Turning Back the Hands of Entropy

If you have time for it, here's something a bit different from usual:

What Keeps Time Moving Forward? Blame It on the Big Bang, by John Matson, Scientific American: ...In his new book, From Eternity to Here..., theoretical physicist Sean Carroll of the California Institute of Technology sets out to explain why time marches along unfailingly in one direction. Expanding on the concepts in his June 2008 feature for Scientific American, "The Cosmic Origins of Time's Arrow," Carroll argues for the necessity of marrying three seemingly disparate concepts: time, entropy and cosmology.

Entropy, which in rough terms is the measure of a system's disorder, creeps up over time, as dictated by the second law of thermodynamics. To illustrate entropy's inexorable growth, Carroll takes us to the breakfast table—you can't unscramble an egg, he points out, and you can't unstir the milk out of your coffee. These systems invariably proceed to disordered, or high-entropy, arrangements. Each of these examples shows how the continual growth of entropy fills the world with irreversible processes that divide the past from the future: The making of an omelet and the mixing of milk into a cup of coffee are events that work in only one temporal direction.

But why should entropy always increase? This is where Carroll turns to cosmology, which must explain why the universe began in a uniquely low-entropy state. We spoke to the physicist...

What's so interesting about time? To a naive observer it's something that just passes by and that we can't do anything with; it's unchanging.
...The fundamental laws of physics treat the past and the future [as being] exactly the same, whereas the world does not. ... So it would be nice to know how to reconcile that. That's the arrow of time problem as it's been thought about for at least a couple hundred years now. ... But there is something that I think makes this problem a little bit special ... I wanted to draw attention to this connection between the arrow of time and cosmology... I think this is something that we really should keep in mind as one of the fundamental puzzles facing us in modern science. ...

[H]ow does the concept of entropy intertwine with the arrow of time?
Well, I think people have probably heard the word entropy...; that's the second law of thermodynamics. ... I believe ... what .. is ... underappreciated is that just about everything about the arrow of time..., the fact that the past is set in stone while the future can still be altered—is all because of entropy. The fact that you can remember yesterday but not tomorrow is because of entropy. The fact that you're always born young and then you grow older,... it's all because of entropy. So I think that entropy is underappreciated as something that has a crucial role in how we go through life. ...

Once you assume that the universe had a low entropy for whatever reason, everything else follows, and that's all we ever talk about in textbooks. But we're being a little bit more ambitious than that. We want to understand why it was that way—why was it that the entropy was lower yesterday than it is today?

To understand why the entropy was lower yesterday really requires cosmology. And I think that if you sit down and think about it carefully there is absolutely no question that that is true, yet a lot of people don't quite accept it yet.

If you take this approach and look at time from a cosmological standpoint, what is this low-entropy condition in the past? What does that look like?

We're not learning anything about the early universe by making this observation. We already know what the early universe was like...—it's that in trying to explain that, in trying to come up with a theory, whether it's inflation or the cyclic universe or a big bounce, you haven't succeeded in explaining the early universe unless you've explained why it has low entropy. And I just think a tremendous number of contemporary cosmological theories fail at that requirement; they sort of sidestep their way around that question rather than addressing it head-on. ...

I was disappointed that he doesn't explain his theory of how the low entropy state comes about. However, there is this graphic from the article above that shows how the appearance of the low entropy state is a temporary deviation from the universe's usual high entropy equilibrium. As you look at the figure, this passage from the article might help fill in what happens between the 2nd and 3rd diagrams (the 4th diagram shows a low entropy state; the endpoints are both high entropy states):

[L]et us suppose that the universe started in a high-entropy state, which is its most natural state. A good candidate for such a state is empty space. Like any good high-entropy state, the tendency of empty space is to just sit there, unchanging. So the problem is: How do we get our current universe out of a desolate and quiescent spacetime? The secret might lie in the existence of dark energy.

In the presence of dark energy, empty space is not completely empty. Fluctuations of quantum fields give rise to a very low temperature—enormously lower than the temperature of today’s universe but nonetheless not quite absolute zero. All quantum fields experience occasional thermal fluctuations in such a universe. That means it is not perfectly quiescent; if we wait long enough, individual particles and even substantial collections of particles will fluctuate into existence, only to once again disperse into the vacuum. ...

Among the things that can fluctuate into existence are small patches of ultradense dark energy. If conditions are just right, that patch can undergo inflation and pinch off to form a separate universe all its own—a baby universe. Our universe may be the offspring of some other universe. ...

This scenario ... provides a provocative solution to the origin of time asymmetry in our observable universe: we see only a tiny patch of the big picture, and this larger arena is fully time-symmetric. Entropy can increase without limit through the creation of new baby universes.

Best of all, this story can be told backward and forward in time. Imagine that we start with empty space at some particular moment... Baby universes fluctuate into existence in both directions of time, eventually emptying out and giving birth to babies of their own. On ultralarge scales, such a multiverse would look statistically symmetric with respect to time—both the past and the future would feature new universes fluctuating into life and proliferating without bound. Each of them would experience an arrow of time, but half would have an arrow that was reversed with respect to that in the others....