Engines of Our Ingenuity

No. 946:
WRONG HILL TO DIE UPON

by John H. John H. Lienhard

Click here for audio of Episode 946.

Today, a great scientist chooses the wrong hill to die upon. 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.

On Sept. 5th, 1906, the 62-year-old physicist Ludwig Boltzmann slipped a noose around his neck and hanged himself. Boltzmann, more than anyone, had shown us how to predict the behavior of gases by describing moving molecules.

But he lived at poor peace with himself, and now he despaired of being understood. He probably committed that irreversible act because scientists attacked his ideas about irreversibility.

I need to explain that: When molecules collide, they bounce off one another's force fields with no friction, no energy loss. If time ran backward, the collision would reverse itself perfectly. But that sets up an absurdity: Suppose you open an air tank and air molecules begin rushing out. Then suppose the motion of each molecule could somehow be reversed. Wouldn't history itself run in reverse? Wouldn't the molecules rush back into the tank?

That's as silly as it is logical. Time looks directionless on the molecular level, where motion is perfectly reversible. But nothing is so perfect in our larger scale of sensory awareness. Here in the visible world the past cannot be undone. Time's arrow flies from past to future. Air never flows back into the tank.

Boltzmann turned superb mathematics on the question. He showed how rules of averaging won't let such a reversal occur. In any large collection of molecules, disorder continues increasing after you reverse the motions. The gas must keep flowing out.

The trouble is, his math didn't say why reversed molecular motions won't reverse history. Classical physicists, who hadn't bought his molecular mechanisms, attacked Boltzmann. Soon after he died, quantum mechanics took shape, and Heisenberg's Uncertainty Principle said it isn't possible to specify reversed motions accurately. In a quantum universe, Boltzmann's math still makes perfect sense, and the idea that you can reverse time is nonsense.

Boltzmann was brilliant, but he had a history of depression and mental illness. Now he couldn't answer his critics, yet he knew he was right. He said,

[theory] fills my thought and action ... no sacrifice for it is too much for me ... [it is] the content of my whole life.
Boltzmann's theory was, as we say, the hill he chose to die upon. He despaired and committed his terrible irreversible suicide just as Einstein and the new breed of physicists were taking him very seriously. Had he waited just a little longer, he would have seen his genius triumph. His belief faltered, but he'd put irreversible change in motion. Time's arrow was in full flight. His ideas continued moving outward, and, by now, they have touched the whole of 20th-century physics.

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.L., Statistical Thermodynamics, (revised printing) New York: Hemisphere Pub. Corp., 1971, 1979. See especially, Section 12.3.

Coveney, P., and Highfield, R., The Arrow of Time: A Voyage Through Science to Solve Time's Greatest Mystery, New York: Fawcett Columbine, 1990.

The theoretical apparatus that Boltzmann put in place was truly immense. He took James Clerk Maxwell's ideas as a starting point and showed how to describe macroscopic behavior from the behavior of molecular movement. He built the bridges that connect the kinetic theory of gases to continuum thermodynamics.

He directed that his tombstone have carved upon it his equation relating entropy to molecular probability. That reflected justifiable pride in his most important theoretical result.

The demonstration that I refer to in the episode is his so-called H-theorem. It proves that increasing entropy is inevitable in any spontaneous process in an ensemble of molecules. In other words, the second law of thermodynamics is derivable from molecular considerations, with minimal assumptions.


The Engines of Our Ingenuity is Copyright © 1988-1997 by John H. Lienhard.

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