Scientists have known for nearly a century that matter is composed of atoms, which are various combinations of electrons, protons, and neutrons. In the 1960s, physicists uncovered a deeper level to matter when they found that protons and neutrons in turn are composed of particles whimsically called quarks. We now know of six kinds of quarks, and combinations of them (in pairs or triplets) explain all of the heavier particles in the universe — protons, neutrons, and many other exotic particles (like gluons and bosons) that turn up in experiments.

That’s the basic understanding of the matter in the universe, but how do particles interact? Beginning in the 1930s, physicists developed a detailed set of mathematical models of four fundamental forces in the universe: gravitation, electromagnetism, and the strong and weak nuclear forces. We can think of each of them in terms of fields acting in space. More amazingly, these four basic “force fields” are themselves constructed from the exchanges between new families of particles and the elementary electrons and quarks. The photon transmits electromagnetic forces; eight different gluons transmit the strong nuclear force that holds quarks together inside protons; three intermediate vector bosons transmit the weak nuclear force, which is responsible for radioactivity; and some physicists believe that gravitons transmit gravitational forces, but these particles remain undiscovered.

In the “standard model,” scientists group the description of matter and forces by these various detailed mathematical theories. It forms the backbone of every calculation that physicists perform when they try to predict what will happen in one of their expensive “atom smashers.” Whenever they design new technologies, perform new experiments, or even study the nature of black holes, they begin with the heavily tested mathematical equations of the standard model.

The standard model is beautiful and simple, but it also seems to be incomplete. Scientists can “unify” two of the forces — electro-magnetism and weak nuclear — into a single mathematical theory. And they can combine this with the strong nuclear force in the “grand unification theory.” But the mathematics of gravity remains stubbornly different, and thus physicists need two separate descriptions of how the four forces work in nature. Wouldn’t it be wonderful if they had only one description instead? This is what some have called the search for a “theory of everything,” and the most promising approach is “super-string theory.” So why did physicists have to reach for strings to fix the standard model, and what does it tell us about the universe?

## Into the depths

Over the past 70 years, scientists have proposed many technical approaches for achieving grand unification, but most of these theories suffered from severe mathematical flaws. For example, sometimes a calculation would result in probabilities that were negative or exceeded 100 percent. According to one model, calculations spewed out legions of faster-than-light particles called tachyons. But one interesting approach has gained a huge following among physicists since the early 1980s — strings.

According to the standard model, particles are pointlike; no matter how deeply scientists try to probe one’s interior, all they would find was a still-smaller “point” of energy that represents all of the particle’s properties, such as its mass, charge, and spin. This turns out to be a huge mathematical problem. Imagine trying to crowd the mass and energy of, say, an electron into a smaller and smaller sphere. Eventually, it would become a vanishingly small point in space, and the particle’s density and energy would reach infinity. This infinity would then cause any calculation that incorporates density and energy to “blow up” into nonsense. So about 30 years ago, physicists came up with a solution to replace the internal shape of a particle with some other kind of shape that didn’t have a vanishing point: a mysterious, closed loop of energy called a string.

The basic idea is that every particle of matter (an electron, quark, ghostlike neutrino, etc.) and every particle that transmits a force (photon, gluon, intermediate vector boson, and graviton) is actually a small one-dimensional loop of something. It can be either open with two ends or closed in a loop. As this 1-D loop of string moves forward in time, it sweeps out a two-dimensional surface. It also can split to form two separate loops of string that in turn shape two other closed surfaces. These surfaces are called “worldsheets,” and the splitting of one string into two is a model for the decay of one particle into two. (To visualize this, imagine that the string is a belt on a pair of pants. As the belt slides down to the ground, it sweeps out the surface of the pants, and splits into the two pant legs to form two other closed belts that continue down to the ground to form the surface of the legs.) Going the other direction, two strings change into one as two particles collide and combine.

