Greetings from sunny Santa Cruz, where we’re in week three of the Summer School on Philosophy of Cosmology. I gave two lectures yesterday afternoon, and in a technological miracle they’ve already appeared on YouTube. The audio and video aren’t perfect quality, but hopefully viewers can hear everything clearly.
These are closer to discussions than lectures, as I was intentionally pretty informal about the whole thing. Rather than trying to push any one specific model or idea, I gave an overview of what I take to be the relevant issues confronting someone who wants to build a cosmological model that naturally explains why the early universe had a low entropy. They are a little bit technical, as the intended audience is grad students in physics and philosophy who have already sat through two weeks of lecturing.
If there is one central idea, it’s the concept of a “cosmological realization measure” for statistical mechanics. Ordinarily, when we have some statistical system, we know some macroscopic facts about it but only have a probability distribution over the microscopic details. If our goal is to predict the future, it suffices to choose a distribution that is uniform in the Liouville measure given to us by classical mechanics (or its quantum analogue). If we want to reconstruct the past, in contrast, we need to conditionalize over trajectories that also started in a low-entropy past state — that the “Past Hypothesis” that is required to get stat mech off the ground in a world governed by time-symmetric fundamental laws.
The goal I am pursuing is to find cosmological scenarios in which the Past Hypothesis is predicted by the dynamics, not merely assumed. We imagine a “large universe,” one in which local macroscopic situations (like a box of gas or a lecture hall full of students) occur many times. Then we can define a measure over the microconditions corresponding to such situations by looking at the ways in which those situations actually appear in the cosmic history. The hope — still just a hope, really — is that familiar situations like observers or lecture halls or apple pies appear predominantly in the aftermath of low-entropy Big-Bang-like states. That would stand in marked contrast to the straightforward Boltzmannian expectation that any particular low-entropy state is both preceded by and followed by higher-entropy configurations. I don’t think any particular model completely succeeds in this ambition, but I’m optimistic that we can build theories of this type. We shall see.