Collider: The Search for the World's Smallest Particles - Paul Halpern (2009)

Chapter 10. The Brane Drain

Looking for Portals to Higher 
Dimensions

If this is the best of all possible worlds, what are the others like?

—VOLTAIRE, CANDIDE (1759)

The LHC, with its matter-changing properties, could be said to offer a modern-day “philosopher’s stone.” Interestingly, its region’s stone has already been used to build a philosopher’s house. That philosopher was François-Marie Arouet, better known as Voltaire.

The Chateau de Ferney, where the witty writer lived from 1758 almost until his death in 1778, is situated within a mile of the ring traced by the LHC. Within that mansion he completed his most famous work, Candide, a cutting satire of the optimism of the German thinker Gottfried Leibniz. At first glance, the LHC and Leibniz (and Voltaire’s parody thereof) might seem to have little in common. However, they are profoundly connected through the concept of parallel universes and alternative realities.

A rival of Newton in developing calculus, Leibniz believed that our world represents the optimum among the set of all possibilities. Leibniz drew his conclusions from the calculus of variations—the method he developed for finding shortest paths along a surface and related problems. An example of such a situation considers the ideal way to cross a hill—among the myriad routes there is one that minimizes the length. Leibniz pondered that God, in designing the universe, would choose the optimal solution whenever there are alternatives.

Voltaire’s farcical character Dr. Pangloss, a teacher of “metaphysico-theologico-cosmolonigology,” takes this concept to the extreme by concocting a convoluted rationale for anything that happens in this “best of all possible worlds.”

“Observe that noses were made to support spectacles,” remarks Pangloss. “Hence we have spectacles. Legs were obviously instituted to be clad in breeches, and we have breeches.”1

Even after Pangloss, along with his pupil Candide, suffers through the most horrific series of events imaginable, including the destruction wrought by the Lisbon earthquake and the terror of the Inquisition, he continues to rationalize his experiences. He concludes that if a solitary link were broken in the cosmic chain of events, no matter how dreadful the occurrence seemed at the time, ultimate good would never ensue—in their case, the possibility to cultivate a small garden. No one following the dismal adventure could miss Voltaire’s irony.

Could we be living in the “best of all possible worlds?” The concept implies the existence of alternative realities—perhaps even universes parallel to our own. Until recently the concept of parallel universes lay exclusively in the realm of speculation. However, remarkably, one of the projects planned for the LHC is to test a new type of parallel universe idea, called the “braneworld” hypothesis, positing that everything we observe resides within a three-dimensional island surrounded by a sea of higher dimensions. “Brane” is short for “membrane,” a description of structures such as the one theorized to support the observable cosmos. According to this hypothesis, the only particles able to leave our brane are gravitons, which are the carriers of gravity. Consequently, researchers plan to use the LHC to search for gravitons leaking into higher dimensions. If such extra dimensions are found, perhaps there are other branes parallel to our own. If these other branes turn out to be lifeless structures, perhaps we do indeed live in the optimum world.

The concept of parallel universes first entered physics in a kind of abstract, mathematical way through Richard Feynman’s diagrammatic method of calculating the likelihoods of certain types of exchanges between charged particles. Each possibility is assigned a certain weight and added up. One way of expressing this “sum over histories” makes use of Leibniz’s calculus of variations through what is called the path integral formulation. According to this approach, if you know the starting and ending states of any quantum interaction, what happens in between is like a “hill” of multiple trajectories. You never know exactly which way the players in the interaction breached the hill; in fact, they traversed it many ways at once. All you can calculate is the most probable means of crossing, which works out to be the shortest distance.

Feynman did not intend his method, which he began to develop in the early 1940s under the supervision of his thesis adviser John Wheeler, to represent paths through a labyrinth of actual parallel universes. The math worked out splendidly and the predictions turned out perfectly accurate, that’s all. However, in 1957, another of Wheeler’s students, Hugh Everett, took matters a step further through his “Many Worlds Interpretation” of quantum mechanics.

