Last year, in a series of posts, I gave you a tour of quantum field theory, telling you some of what we understand and some of what we don’t. I still haven’t told you the role that string theory plays in quantum field theory today, but I am going to give you a brief tour of string theory before I do.

What IS String Theory? Well, what’s Particle Theory?

What is particle theory? It’s nothing other than a theory that describes how particles behave.  And in physics language, a theory is a set of equations, along with a set of rules for how the things in those equations are related to physical objects.  So a particle theory is a set of equations which can be used to make predictions for how particles will behave when they interact with one another.

Now there’s always space for confusion here, so let’s be precise about terminology.

• “Particle theory” is the general category of the equations that can describe particles, of any type and in any combination.
• “A particle theory” is a specific example of such equations, describing a specific set of particles of specific types and interacting with each other in specific ways.

For example, there is a particle theory for electrons in atoms. But we’d need a different one for atoms with both electrons and muons, or for a bottom quark moving around a bottom anti-quark, even though the equations would be of a quite similar type.

Most particle theories that one can write down aren’t relevant (or at least don’t appear to be relevant) to the real world; they don’t describe the types of particles (electrons, quarks, etc.) that we find (so far) in our own universe.   Only certain particle theories are needed to describe aspects of our world.  The others describe imaginary particles in imaginary universes, which can be fun, or even informative, to think about.

Modern particle theory was invented in the early part of the 20th century in response to — guess what? — the discovery of particles in experiments. First the electron was discovered, in 1897; then atomic nuclei, then the proton, then the photon, then the neutrino and the neutron, and so on… Originally, the mathematics used in particle theory was called “quantum mechanics”, a set of equations that is still widely useful today. But it wasn’t complete enough to describe everything physicists knew about, even at the time. Specifically, it couldn’t describe particles that move at or near the speed of light… and so it wasn’t consistent with Einstein’s theory (i.e. his equations) of relativity.

What is Quantum Field Theory?

To fix this problem, physicists first tried to make a new version of particle theory that was consistent with relativity, but it didn’t entirely work.  However, it served as an essential building block in their gradual invention of what is called quantum field theory, described in much more detail in previous posts, starting here. (Again: the distinction between “quantum field theory” and “a quantum field theory” is that of the general versus the specific case; see this post for a more detailed discussion of the terminology.)

In quantum field theory, fields are the basic ingredients, not particles. Each field takes a value everywhere in space and time, in much the same way that the temperature of the air is something you can specify at all times and at all places in the atmosphere. And in quantum field theory, particles are ripples in these quantum fields.

More precisely, a particle is a ripple of smallest possible intensity (or “amplitude”, if you know what that means.)  For example, a photon is the dimmest possible flash of light, and we refer to it as a “particle” or “quantum” of light.

We call such a “smallest ripple” a “particle” because in some ways it behaves like a particle; it travels as a unit, and can’t be divided into pieces.  But really it is wave-like in many ways, and the word “quantum” is in some ways better, because it emphasizes that photons and electrons aren’t like particles of dust.

To sum up:

• particles were discovered in experiments;
• physicists invented the equations of particle theory to describe their behavior;
• but to make those equations consistent with Einstein’s special relativity (needed to describe objects moving near or at the speed of light) they invented the equations of quantum field theory, in which particles are ripples in fields.
• in this context the fields are more fundamental than the particles; and indeed it was eventually realized that one could (in principle) have fields without particles, while the reverse is not true in a world with Einstein’s relativity.
• thus, quantum field theory is a more general and complete theory than particle theory; it has other features not seen in particle theory.

Now what about String Theory?

In some sense, strings also emerged from experiments — experiments on hadrons, back before we knew hadrons were made from quarks and gluons.  The details are a story I’ll tell soon and in another context. For now, suffice it to say that in the process of trying to explain some puzzling experiments, physicists were led to invent some new equations, which, after some study, were recognized to be equations describing the quantum mechanical behavior of strings, just as the equations of particle theory describe the quantum mechanical behavior of particles.  (One advantage of the string equations, however, is that they were, from the start, consistent with Einstein’s relativity.) Naturally, at that point, this class of equations was named “string theory”. (more…)