Stringing Together a Theory
of Everything
“There is no such thing as perfection. The world itself
is imperfect. That’s what makes it so beautiful.”
—Colonel Roy Mustang, FULLMETAL ALCHEMIST
Itching to get back into physics after her five-year exile in Pylea, Fred publishes a scholarly paper on “Superstring Theory and p-Dimensional Subspace,” which causes quite a stir in the local scientific community. As a result, she is invited to give a presentation on her findings at a special colloquium held at the fictional California Physics Institute. She purportedly shares the stage with none other than noted real-life string theorists Edward Witten and Brian Greene. While other budding young physicists struggle to build their reputations in the minor leagues of science, Fred appears to have leapfrogged straight into the majors.
“Supersymmetry” (A-4) is perhaps the most overtly physics-intensive episode in the Buffyverse oeuvre—the other candidate being Gene’s time-stopping activities in “Happy Anniversary” (A-2). Let’s overlook the unlikelihood that an unknown physics student would ever share a podium with scientists of Greene’s and Witten’s stature. Witten is one of the top string theorists in the world, and Greene is the field’s greatest ambassador; his bestselling book The Elegant Universe propelled string theory into the popular imagination. Fred’s dialogue in other episodes is peppered with vague scientific references that, when parsed, often don’t make a lot of sense. But in this case, she’s not just spouting random technobabble when she delivers her lecture. D-branes, p-dimensions, T-dualities, Dirichlet boundary conditions, and compactification are all bona fide terms in string theory, and Fred uses them correctly—not that anyone who wasn’t a string theorist could tell the difference offhand. And while the journal in which Fred’s paper appears, Modern Physics Review, is fictional, its name bears an uncanny resemblance to Reviews of Modern Physics, one of the most prestigious real-world physics journals. So give the writers due credit for doing their homework.
To a layman’s ears, the subject of Fred’s paper sounds impossibly abstract and esoteric, and it should: It addresses one of the most ambitious long-term objectives in physics. Real-world physicists are indeed searching for a theory of everything (TOE), “something that combines quantum mechanics and general relativity, accounting for both the behavior of the smallest subatomic particles and the largest forces of nature,” as Fred puts it. A bona fide TOE would describe how the universe works at all size scales, instead of having two competing sets of rules for the separate realms of small and large. String theory is the top contender to date for that honor.
Fred arrives at the institute to deliver her lecture and soon encounters her old academic advisor, Oliver Seidel, who reminisces about how quickly Fred’s aptitude for physics became apparent in his introductory physics course: “By the end of the semester, she was taking on WIMPs!” A confused Gunn naturally associates the term with weak-kneed milquetoasts, and boasts of his girlfriend’s budding pugilistic abilities. Fred gently explains that the acronym stands for weakly interacting massive particles, one of the candidates for the strange dark matter that physicists believe makes up the bulk of matter in the universe.
WIMPs may be mentioned primarily as comic relief, but they are a very real, very active field of physics, and any first-year physics student capable of studying them would indeed be quite exceptional. Her scientific credentials thus established, Fred makes an appointment with Seidel the next day to discuss some of the implications of her new theory, specifically how it fits with “Kaluza-Klein models.” This is a direct reference to an early-twentieth-century attempt to unify gravity and electromagnetism.
Einstein unified three-dimensional space with the fourth dimension of time, and merged gravity and acceleration, attributing the force of gravity to the warping of the fabric of space-time. He dreamed of one day unifying the strong and weak nuclear forces as well. In 1919, a Polish mathematician named Theodr Kaluza proposed that another force, electromagnetism, might be due to a similar warping of an unseen fifth spatial dimension. By reworking Einstein’s equations in five dimensions (four spatial, one temporal) instead of four, Kaluza believed that he could merge the two forces of gravity and electromagnetism. Light could therefore be envisioned as a disturbance caused by the rippling of the higher dimension just beyond human perception, much as fish in a pond can only see the shadows of the ripples across the water’s surface caused by raindrops.
This is a difficult concept for most of us to visualize, since we live in a three-dimensional world. The prospect of a higher spatial dimension is beyond our limited perspective. Most of the inhabitants of the Buffyverse share a similar limited worldview. However, Cordelia eventually makes so much progress in her personal development while working for Angel Investigations that the Powers That Be elevate her to the status of Higher Being (“Tomorrow,” A-3). In her new incarnation, Cordelia ascends to a higher dimension, where time’s arrow no longer exists, making her immortal. Stuck in their lower dimensional reality, the members of Team Angel are mystified by Cordelia’s disappearance.
Let’s imagine for a moment that Cordelia is a tiny person living in TV Land instead of an electronic representation of an actress playing a role. Her perspective would necessarily be limited to the TV world of the Buffyverse—whatever she can touch, see, smell, taste, and hear around her in any given episode. She would have no concept of anything outside that boxed-in reality. But if she were suddenly lifted from the television screen, and landed, life-size, in our living room, she would see the characters and events in the Buffyverse unfolding from an entirely new perspective. In fact, she’d be largely omniscient, with the all-seeing eyes of the divine. The same concept applies to the dimension of Higher Beings.