According to Everett’s hypothesis, each time particles interact on the microscopic level, the universe responds by bifurcating into a maze of alternatives, each slightly different. When an experimenter measures the result, he or she replicates into versions corresponding to each alternate reality. Each copy records a different result of the measurement, attributing the outcome to chance. But in reality, there is no chance involved, because every possibility is actually realized by a replica researcher—unable to communicate with other versions and compare results. Over time, the number of parallel universes—and occupants within—grows into a staggering figure, dwarfing even the number of atoms in all of visible space.

Despite this shocking conclusion, in the 1970s noted theorist Bryce DeWitt became convinced of the importance of Everett’s conjecture. DeWitt named and popularized the concept, arguing that it was the only reasonable way to make quantum mechanics objective, rather than dependent on the subjective act of measurement. After all, who could step outside of the universe itself, take readings, and cause its wave function to collapse into various possibilities? As crazy as the Many World Interpretation sounds, he argued, isn’t it crazier to think of humans influencing the cosmos through their sensory perceptions? Although by then Everett had left theoretical physics (and would die in 1982 at the age of fifty-one), DeWitt was very effective in promoting the idea that we live in an ever-expanding web of parallel universes.

Along with Wheeler, DeWitt had already made inroads into the question of applying quantum principles to gravity. Wheeler was very interested in developing a sum-over-histories method for encapsulating the solutions of Einsteinian general relativity. In quantum mechanics, states can have different positions, momenta, spins, and so forth. These are like the distinct musical notes that make up a composition. What would be the equivalent keyboard for general relativity? Eventually, it occurred to him that the range of possible three-dimensional geometries would offer the medley of tones needed to compose his symphony. Exuberantly, he prodded DeWitt to help him develop the mathematical notation for this idea. As DeWitt recalled:

Wheeler used to bug everybody. I got a telephone call from him one day around 1964 saying he would be passing through the Raleigh-Durham airport—that’s when I was in North Carolina—between planes for two hours. Would I please come out there and we would discuss physics? I knew that he was bugging everybody with the question “What is the domain space for quantum gravity?” And I guess he had it finally figured out in his mind that it was the space of three-geometries. This was not the direction I was really concentrating my efforts, but it was an interesting problem so . . . I wrote down this equation. I just found a piece of paper out there in the airport. Wheeler got very excited about this.2

The result was the Wheeler-DeWitt equation: a way of assigning weights to three-dimensional geometries and summing them up to determine the most probable evolution of the universe. In theory, it was supposed to help researchers understand how reality as we know it emerged from the chaotic jumble of possibilities. In practice, however, the equation would become unwieldy if applied to complex situations.

In 1973, C. B. Collins and Stephen Hawking considered this question classically in their influential paper “Why Is the Universe Isotropic?” Pondering the myriad possible general relativistic solutions—including isotropic as well as anisotropic cosmologies—they wondered which could evolve into the familiar present-day universe. The difference between isotropic and anisotropic cosmologies is that while the former expands evenly in all directions, like a spherical balloon being filled with air, the latter blows up at unequal rates depending on which way you look, more like a hotdog-shaped balloon becoming longer and longer as it is inflated but not much wider.

Not surprisingly, according to astronomers, the present-day universe on the largest scales is close to isotropic. Space seems to be expanding close to the same rate in all directions. The cosmic microwave background, a snapshot of the “era of recombination” three hundred thousand years after the birth of the universe, is similarly very close to being isotropic. (As we discussed, the COBE [Cosmic Background Explorer] and WMAP [Wilkinson Microwave Anisotropy Probe] satellites mapped out minute anisotropies.) Collins and Hawking wondered whether the very early universe, instants after the Big Bang, needed to have been isotropic as well. Why couldn’t it have been arbitrarily chaotic like the hodgepodge of sand dunes on a rugged beach?

