Allegro
(
Ma Non Troppo
) Passage for Strings
I’ve got the world on a string.
Frank Sinatra
Fast forward a millennium.
Icarus Rushmore XLII was trying out his new Alicxvr Device, Model 6.3, that he had recently purchased from the Spacernet. (Icarus III’s interest in speed and gadgets had apparently been passed down through many generations.) The Alicxvr was designed to let the user view things of any size, from the very small to the very large. Ike was pretty sure that all of his friends who had purchased the Alicxvr Device would first try the large settings, of many megaparsecs, so they could see into outer space beyond the known universe. But Ike thought, “I know just as little about what is happening at extremely tiny distances,” and decided to investigate a minuscule size instead.
However, Ike was an impatient sort. He couldn’t be bothered to read the extensive instruction manual accompanying his device and instead decided to plunge right in. Blithely ignoring the red indicator overlapping the smallest sizes, he adjusted his dial to the 10
-33
cm setting and pressed the button labeled “Go.”
To his horror, he found himself space-sick in a wildly oscillating, precipitous landscape filled with strings. Space was no longer the smooth, anonymous background he was accustomed to. Instead it was jiggling rapidly in places, heading into pointy sections in others, or wandering off into loops that pinched off or later rejoined the surface. Ike fumbled desperately for the “Stop” button and only just managed to press it in time to return to normal with his senses intact.
After recovering his stability, Ike decided he probably should have read the manual after all. He turned to the “Warning” section and read: “Your new Alicxvr Device Model 6.3 works only for sizes larger than 10
-33
cm. We have not yet incorporated the latest string theory developments, whose predictions physicists and mathematicians connected to the physical world only last year.”
Ike was very disappointed when he realized that only the newer Model 7.0 included the latest results. But Ike then caught up with the most recent string theory developments, souped up his Alicxvr, and never got space-sick again.
Einstein’s theory of general relativity was monumental. With it, physicists understood the gravitational field more deeply and could calculate gravity’s influence with unprecedented precision. Relativity gave physicists the tools to predict the evolution of all gravitational systems—even that of the entire universe. However, despite all of its successful predictions, general relativity cannot be the final word on gravity. General relativity fails when it is applied to extremely short distances. At very tiny length scales, only a new gravitational paradigm can succeed. Many physicists believe that that paradigm must be string theory.
If string theory is correct, it embraces the successful predictions of general relativity, quantum mechanics, and particle physics. But it also extends physics to distance and energy domains that these other theories are not equipped to handle. String theory is not yet sufficiently developed for us to evaluate its high-energy predictions and validate its efficacy in these elusive distance and energy regimes. But string theory does have several remarkable features that lend credence to this promising picture.
We’ll now take a look at string theory and how this dramatic new theory evolved, culminating in the “superstring revolution” of 1984, when physicists demonstrated that pieces of string theory fit together miraculously well. The superstring revolution was only the beginning of an intense research program that actively engages many physicists
today. In this and the following chapters, we’ll review the history of string theory and some of the recent exciting string theory developments. We’ll see that string theory has made remarkable advances and has numerous promising aspects. But we’ll also see that string theory faces many crucial challenges that physicists will have to resolve before using it to make predictions about our world.
Incipient Unrest
Quantum mechanics and general relativity peacefully coexist over a wide range of distances, including all those that are accessible to experiments. Although both theories should apply on all length scales, the two theories have a mutual understanding about which of them dominates at measurably long and short distances. Quantum mechanics and general relativity can peacefully share territory because each respects the other’s authority in its designated domain. General relativity is important for massive extended objects, such as stars or the galaxy. But gravity’s influence on an atom is negligible, so you can safely study an atom ignoring general relativity. Quantum mechanics, on the other hand, is critical at atomic distances because its predictions for an atom are substantial and differ significantly from those of classical physics.
However, quantum mechanics and relativity do not have an entirely harmonious relationship. These two very different theories never adequately negotiated the extremely tiny distance known as the Planck scale length, 10
-33
cm. From Newton’s gravitational force law, we know that the strength of gravity is proportional to masses and inversely proportional to distance squared. Even though on atomic scales, gravity is weak, the gravitational force law tells us that on even tinier scales, the force of gravity is enormous. Gravity is important not only for very massive extended objects, but also for objects that are in extremely close proximity, separated by the minuscule Planck scale length. If we try to make predictions about this unmeasurably small distance, both quantum mechanics and general relativity would contribute significantly, and the two theories’ contributions would be incompatible. Neither quantum mechanics nor gravity can be
neglected in this contested territory, where quantum mechanical and general relativity calculations fail to cooperate, and predictions are bound to fail.
General relativity works only when there are smooth gravitational fields encoded in a gradually curving spacetime. But quantum mechanics tells us that anything that can probe or influence the Planck scale length has huge momentum uncertainty. A probe with sufficient energy to probe the Planck scale length would induce disruptive dynamical processes, such as energetic eruptions of virtual particles, that would dash any hope of a general relativity description. According to quantum mechanics, at the Planck scale length, instead of a gradually undulating geometry, there should be wild fluctuations and loops and handles of spacetime branching off, the sort of topography that the futuristic Ike encountered. General relativity cannot be used in such untamed territory.
Nor does general relativity step aside to give quantum mechanics free rein, for at the Planck scale length gravity exerts a substantial force. Although gravity is feeble at the particle physics energies we are accustomed to, it is enormously powerful at the high energies required to explore the Planck scale length.
