaxy, we can rightly celebrate the magnificent picture science has since painted.

Sometimes science does something else. Sometimes it challenges us to reexamine our views of science itself. The usual centuries-old scientific framework envisions that when describing a physical system, a physicist needs to specify three things. We’ve seen all three in various contexts, but it’s useful to gather them together here. First are the mathematical equations describing the relevant physical laws (for example, these might be Newton’s laws of motion, Maxwell’s equations of electricity and magnetism, or Schrödinger’s equation of quantum mechanics). Second are the numerical values of all constants of nature that appear in the mathematical equations (for example, the constants determining the intrinsic strength of gravity and the electromagnetic forces or those determining the masses of the fundamental particles). Third, the physicist must specify the system’s “initial conditions” (such as a baseball being hit from home plate at a particular speed in a particular direction, or an electron starting out with a 50 percent probability of being found at Grant’s Tomb and an equal probability of being found at Strawberry Fields). The equations then determine what things will be like at any subsequent time. Both classical and quantum physics subscribe to this framework; they differ only in that classical physics purports to tell us how things will definitely be at a given moment, while quantum physics provides the probability that things will be one way or another.

When it comes to predicting where a batted ball will land, or how an electron will move through a computer chip (or a model Manhattan), this three-step process is demonstrably powerful. Yet, when it comes to describing the totality of reality, the three steps invite us to ask deeper questions: Can we explain the initial conditions—how things were at some purportedly earliest moment? Can we explain the values of the constants—the particle masses, force strengths, and so on—on which those laws depend? Can we explain why a particular set of mathematical equations describes one or another aspect of the physical universe?

The various multiverse proposals we’ve discussed have the potential to profoundly shift our thinking on these questions. In the Quilted Multiverse, the physical laws across the constituent universes are the same, but the particle arrangements differ; different particle arrangements now reflect different initial conditions in the past. In this multiverse, therefore, our perspective on the question of why the initial conditions in our universe were one way or another shifts. Initial conditions can and generally will vary from universe to universe, so there is no fundamental explanation for any particular arrangement. Asking for such an explanation is asking the wrong kind of question; it’s invoking single-universe mentality in a multiverse setting. Instead, the question we should ask is whether somewhere in the multiverse is a universe whose particle arrangement, and hence initial conditions, agrees with what we see here. Better still, can we show that such universes abound? If so, the deep question of initial conditions would be explained with a shrug of the shoulders; in such a multiverse, the initial conditions of our universe would be in no more need of an explanation than the fact that somewhere in New York is a shoe store that carries your size.

In the inflationary multiverse, the “constants” of nature can and generally will vary from bubble universe to bubble universe. Recall from Chapter 3 that environmental differences—the different Higgs field values permeating each bubble—give rise to different particle masses and force properties. The same holds true in the Brane Multiverse, the Cyclic Multiverse, and the Landscape Multiverse, where the form of string theory’s extra dimensions, together with various differences in fields and fluxes, result in universes with different features—from the electron’s mass to whether there even is an electron to the strength of electromagnetism to whether there is an electromagnetic force to the value of the cosmological constant, and so on. In the context of these multiverses, asking for an explanation of the particle and force properties we measure is once again asking the wrong kind of question; it’s a question borne of single-universe thinking. Instead, we should ask whether in any of these multiverses there’s a universe with the physical properties we measure. Better would be to show that universes with our physical features are abundant, or at least are abundant among all those universes that support life as we know it. But as much as it’s meaningless to ask for the word with which Shakespeare wrote Macbeth, so it’s meaningless to ask the equations to pick out the values of the particular physical features we see here.

The Simulated and Ultimate Multiverses are horses of a different color; they don’t emerge from particular physical theories. Yet, they too have the potential to shift the nature of our questions. In these multiverses, the mathematical laws governing the individual universes vary. Thus, much as with varying initial conditions and constants of nature, varying laws suggest that it’s as misguided to ask for an explanation of the particular laws in operation here. Different universes have different laws; we experience the ones we do because these are among the laws compatible with our existence.

Collectively, we see that the multiverse proposals summarized in Table 11.1 render prosaic three primary aspects of the standard scientific framework that in a single-universe setting are deeply mysterious. In various multiverses, the initial conditions, the constants of nature, and even the mathematical laws are no longer in need of explanation.

Should We Believe Mathematics?

Nobel laureate Steven Weinberg once wrote, “Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world.”1 Weinberg was referring to the pioneering results of Ralph Alpher, Robert Herman, and George Gamow on the cosmic microwave background radiation, which I described in Chapter 3. Although the predicted radiation is a direct consequence of general relativity combined with basic cosmological physics, it rose to prominence only after being discovered theoretically twice, a dozen years apart, and then being observed through a benevolent act of serendipity.

To be sure, Weinberg’s remark has to be applied with care. Although his desk has played host to an inordinate amount of mathematics that has proved relevant to the real world, far from every equation with which we theorists tinker rises to that level. In the absence of compelling experimental or observational results, deciding which mathematics should be taken seriously is as much art as it is science.

Indeed, this issue is central to all we’ve discussed in this book; it has also informed the book’s title. The breadth of multiverse proposals in Table 11.1 might suggest a panorama of hidden realities. But I’ve titled this book in the singular to reflect the unique and uniquely powerful theme that underlies them all: the capacity of mathematics to reveal secreted truths about the workings of the world. Centuries of discovery have made this abundantly evident; monumental upheavals in physics have emerged time and again from vigorously following mathematics’ lead. Einstein’s own complex dance with mathematics provides a revealing case study.

