What is heat?

Heat is amazing. The energy you could in principle extract, by lowering the temperature of any amount of water by a barely perceptible one degree Celsius, would be enough to lift that same amount of water to a height of over four hundred meters. And the energy you could extract by condensing any amount of steam into liquid water would be enough to lift that same amount of water into space. This is why the Industrial Revolution was such a big deal. Harnessing heat, in fuel-burning engines that drive pistons or spin turbines with hot gases, is what has let us hair-challenged primates conquer the planet. Heat is magic. What is it?

Until the mid 19th century, people thought that heat was a special kind of fluid, like air or water but different, and invisible. They called it "phlogiston", or "caloric". Some considered that cold was a distinct fluid, "frigoric", while others argued that cold was simply absence of heat. These were by no means stupid or crazy theories. Electrical charge is a phenomenon which is about as basic and important as heat, and it really is carried by two different kinds of stuff, namely electrons and protons (as well as other much less common particles), which each carry opposite charge. Objects can become positively or negatively charged if they pick up excess protons or electrons. It was not silly to imagine that objects might become hot or cold by picking up excess caloric or frigoric.

But early physicists figured out that this was wrong, mainly from carefully observing how grinding metal keeps on making it hotter, even when the grinder and the metal are kept well apart from any other objects that might conceivably be able to inject a steady supply of caloric into them. They concluded that heat is actually some form of energy, and that the more familiar kinds of energy carried by moving objects can be converted into heat, through friction; while heat may in turn be converted into motion and useful work, in engines.

But then just what is the difference between heat and work, as forms of energy? It's not easy to get a straight answer even from a fully trained physicist, because the truth is that we're still not completely sure what heat is. If I have many bazillions of atoms all zipping around in a big box, bouncing rapidly off each other and the walls, making up a gas, then I can use statistical mechanics to say an awful lot about heat and pressure and temperature for this gas. But if I have one single atom, perhaps ionized and trapped in a strong electric field, I know that the concept of heat is not even relevant. With one atom, I can compute the motions of its nucleus and of its electrons, rather as I worked out the motion of solid objects in freshman physics. It does not even make sense to ask whether the atom is hot or cold. Usually no single atom has heat, but a billion atoms do. So heat is somehow an emergent property of large numbers of atoms together.

"Emergent property" is a fine bit of fashionable philosophical mumbo-jumbo, which spends rather too much time in the blogs of wild-eyed crackpots and tenured philosophers, to be comfortably welcome among respectable scientists. But in the case of heat, you can slurp an emergent property from a cup of coffee. Heat rules the world. It's quite concretely real. So what is it?

Well, we're working on it. There is ample precedent in perfectly well understood physics for new behavior to emerge in larger systems; it's just that in this particularly fundamental case of heat there are still some major obscurities in exactly how it works. But in just the past few years, atomic and optical physicists have gained the capability to make extremely precise and direct measurements on small samples of gas, with only hundreds to thousands of atoms. If heat emerges, we're soon going to be able to catch it in the act. Watch this space.

Statistical Mechanics

Most people these days have heard of quantum mechanics, and how it somehow brings chance and probability into physics on a basic level. This is a misleading truth, because actually quantum mechanics is perfectly deterministic, and not probabilistic at all, until we come to measure anything. Then the probabilities come in, and only then. The problem is that quantum measurement is a very subtle thing that is far from fully understood. And one thing we do know is that inferring how things really are, from how things look, is uniquely tricky in quantum mechanics.

To appreciate the subtlety of quantum mechanics, it helps to know about the older and less tricky place that probability has in physics: statistical mechanics. I doubt that most non-physicists have ever heard of statistical mechanics. In many places one can even earn a Bachelor's degree in physics without ever taking a course in it. This is unfortunate, because statistical mechanics is so important, that a physicist who doesn't know about it is like a Scout who doesn't know that fire needs air. Statistical mechanics is a sort of post-processing stage that has to be performed on virtually all the rest of physics — even including quantum mechanics — in order to make sense of anything but the very simplest and most controlled experiments.

Mechanics without statistics is the physics we learn in school. A rock flies through the air, falling under gravity. Ignore air friction, and model the rock as a point with a given mass — a particle. Apply Newton's Laws to particles: that's mechanics.

'In principle,' we may be told, 'the universe is a large number of particles, governed by Newton's Laws.' In practice, of course, most of these particles are beyond our control, beyond our observation, or at least beneath our notice. We do not see the vast swarms of air molecules that surround us and fill our lungs. And even if we could mark their paths, solving Newton's equations for so many interacting particles is far beyond our computational power. Thus do we see the vast gap between the pristine principles of physics, and the practical real world.

Bah. Physics doesn't care about pristine. Sure, part of physics is about trying to reduce everything, 'in principle', to some elegant little Theory of Everything. We're writing one big long footnote to Plato, who wanted everything to boil down to the five regular polyhedra. But that whole grand unified simplicity thing is really the hood ornament of physics, not the engine. The thing that drives physics is putting principles into practice, and codifying practice into principle. So no, the fact that we can't follow every atom does not make a huge gap between physics and reality. There is a whole huge branch of physics which is all about the principles and the practice of dealing with huge numbers of particles that cannot be individually observed, predicted, or controlled.

And that is the branch of physics called statistical mechanics. It uses probability theory to get the best results we can from what we do know, in spite of what we don't. Whether or not God plays dice with the universe, physicists do, to make up for the fact that we're not God.