Second Thermo

The Second Law of Thermodynamics is a Quantum-Mechanical Effect

June 15th, 1998

This is the title of a paper I wrote way back in 1976. I submitted it to a technical journal for publication and it was rejected; the referees thought I was wrong. I’m quite certain of the correctness of the thesis; this only goes to demonstrate the truth of Kuhn’s observation that scientific revolutions don’t happen until there is a perceived need for a major shift in thinking. My thesis is, admittedly, radical; I’m sure that its extremism is the cause of its rejection. Yet in the last two decades, the world of physics has bumbled forward and my thesis doesn’t seem so radical now. Perhaps somebody else has already demonstrated it, and my thesis has gone from heresy to dogma while I wasn’t looking. In any event, you can decide for yourself. Here’s the reasoning:

The starting point is Maxwell’s Demon, a truly odd notion cooked up by J. C. Maxwell back in 1871. He noted that, if an appropriate device (the demon) were placed at a microscopic doorway between two chambers, with the ability to detect molecules approaching the doorway, and the ability to open and close the door, it could preferentially open or close the door in such a way as to introduce more molecules into one side than the other, or perhaps to permit only fast-moving (high temperature) molecules into the preferred chamber. This would create a pressure difference between the two chambers that could be exploited by a heat engine to extract energy from the system -- a clear violation of the Second Law of Thermodynamics.

Maxwell’s Demon thereby challenges the validity of the Second Law of Thermodynamics. Nobody ever really believed in the Demon, but neither could anybody explain why he couldn’t operate as Maxwell assumed. Technically, the Second Law of Thermodynamics was invalidated by Maxwell’s Demon. But nobody took it seriously.

In 1950 Leon Brilloun solved the problem. He observed that the Demon had to see the molecules in order to act on them, and the ambient photons in the chambers would be at thermal equilibrium with the system, so he would see just a blank when he looked into either chamber. He could, of course, illuminate the chambers with a flashlight, but Brilloun showed that, even in the theoretically perfect case, the amount of entropy gained in scattering one photon off of one molecule would exceed the amount of entropy lost in moving the molecule from one chamber to the other. In other words, the cost of making the transfer would always exceed the profit made from it.

Brilloun’s paper didn’t attract much attention; after all, everybody knew that Maxwell’s Demon couldn’t work anyway. This was just confirmation of their expectations. Indeed, I have seen discussions of Maxwell’s Demon that are apparently unaware of Brilloun’s solution.

But that isn’t the end of the story, at least not from my point of view. For me, the crucial trick was the fact that Brilloun had to appeal to quantum mechanics to kill the Demon. If quantum mechanics didn’t exist (that is, if the Heisenberg constant were equal to zero), then Brilloun’s proof wouldn’t work, the Demon would still be in business -- and the Second Law of Thermodynamics would be invalid.

My big idea, which really isn’t very big at all, is to observe that the Second Law of Thermodynamics is only valid in the case where Heisenberg’s constant is greater than zero -- that is, when quantum mechanics is "turned on" in the universe.In other words, the Second Law of Thermodynamics is a quantum-mechanical effect.

As I said, the physicists of 1976 rejected this thinking; it was just too weird back then. But now let me expand on the idea, providing some background, some illustrative material that doesn’t provide the proof that you need in a scientific paper, but helps make everything fit together.

The first concept here is the notion of information. There’s been lots of excitement in the last few years about information stuff, entropy, and chaos. I haven’t bothered following it, but it does seem that the intellectual community is putting a lot of pieces together. First, some terminology, then two key points.

Terminology: there is one basic duality with many, many words to express the poles of the duality. At one pole we have the following terms: information, orderliness, organization, negentropy, usable energy. At the other pole we have these terms: chaos, randomness, entropy, disorderliness, equilibrium.

Key point #1: the total information content of the universe is finite. This, after all, is the purport of the Uncertainty Principle: you can’t know anything about even a simple particle with unlimited precision. You can know a lot about it, up to a certain limit, but there’s a tradeoff that limits the total amount of information you can have about that particle. And since particles make up much of the universe, the summation of all this is that you can’t know everything about the universe with infinite precision. The sum of all the information in the universe is finite.

Key Point #2 (this one is my contribution): Information and time have an interesting relationship. If it weren’t for one nasty little catch, you could use time as an instrument to extend the precision of your information. Measure the position and velocity of a particle now, wait a while, then measure its position and velocity again, and you can use the difference in positions and the time delay to calculate its velocity with greater precision. If you want more precision, you just wait longer. The nasty little catch is that the act of measurement changes both its position and velocity by just enough to rob your measurement of utility. This is actually a variation on the Schroedinger’s Cat thought experiment; both concern the nature of information as time passes and observations are made.

But the nasty little catch comes from quantum mechanics, and is really just another expression of the statement in Key Point #1. If the total information content of the universe is to remain constant, then we have to degrade information with the passage of time, lest some noisome physicist use the time-delay method to acquire more information than exists.

Let’s shift gears and think in terms of looking backwards in time using measured information. Suppose that you’re floating in space and you don’t know where you came from. You could figure it out by charting star positions, calculating your position relative to the visible stars, then waiting and repeating the process later. The difference in positions divided by the time delay gives you your velocity. You extrapolate backwards to get your starting point. Of course, minor inaccuracies in your measurements yield major inaccuracies in your extrapolation, but if you wait long enough, you can reduce those inaccuracies to as low as you want -- except for the interference of that damned information degradation arising from quantum mechanics. This insures that, no matter how long you wait, you’ll never get your starting point with more precision than the theoretical limit.

Now let’s apply this thinking to the history of the universe. After all, we’re in exactly the same position described above: we’re floating through space, trying to figure out where we came from. If information didn’t degrade with time, we’d be able to wait a few billion years and figure out everything about the universe. We could calculate the starting points of everything, the past behavior of everything -- sheesh, this could get embarrassing. You’d better watch what you do next Saturday night, lest astronomers a billion years from now deduce your indiscretions from the subsequent motions of galaxies over the intervening time.

It gets worse: if information didn’t degrade, then we should be able to wait long enough to gather enough information to see backwards through the Big Bang, learning what happened before time began. This is too weird even for me; I think we’d better accept the concept of information degradation over time as part of a limit on the amount of information in the universe.