To examine the possibility of cosmic evolution from chaos to order, they considered what is now called the multiverse: a kind of universe of universes embodying the range of all geometric possibilities. Of this cosmic zoo, they wondered, which kind of creatures could evolve into the tame entity with which we are familiar: isotropic space as we see it today. Surprisingly, according to their calculations, only an infinitesimally minute percentage could make the leap. Only universes that were extraordinarily isotropic to begin with could end up with ordinary present-day conditions. Any deviation from perfection in the beginning would blow up over time into a cosmic monstrosity. How then to justify the improbable normality of today?

In lieu of an explanation based exclusively on physical laws, Collins and Hawking decided to invoke what Australian physicist Brandon Carter dubbed the anthropic principle: the concept that the existence of humans constrains the nature of the universe. If the universe were sufficiently different, anthropic reasoning asserts, stars like the Sun wouldn’t have formed, planets like Earth would be absent, beings like humans would not exist, and there would be nobody to experience reality. Therefore the fact that we, as intelligent entities, are around implies that the universe must have been close enough to its present form to guarantee the emergence of such cognizant observers. Collins and Hawking applied the anthropic principle as follows to explain why the universe is isotropic:

Suppose there are an infinite number of universes with all possible different initial conditions. Only those universes which are expanding just fast enough to avoid recollapsing would contain galaxies, and hence intelligent life. [These] would in general approach isotropy. On this view, the fact that we observe the universe to be isotropic would be simply a reflection of our own existence.3

The use of anthropic reasoning is akin to compiling news clippings about lottery results around the world and realizing that the reason for all of the success stories is that coverage is biased in favor of winners. Although there are millions of “parallel histories” of people who buy lottery tickets, only those who hit the jackpot generally make the news. If you perused all lottery stories without knowing this, you might wonder if lotteries almost always pay off handsomely. Not only would this seem unprofitable for those running such contests, it would also appear to violate the laws of chance. However, the selection principle of newsworthiness strongly favors the minute subset of parallel histories that end up in success. Similarly, the selection principle of conscious observation strongly favors the minute subset of parallel universes that end up producing intelligent life.

Throughout the final decades of the twentieth century—with respected physicists such as DeWitt, Collins, and Hawking referring in their research to a large or even infinite tally of universes—the speculative concept of alternative realities became a serious scientific talking point. Theorists grew bolder in their allusions to parallel realms beyond the reach of telescopic surveys. If a physical parameter couldn’t be nailed down through an analysis of the observed universe, many researchers began to rely on a toolbox of effects based on the supposition of a largely unseen multiverse.

In 1980, American physicist Alan Guth proposed cosmic inflation as a potential solution of a number of issues in modern cosmology, including the question of why the present-day universe is so uniform. Instead of invoking anthropic reasoning, he suggested that the very early universe went through a stage of ultrarapid expansion that stretched out all abnormalities beyond the point of observability—similar to pulling on a bed sheet to smooth out the wrinkles. Guth’s initial theory, though promising, presented a number of quandaries, including a prediction of observable transition zones between sectors of the universe possessing different conditions. Because astronomy doesn’t record such barriers, the theory required modification.

Three years later, Russian cosmologist Andrei Linde linked the inflationary concept with the multiverse idea through a novel proposal called chaotic inflation. In Linde’s variation, the multiverse is a nursery harboring the seeds of myriad baby universes. These seeds are sown through a randomly fluctuating scalar field (something like the Higgs but more variable) that sets the value of the vacuum energy for each region. Through the general relativistic principle that mass and energy govern geometry, the places where this energy is highest stimulate the fastest-growing areas—such as the abundance of jobs triggering growth in certain communities. As in sprawling suburbs plowing over fallow farms, the most rapidly expanding parts of the universe—the inflationary regions—quickly dominate all of the others. Linde’s conclusion was that we live in one of these hyperexpanded megalopolises—with any others long since nudged away beyond possible detection.

