Sean Carroll

At the most basic level, let's just simplify the question.

If the lower level is deterministic, how can the higher level not be?

If the higher level is just made of the lower level, right?

What else is there?

I put it in those simple terms because the answer in those terms is super duper simple.

The emergence involves coarse graining, right?

Coarse graining means you're throwing away information.

So when I flip a coin,

I cannot predict, if I do a good job of flipping the coin, I cannot predict whether it's going to heads or tails, right?

And even though, even if I thought, incorrectly, that the fundamental laws of physics were deterministic and really there was an answer embedded in the microstate of me and the air molecules and the coin and all that stuff, I don't know that microstate.

As you may have heard, I am not Laplace's demon.

I'm going to have to get the t-shirts made saying that I am not Laplace's demon.

That's definitely something I'm going to have to do.

What that means is in the same macro state that I used to describe the world at the level of people and coins being flipped and things like that, there are included both micro states that will end up with the coin landing heads and micro states that will end up with the coin landing tails.

And from my macroscopic level of observation, I am not able to distinguish those microstates.

So the macro theory, even at its best, even doing as much as it can possibly do, can make at best probabilistic predictions.

It is not a deterministic theory.

You can know everything you want to know about the standard model of particle physics, but if you want to predict when a volcano is going to erupt, good luck with that.

That's not what geologists try to do.

I mean, you can do better and better by collecting more and more data, but typically what you actually do is have theories of frequencies, predictions, probabilities for things.