These loops also can vibrate like closed guitar strings, and the precise way that one vibrates determines the exact properties of the fundamental particles it represents or transmutes into. The vibration’s frequency is higher for more-massive particles and lower for less-massive ones.

So, out of what are these strings fashioned? Well, when was the last time you encountered something that was 1-D? I’ve never experienced a 1-D object, and thus I have no expectation of what characteristics to assign to its appearance, like color, mass, size, etc. Every property we would want to describe a string by is rooted in our 3-D experience, so the very question of what such a physical object should represent is beyond our experiences. Fortunately in mathematics, this is not a problem at all. That’s why physicists can work with 1-D strings in such a precise, and logical, way.

Plus, scientists know that particles like the electron are not just tiny spheres with a surface. In fact, these objects have nothing like a surface at all. They are just infinitesimal knots of energy that have specific properties. It is a major challenge to the human Exploring different dimensions

The story gets even weirder because the mathematics that relates these strings to normal particles and their properties cannot exist unless these 1-D strings are moving in a 10-dimensional universe of space and time. Our normal universe has three dimensions of space and one of time, so string mathematics requires that there be an additional six that are completely closed upon themselves and that have finite sizes close to 10-on-33 centimeter.

Take a 2-D piece of paper and crumple it up tightly. Now, stuff that paper into a pingpong ball and crush this ball down to a size of only 10-on-33 centimeter across — some scientists say six dimensions could be hiding in that object. Now, repeat this exercise again and again with different crumpled sheets of paper and pingpong balls at every possible point in 3-D space; string theory says that every time you compact the six dimensions like this, you can end up with a different kind of universe. The exact geometry of these compact dimensions determines exactly what kinds of particles the universe has and their detailed properties.

A 3-D sphere has a certain geometry that allows particles on its surface to move in certain ways; similarly, the string tension and geometry formed by the spaces of these compact dimensions control the vibrations of a string (and what particle it corresponds to). Every kind of particle has a specific six-number address in this compact space, just as Paris has a unique latitude and longitude on the 2-D curved surface of spherical Earth.

It is, of course, difficult to draw a 6-D object, which physicists call Calabi-Yau manifolds. Even if we could, we would be busy trying to draw all of the possible ways they could look: In string theory, there are an estimated 10500 of these spaces, and each one describes a separate mathematical universe of particles and fields. In some of these spaces, electrons do not exist, while perhaps in others we could have a dozen different kinds of quarks, but no photons. These spaces, for example, would not allow rainbows to form.

## But wait, there’s more

If all we had were a new model for what particles look like — vibrating loops in space rather than points — we would not have simplified or unified our standard model. We only would have gained more complex mathematics to account for things we already know. But string theory also has a second ingredient, called “super-symmetry.” As any geometry student has learned, symmetry often makes solving problems easier.

Because of a cube’s symmetry, one can rotate it in the three dimensions of space by 90” and see a new face, but the shape of the cube remains exactly the same. Scientists call this “rotation symmetry.” In the early 1970s, physicists discovered that the particles in the standard model also could be “transformed” into each other by using supersymmetry. (This operation involves quantum mechanics and one of the particle’s intrinsic properties, called spin.) What makes this theory so super is that it automatically includes gravity as a consequence of supersymmetry among the known kinds of particles — finally, all four forces fit naturally in a theory.

But in nature, you never get something for nothing, so scientists had to add a new ingredient to make the math work. In this case, every particle in the standard model has a new superpartner particle to make the transformations work out mathematically. By extending the standard model in this way, scientists now have what is called the Minimal Supersymmetric Standard Model (MSSM). Not only does MSSM correct a number of problems with the standard model, but it also introduces a new candidate particle for the mysterious material that makes up about 85 percent of the universe’s mass — dark matter. The standard model has no way to explain this invisible mass, but the least massive “neutralino” of MSSM has exactly the right properties to account for dark matter.

