by Brian Greene
When I first learned of the Quilted and Inflationary Multiverses, it was the inflationary variety that struck me as more plausible. Inflationary cosmology resolves a number of long-standing puzzles while yielding predictions that match up well with observations. And by the reasoning we’ve recounted, inflation is naturally a process that never ends; it produces bubble universes upon bubble universes, of which we inhabit but one. The Quilted Multiverse, on the other hand, by having its full force when space is not just large but truly infinite (you might have repetition in a large universe, but you are guaranteed repetition in an infinite one), seemed avoidable: it might be the case, after all, that the universe has finite size. But we now see that eternal inflation’s bubble universes, when properly analyzed from the viewpoint of their inhabitants, are spatially infinite. Inflationary parallel universes beget quilted ones.
The best available cosmological theory for explaining the best available cosmological data leads us to think of ourselves as occupying one of a vast inflationary system of parallel universes, each of which harbors its own vast collection of quilted parallel universes. Cutting-edge research yields a cosmos in which there are not only parallel universes but parallel parallel universes. It suggests that reality is not only expansive but abundantly expansive.
*Equivalently, superfast accelerated expansion means that today’s distant regions would have been much closer together in the early universe than is suggested by the traditional big bang theory—ensuring that a common temperature could be established before the burst separated them.
*You might think that negative pressure would pull inward and thus be at odds with repulsive—outward-pushing—gravity. Actually, uniform pressure, regardless of its sign, doesn’t push or pull at all. Your eardrums pop only when there is nonuniform pressure, lower on one side than the other. The repulsive push I’m describing here is the gravitational force generated by the presence of the uniform negative pressure. This is a difficult but essential point. Again, whereas the presence of positive mass or positive pressure generates attractive gravity, the presence of negative pressure generates the less familiar repulsive gravity.
*The rapid expansion of space is called inflation, but following the historical pattern of invoking names that end in “on” (electron, proton, neutron, muon, etc.), when physicists refer to the field driving inflation, they drop the second “i.” Hence, inflaton field.
*Among those who played a leading role in this work were Viatcheslav Mukhanov, Gennady Chibisov, Stephen Hawking, Alexei Starobinsky, Alan Guth, So-Young Pi, James Bardeen, Paul Steinhardt, and Michael Turner.
*I stress fundamental particles, like electrons and quarks, because for composite particles, like protons and neutrons (each made from 3 quarks), much of the mass arises from interactions between the constituents (the energy carried by gluons of the strong nuclear force, which bind the quarks inside protons and neutrons, contributes most of the mass of these composite particles).
CHAPTER 4
Unifying Nature’s Laws
On the Road to String Theory
From the big bang to inflation, modern cosmology traces its roots to a single scientific nexus: Einstein’s general theory of relativity. With his new theory of gravity, Einstein upended the accepted conception of a rigid and immutable space and time; science now had to embrace a dynamic cosmos. Contributions of this magnitude are rare. Yet, Einstein dreamed of scaling even greater heights. With the mathematical arsenal and geometric intuition he’d amassed by the 1920s, he set out to develop a unified field theory.
By this, Einstein meant a framework that would stitch all of nature’s forces into a single, coherent mathematical tapestry. Rather than have one set of laws for these physical phenomena and a different set for those, Einstein wanted to fuse all the laws into a seamless whole. History has judged Einstein’s decades of intense work toward unification as having had little lasting impact—the dream was noble, the timing was early—but others have taken up the mantle and made substantial strides, the most refined proposal being string theory.
My previous books The Elegant Universe and The Fabric of the Cosmos covered the history and essential features of string theory. In the years since they appeared, the theory’s general health and status have faced a spate of public questioning. Which is completely reasonable. For all its progress, string theory has yet to make definitive predictions whose experimental investigation could prove the theory right or wrong. As the next three multiverse varieties we will encounter (in Chapters 5 and 6) emerge from a string theoretic perspective, it’s important to address the current state of the theory as well as the prospects for making contact with experimental and observational data. Such is the charge of this chapter.
A Brief History of Unification
At the time Einstein pursued the goal of unification, the known forces were gravity, described by his own general relativity, and electromagnetism, described by Maxwell’s equations. Einstein envisioned melding the two into a single mathematical sentence that would articulate the workings of all nature’s forces. Einstein had high hopes for this unified theory. He considered Maxwell’s nineteenth-century work on unification an archetypal contribution to human thought—and rightly so. Before Maxwell, the electricity flowing through a wire, the force generated by a child’s magnet, and the light streaming to earth from the sun were viewed as three separate, unrelated phenomena. Maxwell revealed that, in actuality, they formed an intertwined scientific trinity. Electric currents produce magnetic fields; magnets moving in the vicinity of a wire produce electric currents; and wavelike disturbances rippling through electric and magnetic fields produce light. Einstein anticipated that his own work would carry forward Maxwell’s program of consolidation by making the next and possibly final move toward a fully unified description of nature’s laws—a description that would unite electromagnetism and gravity.