Add in the immortality, and it sounds like a decent gig, but Cordelia is quickly disillusioned and utterly bored with her new role. Since there is no time in this all-seeing realm, nothing ever changes. Plus, she is unable to interact with her former world, or interfere in any way to alter the course of events therein, much like frustrated television viewers are helpless to change how events unfold on their favorite programs. All they can do is change the channel. Ghost-Spike faces a similar dilemma when he finds himself flitting back and forth between the “reality” of Los Angeles and a separate spectral dimension in “Hellbound” (A-5). We’ve seen how if that dimension consisted of four spatial dimensions instead of three, Ghost-Spike would be able to see and hear Fred and the rest of Team Angel, but they wouldn’t be able to see and hear him. And this does indeed seem to be the case. Like Cordelia, Ghost-Spike is aware of what is happening in that lower dimension, but he can’t interact with it in any meaningful way.
There is other internal evidence that this spectral realm has more than three spatial dimensions: Ghost-Spike disappears from view and then reappears at random moments as he pops in and out of the higher dimension. At least that’s how it seems to Team Angel. In the real world, we lack such definitive evidence, so Kaluza’s theory raised an obvious question when it was first proposed: If there is a fifth dimension, why don’t we experience it in the same way that we experience our four-dimensional space-time? Case in point: If one of Fred’s scientific experiments causes a small explosion, the resulting smoke will gradually disperse throughout the room until its molecules reach a state of equilibrium with the rest of the molecules in the air. The smoke molecules never magically disappear the way Ghost-Spike does when popping off into the spectral world, but they should if the smoke could seep into a higher dimension.
That’s where the “Klein” in Kaluza-Klein theory comes in. Oskar Klein was a Swedish mathematician who found a solution to the conundrum. He argued that this hypothetical fifth dimension could simply be so tiny that not even the atoms that comprise the smoke from Fred’s explosive experiment could pass into it. According to Klein’s calculations, it would have to be curled up (“compactified”) into a tiny ball much, much smaller than an atom. This size scale is known as the Planck length.
Kaluza-Klein models experienced a resurrection of sorts in the 1970s, when string theorists adapted this extradimensional approach to unify not just gravity and electromagnetism, but the strong and weak nuclear forces as well. It’s not an easy task, since the four fundamental forces differ greatly in terms of strength. Add in the mishmash of 57 or so subatomic particles, and it calls to mind the bickering horde of disparate demon species that make up the bulk of Wolfram & Hart’s clientele. The firm’s lawyers are masters at smoothing over disputes and finding ways to get their clients to work together. Similarly, some kind of mediating model is needed to bring together all the disparate elements of the cosmos.
Over the course of the twentieth century, physicists painstakingly cobbled together a reasonably efficient “standard model” of physics. The model they came up with almost works without resorting to extra dimensions. It merges electromagnetism with the strong and weak nuclear forces (at almost impossibly high temperatures) despite the differences in their respective strengths, and provides a neat theoretical framework for the big noisy “family” of subatomic particles. But there is a gaping hole. The standard model doesn’t include the gravitational force. That’s like building a model incorporating all the characters and various elements of the Buffyverse, but inexplicably leaving out vampires. Vampires, like gravity, appear to be strong from the perspective of the humans who populate the Buffyverse, but they are surprisingly weak compared to some of the other demons (their sensitivity to sunlight, for example, puts them at a disadvantage), just like gravity is weak compared to the other fundamental forces. Yet vampires are an integral aspect of the Buffyverse. One ignores them at one’s peril. The same is true of gravity. It’s the proverbial thorn in the standard model’s side, the pink polka-dotted elephant—or fanged, yellow-eyed bloodsucker—in the middle of the room that nobody likes to mention. It’s the piece that doesn’t quite fit into the rest of the jigsaw puzzle.
In contrast, string theory incorporates gravity quite elegantly. Einstein’s equations emerge naturally from the broader mathematical framework. But it achieves its grand unification at a price: It requires extra dimensions. Much like Cordelia ascending to a higher plane of existence, string theory extends Kaluza and Klein’s basic approach to dizzying new heights, calling for a whopping nine dimensions of space and one dimension of time. That’s how many it takes to merge the four fundamental forces into a single TOE, because our own four-dimensional space-time simply doesn’t have enough room to accommodate them all. And just as with Kaluza-Klein models, those extra dimensions may be compactified down to the subatomic scale, and can’t be seen.
PULLING STRINGS
The crux of Fred’s paper concerns the notion of string compactification, which is tied to the crumpled-up extra dimensions of space we’ve just discussed. To quote Fred, “If space-time can undergo massive rearrangement of its structure—and I believe it can—tearing and reconnecting according to a predetermined disposition, then T-duality would allow for the compactification of extra spatial dimensions.” Stripped of the jargon and translated into everyday English, it appears that Fred is looking to this aspect of string theory to explain the mechanism behind dimensional portals in the Buffyverse. Indeed, she credits her experiences in Pylea with inspiring her new insights into string theory: “If I hadn’t been sucked into that portal, I never would have figured out my string compactification theory.” Most of us would respond to that statement much like Gunn does in the episode: “Exactly, ’cause, you know, strings…need…to compactify.”
