Unlike model builders, more mathematically inclined physicists try to work from pure theory. The hope is to start with a single elegant theory and derive the consequences, and only then apply the ideas to data. Most any attempt at a unified theory embodies such a top-down approach. String theory is perhaps the most prominent such example. It is a conjecture for the ultimate underlying framework from which all other known physics phenomena would in principle follow. String theorists take a major leap in the physics scales they try to conquer’jumping from the weak scale to the Planck scale at which gravity becomes strong. Experiments probably won’t directly test these ideas anytime soon. But even though string theory itself is difficult to test, elements of string theory do provide ideas andconcepts that potentially observable models have incorporated.

The question physicists ask when deciding on model building versus string theory is whether to follow the Platonic approach, which tries to gain insights from some more fundamental truth, or the Aristotelian one, rooted in empirical observations. Do you take the ‘top-down’ or the ‘bottom-up’ approach? The choice could also be phrased as ‘Old Einstein versus Young Einstein.’ Einstein originally did thought experiments that were grounded in physical situations. Nonetheless, he also valued beauty and elegance. Even when an experimental result contradicted his ideas about special relativity, he confidently (and ultimately correctly) decided that the experiment had to be wrong since its implications would have been too ugly to believe. Einstein became more mathematically inclined after mathematics helped him finally complete his theory of general relativity. Since mathematical advances were crucial to completing his theory, he had more faith in theoretical methods later in his career. Looking to Einstein won’t resolve the issue, however. Despite his successful application of mathematics to general relativity, his later mathematical search for a unified theory never reached fruition.

The Grand Unified Theory proposed by Howard Georgi and Sheldon Glashow was also a top-down idea. GUTs, as they were known, were rooted in data’the inspiration for their conjecture was the particular set of particles and forces that exist in the Standard Model and the strength with which they interact’but the theory extrapolated from what we know to what might be happening at very distant energy scales.Interestingly, even though the unification would happen at an energy much higher than a particle accelerator could achieve, the initial model for a GUT made a prediction that was potentially observable. The Georgi-Glashow GUT model predicted that the proton would decay. The decay would take a long time, but experimenters set up giant vats of material with the hopes that at least one of the protons inside would decay and leave a visible signal. When that didn’t happen, the original GUT model was ruled out. Since that time neither Georgi nor Glashow has chosen to work on any top-down theory that makes such a dramatic leap in energies from those we can directly access in accelerators to those so far removed that they might have only subtle experimental consequences’or likelier still, not any. They decided it would just be too ridiculously unlikely to make a correct guess about a theory so many orders of magnitude away in distance and energy from anything we currently understand. Despite their reservations, many other physicists decided that a top-down approach was the only way to attack certain difficult theoretical issues. String theorists chose to work in a netherworld that isn’t clearly traditional science but has led to a rich, if controversial, set of ideas. They understand some aspects of their theory, but they are still piecing it together’ looking for the key underlying principles as they go along and develop their radical ideas.

The motivation for string theory as a theory of gravity didn’t come from data, but from theoretical puzzles. String theory provides a natural candidate for the graviton, the particle quantum mechanics tells us should exist and communicate the force of gravity. It is currently the leading candidate for a fully consistent theory of quantum gravity’a theory that includes both quantum mechanics and Einstein’s theory of general relativity, and that works at all conceivable energy scales.

Physicists can use known theories to reliably make predictions at small distances, such as the inside of an atom, where quantum mechanics plays a big role and gravity is negligible.

Because gravity has such feeble influence on atomic-mass particles, we can use quantum mechanics and safely ignore gravity. Physicists can also make predictions about phenomena at large distances, such as inside galaxies, where gravity dominates predictions and quantum mechanics can be ignored. However, we lack a theory that includes both quantum mechanics and gravity’and works at all possible energies and distances.

In particular, we don’t know how to calculate at enormously high energies and extremely shortdistances’comparable to the Planck energy or length. Because the influence of gravity is bigger for heavier and more energetic particles, gravity acting on Planck mass particles would play an essential role. And at the tiny Planck length, quantum mechanics would too.

Although this problem doesn’t spoil any calculations for observable phenomena’certainly not those at the LHC’it does mean theoretical physics is incomplete. Physicists don’t yet know how to consistently include quantum mechanics and gravity at extremely high energies or short distances where both have comparable importance for predictions and neither can be neglected. This important gap in our understanding could potentially point the way forward. Many think string theory could be the resolution.

The name ‘string theory’ derives from the fundamental oscillating string that formed the core of the initial formulation. Particles exist in string theory, but they arise from the vibrations of a string. Different particles correspond to different oscillations, much as different notes arise from a vibrating violin string. In principle, experimental evidence for string theory should consist of new particles that would correspond to the many additional vibrational modes that a string can produce. However, most such particles are likely to be much too heavy to ever observe, and that’s why it’s so difficult to experimentally verify whether string theory is realized in nature. String theory’s equations describe objects that are so incredibly tiny and that possess such extraordinarily high energy that any detector we could even imagine would be unlikely to ever see them. It is defined at an energy scale that is about 10 million billion times larger than those we can experimentally explore with current instruments. At present, we still don’t even know what will happen when the energy of particle colliders increases by a factor of 10.

String theorists can’t uniquely predict what happens at experimentally accessible energies since the particle content and other properties depends on the as yet undetermined configuration of fundamental ingredients in the theory. String theory’s consequences in nature depend on how the elements arrange themselves. As it is currently formulated, string theory contains more particles, more forces, and more dimensions than we see in our world. What is it that distinguishes those particles, forces, and dimensions that are visible from those that are not?

For example, space in string theory is not necessarily the space we see around us’space with three dimensions. Instead, string theory’s gravity describes six or seven additional dimensions of space. A workable version of string theory has to explain how the invisible extra dimensions are different from the three we know. As fascinating and remarkable as string theory is, puzzling features like its extra dimensions obscure its connection to the visible universe. To get from the high energy at which string theory is defined to predictions about measurable energies, we need to deduce what the original theory will look like with the heavier particles removed. However, there are many possible manifestations of string theory at accessible energies, and we don’t yet know how

to distinguish among the enormous range of possibilities, or even how to find the one that looks like our world. The problem is that we don’t yet understand string theory sufficientlyn well to derive its consequences at the energies we see. The theory’s predictions are hindered by its complexity. Not only is the challenge mathematically difficult, it is not even always clear how to organize string theory’s ingredients and determine which mathematical problem to solve. On top of that, we now know that string theory is much more complex than physicists originally thought and involves many other ingredients with different dimensionalities’ notably branes. The name string theory still generally survives, but physicists also talk about M-theory, although no one really knows what the ‘M’ stands for.

String theory is a magnificent theory that has already led to profound mathematical and physical insights, and it might well contain the correct ingredients to ultimately describe nature. Unfortunately, an enormous theoretical gulf separates the theory as it is currently understood from predictions that describe our world. Ultimately, if string theory is correct, all the models that describe real-world phenomena should be derivable from its fundamental premises. But its initial formulation is abstract, and its connection to observable phenomena is remote. We would have to be very lucky to find all the correct physical principles that will make string theoretical predictions match our world. That is string theory’s ultimate goal, but it is a daunting task. Although elegance and simplicity can be the hallmarks of a correct theory, we can only really judge a theory’s beauty when we have a reasonably comprehensive understanding of how it works. Discovering how and why nature hides string theory’s extra dimensions would be a stunning achievement. Physicists want to figure out how this occurs.

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