Tachyons today

Much of my work as a Pappalardo Fellow has involved some puzzles that arise in certain string theories because of a very peculiar type of particle, called a tachyon. Here I’ll explain what a tachyon is and why it’s important to solve these puzzles. Along the way we’ll compare and contrast string theories with conventional particle theories. I should first clarify that when I say “theory” here I mean an abstract mathematical construct, which is physical in the sense that it satisfies the basic rules of physics like quantum mechanics and special relativity, but is not necessarily intended to be an accurate description of the real world. Of course, ultimately our goal is to construct a string theory that describes the real world, but in order to do so we need to understand more about the mathematical properties of string theories. What is the difference between a string theory and a conventional particle theory? Both kinds of theories describe particles and their interactions, but in the latter case the particles are the fundamental entities, whereas in the former case they are made of something more fundamental (the string). When constructing a conventional particle theory, the theorist is more or less free to decide what types of particles to include and what properties to endow them with, such as what their masses are, whether they are bosons or fermions, and how they interact with each other. For example, the theorist might include only electrons and photons, to make a simple theory called quantum electrodynamics (one of the first modern particle theories, developed in the 1940’s). Or she could add neutrinos, quarks, gluons, W and Z bosons, and Higgs bosons, to make the Standard Model of particle physics (which was developed in the 1970’s and describes all the particles and interactions that have been observed up to now, except for gravity). These are examples of realistic theories, meaning that they describe the real world (or at least aspects of it), but there are countless other theories one can construct that are equally mathematically consistent (and also satisfy basic physical requirements like quantum mechanics and special relativity). The framework of conventional particle theories is thus extremely flexible, which can be very useful to theorists. This permissiveness, however, means we have no hope of using such theories to explain why the real world has the particular types of particles present in the Standard Model, when some other combination seems equally allowed by the math: the Standard Model lacks inevitability. There is another problem with conventional particle theories: although we can include many different types of particles in a mathematically consistent theory, we cannot include gravitons. Since the graviton is the massless particle that carries the force of gravity (just as the photon carries the electromagnetic force), using a conventional particle theory to describe this important aspect of nature is unfortunately ruled out. Like particle theories, string theories describe the world in terms of particles and their interactions; unlike in particle theories, however, these are derived concepts. Just as in the Standard Model neutrons and protons are made of more elementary constituents—quarks and gluons—in a string theory the particles are made of a more elementary constituent, a short segment or loop of string. The string is a one-dimensional object moving in space. It has a certain mass density and tension, but otherwise is endowed with (almost) no intrinsic properties. Its tension is so large that it can exist only in very short segments or loops, which are so small that they behave essentially like particles (just as protons and neutrons can be considered particles for many purposes, even