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

Chapter 2. The Quest for a Theory of Everything

What immortal hand or eye
Dare frame thy fearful symmetry?

—WILLIAM BLAKE (“THE TYGER,” 1794)

In the heart of Geneva’s old town stands the majestic Cathedral of St. Pierre. Between 1160 and 1232, it was constructed in the austere, measured Romanesque style characteristic of the times. Emphasizing the basic unity of God’s plan, its vaulting arches and lofty towers were planned to form a careful equilibrium—the left side balancing the right.

Over the ages, the shifting currents of religious belief eroded the cathedral’s original design. In the sixteenth century, the Reformation ushered in a fanatical desecration of its interior artwork, including the destruction of statues and the whitewashing of frescoes painted on the walls. Adding to the architectural jumble, the original frontage was replaced with a neoclassical facade in 1750.

Many physicists believe that the universe was once a simple cathedral, elegant and balanced. According to this view, like a perfectly fashioned nave, the cosmos began with an equal mixture of opposites—positive and negative charge, matter and antimatter, leptons and quarks, fermions and bosons, and so forth. As the universe cooled down from its initial hot, ultracompact state, these symmetries spontaneously broke down. Presently the cosmos is thereby a bit of a jumble, like St. Pierre’s.

One of the principal missions of the Large Hadron Collider (LHC) involves a kind of archeological expedition—attempting to piece together some of nature’s original symmetries. Searching for these symmetries pertains to the ultimate quest to unify all of the particles and forces in the universe under a single umbrella. Looking back to the first moments of the universe could provide the answer. The LHC’s extraordinary energies, when applied on the particle scale, reproduce some of the conditions a tiny fraction of a second after the Big Bang. On a minuscule level, it offers a kind of journey back in time.

The LHC isn’t re-creating the actual Big Bang itself. Although the LHC’s experiments involve comparable energy per particle, they produce incomparably less energy overall. It’s like pouring a thimbleful of water on a smidgen of sand to test beach erosion; although it might simulate the effect of a lap of the ocean on a bit of the beach, it would hardly reproduce the might of the entire Pacific.

Theoretical clues as to the original state of symmetry present themselves through conserved or near-conserved quantities in nature today. This near-symmetry led to the development of the elegant Standard Model. The Standard Model is a mathematical way of expressing two of nature’s fundamental forces—electromagnetism and the weak interaction (a cause of certain types of radiation). There have been numerous attempts to unify these interactions with either or both of the two other natural forces, the strong interaction (that binds nuclei together) and gravity.

For example, Einstein spent the final decades of his life trying to unite electromagnetism with gravity through various extensions of general relativity. He believed that the laws of nature offered subtle signs of an original harmony. These hidden universal principles, he hoped, would eventually reveal themselves through diligent mathematical exploration. Alas, all of his efforts were to no avail. He died in 1955 without finding a satisfactory resolution of his quest.

In the decades after Einstein’s death, the Standard Model of the electroweak interaction—as the merger of electromagnetism with the weak interaction is called—took shape as the only fully successful unification model to date. Even this matchup took much hard work and creative thinking. Under mundane conditions, electromagnetism and the weak interaction have several noticeable distinctions. Electromagnetism acts over an incredibly wide range of distances, from the minute scale of atoms to the colossal spans of lightning bolts. The weak interaction, in comparison, acts exclusively on the subatomic level. Moreover, while the electromagnetic force can bring together or push apart charged particles, it never alters their actual charges or identities. Thus, a positively charged proton tugging on a negatively charged electron each remain just that. In contrast, the weak interaction, in its typical dealings, acts like a minuscule marauder, robbing particles of their charge and other properties. For example, it causes beta decay, a process that involves the transformation of a neutral neutron into a proton (along with other particles).