Inflation has become a popular way of understanding the overall uniformity of the observable cosmos. One of its key advantages over pure anthropic argumentation is that it doesn’t rely on the existence of humans to explain how tapioca pudding-like blandness emerged from the bubbling chaos of the primordial universe. Yet, by literally pushing alternative versions of our universe beyond measurement, inflationary cosmology removes a potential means of verification. Fortunately, it offers predictions about the distribution of matter and energy in the stages of the universe after inflation. These characteristic patterns manifest themselves in the cosmic background radiation, which has been analyzed by WMAP and other surveys. The consensus of astrophysicists today is that cosmic inflation in some form remains a viable explanation of how the early universe developed. What form of inflation might have occurred and what could have caused such an era remain open questions.

The latest breed of parallel universe theory, the braneworld hypothesis, relies not on unseen realms of our own space but rather on dimensions beyond the familiar three. The far-reaching idea proposes that ordinary space comprises a three-dimensional membrane—or “brane,” for short—floating in a higher dimensional reality called the bulk. According to this notion, the bulk would be impervious to all particles except gravitons. Because the carriers of the electroweak and strong interactions cannot penetrate its depths, its existence would affect only gravitational interactions. Hence, without photons being able to enter the bulk, we could not see it. The dilution of gravity by means of gravitons leaving our brane and infusing the bulk would explain why gravity is so much weaker than the other forces.

The concept of branes is a variation of string theory that generalizes the jump rope-like vibrations of string into pulsating objects of two, three, or higher dimensions—akin to bouncy trampolines or shimmering raindrops. These could have an enormous span of sizes—ranging from minute enough to represent elementary particles to grand enough to encompass all of observable space. From the latter stems the idea that everything around us, except for gravitons, lives on a brane.

Branes have been under discussion as particle models for several decades. Dirac conceived the idea in the 1960s that particles are extended rather than pointlike. He didn’t push the concept very far, however, and it was scarcely noticed by the physics community. In 1986, Texas researchers James Hughes, Jun Liu, and Joseph Polchinski constructed the first supersymmetric theory of membranes, demonstrating how they could represent various types of particles. The following year, Cambridge physicist Paul Townshend coined the term p-branes to denote higher-dimensional extended objects dwelling in an eleven-dimensional reality—like curiously shaped peas living in an exceptionally spacious and intricate pod. (The “p” takes on values representing the number of dimensions of the membrane.)

Around the same time, Townshend, his colleague Michael Duff, and other theorists revealed deep connections between membranes and strings called dualities. A duality is a kind of mathematical equivalence that allows swaps between the extreme cases of certain variables—for example, exchanging a microscopically small radius for an enormous one—while preserving other physical properties. It is like a card game in which the numbers “1” and “11” are both represented by aces, allowing players with aces to switch their value strategically from low to high to wield the best hand. Similarly, there are cases in membrane theory in which flipping certain variables from small to large serve well in proving certain equivalences.

Membrane theory was little noticed by the mainstream physics community until the mid-1990s, when a combination of dualities developed by researchers in that area served to unite the five kinds of string theory. When string theory first came into prominence in the early 1980s as a potential “theory of everything,” various theorists proposed an embarrassing assortment of types—technically known as Type I, Type IIA, Type IIB, Heterotic-O, and Heterotic-E—each of which seemed suitable. How to distinguish which was the real deal? Surely a theory of everything must be unique.

It would be like different witnesses to a crime scene relating clashing descriptions to a detective—with one saying, “He had a long gray coat,” another indicating, “He was wearing a short blue vest,” and so forth—until the sleuth figured out that shadows and lighting altered the culprit’s appearance. An awning blocking the Sun from a certain angle darkened his jacket and made it seem longer. Similarly, dualities gleaned from membrane theory showed that by changing perspectives all five varieties of string theory can be transformed into one another.