What exactly are these mysterious strings, and how could they possibly have anything to do with portals in the Buffyverse? There are no simple answers to these questions, but we can start by recapping what we’ve learned thus far about black holes. By their very nature, black holes are a paradox. The center of a black hole is both massively heavy and tiny at the same time, and a black hole may even have a wormhole at the center connecting it to another point in space-time—the conceptual foundation for dimensional portals in the Buffyverse. Both quantum mechanics and relativity therefore apply, yet scientists can’t apply two such vastly different theories simultaneously. A master set of equations (a TOE) that could describe the universe at all size scales would enable physicists to do just that, and hopefully resolve the remaining mysteries surrounding black holes, including the question of what really lies at the heart of one.
One of the critical problems in merging the two theories is that relativity requires a space-time fabric that is smooth. But at the quantum level, space-time is bumpy, with virtual particles popping in and out of existence like tiny bubbles frothing in a subatomic foam. Quantum fluctuations are so small that they don’t matter at the macroscale. They become much more significant at the subatomic level, which is why Newton’s laws of motion and Einstein’s relativity—both of which describe gravity—break down on that tiny size scale. String theory attempts to address this contradiction by reenvisioning the nature of subatomic particles, which are traditionally viewed as tiny, fixed points.
Thanks to the uncertainty principle, if we know a particle’s exact location, we can’t know anything about its velocity (or momentum). That’s why we can’t use Newton’s laws to determine the trajectory of a subatomic stake. Classical physics demands that we know the values for both properties. But what if these pointlike particles are, instead, tiny vibrating strings: one-dimensional closed-loop filaments akin to infinitely thin rubber bands? Perhaps strings only appear to be fixed and pointlike because they are so small. If they are vibrating, our knowledge of their position is not so exact. This fuzziness calms the so-called quantum jitters.
According to string theorists, there are the three full-size spatial dimensions that we experience every day, one dimension of time, and six extra dimensions crumpled up at the Planck scale like itty-bitty wads of paper. As tiny as these dimensions are, strings are even smaller. Fred, Gunn, and the rest of Team Angel (and us) are limited to four-dimensional space-time. A string enjoys the same kind of unfettered freedom as a Higher Being in the Buffyverse, able to move through all ten dimensions of space-time. But unlike the frustrated Cordelia, who is unable to interfere with the mortal realm during her yawn-inducing stint as a Higher Being, a string’s multidimensional existence has a very real, observable effect on our physical reality. The little string wriggles as it goes on its merry way, and the geometric shape of those extra dimensions helps determine the resonant patterns of vibration. Those vibrating patterns in turn determine the kind of elementary particles that are formed, and they generate the physical forces we observe around us—in much the same way that vibrating fields of electricity and magnetism give rise to the entire spectrum of light or vibrating strings can produce different musical notes on a violin. All matter, and all forces, are composed of these vibrations.
Impressive, you might be thinking, but what about those portals? This brings us back to wormholes. In order to create a wormhole, the fabric of space-time must rip, yet there is still some debate among physicists as to whether this is possible. And once again, the two prevailing “rule books” disagree. General relativity says that space-time can bend and curve, but it doesn’t allow for punctures or tears; space-time must be smooth. Einstein speculated on the possibility of preexisting wormholes at the heart of black holes—akin to the preexisting “hot spots” that serve as natural gateways to other worlds in the Buffyverse—but nixed the idea that we could one day create a new one. However, quantum fluctuations can give rise to hypothetical wormholes at the subatomic scale: tiny tears in space-time that exist for fractions of a second before closing up again.
Here’s what keeps a theoretical physicist awake at night: If space-time can rip, what’s to prevent that hole from getting bigger, until the entire fabric is split in two? This would be a cosmic catastrophe, as we shall see in the next chapter. Fortunately, the universe appears to have a built-in “cosmic censorship” principle at work to guard against these events, known as “naked singularities.” Black holes provide a safeguard in general relativity. Since nothing can escape their immense gravitational fields, the hypothetical punctures at the singularity are cut off from the rest of space-time, so the rip is unable to spread uncontrollably. And at the quantum level, the tears exist for mere fractions of a second, so there just isn’t enough time for rips to reach catastrophic proportions.
String theory offers its own unique solution to the dilemma. It allows space-time to puncture or tear as it compactifies, but it can also repair itself and “reinflate,” often into a new configuration. Crazy though it may sound, Fred’s theory might just be on the right track. Among their many other useful properties, strings can compactify and reinflate along with a shrinking region of space. The string wraps around the spatial area, just like one could wrap a rubber band around an object. Because it’s so stretchy, the string’s ability to expand and contract in size provides a protective “shrink-wrapping” around any torn patch of space-time. This keeps the tear from ripping out of control, until that bit of space can repair and reinflate.
That’s the working hypothesis, anyway, and it is certainly borne out mathematically in the few specific configurations for which the numbers have been crunched. These have been for the curled-up, six dimensions of space, but there’s no reason the same rules can’t apply to our own four-dimensional space-time—although wormholes (traversable or not) remain a distant hypothetical possibility, even in string theory. The lack of direct experimental evidence for wormholes turns out not to be a problem for Fred. Shortly after she begins her lecture, a portal opens up right behind her on the podium—the kind of dramatic, undeniable, eyewitness proof every physicist dreams of one day finding to support his or her pet theory.
