The Theory That Never Asks What Things Are Made Of

Thermodynamics has a strange position among physical theories. Its laws were worked out before it was settled whether matter is made of atoms, and when the atoms turned up nothing had to be withdrawn. The same apparatus now applies to gases, magnets, living cells, computation and black holes — domains with almost nothing in common at the level of what they are made of. The strangeness goes away once the kind of theory is named.

Einstein named it in 1919, in a distinction he drew for a different purpose. There are, he suggested, two kinds of physical theory.

Constructive theories build complex phenomena up from a simple hypothesised scheme. The kinetic theory of gases is the model case: posit molecules, derive pressure and temperature from their motions. The advantages, in his words, are “completeness, adaptability, and clearness” — you can see the machinery.

Principle theories work the other way. They start from empirically discovered general features of natural processes — that perpetual motion is impossible, say — and deduce what any process must satisfy. Their advantages are “logical perfection and security of the foundations.”

Thermodynamics was his paradigm case of the second kind. A principle theory is about the properties of a context, and at that level it is fully descriptive: it tells you what is going on with the context. What the context is made of is a different question, and the theory does not ask it. The substrate is not underneath the theory so much as beside the point. Carnot found the limit on heat engines in 1824 without knowing what heat was, because the limit was a property of engines and not of what heat was.

That is why it travels. Everywhere a context has those properties, the theory should hold. Reach is not a bonus a principle theory earns; it is what a principle theory is.

Einstein drew the distinction to explain what he had done with relativity, not to praise thermodynamics. The praise came thirty years later, as a retrospective judgement rather than an aside. In the Autobiographical Notes of 1949, having just said that a theory is the more impressive the greater the simplicity of its premises, he singled thermodynamics out — in a line that gets quoted often and usually with a clause removed:

It is the only physical theory of universal content concerning which I am convinced that, within the framework of applicability of its basic concepts, it will never be overthrown.

The missing clause is within the framework of applicability of its basic concepts. He is not saying thermodynamics is eternally true. He is saying that where its concepts apply, it will hold. It puts the question where it belongs: not on whether the theory is right but on where its concepts get a grip. It is the travelling said the other way round.

There is also a ground-up account of why the constraint is substrate-independent, running through Boltzmann’s counting of states; the reference library has it under what entropy is.

What holds for a principle theory holds for any vocabulary that travels. It travels because it was about properties of a context and not about the substance, and which properties is the question its travelling raises.

Which brings me back to black holes, where the sequence is Carnot and Boltzmann again, half a century apart. The principle theory got there first — the four laws, with the area of the horizon standing in for entropy — and what is being sought is the constructive account, the microstates whose count gives the area: Strominger and Vafa counted them for a class of extremal black holes in string theory in 1996, and loop quantum gravity has a count of its own. Whether a horizon has those properties or something shaped like them is the open question, and it is being worked on by building, not by arguing.

This post is part of the conversations series. See also the reference entries on thermodynamics and black holes.

Photo: Natalia Blauth / Unsplash