At a 1995 conference in Southern California, the leading string theorist Ed Witten dramatically announced the discovery of the “duality of dualities” uniting all of the string theory brands into a single approach, which he called “M-theory.” Rather than defining the term, he left its meaning open to interpretation, asserting that the “M” could stand for “magic,” “mystery,” or “matrix.” Others thought immediately of “membranes” and “mother of all theories.” The excitement generated by that announcement and the realization that string theory could be unified heralded what became known as the second string revolution (the first revolution being the 1980s discovery that string theory doesn’t have mathematical anomalies).

In the unification of string theory, one of the parameters found to be adjustable is the size of what is called the large extra dimension. This nomenclature distinguishes several distinct kinds of dimensions. First of all, there are the three dimensions of space, length, width, and height, which, along with the dimension of time, make up four-dimensional space-time. Second, following an approach first suggested by Swedish physicist Oskar Klein, there are the small “compactified” dimensions—those curled up into tight knots too minuscule ever to observe. According to the ideas of Witten and others, these form various types of six-dimensional clusters named Calabi-Yau spaces after mathematicians Eugenio Calabi and Shing-Tung Yau. Finally, there is an eleventh dimension of adjustable size—with dualities enabling it to thicken like dough mixed with yeast. This large extra dimension could conceivably be of detectable proportions.

How can we envision an extra dimension perpendicular to those we normally experience? It’s like describing a hot air balloon ride to people who have never left the ground. Before the age of ballooning, nobody ever experienced Earth from an aerial perspective. Balloons—and later airplanes and space-ships—permitted far greater exploration of the dimension of height. If the eleventh dimension exists, and it is not curled up, what prevents us from experiencing that, too? According to some theorists, the answer may lie in the stickiness of the strings that make up matter and luminous energy.

A critical aspect of M-theory is the concept of the Dirichlet brane, or “D-brane” for short, developed by UC Santa Barbara researcher Joseph Polchinski, along with J. Dai and R. G. Leigh. Polchinski defined these as extended objects to which the end points of open strings can be attached. Open strings are those not connected with themselves, rather hanging loose like strands of spaghetti. The opposite of these are closed strings, which form complete loops like onion rings. Polchinski and his colleagues showed that open strings naturally cling to D-branes as if their ends were made of glue, but closed strings have no such constraint.

String theory represents quarks, leptons, photons, and most other particles as open strings. The exception is gravitons, modeled by closed strings. Therefore, aside from gravitons, all particles would naturally stick to a D-brane. Gravitons, on the other hand, would be free to wander away from one D-brane and head, like migrating birds, toward another.

The dichotomy between the stringy behavior of gravitons and other particles suggested a way to model the relative weakness of gravity using M-theory and resolve the hierarchy problem described earlier. In 1998, Stanford physicists Nima Arkani-Hamed, Savas Dimopoulos, and Gia Dvali (joined for one paper by Ignatius Antoniadas) suggested a scenario called the ADD model (after their initials) involving two D-branes separated by a large extra dimension on the order of ⅟25 of an inch in size. The second D-brane would represent a parallel universe, or another section of our own universe, right in front of our eyes but completely invisible. Because all standard model fields would remain confined to our own brane, photons would never be able to make the leap and illuminate the parallel brane. The strong and weak forces would similarly keep mum about the close but hidden realm. Instead, the only means of discerning its existence would be through the unseen tugs of gravity.

Due to its ability to fill the bulk in between our brane and the parallel brane, gravity would become diluted—making it much less powerful than the other interactions. It would be similar to four boilers in the basement of a ten-story apartment building, with the first three used to provide steam for a spa and sauna in an adjacent room, and the fourth pumping out heat for the other floors. While those in the spa might enjoy the full force of the steam, those on the highest floor might be huddled under blankets in chilly rooms. The strength of the boilers might be the same, but the dilution of the steam the fourth one produced would make it much less effective. Similarly, the leakage of gravitons from our brane would allow them to have the same interactive strength in principle as other exchange particles—weakened only because of their seepage into the bulk.

