Existential Physics: A Scientist's Guide to Life's Biggest Questions

by Sabine Hossenfelder

Now that you know how entropy is formally defined, let us have a closer look at this definition: entropy counts the number of microstates that can give rise to a certain macrostate. Notice the word can. The state of a system is always in only one microstate. The statement that it “can” be in any other state is counterfactual—it refers to states that do not exist in reality; they exist only mathematically. We consider them just because we do not know exactly what the true state of the system is.

Entropy thus is really a measure of our ignorance, not a measure for the actual state of the system. It quantifies which differences between microstates we think aren’t interesting. We don’t think the specific distribution of the molecules in the batter is interesting, so we lump them together in one macrostate and declare that “high entropy.”

When we lump together “similar” states in a macrostate, we need a notion of “similarity.” We derive this notion from current theories that are based on what we ourselves think of as similar. But change the notion of similarity and you change the notion of entropy. To borrow the terms coined by David Bohm, the explicate order, which our current theories quantify, might one day reveal an implicate order that we have missed so far.

Finally, we don’t actually know how to define entropy for gravity or for space-time, but this entropy plays a most important role in the evolution of the universe. You might have noticed that, according to our current theories, matter in the universe starts out as an almost evenly distributed plasma. That plasma must have had low entropy according to the past-hypothesis. But I told you earlier that the smooth batter had high entropy. How does this fit together?

It fits together if you take into account the fact that gravity makes the almost even, high-density plasma in the early universe extremely unlikely. Gravity wants to clump things, but for some reason they weren’t very clumped when the universe was young. That’s why the initial state had low entropy. Once it evolves forward in time, sure enough, the plasma begins to clump, forming stars and galaxies—because that’s likely to happen. This doesn’t happen in the batter, because the gravitational force isn’t strong enough for such a small amount of matter at comparably low density. It’s because of the different role of gravity that the batter and the early universe are two very different cases, and why the one has high entropy, the other one low entropy.

However, to make this case quantitative, we’d have to understand how to assign entropy to gravity. While physicists have made some attempts at doing that, we still don’t really know how to d...