IT TAKES BRANES
Not only does string theory offer a convincing mechanism for portals in the Buffyverse, it can also account for the origin of its myriad dimensional worlds. When Fred meets with Seidel the day after her horrific close call, she explains about her exile to Pylea, prompting bemused skepticism in the physics professor. It’s a perfectly understandable reaction from a scientist who has witnessed a truly otherworldly occurrence but is still cautious about drawing wildly speculative conclusions. He’s more inclined to attribute the portal’s unexpected appearance to subconscious suggestion or a form of mass hysteria. As for Pylea, Seidel admits to Fred that, as a theoretical physicist, he is open to the possibility that other worlds exist, “but you’re naming them.”
Of course, when Fred speaks of other dimensions in this context, she does not mean the crumpled-up, tiny extra dimensions of string theory. Because they are so tiny, those dimensions are not the sort that might house ghosts, demon races, Higher Beings, or shy physics students who’ve been sucked through a portal by mistake. So those dimensions can’t intermingle with the four dimensions of space-time in which we exist, and we can’t, in turn, enter them. Fred is using the term to describe the equivalent of parallel universes. The Buffyverse, as we have seen, is a multiverse. All those parallel worlds, like Pylea, may have started out as baby universes, budding off from tiny wormholes that popped up in the quantum foam before inflating to their full size. It just so happens that the latest incarnation of string theory offers an alternative explanation for the origin of parallel universes.
Strings are really stretchy, so hypothetically a tiny string can stretch into an object resembling a membrane. String theorists have dubbed these structures “branes.” Unlike strings, branes might be quite large, but still invisible to the standard ways scientists probe the universe. A brane can exist in any dimension less than ten. Point particles are “zero branes.” A string is one-dimensional, like a line, so it is called a “one-brane.” A membrane is two-dimensional, defined only by length and width; this is a “two-brane.” If a brane has length, width, and breadth (three spatial dimensions), it is a “three-brane.” And so forth. The so-called p-branes are simply scientific shorthand for denoting various possible dimensions for branes without specifically designating one; p can equal any whole number less than 10. The same concept applies when Fred talks about p-dimensional subspace.
So not all extra dimensions must be wrapped into a tight little Planckian ball. Some can be huge, as large as a universe. In fact, it’s possible to view our entire universe as a gigantic three-brane floating in a much larger dimensional brane-world, much like the world of the Buffyverse exists in TV Land, which is in turn part of our much larger living-room reality. Brian Greene likens it to living inside a loaf of bread, where our universe is just one slice in a much larger loaf. There could be parallel universes floating right next to ours as little as one millimeter away, and we are simply oblivious to their existence. We’re back in multiverse territory, with other worlds—like Pylea, or Quor-Toth—that may, or may not, resemble ours in terms of physical laws.
Instead of springing up out of the quantum foam and budding off the parent universe, perhaps parallel universes arise from collisions between large brane-worlds. This is admittedly highly speculative, even among string theorists, but it’s an intriguing notion. What happens when two giant branes floating in hyperspace collide? The working hypothesis is that the kinetic energy from any such collision would be so immense, it would convert into matter and energy, much like the spark from a flint striking stone can start a fire. The intense temperatures produced by the collision would then cool rapidly as the two membranes move apart.
So our universe might be the result of a “big splat” instead of a big bang. And it could happen again in the distant future, because the expansion of our universe is accelerating. Physicists aren’t sure why this is the case, but many hypothesize that it’s due to the existence of “dark energy,” a type of antigravity (similar to the negative energy discussed in the previous chapter) that is pushing the galaxies farther and farther apart. But there is another option. If the colliding-branes scenario were to prove correct, there is no need for dark energy. The accelerated expansion rate could be due to the gravitational attraction that still exists between our brane and a second brane with which we once collided. The two branes could once again be moving toward each other at an ever-faster rate, which means another collision could happen billions of years from now, vaporizing our world in a cosmic fireball even as it creates another baby universe in our stead. In fact, such collisions could have happened countless times, giving rise to any number of nascent universes.
We might not be able to see these parallel universes, and we certainly can’t travel to and from those other worlds via mystical portals as in the Buffyverse. But perhaps one day we will be able to sense them through gravity. Among its many other insights, string theory offers a potential explanation for why the gravitational force is so much weaker than the other forces. Originally string theorists conceived of strings that were closed loops, like rubber bands, able to travel freely among the higher dimensions. But now they believe that there could also be open-ended strings, where each endpoint is tied down to a brane. Such strings have set boundaries. They are limited to just those dimensions of the particular branes to which they are attached—the “D-branes” Fred mentions in her lecture.* Much like Team Angel is confined to the three-dimensional world of Los Angeles, matter and light would be made of open-ended strings, and are thus confined to our three-dimensional D-brane. The same goes for the “messenger” particles (bosons) that carry the weak and strong nuclear forces. These are the ways in which physicists normally explore the universe.