*
The Planck scale energy—the energy needed to explore the Planck scale length—is exactly the energy at which gravity is no longer dismissible as a feeble force. At the Planck scale length, gravity cannot be ignored.
In fact, at the Planck scale energy, gravity constructs barriers that make conventional quantum mechanical calculations impossible. Anything sufficiently energetic to probe 10
-33
cm would be snapped up into a black hole that imprisons whatever enters. Only a quantum theory of gravity can tell us what is really going on inside.
At tiny distances, quantum mechanics and gravity cry out for a more fundamental theory. Given the conflict between them, there is no choice but to bring in an external arbiter as an alternative to both. The new regime must allow quantum mechanics and general relativity free rein in their undisputed home territories, but have adequate
authority to govern the disputed region where neither of the older theories is in control. String theory might be the answer.
The incompatibility of quantum mechanics and gravity also reveals itself through conventional gravity’s nonsensical predictions for the high-energy interactions of a particle called the
graviton
—the particle that communicates the gravitational force in a quantum theory of gravity.
According to classical gravitational theory, gravity is communicated between massive objects through a gravitational field in much the same way that, according to Maxwell’s classical electromagnetic theory, electromagnetism is communicated from one charged particle to another via a classical electromagnetic field. But quantum electrodynamics (QED), the quantum field theory of electromagnetism, reinterprets this classical electromagnetic force in terms of the exchange of a particle, the photon.
*
QED, the theory of the photon, is the extension of the classical theory of electromagnetism that incorporates quantum mechanical effects.
Quantum mechanics dictates that, similarly, there must be a particle to transmit the gravitational force. That particle is the graviton. In a quantum theory of gravity, the exchange of a graviton between two objects reproduces Newton’s law of gravitational attraction. Although gravitons have not been directly observed, physicists believe that they exist because quantum mechanics tells us they do.
Later on, the distinctive spin of the graviton will be important to us. Because gravitons communicate gravity, a force inherently connected with space and time, they have a different spin from all other known force carriers such as the photon. We will not delve into the reasons here, but the graviton is the only known massless particle whose spin is 2—not 1, as for other gauge bosons, or ½, as for quarks and leptons. The fact that it has spin-2 is important when it comes to finding convincing evidence of extra-dimensional theories. And, as we will soon see, the graviton’s spin was also the key to recognizing string theory’s potential implications.
However, the quantum field theory description of gravity cannot be complete. No quantum field theory for the graviton can predict its
interactions at all energies. When a graviton is as energetic as the Planck scale energy, quantum field theory breaks down. Theoretical reasoning demonstrates that extra graviton interactions that wouldn’t make a difference at low energies become important at high energies, but the logic of quantum field theory is not sufficient to tell us what they are or how to include them. If we incorrectly used a quantum field theory of gravity, ignoring the interactions that don’t matter at low energies, and attempted to make predictions for extremely energetic gravitons, we would conclude that graviton interactions occur with probability greater than one—something which is clearly impossible. At the Planck scale energy, or equivalently (according to quantum mechanics and special relativity) at the Planck scale length, 10
-33
cm, the quantum mechanical description of the graviton obviously breaks down.
The Planck scale length, nineteen orders of magnitude smaller than the size of a proton, would be much too small for physicists to care about were it not for the fundamental issues that a more comprehensive theory can potentially address. For example, current theories of cosmology conjecture that the universe began as a tiny ball, a Planck scale length in size. But we have no understanding of the “Bang” of the Big Bang. We understand many aspects of the universe’s later evolution, but not how it began. Deducing the physical laws that apply to sizes less than the Planck scale length should shed light on the earliest stage of the evolution of our universe.
Furthermore, there are many mysteries about black holes. Important unresolved questions include what exactly is happening at the black hole’s
horizon
, the place of no return beyond which nothing can escape, and at the
singularity
, the place in the center of the black hole where general relativity no longer applies. Another unanswered question is how information about objects that fall into a black hole is stored. Unlike the gravitational force we experience, gravitational effects inside a black hole are strong, as strong as effects from objects with the Planck scale energy in ordinary flat space. We will never solve these black hole mysteries until we resolve the problem of finding a single theory that consistently includes both quantum mechanics and general relativity—a theory of
quantum gravity
on the Planck scale length, 10
-33
cm. Black holes exemplify some of the questions about
strong gravitational effects that will be resolved only by a quantum theory of gravity. String theory is the best known candidate for such a theory.
String Training
String theory’s view of the fundamental nature of matter differs significantly from that of traditional particle physics. According to string theory, the most basic indivisible objects underlying all matter are
strings
—vibrating, one-dimensional loops or segments of energy. These strings, unlike violin strings, say, are not made up of atoms which are in turn made up of electrons and nucleons which are in turn made up of quarks. In fact, exactly the opposite is true. These are fundamental strings, which means that everything, including electrons and quarks, consists of their oscillations. According to string theory, the yarn a cat plays with is made of atoms that are ultimately composed of the vibrations of strings.
String theory’s radical hypothesis is that particles arise from the resonant oscillation modes of strings. Each and every particle corresponds to the vibrations of an underlying string, and the character of those vibrations determines the particle’s properties. Because of the many ways in which strings can vibrate, a single string can give rise to many types of particle. Theorists initially thought there was only a single type of fundamental string that is responsible for all known particles. But that picture has changed in the last few years, and we now believe that string theory can contain different, independent types of string, each of which can oscillate in many possible ways.