Unlike the MSSM (Minimal Supersymmetric Standard Model) method of augmenting the Standard Model with supersymmetry, the large extra dimensions approach offers the advantage of a single unification energy rather than several. Everything would be united on the TeV scale, which is, conveniently, the energy of the LHC. Gravity would just appear weaker because of its secret excursions to a nether realm. The tremendous energy of the Planck scale, which is much higher than the TeV scale, would never have to be approached to test unification. If that’s true, it would sure save a lot of money.

Large extra dimensions also offer the enticing possibility of helping astronomers understand dark matter. In a variation of the scheme, called the Manyfold Universe, the ADD team, along with Stanford physicist Nemanja Kaloper, pondered what would happen if our brane were folded up like an accordion. Stars that are distant along our brane—their light taking millions of years to reach us—could be close together by way of a shortcut through the eleventh dimension. It would be the same as standing at the end of a serpentine line winding around a zigzag chain-link fence and then having someone lift a chain that allows you suddenly to be right next to the person formerly well ahead of you.

Because gravitons could breach the shortcut through the bulk, two otherwise distant stars could gravitationally influence each other. This influence would be felt but not seen, offering a possible explanation for at least one form of dark matter. In other words, some types of dark matter would actually be luminous matter pulling on other luminous matter through the curtain of the bulk.

One of the appealing aspects of the ADD scenario is that it offers testable predictions. It presages modifications to the law of gravity on scales less than ⅟25of an inch. In contrast to the conclusions of both Newton and Einstein, it hypothesizes that gravitational attraction, for those short distances, would no longer follow an inverse-squared behavior but would rather be modified by an additional factor. For large distances, such as the radius of the moon’s orbit around the Earth, this factor would be insignificant, explaining why the discrepancy has never been noticed. Unfortunately for the success of the theory, despite numerous tests using sensitive instruments, the discrepancy has yet to be detected on the smallest scales, either. For example, experiments by a group led by Eric Adelberger at the University of Washington using a delicate kind of twisted pendulum called a torsion balance have measured gravitational attraction to be an inverse-squared relationship for distances much smaller than⅟25 inch. This has cast doubt upon at least the simplest form of the theory.

In 1999, physicists Lisa Randall and Raman Sundrum proposed a different kind of braneworld scheme that doesn’t require the same stark modifications of the law of gravity. Although, like the ADD model, the Randall-Sundrum model posits two three-dimensional branes—one representing the observable universe where the Standard Model lives; and the other, a kind of forbidden zone where only gravitons dare venture—it doesn’t require the distance between the branes to be measurably large. Rather, the parallel branes could be so close together to elude even the most sensitive instruments.

To achieve this feat, Randall and Sundrum found a clever way to dilute gravity without the need for a large extradimensional arena. They proposed a warping of the bulk that would concentrate the greatest part of the gravitons’ wave function away from our brane. This warping would be a function of the distance from our brane in the extra dimension—growing deeper like the ocean away from the shore. Consequently, gravitons would have a much higher probability of being in the region near the other brane than touching ours. They would have minimal interaction with the particles on our brane—rendering gravity much weaker than the other forces.

We can envision the distinction between the ADD and Randall-Sundrum models in terms of choices an urban planner might make about accommodations for parking to keep cars away from the main street of a town. One option, analogous to the ADD approach, would be a spacious, flat parking lot nearby. Most cars would be scattered around its interior, far from the street. If there isn’t much space to spare, however, the planner might choose instead to dig deep and build an underground garage. Cars entering the garage would follow a ramp downward. As in the flat case, the cars would be well off the street—with the advantage of minimizing the impact on the cityscape. That second option would be more akin to the Randall-Sundrum approach.