In contrast, gravity might be more like a Higher Being in the Buffyverse. A closed-loop string that has been dubbed a graviton—the hypothetical messenger particle for gravity—has no loose ends that are tied onto a brane, and hence no boundaries, so gravitons can escape into higher dimensions. It could be that gravity isn’t such a weakling after all. We just can’t feel its full impact, because it dissipates into extra dimensions. The atoms and particles of our universe stay on our brane, in much the same way that Spike’s billiard balls stay on the surface of the pool table in the Bronze. But whenever he makes a shot, balls collide and sound waves—mechanical vibrations in the air—travel off the table and into the surrounding atmosphere. Other people can hear the collision even if they aren’t in the same room. Gravity, too, might be able to escape the confining parameters of its source and seep into other dimensional “rooms,” thus diluting its strength.
Physicists might one day be able to detect interference patterns from these hypothetical branes, encoded in gravitational waves. These are ripples in the fabric of space-time caused by violent events in the universe: colliding black holes, shock waves from exploding supernovae, perhaps even the remnant of the shock wave produced by the big bang itself. Of course, first we must be able to sense gravitational waves, which are very faint. Any information encoded in those ripples would be even fainter. The good news is that scientists may be on the verge of observing gravitational waves directly for the first time with the Laser Interferometer Gravitational-Wave Observatory (LIGO), which began operation in 2005, as well as the space-based Laser Interferometer Space Antenna (LISA), slated for launch around 2015. Should they succeed in observation, even the skeptical Seidel might be forced to accept the existence of extradimensional brane-worlds as a real scientific possibility.
It’s not branes, but bodies that collide in “Supersymmetry” (A-4). The episode opens with Fred and Gunn making love to celebrate the publication of her paper. And it’s not the only romantic coupling that takes place. Wesley is mired in a passionate entanglement with Lilah Morgan, a high-powered lawyer with Wolfram & Hart. And a budding romance between Angel and Cordelia has been complicated by the growing attraction between Cordelia and Angel’s eighteen-year-old son, Connor, setting up an awkward (and slightly incestuous) love triangle. Who knew string theory could be so steamy? It just so happens that string theory contains its own elaborate network of couplings, in the form of “stringy dualities.”
Dualities in physics refers to theoretical models that appear to be different but can be shown to describe exactly the same thing. It’s a bit like how ice, water, and vapor are three different phases of the same chemical substance, except that a duality looks at the same phenomenon in two different ways that are inversely related. Remember the kindly Sunnydale doctor, Ben, and his hell god alter ego, Glory? We learned in chapter 6 that subatomic particles like photons and electrons also exhibit wavelike behavior, but uncertainty dictates that we can’t see both of these aspects at the same time. The more accurately we observe its particle nature, the less we can see the wavelike nature of the object, and vice versa. This is a duality. The particle/wave identities are inversely related, different “faces” of the same underlying reality, just like Ben and Glory are inverse (male and female) personas inhabiting the same body.
String theory has its own set of dualities. Fred rightly says that there are several competing dimensional theories—five, in fact—and as recently as 1995, no one knew which version was correct. Then Edward Witten stepped in and demonstrated that the five different string theories weren’t so contradictory after all. He united all five under a single theoretical umbrella that he dubbed M theory,* adding a tenth spatial dimension to bring the total number of required dimensions to eleven.
M theory indicates that mathematically, the five versions of string theory are merely five different ways of looking at the same thing. Just like the couplings that take place between the various characters in the Buffyverse, each iteration of string theory is connected in some way to another through various dualities in an intricate web of interconnections that ultimately links all five to one another and to M theory. But whereas the complex social network of relationships in the Buffyverse usually leads to conflict and broken hearts, stringy dualities can help physicists simplify difficult calculations through a kind of “bait-and-switch” approach. Fred is referring to these intrinsic dualities when she asks her audience to “consider the nonperturbative properties of string theory” during her lecture.
To understand what this is, we must first understand what it isn’t. Perturbation theory is a calculating method that makes approximations to get a rough answer and then refines it bit by bit, according to how given physical systems are known to behave. Let’s say that Xander, in his role as construction manager, makes an initial estimate for a prospective client to rebuild Sunnydale High School. Xander can then gradually make refinements to that estimate by filling in the missing details as they emerge to calculate the final bill: the actual materials and labor costs, for example. These details are “perturbations” to the original estimate. Physicists employ a similar approach when determining the trajectory of a satellite. They use Newton’s laws for the initial calculation and then make small refinements by calculating the effects of other, minor factors that might influence the trajectory: pressure from the solar wind, for instance, or the effects of heating on one side of the satellite.
Ideally, there should be only small discrepancies between Xander’s original estimate and the final bill, just as there should be only small discrepancies between the predicted properties of a physical system and those that actually emerge. But as anyone who has ever hired a contractor knows, the final bill is sometimes way off target. Complications may ensue. There could be massive cost overruns from a labor strike, rising materials costs, or unexpected damage from demon attacks or marauding students driven mad by the percolating Hellmouth energy below the school. In those cases, the refinements result in large changes to the ballpark estimate: “contract-y goodness” for Xander, who stands to make a tidy profit from the overruns, but a financial disaster for the client, who probably didn’t budget for those eventualities.
Something similar happens when physicists try to calculate the highly turbulent air flow patterns of a tornado, for instance, or the properties of a rapidly rotating wormhole. Their perturbative approximations break down because they are dealing with sudden, large changes to the original value, instead of small, predictable increments. If Fred were trying to calculate the properties of a swirling dimensional portal in the Buffyverse—which would be similar to the physics of a rotating wormhole—she wouldn’t be able to use a perturbative approach, because the numbers involved would be too large. Stringy dualities could help simplify her calculations.
