1. Introduction¶

Depending on how you look at it, statistical mechanics is either the least fundamental or most fundamental of all fields of physics. That is because it is not really science at all. It is pure mathematics.

In other subjects, you learn about “natural laws”: Newton’s second law, Maxwell’s equations, Schr√∂dinger’s equation, etc. These laws are not derived from anything else. They were discovered experimentally and then assumed to reflect fundamental aspects of reality. But statistical mechanics does not involve any natural laws of this sort. Instead, it is a set of techniques that can be applied to nearly any physical system, no matter what laws that system obeys. That is why I call it the most fundamental field of physics. New theories may replace old ones, and natural laws may turn out to be merely approximations to deeper laws. But statistical mechanics remains valid through it all, and whatever new laws are discovered, it will almost certainly work just as well with them as it did with the old ones.

Statistical mechanics was developed in the second half of the 19th century. It was primarily the work of Ludwig Boltzmann, who personally published more than a hundred papers on the subject during his lifetime. Other scientists also contributed to it, of course, especially James Clerk Maxwell (the same one Maxwell’s equations are named after) and Josiah Willard Gibbs.

It grew out of thermodynamics, an earlier theory that described the behavior of a mysterious substance called “heat” or “caloric”. Thermodynamics was a physical theory of the more conventional sort. It involved natural laws discovered by experiment, and made no claims about why those laws happened to hold. Caloric was supposed to be a substance much like other forms of matter. But this view turned out to be incorrect. Heat is actually an emergent phenomenon: a mathematical quantity defined in terms of a more detailed theory (the movement of individual atoms). The “laws” of thermodynamics can be derived from that deeper theory by applying statistical techniques. If you ignore the details of how each atom is moving, you find they collectively behave in a way that resembles a continuous fluid. That is what statistical mechanics is all about: deriving high level descriptions by starting from lower level ones and then averaging out lots of details.

Is it possible other theories could be explained in the same way? That is an open question, and a fascinating one. Many physicists suspect gravity is an emergent phenomenon, that it arises from the collective behavior of some deeper degrees of freedom. Statistical interpretations have also been proposed for quantum mechanics. These are all very speculative, of course, and they could easily turn out to be wrong. But they also could easily turn out to be right. Based on what we know today, it is entirely possible that the very structure of spacetime is a consequence of statistical mechanics.