Clever theorists noted, however, that neutrons and protons have similar (but not identical) mass. They pondered, therefore, if the transformation of one into the other could be a one-time symmetry that somehow cracked. Like the Liberty Bell, perhaps it once rang like others forged in the same foundry but then acquired imperfections over the course of time. Could it be that electromagnetism and the weak interaction were born twins but had distinct formative experiences?

The concept of spontaneous symmetry breaking, on which the Standard Model is based, stems from a completely different field of physics: the study of superconductivity. Certain materials, when extremely cold, lose all resistance and conduct electricity perfectly. The “supercurrents” block external magnetic fields from entering and keep internal fields intact. Superconducting magnets are used throughout the LHC to generate the ultrahigh fields needed to steer particles around the ring and to keep them focused in tight bunches.

In 1957, John Bardeen, Leon Cooper, and J. Robert Schrieffer (BCS) developed a successful quantum theory of how materials organize themselves to produce such a superconducting state. The theory relies on special correlations between electrons, known as Cooper pairs. The paired electrons organize themselves and, like dutiful soldiers, march in unison. Hence, they are able to overcome all resistance and become perfect electrical conductors.

The reason paired electrons are able to move in lockstep while single electrons cannot has to do with a feature called the Pauli exclusion principle. Elementary particles fall into two different categories called fermions and bosons. Electrons (if not in Cooper pairs) are an example of fermions and photons are an example of bosons. The Pauli exclusion principle, a critical rule of quantum mechanics, states that no two fermions can share the same quantum state. The principle doesn’t apply to bosons, for which any quantity can occupy the same state. It’s like a summer camp for which any number of kids (the bosons) are allowed to share the same bunk, but counselors (the fermions) each get a room to themselves. Naturally the former would be much more clustered than the latter—explaining why bosons can act in tandem more easily. Although composed of two fermions each, Cooper pairs behave like bosons, explaining their lockstep behavior.

The mortal enemy of superconductivity is heat. At a sufficiently high temperature, depending on the material, synchronized motion breaks down and superconductivity reverts to normal electrical behavior. The changeover resembles the transformation from crystalline ice into liquid water and is called a phase transition.

Four years after the BCS theory was published, Japanese-born physicist Yoichiro Nambu cleverly demonstrated that its assumptions could similarly describe how symmetry could spontaneously break down in particle physics. With a lowering of temperature, such as in the instants after the Big Bang, a phase transition could occur in which bosons suddenly synchronize themselves and turn aimless behavior into coordinated patterns. He would share the 2008 Nobel Prize for this key finding.

Then, in 1964, British physicist Peter Higgs proposed a new type of boson that would acquire mass through a special kind of spontaneous symmetry breaking. In acquiring mass it would also bestow mass on other particles. Although the boson ended up being named after him, there were several other similar mechanisms proposed independently at the time, including in one paper by Gerald Guralnik, C. Richard Hagen, and Tom Kibble, and another by François Englert and Robert Brout.

In quantum physics, energetic fields take shape due to the potentials they live in. A potential is a kind of a slope, well, or barrier that delineates how energy changes with position. A clifflike potential, for instance, represents a much steeper energy transformation than a plateaulike potential. Higgs assigned his boson a peculiar potential shaped like the bottom of a basin for higher temperatures but like the rim of a basin for lower temperatures. By lowering the temperature below a critical value, the boson is forced from the center of the basin (a zero-energy state, known as the true vacuum), to a place along the rim (a non-zero energy state, called the false vacuum). The arbitrary place on the rim where the Higgs boson ends up—indicating its phase (a type of internal parameter that can assume different angles, like the hands on a clock)—locks in the phase of the ground state of all of space. That’s because, unlike an individual particle, a vacuum must be unique and can’t have different phases at each point. Hence, the original symmetry is spontaneously broken.