This wasn’t a modest goal, and Einstein didn’t take it lightly. He had an unparalleled capacity for single-minded devotion to problems he’d set for himself, and during the last thirty years of his life the problem of unification became his prime obsession. His personal secretary and gatekeeper, Helen Dukas, was with Einstein at the Princeton Hospital during his penultimate day, April 17, 1955. She recounts how Einstein, bedridden but feeling a little stronger, asked for the pages of equations on which he had been endlessly manipulating mathematical symbols in the fading hope that the unified field theory would materialize. Einstein didn’t rise with the morning sun. His final scribblings shed no further light on unification.1
Few of Einstein’s contemporaries shared his passion for unification. From the mid-1920s through the mid-1960s, physicists, guided by quantum mechanics, were unlocking the secrets of the atom and learning how to harness its hidden powers. The lure of prying apart matter’s constituents was immediate and powerful. While many agreed that unification was a laudable goal, it was of only passing interest in an age when theorists and experimenters were working hand in glove to reveal the laws of the microscopic realm. With Einstein’s passing, work on unification ground to a halt.
His failure was compounded when subsequent research showed that his quest for unity had been too narrowly focused. Not only had Einstein downplayed the role of quantum physics (he believed the unified theory would supersede quantum mechanics and so it needn’t be incorporated from the outset), but his work failed to take account of two additional forces revealed by experiments: the strong nuclear force and the weak nuclear force. The former provides a powerful glue that holds together the nuclei of atoms, while the latter is responsible for, among other things, radioactive decay. Unification would need to combine not two forces but four; Einstein’s dream seemed all the more remote.
During the late 1960s and 1970s, the tide turned. Physicists realized that the methods of quantum field theory, which had been successfully applied to the electromagnetic force, also provided descriptions of the weak and strong nuclear forces. All three of the nongravitational forces could th
us be described using the same mathematical language. Moreover, detailed study of these quantum field theories—most notably in the Nobel Prize–winning work of Sheldon Glashow, Steven Weinberg, and Abdus Salam, as well as in the subsequent insights of Glashow and his Harvard colleague Howard Georgi—revealed relationships suggesting a potential unity among the electromagnetic, weak, and strong nuclear forces. Following Einstein’s nearly half-century-old lead, theoreticians argued that these three apparently distinct forces might actually be manifestations of a single monolithic force of nature.2
These were impressive advances toward unification, but set against the encouraging backdrop was a pesky problem. When scientists applied the methods of quantum field theory to nature’s fourth force, gravity, the math just wouldn’t work. Calculations involving quantum mechanics and Einstein’s general relativistic description of the gravitational field yielded jarring results that amounted to mathematical gibberish. However successful general relativity and quantum mechanics had been in their native domains, the large and the small, the nonsensical output from the attempt to unite them spoke to a deep fissure in the understanding of nature’s laws. If the laws you have prove mutually incompatible, then—clearly—the laws you have are not the right laws. Unification had been an aesthetic goal; now it was transformed into a logical imperative.
The mid-1980s witnessed the next pivotal development. That’s when a new approach, superstring theory, captured the attention of the world’s physicists. It ameliorated the hostility between general relativity and quantum mechanics, and so provided hope that gravity could be brought within a unified quantum mechanical fold. The era of superstring unification was born. Research proceeded at an intense pace, and thousands of journal pages were quickly filled with calculations that fleshed out aspects of the approach and laid the groundwork for its systematic formulation. An impressive and intricate mathematical structure emerged, but much about superstring theory (string theory, for short) remained mysterious.3
Then, beginning in the mid-1990s, theorists intent on unraveling those mysteries unexpectedly thrust string theory squarely into the multiverse narrative. Researchers had long known that the mathematical methods being used to analyze string theory invoked a variety of approximations and so were ripe for refinement. When some of those refinements were developed, researchers realized that the math suggested plainly that our universe might belong to a multiverse. In fact, the mathematics of string theory suggested not just one but a number of different kinds of multiverses of which we might be a part.
To fully grasp these compelling and contentious developments, and to assess their role in our ongoing search for the deep laws of the cosmos, we need to take a step back and first evaluate the state of string theory.
Quantum Fields Redux
Let’s begin by taking a closer look at the traditional, highly successful framework of quantum field theory. This will prepare us to string unification as well as highlight pivotal connections between these two approaches for formulating nature’s laws.
Classical physics, as we saw in Chapter 3, describes a field as a kind of mist that permeates a region of space and can carry disturbances in the form of ripples and waves. Were Maxwell to describe the light that’s now illuminating this text, for example, he’d wax enthusiastic about electromagnetic waves, produced by the sun or by a nearby lightbulb, undulating across space on their way to the printed page. He’d describe the waves’ movement mathematically, using numbers to delineate the field’s strength and direction at each point in space. An undulating field corresponds to undulating numbers: the field’s numerical value at any given location cycles down and up again.
When quantum mechanics is brought to bear on the concept of a field, the result is quantum field theory, which is characterized by two essential new features. We’ve already encountered both, but they’re worth a refresher. First, quantum uncertainty causes the value of a field at each point in space to jitter randomly—think of the fluctuating inflaton field from inflationary cosmology. Second, quantum mechanics establishes that, somewhat as water is composed of H2O molecules, a field is composed of infinitesimally small particles known as the field’s quanta. For the electromagnetic field, the quanta are photons, and so a quantum theorist would modify Maxwell’s classical description of your lightbulb by saying that the bulb emits a steady stream comprising 100 billion billion photons each second.