Among the jargon Fred employs in her lecture is something called T-duality. Because it’s a duality, we know it describes an inverse mirror relationship between two of the five permutations of string theories. It also pertains to transformations of space-time, a critical requirement for the creation of a wormhole or portal. Here’s how it works: if the radius (r) of a circular area of space has a large value (r = 1,000) in one of the five versions of string theory, it is difficult for Fred to calculate. However, that value will be inverted, and therefore small (r = 1/1000) in one of the other versions. This is a small perturbation, and easier for Fred to calculate. Because both theories describe the same underlying physics, Fred can use the dual theory where the value is small to calculate the quantity, then plug it back into the original theory to complete the calculation. No doubt that’s how she arrives at her revolutionary breakthrough in string theory (as it exists in the Buffyverse): Space-time can shrink, tear, repair, and reinflate, thereby rearranging itself into exotic configurations like portals to other dimensions.
Dualities are a type of symmetry, and it’s no accident that this episode is entitled “Supersymmetry.” The concept is a natural extension of the many different kinds of symmetry we see every day around us in the physical world. For instance, rotate a snowflake by 60 degrees, and you’ll find that it looks exactly the same. This is spatial symmetry. A second type of symmetry occurs when one shuffles a series of similar objects, as in a shell game, where the player must guess under which of three shells a marble might be found after the three are randomly shuffled in quick succession. Regardless of where the marble turns out to be, mathematically there are six different ways in which three identical objects can be interchanged. The equations that appear in the background in the episode don’t come from string theory, but from quantum chromodynamics (QCD), a theory that describes the strong nuclear force and the way various quarks interact with one another. There are quarks of three different “colors” that can be randomly interchanged, just like the shells, so those quarks share a similar internal symmetry.
Supersymmetry extends this interchangeable shuffling to incorporate all known subatomic particles. Not all potential couplings are feasible in the current standard model. Fermions (the particles that make up matter) and bosons (messenger particles that carry fundamental forces) can’t mix at all because they have such vastly different properties. It’s a bit like how certain demons in the Buffyverse have “anatomical peculiarities” that prevent them from mating with any creature outside their species—at least not without causing severe internal damage. Supersymmetry allows us to engage in “cross-species” mating, interchanging a fermion with a boson. In order to accomplish this, however, it requires some sort of “adapter”—in this case, the existence of hypothetical super partners, called sparticles. Each fermion is paired with a super-boson partner, and each boson has a super-fermion partner. Now they can be mixed via their super partners, but the price is a doubling of the number of subatomic particles. Never one to shy away from a little added complexity, string theory incorporates supersymmetry.
If it turns out to be true, supersymmetry would provide physicists with a powerful calculating tool for understanding the most elusive mysteries of our universe, since everything would be connected to everything else through various kinds of dualities. Fred gained revolutionary new insights into Buffyverse physics using just one kind of duality. Imagine the major theoretical breakthroughs she could make were she able to simplify all her most difficult calculations in this way. The same goes for real-world physicists. Alas, supersymmetry is broken. Our universe today is an imperfect shadow of its former majestic self.
As Fred waits in Seidel’s office, she notices that a textbook, Plasma and Fluid Turbulence, is inexplicably sandwiched between books on neutrino physics on the shelf. When she opens it, she finds ancient pages from a mystical text with instructions on how to open a dimensional portal. Horrified, Fred realizes that her beloved mentor has been lying about his professed ignorance regarding other dimensions. He is the one responsible not only for opening the portal during her lecture, but also for sending her to Pylea six years earlier.
It seems he’s even figured out how to open portals wirelessly. As a vengeance-minded Fred confers with Wesley over a suitable punishment for Seidel, she receives a call on her cell phone. When she flips it open, strange symbols—no doubt the “consonant representations of mathematical formulae” with which she has become so familiar—appear on the display screen, and a portal opens up right there in the room. That makes Seidel pretty cutting-edge in terms of real-world technology. Wireless devices have become mainstays of our daily lives, from cell phones, BlackBerries, and laptops to embedded wireless sensors in buildings and bridges to monitor structural integrity. Perhaps he should have been an experimentalist instead of a theorist.
Fred survived her five-year ordeal in Pylea, then built a well-ordered life in Los Angeles as part of Team Angel. But by the episode’s end, her carefully structured world has come apart at the seams. The symmetry has been broken, and she must once again piece the broken shards of her life back together. It’s a useful metaphor for the supersymmetry that string theorists believe characterized the early universe. Before the big bang, the cosmos was a perfectly symmetrical ten-dimensional universe with all four fundamental forces unified at unimaginably high temperatures—a state of extremely low entropy. But this universe was highly unstable and cracked in two, sending an immense shock wave reverberating through the cosmos. The result was two separate space-times: the unfurled four-dimensional one that we inhabit, and a six-dimensional one that contracted as violently as ours expanded, shrinking into a tiny Planckian ball. As our universe expanded and cooled, the four forces split off one by one, beginning with gravity. Everything we see around us today is a mere shard of the original shattered ten-dimensional universe.