To envision this situation, consider a new property development that is a checkerboard of perfectly square tracts. Before houses are built on the land, each tract is absolutely symmetric with no features distinguishing the north side from the south. Now suppose that a regional ordinance mandates that houses must be spaced a certain distance apart. If the house to be built sits precisely in the center of one of the tracts, then all of the others could follow, and the tracts would each remain symmetric. That’s similar to the high-temperature case for Higgs bosons. However, suppose the first house appears in the southwest corner of one of the tracts. The neighboring houses, required to be a specific distance from others, would have to do the same. Eventually, all of the tracts would be occupied with houses on their southwest corners—breaking their original symmetry because of a single, arbitrary, local decision. If the first house had been built in the northeast corner instead, perhaps that would have set the overall trend as well. Similarly, the phase choice of a Higgs boson locally sets the overall phase globally.

As Higgs demonstrated, once the boson field’s phase is set, it acquires a mass associated with its nonzero energy. This mass does not arise out of the blue; rather it represents the transformation of energy into mass described by Einstein’s special theory of relativity that takes place during the transition between the different vacuum states. Moreover, the Higgs boson interacts with other particles and bestows them with their own masses. Thus, the Higgs could well have set the masses for all of the massive particles in the universe. Because of its ability to seemingly pull mass out of the blue, it has been nicknamed the “God particle”—an epithet with which Higgs himself is not particularly comfortable. It took awhile for the modest professor to get used to a particle named after himself, let alone one assigned divine features.

Higgs’s idea was so radical that his original paper was rejected by the leading European journal, Physics Letters. He later recalled his disappointment:

I was indignant. I believed that what I had shown could have important consequences in particle physics. Later my colleague … at CERN told me that the theorists there did not see the point of what I had done …

Realizing that my paper had been short on salestalk, I rewrote it with the addition of two extra paragraphs, one of which discussed spontaneous breaking of the currently fashionable SU(3) flavor [quark type] symmetry, and sent it to Physical Review Letters… . This time it was accepted.¹

Higgs’s paper stimulated a novel look at unifying the electromagnetic and weak forces into a single theory. The critical idea is that these forces are conveyed by means of a quartet of exchange particles, three of which acquire mass through the Higgs mechanism. An exchange particle is a boson that cements the connection between a set of matter particles, causing attraction, repulsion, or transformation. The more massive the exchange particle, the shorter the range of the corresponding interaction.

As the carriers of a force with indefinite range—electromagnetism—photons are massless. Moreover, because they don’t affect the charge of interacting particles, they are electrically neutral. Two of the exchange particles for the weak force, however, called the W⁺ and W^- bosons, are charged and massive, reflecting the properties of the interaction they convey—charge-transforming and short-ranged. There is also a neutral weak force carrier, called the Z boson. Its existence was proposed in 1960 by Harvard theorist Sheldon Glashow. All three of the weak exchange particles have since been found.

Once Higgs’s mechanism was included, along with representations of the exchange particles and fields representing various types of matter, all of the pieces for uniting electromagnetism with the weak interaction snapped into place. In 1967, American physicist Steven Weinberg, working at MIT, and Pakistani physicist Abdus Salam, working at Cambridge, independently developed a successful theory of electroweak unification. It is a masterful theory—the crowning achievement of decades of experimental and theoretical explorations of the nature of subatomic particles. Its designation as the Standard Model is a recognition of its extraordinary importance.

According to theoretical predictions, a remnant of the original Higgs field ought to be leftover and detectable. Surprisingly, despite several decades of experimental investigations at that energy, the Higgs boson has yet to be found. Through the LHC, the physics community hopes at long last to identify the Higgs boson and establish the Standard Model on debt-free grounds.

LHC researchers are fully aware that the Standard Model could prove to be incomplete. Too many mysteries remain about inequities in the universe for the Standard Model to be the be-all and end-all, anyway. Because the Higgs has yet to be found and other interactions are yet to be united satisfactorily, among other things, many physicists today are agnostic about the Standard Model’s ultimate validity. Although it has been enormously successful in explaining most particle phenomena, like many beautifully painted old frescoes it has acquired cracks.

