The Order of Time

My students enjoy my occasional digressions into speculative science. These are often prompted by a student question, thus encouraging them to ask interesting relevant questions. Sometimes I pose the question instead, and every spring semester when we discuss thermodynamics I bring up the issue of entropy and time’s arrow.

Time is a strange and funny thing. We don’t really know what it is. But unlike all the other laws of physics, where symmetry plays an important role and there is no difference between forwards and backwards, time is different. Or maybe I should say heat is different. Heat is the ‘thermo’ of thermodynamics. It’s stranger than you think. Exploring this strangeness is Carlo Rovelli’s The Order of Time. Rovelli is a wonderful writer with engaging prose. I’ve quoted one of his earlier books in a previous post on – you might have guessed – thermodynamics!

Heat spontaneously moves in one direction. Never the other way around. A quantity was invented by Rudolf Clausius to describe this behavior: Entropy, from the Greek word for transformation. Rovelli has only one simple equation in his book. It represents the second law of thermodynamics. He writes: “It is the only equation of fundamental physics that knows any difference between past and future. The only one that speaks of the flowing of time. Behind this unusual equation, an entire world lies hidden. Revealing it will fall to an unfortunate and engaging Austrian, the grandson of a watchmaker, a tragic and romantic figure, Ludwig Boltzmann.”

In my class, I illustrate the counting of different configurations (microstates) with coin-tossing examples. We calculate probabilities, certainly at the G-Chem level, and in P-Chem we derive the Boltzmann distribution in all its glory. (My students would say “gory”.) Why does the Second Law ‘work’? As the sample size increases the Boltzmann distribution becomes overwhelmingly the most probable. It’s the one that maximizes that strange quantity called entropy. The experience of observing low entropy situations changing to high entropy situations gives us that feeling of the unidirectional ‘flow’ of time.

But time doesn’t really flow. A crucial point that Rovelli makes, and one that I try to emphasize in my classes is that entropy-counting is not just a matter of probability, but also one of perception. It depends on how you lump the microstates together and count them. You are counting what you cannot see. Weird, huh? Rovelli puts it this way: “Boltzmann has shown that entropy exists because we describe the world in a blurred fashion… The difference between past and future is deeply linked to this blurring…” If I was the size of an atom (molecular-me!), there might be no distinction between the future and the past. You would not be able to tell if you were moving forwards or backwards. My students find this idea crazy!

Rovelli goes on: “This is the disconcerting conclusion that emerges… the difference between the past and the future refers only to our own blurred vision of the world… is it really possible that a perception so vivid, basic, existential – my perception of the passage of time – depends on the fact that I cannot apprehend the world in all of its minute detail?” There’s a word for this activity of blurring things. Computational scientists use it all the time. It’s called ‘coarse-graining’. It’s uncanny when and where coarse-graining shows up. For example, it is used to describe complex systems and might even be involved in the origin of life (and complexity). And if we could get over our perception limitations, perhaps we could time-travel?

The ancients make their appearance in Rovelli’s book. It's a topic I encountered as an undergraduate when I wrote an essay in a philosophy class on Augustine’s description of Time in Book XI of The Confessions. Rovelli discusses these ideas and more. The strongest parts of the book are when Rovelli distils complicated concepts in physics to thinks a non-physicist can follow. I now have some idea why quantum loop gravity is interesting. He has a knack for communicating why physics is both interesting and strange. The weakest parts of the book are at the end when he ventures into speculative areas far afield. One should take these with a grain of salt or whimsy, depending on your disposition. But all in all, it’s an engaging little book and I will be pointing my students to it!