Physicists aren’t sure why it happened, but they suspect that it might be due to the incredible tension and high energy required to maintain such a highly ordered supersymmetric state, which could render it inherently unstable. Imagine that Fred and Gunn are making their shared bed on laundry day, but the bedsheet has shrunk slightly in the wash. They manage to get it to fit around all four corners of the bed, but the sheet is stretched so tightly that it just won’t stay in place. There is too much strain on the fabric, so one corner inevitably pops loose, causing the bedsheet to curl up in that spot. Fred and Gunn can force that corner back into place, but again, the strain will prove to be too much and another corner will pop. Like the bedsheet, the original ten-dimensional fabric of space-time was stretched tight in a supersymmetric state. But the tension became too great, and space-time cracked in two. One part curled up into a tight little ball, while the aftershock from the cataclysmic cosmic cracking caused the other part to expand outward rapidly. This became our visible universe.
For a ten-dimensional universe, there are apparently millions of ways for supersymmetry to break, although there does seem to be something special about three spatial dimensions that causes that configuration to be favored. We’ve seen that the way the remaining dimensions curl up (their shape) gives rise to all the fundamental constants, the respective strengths of the various forces, and ultimately the structure of the universe. If we apply symmetry breaking to the multiverse—or the many different parallel dimensions that exist in the Buffyverse—it gives us a potential explanation for why the laws of physics may (or may not) be different in such universes. Each time a baby universe forms, whether it arises from the quantum foam or from the energy of colliding branes, the symmetry will break randomly in a different dimensional configuration, which in turn determines what kind of universe is born.
Scientists still don’t understand the origin of symmetry breaking, but on a less-cosmic scale, some version of it appears to be a crucial component in many basic physical processes, including simple phase transitions, such as the critical temperature/pressure point where water turns into ice. In fact, some kind of symmetry breaking is woven into every aspect of our existence, right down to the mutual (one assumes) orgasms Fred and Gunn experience while making love. The sexual energy between them builds and builds, until finally the tension becomes so great that something quite literally has to give.
Paradoxically, it is shattered symmetries that make life possible, and not just in the context of human sexuality and reproduction. Remember that tiny amount of extra matter that led to its victory over antimatter, and gave rise to everything in our universe? That’s just one example of symmetry breaking that proved critical to our existence. It’s called CP symmetry, where C = charge and P = parity. All this means is that matter and antimatter have opposite charges, and there should be equal amounts of each—except there wasn’t. That tiny asymmetry in favor of matter literally determined our fate.
The same is true of time. We’ve seen that all the major physics theories exhibit time-reversal symmetry: Time can flow in both directions. At the subatomic level, this does indeed appear to be the case. If you could videotape a particle and antiparticle popping out of the quantum vacuum and annihilating into radiation, and then ran the tape backward, it would be impossible to tell the difference between the two directions. It’s a quantum palindrome. Yet in our macroscale day-to-day world, the symmetry of time has been broken. Entropy holds sway. For us, time is a one-way street.
That’s not necessarily a bad thing. Nothing could ever change if there were no distinction between the forward and backward motion of time. Not only would we be bored out of our minds by the relentless sameness of our surroundings, like Cordelia, the reluctant Higher Being, there wouldn’t be much of a universe at all, because nothing could ever permanently form. Think about it: if an object forms, it creates a distinction between past (when there was no object) and present (in which the object now exists), which means we can tell the difference between time moving forward or backward. Human memory serves the same purpose. We can remember the past, and this establishes a time line moving in one direction: forward. The downside, as Wesley warns Fred about the price of vengeance, is that “once you’ve acted, you can’t go back. You’ll have to live with your actions forever.”
Scientists aren’t sure about the origin of time’s arrow, but they found a potential clue with the discovery of an extremely rare elementary particle called the kaon. As elementary particles go, the kaon has a much longer life span—still mere fractions of a second, but those fractions are significantly greater than for the rest of the subatomic family. And unlike its subatomic siblings, the kaon doesn’t exhibit time symmetry (nor does another particle called the B meson). As with matter and antimatter, there is a very slight asymmetry, favoring the forward rather than backward motion of time. The kaon and the B meson could hold the secret to time’s arrow, which is why they are the focus of such intensive research.
Oddly, the broken symmetry of time’s arrow appears to be linked to heart health. In 2005, a team of scientists from Harvard Medical School and the University of Lisbon discovered that too-perfect symmetry in human heartbeats—a cardiogram that looks the same whether run forward or backward in time—is one sign of an unhealthy heart. Young, healthy study subjects showed the most asymmetrical heartbeats.
Unfortunately, symmetry breaking leads not to heart health, but to heartbreak for poor Fred. The pernicious physics professor is sucked into one of his own portals, but not before Gunn ruthlessly snaps his neck. The exacting of vengeance rips the couple apart. Their personal symmetry is shattered just like our nascent cosmos. And as Wesley forewarned, they can’t go back to their former idyllic state.
