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THE FABRIC of the COSMOS, Brian Greene, 2004
```(annotated and with added bold highlights by Epsilon=One)
```(annotated and with added bold highlights by Epsilon=One)
Chapter 12 - The World on a String
Particle Properties in String Theory
To understand string theory's new explanatory framework, we need to have a better feel for how string vibrations produce particle properties, so let's consider the simplest property of a particle, its mass.
From E=mc^2, we know that mass and energy are interchangeable; like dollars and euros, they are convertible currencies (but unlike monetary currencies, they have a fixed exchange rate, given by the speed of light times itself, c^2). Our survival depends on Einstein's equation, since the sun's life-sustaining heat and light are generated by the conversion of 4.3 million tons of matter into energy every second; one day, nuclear reactors on earth may emulate the sun by safely harnessing Einstein's equation to provide humanity with an essentially limitless supply of energy.
In these examples, energy is produced from mass. But Einstein's equation works perfectly well in reverse — the direction in which mass is produced from energy — and that's the direction in which string theory uses Einstein's equation. The mass of a particle in string theory is nothing but the energy of its vibrating string. For instance, the explanation string theory offers for why one particle is heavier than another is that the string constituting the heavier particle is vibrating faster and more furiously than the string constituting the lighter particle. Faster and more furious vibration means higher energy, and higher energy translates, via Einstein's equation, into greater mass. Conversely, the lighter a particle is, the slower and less frenetic is the corresponding string vibration; a massless particle like a photon or a graviton corresponds to a string executing the most placid and gentle vibrational pattern that it possibly can.* 14
Other properties of a particle, such as its electric charge and its spin, are encoded through more subtle features of the string's vibrations. Compared with mass, these features are harder to describe nonmathematically, but they follow the same basic idea: the vibrational pattern is the particle's fingerprint: all the properties that we use to distinguish one particle from another are determined by the vibrational pattern of the particle's string.
In the early 1970s, when physicists analyzed the vibrational patterns arising in the first incarnation of string theory — the bosonic string theory — to determine the kinds of particle properties the theory predicted, they hit a snag. Every vibrational pattern in the bosonic string theory had a whole-number amount of spin: spin-0, spin-1, spin-2, and so on. This was a problem, because although the messenger particles have spin values of this sort, particles of matter (like electrons and quarks) don't. They have a fractional amount of spin, spin-1/2. In 1971, Pierre Ramond of the University of Florida set out to remedy this deficiency; in short order, he found a way to modify the equations of the bosonic string theory to allow for half-integer vibrational patterns as well.
In fact, on closer inspection, Ramond's research, together with results found by Schwarz and his collaborator Andre Neveu and later insights of Ferdinando Gliozzi, Joel Scherk, and David Olive, revealed a perfect balance — a novel symmetry — between the vibrational patterns with different spins in the modified string theory. These researchers found that the new vibrational patterns arose in pairs whose spin values differed by half a unit. For every vibrational pattern with spin-1/2 there was an associated vibrational pattern with spin-0. For every vibrational pattern of spin-1 there was an associated vibrational pattern of spin-1/2, and so on. The relationship between integer and half-integer spin values was named supersymmetry, and with these results the supersymmetric string theory, or superstring theory, was born. Nearly a decade later, when Schwarz and Green showed that all the potential anomalies that threatened string theory canceled each other out, they were actually working in the framework of superstring theory, and so the revolution their paper ignited in 1984 is more appropriately called the first superstring revolution. (In what follows, we will often refer to strings and to string theory, but that's just a shorthand; we always mean superstrings and superstring theory.)
With this background, we can now state what it would mean for string theory to reach beyond broad-brush features and explain the universe in detail. It comes down to this: among the vibrational patterns that strings can execute, there must be patterns whose properties agree with those of the known particle species. The theory has vibrational patterns with spin-1/2, but it must have spin-1/2 vibrational patterns that match precisely the known matter particles, as summarized in Table 12.1. The theory has spin-1 vibrational patterns, but it must have spin-1 vibrational patterns that match precisely the known messenger particles, as summarized in Table 12.2. Finally, if experiments do indeed discover spin-0 particles, such as are predicted for Higgs fields, string theory must yield vibrational patterns that match precisely the properties of these particles as well. In short, for string theory to be viable, its vibrational patterns must yield and explain the particles of the standard model.
Here, then, is string theory's grand opportunity. If string theory is right, there is an explanation for the particle properties that experimenters have measured, and it's to be found in the resonant vibrational patterns that strings can execute. If the properties of these vibrational patterns match the particle properties in Tables 12.1 and 12.2, I think that would convince even the diehard skeptics of string theory's veracity, whether or not anyone had directly seen the extended structure of a string itself. And beyond establishing itself as the long-sought unified theory, with such a match between theory and experimental data, string theory would provIde the first fundamental explanation for why the universe is the way it is.
