Maxwell's demon and Schrodinger's cat

And lesser flights of fancy

In the days when intuition indicated that the earth was flat, some people asked what would happen if a ship sailed to the edge. Would it fall over? Did the sea go over the edge in a giant waterfall? Where did the water go?

The questions were a thought experiment. No one ever did sail to the edge of the ocean. There's no record anyone tried. But the very questioning tested the flat-earth model and suggested its weaknesses.

The thought experiments continued and became more subtle as science probed realms too small, too fast or too distant for humans to observe directly. In the 19th century Robert Clerk Maxwell questioned the second law of thermodynamics, which declared that in a closed system, entropy can only increase — order tends toward disorder. Maxwell imagined a box filled with gas at a given temperature. This temperature represents the average kinetic energy of the gas molecules. But it is only an average. At any moment some molecules have more energy — are moving faster — than the average. And some molecules have less energy.

Maxwell supposed a tiny being — later called Maxwell’s demon — sitting inside the box, which the demon has divided by a partition that has a microscopic window that can be opened and closed. The demon observes molecules as they streak toward the window. When a molecule moving faster than average approaches the window from the left side of the partition, the demon opens the window and lets it pass through. When a slow molecule approaches from the left, the demon closes the window and the slowpoke bounces back to the left, trapped on that side.

Meanwhile the demon also monitors molecules approaching the partition from the right. Now the slow ones are let through and the fast ones retained.

Gradually the fast molecules and the slow molecules are separated from each other. As they are, the right half of the chamber, filling with speedy molecules, grows warmer. The left half grows cooler. Order increases — which is to say that entropy decreases. The second law of thermodynamics is broken.

All this was a thought experiment. No such demon could ever be constructed or conjured into being.

Even so, the principle behind the experiment was unnerving. No energy from outside the system was being introduced, and yet entropy was decreasing. Something was amiss.

One possibility was that the second law was wrong. Albert Einstein would win his reputation with thought experiments that showed that Isaac Newton’s law of gravity, while useful in most cases, was wrong when pushed to extremes. Maybe Maxwell's demon showed something similar about the second law: good enough for everyday use but unreliable at the limits.

This wasn't what happened. Or hasn't happened yet. Instead the demon inspired closer looks at the role of information in entropy. Even if no work is done upon the molecules — no energy added or subtracted — by the demon, something is done. Information is extracted and deployed.

Theorists are still wrestling with the connection between entropy and information. So far the second law has survived. Most physicists consider it a pillar of thermodynamics. The wrestling has yielded advancements in cosmology, involving black holes for instance, and communication theory. But the bout’s not over, and the final decision has yet to be rendered.

Another celebrated thought experiment involves a cat. Erwin Schrodinger, puzzling over some ramifications of quantum theory and Werner Heisenberg’s uncertainty principle, imagined a cat in a box with a vial of poison, a sample of radioactive material and a Geiger counter. In a given period of time, there is a 50 percent chance the material will give off radiation that triggers the Geiger counter, which in turn releases the poison that kills the cat. One would think that at any particular moment, the cat is either dead or alive. Yet according to a common interpretation of quantum theory, the radiation has neither happened nor not happened until someone observes it. More precisely, if confusingly, the radiation both has and has not happened until observed. Extrapolating, the cat is both dead and alive until somebody opens the box.

In this case the conundrum arises from the fact that the world behaves differently at atomic scale than it does at cat scale. Superposition — the dual state — provides a useful interpretation of radioactive decay and other such micro phenomena. But it defies all observations at the macro level of the everyday.

Most thought experiments are more mundane. We do our own whenever we weigh alternative courses of action. What might happen if I slip away from the office early today? Will the boss notice? Will I be punished if caught? Arguably our penchant for thought experiments is what makes us human — except that animals appear to weigh decisions too. A gopher peeks from its hole and ponders whether it can safely venture out. A hyena waits for reinforcements before trying to drive a lion from its dinner.

Thought experiments have the great advantage of risking nothing but brain time. Our brains model the universe, or some salient part of it, and test courses of action. In our models our ships sail off the edge of the ocean, so we don't have to. And the only cats that die are imaginary ones.