TRIAL BY FIRE
Fred and Gunn’s relationship is put to the test and, ultimately, it fails. String theory is undergoing its own intellectual trial by fire, facing mounting criticism from others in the physics community who believe that the theory is inherently untestable. The crux of the criticism is valid. Science currently lacks the means to directly observe strings, so their existence, and that of any extra dimensions, can only be inferred from the underlying mathematics. As with the Many Worlds hypothesis, if a theory can’t be tested, it is not so much a science as a philosophy—at least in the minds of most physicists—no matter how impressively complex and elegant the math.
That’s why the focus of string theory is shifting more toward developing testable predictions—those that can be verified by practical experiments. The problem is that the energies required to test any of string theory’s predictions are literally astronomical. A particle accelerator roughly the size of our own solar system might do the trick, but we can’t build something of that magnitude. String theorists have countered that certain predictions could conceivably be tested within the next decade if plans for the next generation of particle accelerators continue on schedule.
The Large Hadron Collider (LHC) now being built in Switzerland should be operating by 2008. Remember Spike’s colliding billiard balls? When the balls collide, some of their kinetic energy will be transformed into heat or noise upon impact, but energy conservation dictates that if we add up all the different kinds of energy, there should be the same amount after the collision as there was before. If experiments at the LHC show that there is less energy after a high-energy collision between subatomic particles than at the start, it would constitute an apparent violation of the first law of thermodynamics. But just as mechanical sound waves from the collision of Spike’s billiard balls can seep into other rooms, any shortfall in energy following a particle collision could be attributed to some of that energy seeping into extra dimensions—strong circumstantial evidence of their existence. Likewise, if evidence is observed for any of the supersymmetric sparticles, that, too, would bolster string theory’s reputation. Discovery of the hypothetical graviton is also a long shot, but this would be another evidentiary feather in string theory’s cap.
Not all the criticism of string theory rests on testable predictions. Elegant though it may be, string theory makes one very big assumption: the preexistence of the fabric of space-time. It’s a bit like a master painter who produces great works, yet never stops to wonder where the canvas comes from. In truth, referring to space-time as a “fabric” is somewhat misleading. It isn’t canvas, cotton, silk, or some cheap polyester blend (a prospect the nattily dressed Lorne would find horrifying). It isn’t any kind of material at all, although physicists speak of curving and twisting space-time as if it were a tangible thing. Space-time is little more than a mathematical construct on which to drape the master equations of the cosmos, but an explanation of its origin is nonetheless necessary for physicists to lay claim to a bona fide TOE.
Even string theorists acknowledge this shortcoming, and are in hot pursuit of a “background-independent formulation,” one that can account for the cosmic canvas. They might get some help, ironically, from string theory’s primary competitor: loop quantum gravity. While it is not as all-encompassing in scope as string theory, the fabric of space-time emerges directly from the equations of loop quantum gravity. The two approaches are quite different in some respects. String theory starts at the quantum level and builds upward to incorporate general relativity, while loop quantum gravity starts out at the top with general relativity and seeks to incorporate quantum mechanics. But both involve some kind of loop—loops of string in string theory, and the mathematical equivalent to loops of space in loop quantum gravity. This suggests that the two camps may, in fact, turn out to be a sort of duality: opposite ends of the same TOE.
Chances are that string theory will not be verified in one dramatic swoop in the experimental equivalent of the portal that opens up behind Fred during her lecture, but in slow, small increments as physicists painstakingly sift through huge amounts of data and stitch together the bits and pieces needed to support specific predictions. It may turn out that string theory, in its present incarnation, fails the test. That doesn’t spell its doom any more than the shattered supersymmetry of the original ten-dimensional universe ended its existence, or Fred and Gunn’s broken romantic bond ends their underlying friendship. String theory will adapt and continue in a new incarnation, which will in turn be subject to testable predictions, and so on, until physicists arrive at their ultimate goal: a workable theory of everything. That’s how science advances. Failure is an acceptable option, even if it’s not the most desirable one. There is no progress without it.
Symmetry breaking is a kind of failure that, while traumatic, gives rise to life, the universe, and everything. This might provide a modicum of comfort to Fred and Gunn. Change is built into the mechanisms of the cosmos, right down to the level of kaons and B mesons. Perfection is a static and therefore unnatural state that cannot—and probably should not—be maintained, as Gene the temporal physicist learned when he tried to freeze that perfect moment in time and prevent his girlfriend from breaking up with him. The shattering of perfection, in countless tiny different ways, is what gives meaning to human existence. “The wheel keeps turning. You can’t stop it,” Lorne tells a rueful Gene, pointing out that while he can hold a musical note indefinitely, “Eventually that’s just noise. It’s the change we’re listening for, the note coming after, and the one after that. That’s what makes it music.” Lorne’s musical analogy is particularly apt for string theory, since it is the changing vibrations of all those tiny strings that create the diverse “music” of the universe.
*The “D” stands for “Dirichlet” (pronounced “deh-RISH-lay”). Johann Peter Gustav LeJeune Dirichlet was a nineteenth-century mathematician known for applying certain boundary conditions to differential equations. Branes that serve as “sticking points” for open strings set similar boundary conditions for those strings. That’s why they’re known as D-branes.
*Nobody knows for sure what the “M” stands for. Possibilities include “mother,” “membrane,” “matrix,” “mystery,” even an inverted “W” (for Witten). Witten himself isn’t telling.
