The first string theory has become known as bosonic string theory, and it said that all the particles that physicists have observed are actually the vibration of multidimensional “strings.” But the theory had consequences that made it unrealistic to use to describe our reality.
A dedicated group of physicists worked on bosonic string theory between 1968 and the early 1970s, when the development of superstring theory (which said the same thing, but fit reality better) supplanted it. (I explain this superior theory in the later section “Supersymmetry Saves the Day: Superstring Theory.”)
Even though bosonic string theory was flawed and incomplete, string theorists occasionally do mathematical work with this model to test new methods and theories before moving on to the more modern superstring models.
Explaining the scattering of particles with early dual resonance models
String theory was born in 1968 as an attempt to explain the scattering of particles (specifically hadrons, like protons and neutrons) within a particle accelerator. Originally, it had nothing to do with strings. These early predecessors of string theory were known as dual resonance models.
The initial and final state of particle interactions can be recorded in an array of numbers called an S-matrix. At the time, finding a mathematical structure for this S-matrix was considered to be a significant step toward creating a coherent model of particle physics.
Gabriele Veneziano, a physicist at the CERN particle accelerator laboratory, realized that an existing mathematical formula seemed to explain the mathematical structure of the S-matrix. (See the sidebar “Applications of pure mathematics to physics” for more on this formula.) (Physicist Michio Kaku has stated that Mahiko Suzuki, also at CERN, made the same discovery at the same time, but was persuaded by a mentor not to publish it.)
Veneziano’s explanation has been called the dual resonance model, the Veneziano amplitude, or just the Veneziano model. The dual resonance model was close to the correct result for how hadrons interacted, but not quite correct. At the time Veneziano developed the model, particle accelerators weren’t precise enough to detect the differences between model and reality. (Eventually, it would be shown that the alternative theory of quantum chromodynamics was the correct explanation of hadron behavior, as discussed in topic 8.)
Applications of pure mathematics to physics
Physicists frequently find the math they need was created long before it was needed. For example, the equation that physicist Gabriele Veneziano used to explain particle scattering was the Euler beta function, which was discovered in the 1700s by Swiss mathematician Leonhard Euler. Also, when Einstein began to extend special relativity into general relativity, he soon realized that traditional Euclidean geometry wouldn’t work. His space had to curve, and Euclid’s geometry only described flat surfaces.
Fortunately for Einstein, in the mid-1800s the German mathematician Bernhard Riemann had worked on a form of non-Euclidean geometry (named Riemannian geometry). The mathematics that Einstein needed for the general theory of relativity had been created a half century earlier as an intellectual exercise, with no practical purpose in mind. (As fascinating as revolutionizing the foundations of geometry may be, it was hardly practical.)
This happened several times in the history of string theory. Calabi-Yau manifolds, discussed at the end of this topic, are one example. Another example is when string theorists were attempting to determine the appropriate number of dimensions to make their theories stable and consistent. A key to this problem came from the journals of Indian mathematical genius Srinivasa Ramanujan (referenced in the film Good Will Hunting), who died in 1920. The specific mathematics in this case was a function called the Ramanujan function.
After the dual resonance model was formed, hundreds of theoretical papers were published in attempts to modify the parameters a bit. This was the way theories were approached in physics; after all, an initial guess at a theory is rarely precisely correct and typically requires subtle tweaks — to see how the theory reacts, how much it can be bent and modified, and so on — so that ultimately it fits with the experimental results.
The dual resonance model would have nothing to do with that sort of tinkering — it simply didn’t allow for any changes that would still enable it to be valid. The mathematical parameters of the theory were too precisely fixed. Attempts to modify the theory in any way quickly led to a collapse of the entire theory. Like a dagger balanced on its tip, any slight disturbance would send it toppling over. Mathematically, it was locked into a certain set of values. In fact, it has been said by some that the theory had absolutely no adjustable parameters — at least not until it was transformed into an entirely different concept: superstring theory!
This isn’t the way theories are supposed to behave. If you have a theory and modify it so the particle mass, for example, changes a bit, the theory shouldn’t collapse — it should just give you a different result.
When a theory can’t be modified, there are only two possible reasons: either it’s completely wrong or it’s completely right! For several years, dual resonance models looked like they might be completely right, so physicists continued to ponder what they might mean.
Exploring the first physical model: Particles as strings
The basic physical interpretation of string theory was as vibrating strings. As the strings, each representing a particle, collided with each other, the S-matrix described the result.
Consider this very informal way of looking at string theory, shown in Figure 10-1. Each particle is composed of a vibrating string. In the case of a proton, there are three quark strings. When these three strings come in contact, they bond together to form a proton. So the proton is created by the interaction of the three quark strings touching each other. The proton is kind of a knot within the strings.
Figure 10-1:
Most people think of particles as solid spheres. In string theory, scientists view them as vibrating strings instead.
What are these strings like? The strings described were almost like rubber bands. There is a certain “springiness” to them. A phrase that I think describes them well is “filaments of energy” (as string theorist Brian Greene and others have called them). Though most people think of particles as balls of matter, physicists have long thought of them as little bundles of waves (called wave packets), which is in line with describing them as strings. (In some other situations, physicists can treat particles as having no size whatsoever, but this is a simplification to make the math and theory more manageable. The way physicists treat particles depends a lot on the situation they’re working with.)
This interpretation was put forth independently by Yoichiro Nambu, Holger Nielsen, and Leonard Susskind in 1970, earning all three men positions as founders of string theory.
According to Einstein’s work, mass was a form of energy, an insight demonstrated dramatically by the creation of the atomic bomb. Quantum theory showed physicists that matter was represented by the mathematics of wave mechanics, so even a particle had a wavelength associated with it.
In string theory, matter again takes on a new form. Particles of different types are different vibrational modes of these fundamental entities: energetic rubber bands, or strings. (Classical vibrations and strings are discussed in topic 5.) In essence, the more the string vibrates, the more energy (and therefore mass) it possesses.
Through all the transformations that string theory has undergone in the years since its discovery, this central concept remains (fairly) constant, although in recent years new objects in addition to strings have been introduced (which I explain in topic 11 when I discuss branes).
The basic physical model couldn’t have been simpler: The particles and forces in nature are really interactions between vibrating strings of energy.
Bosonic string theory loses out to the Standard Model
The dual resonance model was created for the express purpose of explaining the S-matrix particle scattering, which was now explained in terms of the Standard Model of particle physics — gauge fields and quantum chromodynamics. (See topic 8 for more on these concepts.) There was no point to string theory in light of the success of the Standard Model.
Also, as the measurements of experiments in particle accelerators got more precise, it became clear that dual resonance models were only approximately correct. In 1969, physicists showed that Veneziano had discovered only the first term in an infinite series of terms. Although this term was the most important, it still wasn’t complete. The theory appeared to need some further refinement to match the results perfectly.
Terms could be added (which Michio Kaku did in 1972), correcting for the different ways that the strings could collide, but it made the theory less elegant. There were growing indications that string theory might not work the way everyone had thought it would and that, indeed, quantum chromodynamics explained the behavior of the particle collisions better.
The early string theorists had therefore spent a lot of time giving meaning to a theory that seemed to (almost) accurately predict the S-matrix, only to find that the majority of particle physicists weren’t interested in it. It had to be very frustrating to have such an elegant model that was quickly falling into obscurity.
But a few string theorists weren’t about to give up on it quite yet.
