Paul Dirac, Scientific American, 1963: The Evolution of the Physicist's Picture of NatureThis would be a good update to the history section of the Wikipedia article on the equation; it's also a lovely example for people writing about on the philosophy of science. It's all so much neater in retrospect.

... I might tell you the story I heard from Schrodinger of how, when he first got the idea for this equation, he immediately applied it to the behavior of the electron in the hydrogen atom, and then he got results that did not agree with experiment. The disagreement arose because at that time it was not known that the electron has a spin. That, of course, was a great disappointment to Schrodinger, and it caused him to abandon the work for some months. Then he noticed that if he applied the theory in a more approximate way, not taking into account the refinements required by relativity, to this rough approximation his work was in agreement with observation. He published his first paper with only this rough approximation, and in that way Schrodinger's wave equation was presented to the world. Afterward, of course, when people found out how to take into account correctly the spin of the electron, the discrepancy between the results of applying Schrodinger's relativistic equation and the experiments was completely cleared up...

Those were the glory days of Scientific American. I love the Sci Am news blog, but the magazine is very slight now. It aims for a different market.

There's so much more in this brief essay. It's required reading for the physics fanboy. Consider Dirac's discussion of "137" (Adams should have used 137, not 42):

.... There are some fundamental constants in nature: the charge on the electron (designated e), Planck's constant divided by 2 π (designated h-bar) and the velocity of light (c). From these fundamental constants one can construct a number that has no dimensions: the number h-bar*c/e^2. That number is found by experiment to have the value 137, or something very close to 137. Now, there is no known reason why it should have this value rather than some other number. Various people have put forward ideas about it, but there is no accepted theory. Still, one can be fairly sure that someday physicists will solve the problem and explain why the number has this value. There will be a physics in the future that works when h-bar*c/e^2 has the value 137 and that will not work when it has any other value...Dirac gets numerological about 137. He really doesn't like square roots ...

.... Only two of them can be fundamental, and the third must be derived from those two. It is almost certain that c will be one of the two fundamental ones.... If h-bar is fundamental, e will have to be explained in some way in terms of the square root of h-bar, and it seems most unlikely that any fundamental theory can give e in terms of a square root, since square roots do not occur in basic equations. It is much more likely that e will be the fundamental quantity and that h-bar will be explained in terms of c^2. Then there will be no square root in the basic equations...Genius is sometimes close to dysfunction [1]; it's common in science that elder genius takes odd directions. This stuff is great fodder for crackpots, but there's always the tantalizing possibility that some of it will be borne out one day.

[1] I've lost a recent developmental neurobiology reference that put the old "genius is close to madness" cliche on firm ground. It wasn't this review article, but it was of the same genre. The same mechanisms that make a person creative do seem to make them more prone to "strange loops", perhaps particularly as they age. (Yeah, I'm being self-referential.)

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