So how does string theory fare on this critical test?
From E=mc^2, we know that mass and energy are interchangeable; like dollars and euros, they are convertible currencies (but unlike monetary currencies, they have a fixed exchange rate, given by the speed of light times itself, c^2). Our survival depends on Einstein's equation, since the sun's life-sustaining heat and light are generated by the conversion of 4.3 million tons of matter into energy every second; one day, nuclear reactors on earth may emulate the sun by safely harnessing Einstein's equation to provide humanity with an essentially limitless supply of energy.
In these examples, energy is produced from mass. But Einstein's equation works perfectly well in reverse — the direction in which mass is produced from energy — and that's the direction in which string theory uses Einstein's equation. The mass of a particle in string theory is nothing but the energy of its vibrating string. For instance, the explanation string theory offers for why one particle is heavier than another is that the string constituting the heavier particle is vibrating faster and more furiously than the string constituting the lighter particle. Faster and more furious vibration means higher energy, and higher energy translates, via Einstein's equation, into greater mass. Conversely, the lighter a particle is, the slower and less frenetic is the corresponding string vibration; a massless particle like a photon or a graviton corresponds to a string executing the most placid and gentle vibrational pattern that it possibly can.* 14
Other properties of a particle, such as its electric charge and its spin, are encoded through more subtle features of the string's vibrations. Compared with mass, these features are harder to describe nonmathematically, but they follow the same basic idea: the vibrational pattern is the particle's fingerprint: all the properties that we use to distinguish one particle from another are determined by the vibrational pattern of the particle's string.
In the early 1970s, when physicists analyzed the vibrational patterns arising in the first incarnation of string theory — the bosonic string theory — to determine the kinds of particle properties the theory predicted, they hit a snag. Every vibrational pattern in the bosonic string theory had a whole-number amount of spin: spin-0, spin-1, spin-2, and so on. This was a problem, because although the messenger particles have spin values of this sort, particles of matter (like electrons and quarks) don't. They have a fractional amount of spin, spin-1/2. In 1971, Pierre Ramond of the University of Florida set out to remedy this deficiency; in short order, he found a way to modify the equations of the bosonic string theory to allow for half-integer vibrational patterns as well.
In fact, on closer inspection, Ramond's research, together with results found by Schwarz and his collaborator Andre Neveu and later insights of Ferdinando Gliozzi, Joel Scherk, and David Olive, revealed a perfect balance — a novel symmetry — between the vibrational patterns with different spins in the modified string theory. These researchers found that the new vibrational patterns arose in pairs whose spin values differed by half a unit. For every vibrational pattern with spin-1/2 there was an associated vibrational pattern with spin-0. For every vibrational pattern of spin-1 there was an associated vibrational pattern of spin-1/2, and so on. The relationship between integer and half-integer spin values was named supersymmetry, and with these results the supersymmetric string theory, or superstring theory, was born. Nearly a decade later, when Schwarz and Green showed that all the potential anomalies that threatened string theory canceled each other out, they were actually working in the framework of superstring theory, and so the revolution their paper ignited in 1984 is more appropriately called the first superstring revolution. (In what follows, we will often refer to strings and to string theory, but that's just a shorthand; we always mean superstrings and superstring theory.)
With this background, we can now state what it would mean for string theory to reach beyond broad-brush features and explain the universe in detail. It comes down to this: among the vibrational patterns that strings can execute, there must be patterns whose properties agree with those of the known particle species. The theory has vibrational patterns with spin-1/2, but it must have spin-1/2 vibrational patterns that match precisely the known matter particles, as summarized in Table 12.1. The theory has spin-1 vibrational patterns, but it must have spin-1 vibrational patterns that match precisely the known messenger particles, as summarized in Table 12.2. Finally, if experiments do indeed discover spin-0 particles, such as are predicted for Higgs fields, string theory must yield vibrational patterns that match precisely the properties of these particles as well. In short, for string theory to be viable, its vibrational patterns must yield and explain the particles of the standard model.
Here, then, is string theory's grand opportunity. If string theory is right, there is an explanation for the particle properties that experimenters have measured, and it's to be found in the resonant vibrational patterns that strings can execute. If the properties of these vibrational patterns match the particle properties in Tables 12.1 and 12.2, I think that would convince even the diehard skeptics of string theory's veracity, whether or not anyone had directly seen the extended structure of a string itself. And beyond establishing itself as the long-sought unified theory, with such a match between theory and experimental data, string theory would provIde the first fundamental explanation for why the universe is the way it is.
So how does string theory fare on this critical test?
*The relationship to mass arising from a Higgs ocean will be discussed later in the chapter.