To complete the analogy, we can think of Main Street as corresponding to the three-dimensional space in which we live, the number of parked cars on the street as representing the measured strength of gravity, and satellite photos as signifying scientific observation. The situation with no off-street parking opportunities and cars jammed on Main Street would represent gravity as being much stronger in our three-dimensional space than what we actually detect in nature. The case with the flat parking lot would represent weak gravity and a large extra dimension that could easily be spotted by scientists. Finally, the case with the underground garage would similarly allow for weak gravity, but with the bonus of keeping the extra dimension concealed from direct scientific detection. Someone perusing an aerial shot might mistake the community for a quiet town with few cars—like a physicist mistaking our cosmos for one with a paltry number of dimensions and weak gravity.

If the bulk is scooping up gravitons like a plethora of zealous dustpans, might there be a way of detecting the extradimensional leakage with the LHC? One method, already attempted at the Tevatron, would be to look for events in which the detected particles spray in one direction but not another. This imbalance would indicate that an unseen particle (or set of particles) carried away a portion of the momentum and energy. Although this could represent an escaping graviton, more likely possibilities would need to be ruled out, such as the commonplace production of neutrinos. Unfortunately, even a hermetic detector such as ATLAS can’t account for the streams of lost neutrinos that pass unhindered through almost everything in nature—except by estimating the missing momentum and assuming it is all being transferred to neutrinos. Some physicists hope that statistical models of neutrino production would eventually prove sharp enough to indicate significant differences between the expected and actual pictures. Such discrepancies could prove that gravitons fled from collisions and ducked into regions beyond.

Another potential means of establishing the existence of extra dimensions would be to look for the hypothetical phenomena called Kaluza-Klein excitations (named for Klein and an earlier unification pioneer, German mathematician Theodor Kaluza). These would reveal themselves as shadows in our brane of particles traveling though the bulk. We’d observe these as particles with the same charge, spin, and other properties as familiar particles except for curiously higher masses.

Plato wrote a famous allegory about prisoners shackled to the interior wall of a cave since childhood, unable to observe the outside world directly. They watch the shadows on the opposite wall and mistake these images for real things. For example, they think that the shadows of individuals carrying vessels as they walk by are actual people. Eventually, one of the prisoners escapes, explores the world outside the cave, and informs the others about their delusion.

Similarly, it is possible that the LHC results (from ATLAS or CMS) could serve as a “cave wall” by which we could observe shadows of particles moving in a greater reality. These particles would have an extra component of their momentum corresponding to their ability to travel along an extra dimension. Because of the unobservability of the extra dimension, we couldn’t actually see the particles moving in that direction. Rather, their unseen motion would manifest itself through an additional amount of mass associated with their extra energy and momentum. Researchers hope that the energies of some of the lightest Kaluza-Klein excitations are at the low end of the TeV scale, which could enable them to be observed by LHC researchers.

A host of research articles have offered predictions for potential signals of Kaluza-Klein gravitons and other particles beefed up by extra dimensions. These could decay into electron-positron pairs, muon-antimuon pairs, or other products at energies indicating their possible origin. Studying such excitations would yield valuable information about the size, shape, and other properties of the bulk.

Finding evidence of extra dimensions isn’t one of the primary goals of the LHC. However, discovering unseen romping grounds beyond the view stands of our familiar arena would make particle physics a whole new game. Like Plato’s cave dwellers, we’d have to face the possibility that everything around us is a shadow of a greater reality. Yet if, on the other hand, visible space plus time make up all that there is, the quest for extra dimensions would ultimately prove futile. Theorists would need to concoct other explanations for why all the other forces are so much more potent than gravity.

One can imagine Voltaire’s spirit hovering over the LHC, stirred by the whirlwind of particles circulating beneath his former village of Ferney, and smiling at the search for other possible worlds. Would he have considered it valid science or an exercise in Panglossian “metaphysico-theologico-cosmolonigology”? Perhaps he’d simply be pleased that his haunting grounds remain un jardin ouvert sur le monde, cultivated above and below by motivated gardeners to sustain the body and the mind.