At the LHC, researchers often consider the Standard Model predictions along with several alternatives, hoping that experimental results will distinguish among the possibilities. For example, experimenters are preparing themselves for Higgs bosons of higher mass than the Standard Model forecasts or even, as some theories foretell, a triplet of Higgs particles. As midwives to a possible impending birth, they need to ready themselves for a variety of natal scenarios.

Of the unification models that have emerged in the past few decades, the most popular by far has been string theory. String theory envisions the most elementary constituents of nature as incredibly minuscule (less than 10^-33inches, called the Planck length) vibrating strands of energy instead of point particles (as envisioned in the Standard Model). Thus they have a finite, but unobservably small, rather than infinitesimal extent. An immediate mathematical advantage is that any equations that include inverse length are finite, rather than infinite. This helps avoid certain mathematical maladies that plague standard quantum field theory, in which particular terms become indefinitely and unrealistically large.

String theory is sometimes called the Theory of Everything (TOE) because it purports to include all known interactions. Its finiteness makes it particularly adept to handle gravitation, which has resisted all previous attempts at inclusion within a unified theory—including Einstein’s famous effort. Critics, however, have pointed to string theory’s embarrassment of riches. Not only could it potentially include the Standard Model as one of its subsets, but it also seems to encompass myriad physically unrealistic configurations. Therefore one of the long-term goals of string theory is narrowing it down to a single TOE that precisely models our own universe.

According to string theory, different fields and particles are distinct modes of energetic vibrations. If a guitar is out of tune, you can try to tighten its strings. Similarly the energetic vibrations of string theory respond to changes in tension. They also exhibit harmonic patterns, like the overtones that enrich a musical composition. These string configurations correspond to the assorted masses, spins, and other properties of various types of constituents.

String theory started out as solely a model of the strong interaction. In that guise, it encompassed only carriers of force—in other words, bosons. Bosonic string theory could never describe material particles, represented at the tiniest level by fermions. Theorists were motivated to find a way of describing fermions too and model the stuff of matter along with the agents of attraction.

To include fermionic strings along with bosonic strings, physicist Pierre Ramond of the University of Florida proposed the concept of supersymmetry in 1971. Ramond’s notion of a transformation connecting matter with force quickly caught fire and ignited the interest of all manner of theorists—even those unenthusiastic about strings themselves. A symmetry uniting fermions with bosons seemed to be the ultimate particle democracy.

Moreover, unlike conventional quantum field theory, like the Standard Model, supersymmetry makes ample room for gravity. For the first time in the history of quantum physics, gravity seemed within reach of incorporation into a unified field theory. Suddenly, Einstein’s dormant quest for unification sprang back to life like an antique car equipped with a roaring new engine.

Propelled by the dynamo of supersymmetry, which acquired the nickname “SUSY,” field theorists who believed in its power found themselves with the choice of several different routes. One was to press forward with superstrings, the supersymmetric theory of strings, and to explore their fundamental properties, hoping these would match up with observed aspects of elementary particles. In 1984, an important result by Michael Green and John Schwarz showing that superstring theory lacks certain mathematical blemishes called “anomalies” was cause for celebration. Superstring theory’s vibrant vehicle seemed to gleam even more.

One challenge for those taking the fundamental route, however, was making their case to experimentalists. String theory calculations are often tricky and involve many free parameters. These could be adjusted to accommodate a wide range of predictions. Also, until Ed Witten and other theorists showed their equivalence in the mid-1990s, string theories appeared to come in several different varieties. Given such a multiplicity of parameters and theories, researchers were unsure exactly what to test. At any rate, a realm so tiny that nuclei loomed like galaxies in comparison seemed virtually impossible to explore.