## Tying it together

In the early 1980s, physicists applied supersymmetry to string theory — to form superstring theory — and came up with five different kinds of superstring theory, each explaining the physical world from A to Z but in various ways. Then in 1995, they realized that these five theories were themselves one, which scientists call “M-theory.”

The way these theories are connected is by precise mathematical operations that involve changing length scales — called “duality transformations.” An example of a more familiar kind of transformation that instead involves rotations is a cube with six faces, each a 2-D projection of the 3-D cube. The true shape of a cube in 3-D can be pieced together from its various 2-D projections, which we see as separate faces of the cube. Each 2-D face can be transformed into one of the other faces by rotating the cube in 3-D space. You can think of each face of the 11-D M-theory “cube” as a separate 10-D superstring theory. The detailed mathematics of 11-D M-theory tells scientists how to transform the 10-D superstring theory into one of the other 10-D superstring theories.

## The evidence, so far

Some physicists look at MSSM as the easiest way to move beyond the standard model without adding a drastic amount of assumptions. The theory also provides new predictions they can test at the world’s most powerful particle accelerator, the Large Hadron Collider (LHC) at the European Organization for Nuclear Research. For instance, scientists are scouring the data for evidence of the known particles’ superpartners, and the lightest should have masses of a few teraelectron volts (TeV), which the LHC can access. (An electron volt, eV, is a unit of energy; visible light photons range from 1.5 to 3.5 eV; a TeV is a million million eV.) If researchers don’t find any, then they will need to replace MSSM with more-complicated models that push the masses of the superpartner particles to still higher energies. So where does this search stand today, now that the LHC has been taking data for more than two years?

The good news is that the standard model is pretty well confirmed. In July 2012, physicists announced that they had discovered a particle that looks just like the last standard-model holdout, the Higgs boson, with a mass of 126 billion eV/(speed of light)2, following a search lasting more than four decades.

The bad news is that, in August 2on and again in November 2012, a team of physicists at the LHC reported that its study of the decay of exotic particles called B-mesons turned up no sign of supersymmetry. These particles should have decayed far more quickly with the help of supersymmetry, but scientists have found no indication of this effect among the trillions of decays studied.

More bad news: Scientists haven’t found any evidence for the supersymmetric particles below 7 TeV, which is interpreted as a major failing for the simplest supersymmetry models (and specifically MSSM). Super-symmetry is the simplest mathematical model that scientists have to unify the four fundamental forces, and nature seems to favor the most basic theories that explain our world. If MSSM fails, it will be the biggest bait-and-switch job that nature has ever foisted on scientists.

By early 2013, the LHC shut down; in 2015, it will power back up and will begin operating at its full designed collision energy of 13 TeV. Physicists have only begun to study what the various theories predict for the lightest supersymmetry particles. They’ve calculated the existence of dozens of new particles spread across the full operating energy range of the LHC, so some optimism is warranted.

The stakes are extremely high: If supersymmetry is found, the discovery road will be opened for superstring theory as the next step beyond MSSM. If they continue to find no evidence of supersymmetry at the LHC, then the simplest versions of MSSM must fall, and superstring theory will seem a far less elegant explanation of a theory of everything. And that would be a shame.

The string theory description of loopy particles offers a rich landscape of new particles and phenomenology, and can extend human understanding of space and time’s creation. The down side, however, is that most of these particles have masses that are well beyond the searchable LHC energy scale. And that’s the biggest problem.

No scientist seriously thinks that after a community of world governments has spent billions of dollars to build the LHC to find “new physics” and hasn’t discovered any, it will garner additional funding to create an even larger collider to probe beyond 13 TeV. If there is no sign of new physics or new particles at the LHC, the negative results will force extremely difficult decisions on physicists: Either innovate a completely new (and inexpensive) technology for accelerating particles to high energies, or languish for decades to come with no new data upon which to test an increasing number of “elegant” theories. So, the next few years of accelerator physics may just give us the verdict on the success of superstring theory.