Wednesday, June 30, 2010

Why Isn't Tomorrow Ever Yesterday? Part I

Why does time flow in one direction? The fundamental equations of physics (to the extent that they are known) are essentially symmetrical with respect to time. So why do we remember yesterday and not tomorrow? Why does an ice cube left on the ground on a warm day spontaneously melt, but a puddle of water on the ground never spontaneously become an ice cube?

A recent Science News article addresses this age-old question and discusses the answer proposed by Sean Carroll (of Cosmic Variance fame). Sean has explained his theory in a popular-level book, too.

Fundamentally, the answer boils down (hah!) to entropy, which is just the physicist's way of saying it's all a matter of probability. There are vastly more ways for an ice cube to transform itself into a puddle of water than there are for a puddle to transform itself into an ice cube, so the former process is vastly more likely than the latter. To say it another way, for the puddle to become an ice cube (on a warm day) would require a huge number of exceedingly unlikely coincidences: water molecules oriented perfectly, and with perfectly aligned motion, so that they bond together and channel the excess energy away.

But for the entropy explanation to work, the universe must start out in a low-entropy state, so that there is some room for entropy to increase. If the universe began its existence in a state of maximum entropy, then it would be impossible for entropy to get any bigger. In such a universe, you might see an occasional increase or even an occasional decrease of entropy in some local region, caused by random fluctuations, but the overall trend would be no increase or decrease of entropy. In contrast, what we see in our universe is a universal trend for entropy to increase. So why did the universe start out that way - and doesn't that violate the fundamental time symmetry of the equations of physics?

Carroll suggests that it all has to do with what happened before the Big Bang. The basic idea - and I want to emphasize that this idea is completely speculative at this time - is summed up in this diagram:

The basic idea is this: There is a large slab of spacetime in the middle of the diagram (labelled "de Sitter space") that spits out little baby universe blobs. Our universe is one of these droplet-shaped blobs, and the pointy end - the end nearest to the slab - is our Big Bang. There are, presumably, infinitely many other droplets that are other universes completely separate from our universe, which we will never encounter or even detect in any way.

The clever bit is that there are blobs below the slab as well as above it. For those blobs, the pointy end is at the "top" of the blob: the Big Bang in those universes occurs at what, from the God's-eye perspective of the diagram, we would call a later time than all the other events of that universe. However, for beings living inside one of those universes, the Big Bang would appear to be in the past, not the future, just as in our universe.

Since there are blobs both above and below the slab, the overall picture is (on average) time-symmetric. That is, if you flip the whole diagram upside-down, it looks more or less the same. So Sean's model lets us have our cake and eat it, too: we can have entropy increasing within each little blob, but in the overall picture there is no difference between the "forward" and "backward" time directions.

Now, I don't want to go into the details of the physics of this model, because I don't really understand the details myself. What I want to ask is: What does an explanation like this explain? Is this sort of speculation a matter of physics or of metaphysics? What kind of evidence could we obtain in our little bubble of spacetime that would justify the conjecture of infinitely many other unobservable bubbles?

This post is already getting rather long, so I will leave you to ponder those questions until next time.

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