Moreover, superstrings are mathematically consistent only if they live in a world of ten dimensions or more. To accommodate the fact that people observe only three dimensions of space and the dimension of time, theorists recalled an idea developed by Swedish physicist Oskar Klein in the 1920s and proposed that six of the dimensions are curled into a ball so tiny that it cannot physically be observed. That worked well mathematically but offered no incentive for experimenters to try to probe the theory. Given the inability to obtain experimental proof, string theory’s skeptics—Glashow and Richard Feynman, among the prominent examples—argued that it remained on shaky ground.

Laboratory researchers were enticed to a greater extent by a more conservative application of supersymmetry, called the Minimal Supersymmetric Standard Model (MSSM). Proposed in 1981 by Stanford University physicist Savas Dimopoulos, along with Howard Georgi, it offered a way of extending the Standard Model to include additional fields with the goal of preparing it to be part of a greater unified theory. These fields included supersymmetric companion particles, the lightest of which could potentially be seen in the lab.

The ultimate unification would include gravity. Yet gravity is far weaker than the other forces. Tracing back the history of the universe to a time when gravity could have been comparable in strength to its kindred interactions requires us to ponder its conditions less than 10^-43 seconds after the Big Bang. At that moment, called the Planck time, the cosmos would have been unimaginably hot and compact, so much so that quantum mechanical principles pertaining to nature’s smallest scales would apply to the realm of gravitation. For the briefest instant, the disparate worlds of general relativity and quantum mechanics would be joined through the shotgun marriage of quantum gravity.

Because unification of all of the natural forces would have taken place at such high energies, the particles involved would be extremely heavy. Their mass would be a quadrillion times what could possibly be found at the LHC. Interacting with the Higgs, the Planck scale particles would tug its energy so high as to destabilize the Standard Model. In particular, it would render the weak interaction in theory much feebler than actually observed.

To avoid such a catastrophe, Dimopoulos and Georgi made use of auspicious mathematical cancellations that occurred when they constructed a supersymmetric description of a unified field theory. The cancellations negated the influence of higher mass terms and protected the Higgs from being yanked to unrealistic energies. One caveat is that the Higgs itself would be replaced by a family of such particles—charged along with neutral—including a supersymmetric companion called the higgsino.

If some of the low-mass supersymmetric companions are found, they would offer vital clues as to what lies beyond the Standard Model. They would reveal whether the MSSM or other extensions are correct, and if so, help tune the values of their unspecified parameters (the MSSM has more than a hundred). Ultimately, the findings could provide a valuable hint as to what string theory (or another unified field theory) might look like at much higher energies.

Because string theory has so many different possible configurations and its full energy could be well beyond reach, it is unlikely, however, that any LHC results would either confirm or disprove string theory altogether. At best, they would simply offer more information about string theory’s limits and constraints. The experimental discovery of supersymmetry, for instance, would not validate string theory but might assure some of its proponents that they are on the right track.

One of the groups most desperately seeking SUSY consists of researchers trying to resolve one of the deepest dilemmas facing science today: the missing matter mystery. Astronomers are puzzled by unseen matter, scattered throughout the universe, that makes its presence known only through gravitational tugs—for example, through extra forces on stars in the outer reaches of galaxies. The dark matter mystery is one of the deepest conundrums in astronomy. Some researchers think the answer could be massive but invisible, supersymmetric companion particles. Could a supersymmetric payload be the hidden ballast loading down the cosmic craft? Soon the world’s most powerful high-energy device could possibly reveal nature’s unseen cargo.

Resolving all of these mysteries requires the impact of high-energy collisions monitored carefully by sophisticated detectors to determine the properties of their massive byproducts. Such methods have a long and distinguished history. The story of using collisions to probe the deep structure of matter began a century ago, with gold-foil experiments conducted in 1909. Naturally, the instruments used were far, far simpler back then.

Scientists at that time were trying to explore the inner world of the atom. Little was known about the atomic interior until collisions revealed its secrets. You can’t crack open a coconut through the impact of a palm leaf; you need a sturdy mallet applied with vigor and precision. Revealing the atom’s structure would require a special kind of sledgehammer and the steadiest of arms to wield it.