In the late 1800s when James Clerk Maxwell realized that light was an electromagnetic wave, his equations showed that light’s speed should be about 300,000 kilometers per second—close to the value experimenters had measured. A nagging loose end was that his equations left unanswered the question: 300,000 kilometers per second relative to what? Scientists pursued the makeshift resolution that an invisible substance permeating space, the “aether,” provided the unseen standard of rest. But in the early twentieth century, Einstein argued that scientists needed to take Maxwell’s equations more seriously. If Maxwell’s equations didn’t refer to a standard of rest, then there was no need for a standard of rest; light’s speed, Einstein forcefully declared, is 300,000 kilometers per second relative to anything. Although the details are of historical interest, I’m describing this episode for the larger point: everyone had access to Maxwell’s mathematics, but it took the genius of Einstein to embrace the mathematics fully. And with that move, Einstein broke through to the special theory of relativity, overturning centuries of thought regarding space, time, matter, and energy.

During the next decade, in the course of developing the general theory of relativity, Einstein became intimately familiar with vast areas of mathematics that most physicists of his day knew little or nothing about. As he groped toward general relativity’s final equations, Einstein displayed a master’s skill in molding these mathematical constructs with the firm hand of physical intuition. A few years later, when he received the good news that observations of the 1919 solar eclipse confirmed general relativity’s prediction that star light should travel along curved trajectories, Einstein confidently noted that had the results been different, “he would have been sorry for the dear Lord, since the theory is correct.” I’m sure that convincing data contravening general relativity would have changed Einstein’s tune, but the remark captures well how a set of mathematical equations, through their sleek internal logic, their intrinsic beauty, and their potential for wide-ranging applicability, can seemingly radiate reality.

Nevertheless, there was a limit to how far Einstein was willing to follow his own mathematics. Einstein did not take the general theory of relativity “seriously enough” to believe its prediction of black holes, or its prediction that the universe was expanding. As we’ve seen, others, including Friedmann, Lemaître, and Schwarzschild, embraced Einstein’s equations more fully than he, and their achievements have set the course of cosmological understanding for nearly a century. By contrast, during the last twenty or so years of his life, Einstein threw himself into mathematical investigations, passionately striving for the prized achievement of a unified theory of physics. In assessing this work based on what we know now, one can’t help but conclude that during those years Einstein was too heavily guided—some might say blinded—by the thicket of equations with which he was constantly surrounded. And so, even Einstein, at various times in his life, made the wrong decision regarding which equations to take seriously and which to not.

The third revolution in modern theoretical physics, quantum mechanics, provides another case study, one of direct relevance to the story I’ve told in this book. Schrödinger wrote down his equation for how quantum waves evolve in 1926. For decades, the equation was viewed as relevant only to the domain of small things: molecules, atoms, and particles. But in 1957, Hugh Everett echoed Einstein’s Maxwellian charge of a half century earlier: take the math seriously. Everett argued that Schrödinger’s equation should apply to everything because all things material, regardless of size, are made from molecules, atoms, and subatomic particles. And as we’ve seen, this led Everett to the Many Worlds approach to quantum mechanics and to the Quantum Multiverse. More than fifty years later, we still don’t know if Everett’s approach is right. But by taking the mathematics underlying quantum theory seriously—fully seriously—he may have discovered one of the most profound revelations of scientific exploration.

The other multiverse proposals similarly rely on a belief that mathematics is tightly stitched into the fabric of reality. The Ultimate Multiverse takes this perspective to its furthermost incarnation; mathematics, according to the Ultimate Multiverse, is reality. But even with their less panoptic view on the connection between mathematics and reality, the other multiverse theories in Table 11.1 owe their genesis to numbers and equations played with by theorists sitting at desks—and scribbling in notebooks, and writing on chalkboards, and programming computers. Whether invoking general relativity, quantum mechanics, string theory, or mathematical insight more broadly, the entries in Table 11.1 arise only because we assume that mathematical theorizing can guide us toward hidden truths. Only time will tell if this assumption takes the underlying mathematical theories too seriously, or perhaps not seriously enough.

If some or all of the mathematics that’s compelled us to think about parallel worlds proves relevant to reality, Einstein’s famous query, asking whether the universe has the properties it does simply because no other universe is possible, would have a definitive answer: no. Our universe is not the only one possible. Its properties could have been different. And in many of the multiverse proposals, the properties of the other member universes would be different. In turn, seeking a fundamental explanation for why certain things are the way they are would be pointless. Instead, statistical likelihood or plain happenstance would be firmly inserted in our understanding of a cosmos that would be profoundly vast.

I don’t know if this is how things will turn out. No one does. But it’s only through fearless engagement that we can learn our own limits. It’s only through the rational pursuit of theories, even those that whisk us into strange and unfamiliar domains, that we stand a chance of revealing the expanse of reality.

*Note, as in Chapter 7, that an airtight observational refutation of inflation would require the theory’s commitment to a procedure for comparing infinite classes of universes—something it has not yet achieved. However, most practitioners would agree that if, say, the microwave background data had looked different from Figure 3.4, their confidence in inflation would have plummeted, even though, according to the theory, there’s a bubble universe in the Inflationary Multiverse in which those data would hold.