Last time, I introduced the question of the arrow of time and Sean Carroll's proposed solution of it. Now I want to ask what it is that this solution solves.
First, a little about the nature of physical models. There are the equations of the theory - say, general relativity, or the Standard Model. The equations (we suppose) apply to a wide variety of different situations. In addition, there are boundary conditions that apply to some specific situation that we are trying to model. For instance, if I want to model the water in a beaker, I need the equations of fluid dynamics, but I also need to specify the conditions at the boundary of the water: where the water meets the beaker. In this case, I would need to specify the shape of the beaker and give some condition for what the water does when it hits the edge.
The equations of the theory will respect some symmetries, like the time reversal symmetry I mentioned last time. But the solutions of the equations will not necessarily respect the same symmetries. Take, for example, the simple case of a freely moving object in an otherwise empty spacetime. The equation of motion is:
Acceleration = O
This equation has rotational symmetry: it doesn't single out any particular direction in space. Now consider a solution to the equation for a specific object, say a rock. The solution is that the rock's velocity remains constant. But if the rock is moving at all, it is moving in some particular direction. The solution singles out a special direction in space: the direction of motion. The solution for a particular situation will not, in general, display the same symmetries as the equations of motion.
From this point of view, there's no need to worry about the fact that the universe starts out with low entropy: the low entropy is simply a boundary condition we need to impose in order to produce a model that reflects the universe we live in. The lack of time reversal symmetry is not mysterious: the equations of physics are time reversal invariant, but the boundary conditions are not.
What, then, does Carroll's "explanation" of time reversal asymmetry actually explain? Carroll cannot avoid the issue of boundary conditions. His slab of de Sitter space acts as the boundary condition for the droplets that are the baby universes. He has just replaced one boundary condition with another. True, his choice of boundary condition restores some kind of overall time symmetry to the solution. But that symmetry is completely unobservable, because the other baby universes are causally disconnected from our universe. If Carroll is right, there is no way we will ever know it!
Now, maybe I'm not being fair to Carroll's model. Maybe there is something in the process of spawning baby universes that gives specific, testable predictions. And maybe some day those predictions will be confirmed. But even if they are, the overall picture can never be tested experimentally. Specifically, the time symmetry aspect - which, after all, is what Carroll claims to be explaining - can never be checked.
To me, this removes the model from the realm of science. The existence of other baby universes is a purely metaphysical question: do you prefer a picture which has an overall time symmetry, or can you live without it? Does it bother you to postulate an infinite number of unobservable universes, or are you OK with that? Certainly esthetic principles have played a role in theoretical physics in the past and have led to deeper understanding. But when your esthetic principle leads to a picture that is completely untestable, I wonder whether it has any scientific value.
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