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No. 1239:
Canonical Ensemble

Today, a practical use for an abstract theory. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

First, a simple fact of physics: If you average the velocity of one molecule of the air in your room, as it collides from one molecule to the next, that average comes out the same as for all molecules in the room at one instant.

Now stretch that idea a little: Suppose we want to know how the instant average of a set of molecules fluctuates from moment to moment. This time, we can imagine many similar sets of molecules and then calculate how their averages differ at any instant. In broader terms, physicists find they can simplify their calculations if they replace history with parallel universes.

That's what we call a thought experiment -- one we do only in our minds as an aid to calculation. Now let's pretend that our universe really is replicated over and over -- that our world is just one realization along with all the others.

Let's think about how our lives might fluctuate in those other worlds. Remember that time you almost had an accident -- how you just happened to turn your head at the right moment? Remember that one time in a hundred when you zigged instead of zagging? Our lives are an accumulation of such choices.

If such alternate universes really existed they'd spin themselves out alongside ours with differences that don't come from molecular fluctuations alone, but from free will choices as well. Remember when you teetered over a decision -- buying a house, accepting a job, or just deciding which way to come home from the store.

This thought model isn't a matter of science-fiction speculation. The physicist uses it to predict the most probable state of the universe, along with its fluctuations. But the point is that all those worlds fluctuate. In one, the Germans don't bring Hitler to power. In another, no one invents penicillin. In a third, I zag instead of zigging after all.

We gain perspective by imagining parallel universes out there, with our other selves making other choices, or having different luck. If we hadn't dropped the Hiroshima bomb, full scale nuclear war with Russia might've looked viable in 1962. Someone would've used the accursed thing sooner or later. If you hadn't messed up in 1970, you might be a less worthwhile person today.

The laws of probability say those parallel universes only differ in the small stuff. If your other self out there made one crucial choice you wish you'd made, how different from you would he be? We give too much weight to a few decisions that loom large. Actually, we're formed in a thousand undramatic day-by-day choices.

Physicists call these parallel universes ensembles. I call that a fine reason for rejoicing in the hand life deals us. Ensemble theory reminds us that those other selves would be doing not much better or worse than you and I -- in the only universe we know.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)

Tien, C. L., and Lienhard, J. H., Statistical Thermodynamics, revised edition. Washington, DC: Hemisphere Publishing Corp., 1979. See especially Chapter 8.


(from Tien and Lienhard, above)