All Mixed Up
Posted by midiguru on December 13, 2012
How many of you have heard of Maxwell’s demon? Raise your hand? Okay, that’s what I thought. We’ll start with a little explanation.
The Second Law of Thermodynamics tells us, basically, that things fall apart. Any physical system tends to move toward disorder, also known as randomness, also known as heat (because molecules jittering at random as they bump into one another are what heat is). Because of the Second Law, any engine that you build will be less than 100% efficient: Some energy will always be lost, due to friction or whatever. That’s why perpetual motion machines don’t work.
Another word for disorder is entropy. Entropy is always increasing. If it decreases locally (such as when a plant grows from a seed), it’s always increasing somewhere else. Living things don’t actually violate the Second Law, though they may seem to, because the equation is always balanced if you look at the big picture.
At least, that’s what the best scientific minds assure us. We also have a highly regarded scientific theory that the universe began as an enormous, rapidly expanding cloud of hot gas. As the gas spread out and cooled, galaxies and stars formed. That is to say, the amount of order in the universe apparently increased, and in a rather dramatic, easily visible fashion. I haven’t run into an explanation of this apparent contradiction, but I’m sure some physicist has concocted one.
Toward the end of the 19th century, the physicist James Clerk Maxwell came up with a thought experiment. I don’t know why — maybe it was a slow day in the physics lab. Maxwell imagined a box with two compartments containing gas. Between the two compartments is a partition with a very small trapdoor. Maxwell imagined that this trapdoor was operated by a demon. When the demon sees a hotter-than-average molecule of gas approaching the trapdoor from the left, he opens the trapdoor and lets it through. Conversely, when he sees a cooler-than-average molecule approaching the trapdoor from the right, he opens the trapdoor and lets it through.
The result: Over time, hot gas would accumulate in one compartment, cool gas in the other. This would violate the Second Law. It can’t happen. So where’s the fly in the ointment?
In truth, there are several flies in this ointment. For starters, operating the mechanism that opens and closes the trapdoor would cost energy and release heat. Maxwell waved his magic wand and made that problem go away. (I’ll bet you didn’t know physicists have magic wands.) Also, building (or raising, or hiring) a demon with the necessary keen eyesight and fast reflexes would cost quite a lot of energy — more than you would get back by separating the gas into hot and cold compartments. If the demon was inside the box, his activity would be releasing more heat into the system, and if he was outside the box it wouldn’t be a closed system. The thought experiment requires that the box be a closed system, with nothing coming in or going out — and of course in the real world there’s no such thing as a closed system, so all thought experiments of this type are doomed to failure. But never mind that.
The solution to the conundrum that physicists eventually settled on has something to do with information theory. I’ve just dipped into a book called The Touchstone of Life, by Werner Loewenstein, whose opening chapter presents a rather muddled treatment of the idea. Here is what Loewenstein (who certainly knows more about this stuff than I do) says: “Leo Szilard showed that the demon’s stunt really isn’t free of charge. Though he spends no energy, he puts up a precious commodity called information. The unit of this commodity is the bit, and each time the demon chooses between a hot and a cold molecule, he shells out one bit of information for this cognitive act, precisely balancing the thermodynamics accounts. Thus, the hocus-pocus here has an exact information price.” [Italics in original.]
Apparently, Loewenstein thinks this passage explains something, but it left me scratching my head. If there’s an information price, then each time the demon opens the trapdoor he must be losing information. He must end up with less information than he had before. But where did the information go? If the demon had it before he opened the trapdoor, doesn’t he still have it afterward? An increase in entropy, Loewenstein goes on to tell us, implies a decrease in information. That is, the more mixed up something (such as a box full of gas) is, the less information is contained in the gas. Or something like that. At the level of quantum mechanics, which is where individual molecules live, it all gets a little hazy. Conversely, if something is ordered in a precise way — its entropy then being low — it contains more of an abstract, non-physical “quantity” called information. Information is orderliness, and vice-versa.
In discussing information, Loewenstein refers to a cloud of gas that is at thermal equilibrium (that is, maximum entropy and minimum information) as having no discernible order or structure. That word “discernible” set my antennae quivering. Why? Because the act of discerning requires an observer. This is not a trivial distinction. It suggests that in the absence of an observer, there would be no entropy — no such thing as order or disorder. Is it possible that the Second Law of Thermodynamics rests entirely on the presence of an observer, and could be violated quite casually if no one were watching?
Well, I have to rephrase that a little. The Second Law would neither be violated nor apply, because the thing that it applies to — namely, entropy — wouldn’t exist. We can’t say anything about what would happen if there were no observer, because in the act of saying something about it, we’re observing it.
On a more concrete level, though, we can ask: Where is the observer, and what phenomena is he/she/it prepared to observe? Here’s my thought experiment. We’re going to map the movements of people in a large city. We have a really big computer and a perfect tracking system, and we’ve constructed a time sequence that shows the movements of people as little dots. We would observe, I think, very little order in our time sequence map. During certain periods (night) there would be less movement overall, and our map would tend to show lots of movement along certain routes (streets) and less movement elsewhere — but other than that, the entropy would seem to be pretty widespread. Not much information, that is, can be gleaned.
Now let’s zoom in. You’re a young man waiting impatiently in a park to meet his girlfriend. She hasn’t yet arrived. To this particular observer, the young man waiting, the supposed entropy of the movement of people through the city is nonexistent. He cares only about one special movement of one person — the arrival of his girlfriend — and he has perfect information about it.
Entropy has vanished, and the reason is because we’ve switched to a different observer.
I’m not smart enough to draw any firm conclusions from any of this. Quite possibly a physicist trained in logic could show me where I’ve run off the rails. I just think it’s interesting that maybe entropy only exists when you’re watching. When you’re not watching, the universe could be doing almost anything — as long as you don’t turn around and start watching again. That would spoil it.