Decades of research have established that these features of quantum mechanics as applied to fields are completely general. Every field is subject to quantum jitters. And every field is associated with a species of particle. Electrons are quanta of the electron field. Quarks are quanta of the quark field. For a (very) rough mental image, physicists sometimes think of particles as knots or dense nuggets of their associated field. This visualization notwithstanding, the mathematics of quantum field theory describes these particles as dots or points that have no spatial extent and no internal structure.4
Our confidence in quantum field theory comes from one essential fact: there is not a single experimental result that counters its predictions. To the contrary, data confirm that the equations of quantum field theory describe the behavior of particles with astounding accuracy. The most impressive example comes from the quantum field theory of the electromagnetic force, quantum electrodynamics. Using it, physicists have undertaken detailed calculations of the electron’s magnetic properties. The calculations are not easy, and the most refined versions have taken decades to complete. But they’ve been worth the effort. The results match actual measurements to a precision of ten decimal places, an almost unimaginable agreement between theory and experiment.
With such success, you might anticipate that quantum field theory would provide the mathematical framework for understanding all of nature’s forces. An illustrious coterie of physicists shared this very expectation. By the late 1970s, the hard work of many of these visionaries had established that, indeed, the weak and strong nuclear forces fit squarely within the rubric of quantum field theory. Both forces are accurately described in terms of fields—the weak and the strong fields—that evolve and interact according to the mathematical rules of quantum field theory.
But, as I indicated in the historical overview, many of these same physicists quickly realized that the story for nature’s remaining force, gravity, was far subtler. Whenever the equations of general relativity commingled with those of quantum theory, the mathematics balked. Use the combined equations to calculate the quantum probability of some physical process—such as the chance of two electrons ricocheting off each other, given both their electromagnetic repulsion and their gravitational attraction—and you’d typically get the answer infinity. While some things in the universe can be infinite, such as the extent of space and the quantity of matter that may fill it, probabilities are not among them. By definition, the value of a probability must be between 0 and 1 (or, in terms of percentages, between 0 and 100). An infinite probability does not mean that something is very likely to happen, or is certain to happen; rather, it’s meaningless, like speaking of the thirteenth egg in an even dozen. An infinite probability sends a clear mathematical message: the combined equations are nonsense.
Physicists traced the failure to the jitters of quantum uncertainty. Mathematical techniques had been developed for analyzing the jitters of the strong, weak, and electromagnetic fields, but when the same methods were applied to the gravitational field—a field that governs the curvature of spacetime itself—they proved ineffective. This left the mathematics saturated with inconsistencies such as infinite probabilities.
To get a feel for why, imagine you’re the landlord of an old house in San Francisco. If you have tenants who throw raucous parties, it might take effort to deal with the situation, but you don’t worry that the festivities will compromise the building’s structural integrity. However, if there’s an earthquake, you’re facing something far more serious. The fluctuations of the three nongravitational forces—fields that are tenants
within the house of spacetime—are like the building’s incessant partyers. It took a generation of theoretical physicists to grapple with their raucous jitters, but by the 1970s they’d developed mathematical methods capable of describing the quantum properties of the nongravitational forces. The fluctuations of the gravitational field, however, are qualitatively different. They’re more like an earthquake. Because the gravitational field is woven within the very fabric of spacetime, its quantum jitters shake the entire structure through and through. When used to analyze such pervasive quantum jitters, the mathematical methods collapsed.5
For years, physicists turned a blind eye to this problem because it surfaces only under the most extreme conditions. Gravity makes its mark when things are very massive, quantum mechanics when things are very small. And rare is the realm that is both small and massive, so that to describe it you must invoke both quantum mechanics and general relativity. Yet, there are such realms. When gravity and quantum mechanics are together brought to bear on either the big bang or black holes, realms that do involve extremes of enormous mass squeezed to small size, the math falls apart at a critical point in the analyses, leaving us with unanswered questions regarding how the universe began and how, at the crushing center of a black hole, it might end.
Moreover—and this is the truly daunting part—beyond the specific examples of black holes and the big bang, you can calculate how massive and how small a physical system needs to be for both gravity and quantum mechanics to play a significant role. The result is about 1019 times the mass of a single proton, the so-called Planck mass, squeezed into a fantastically small volume of about 10–99 cubic centimeters (roughly a sphere with a radius of 10–33 centimeters, the so-called Planck length graphically illustrated in Figure 4.1).6 The dominion of quantum gravity is thus more than a million billion times beyond the scales we can probe even with the world’s most powerful accelerators. This vast expanse of uncharted territory could easily be rife with new fields and their associated particles—and who knows what else. To unify gravity and quantum mechanics requires trekking from here to there, grasping the known and the unknown across an enormous expanse that, for the most part, is experimentally inaccessible. That’s a hugely ambitious task, and many scientists concluded that it was beyond reach.