Excerpt from a lecture/Q&A where Sean Carroll discusses the arrow of time as an emergent phenomenon rather than fundamental. He connects the thermodynamic arrow (low-entropy initial conditions after the Big Bang) with a quantum-mechanical perspective (initially a single branch of the wavefunction that has since branched), and distinguishes between ‘time’ itself and the ‘arrow of time’. Examples and thought experiments (planet orbiting the Sun, small fluctuating systems) illustrate when an arrow would be absent or negligible.
Chapters
We talked a little bit about error of time last time, but in many worlds, that there is a kind of implied error of time. Right. So you've talked about the arrow of time that has to do with the second law of thermodynamic dynamics. That's the arrow of time. That's emergent or fundamental? We don't know, I guess. No, it's emergent. Does everyone agree on that? Well, nobody agrees with everything. They should. They should. So that arrow of time, is that different than the arrow of time that's implied by many worlds? It's not different, actually, no. In both cases, you have fundamental laws of physics that are completely reversible. If you give me the state of the universe at one moment in time, I can run the clock forward or backward equally well. There's no arrow of time built into the laws of physics at the most fundamental level. But what we do have are special initial conditions. 14 billion years ago, near the Big Bang. In thermodynamics, those special initial conditions take the form of things were low entropy. And entropy has been increasing ever since, making the universe more disorganized and chaotic. And that's the arrow of time. In quantum mechanics, these special initial conditions take the form of. There was only one branch of the wave function, and the universe has been branching more and more ever since. Okay, so if time is emergent. So it seems like our human cognitive capacity likes to take things that are emergent and assume and feel like they're fundamental. So what? It seem. So if time is emergent and locality like, is space emergent? Yes. Okay, but I didn't say time was emergent. I said the arrow of time was emergent. Those are different. What's the difference between the arrow of time and time? Are you using arrow of time to simply mean this? They're synonymous with the second law of thermodynamics? No, but the arrow of time is the difference between the past and future. So there's space, but there's no arrow of space. You don't feel that space has to have an arrow. Right. You could live in thermodynamic equilibrium. There there'd be no arrow of time, but there'd still be time. There'd still be a difference between now and the future or whatever. Okay, so if nothing changes, there's still time. Well, things could even change. Like if the whole universe consisted of the Earth going around the sun, okay, it would just go in circles or ellipses. Right. That's an equilibrium. Things would change, but it's not increasing. Entropy, there's no arrow. If you took a movie of that and I played you the movie backward, you would never know. So the arrow of time can theoretically point in the other direction. For brief Briefly, to the extent that it points in different directions, it's not a very good arrow. I mean, the arrow of time in the macroscopic world is so powerful that there's just no chance of going back. When you get down to tiny systems with only 3 or 4 moving parts, then entropy can fluctuate up and down SA.
