On occasion, somebody voices the idea that in year [tex]N[/tex], physicists thought they had everything basically figured out, and that all they had to do was compute more decimal digits. I won’t pretend to know whether this is actually true for any values of [tex]N[/tex] — when did one old man’s grumpiness become the definitive statement about a scientific age? — but it’s interesting that not every physicist with an interest in history has supported the claim.
One classic illustration of how the old guys with the beards knew their understanding of physics was incomplete involves the specific heats of gases. How much does a gas warm up when a given amount of energy is poured into it? The physics of the 1890s was unable to resolve this problem. The solution, achieved in the next century, required quantum mechanics, but the problem was far from unknown in the years before 1900. Quoting Richard Feynman’s Lectures on Physics (1964), volume 1, chapter 40, with hyperlinks added by me:
The first great paper on the dynamical theory of gases was by Maxwell in 1859. On the basis of ideas we have been discussing, he was able accurately to explain a great many known relations, such as Boyle’s law, the diffusion theory, the viscosity of gases, and things we shall talk about in the next chapter. He listed all these great successes in a final summary, and at the end he said, “Finally, by establishing a necessary relation between the motions of translation and rotation (he is talking about the 1/2 kT theorem) of all particles not spherical, we proved that a system of such particles could not possibly satisfy the known relation between the two specific heats.” He is referring to γ (which we shall see later is related to two ways of measuring specific heat), and he says we know we cannot get the right answer.
Two years later, in a lecture, he said, “I have now put before you what I consider to be the greatest difficulty yet encountered by the molecular theory.” These words represent the first discovery that the laws of classical physics were wrong. This was the first indication that there was something fundamentally impossible, because a rigorously proved theorem did not agree with experiment. About 1890, Jeans was to talk about this puzzle again [cf.]. One often hears it said that the physicists at the latter part of the nineteenth century thought they knew all the significant physical laws and that all they had to do was to calculate more decimal places. Someone may have said that once, and others copied it. But a thorough reading of the literature of the time shows they were all worrying about something.
When the history lessons handed to us are textbook cardboard, oversimplifications which leave out all the interesting parts of the story, how much insight can we honestly hope for?
UPDATE (1 December 2013): The link to the Feynman lectures now points to the online version of Volume 1′s complete text. This is a good time to point out an erratum, which I noticed when first writing this post but managed to forget to mention explicitly. If “Jeans” does refer to James Jeans (and I don’t know what other physicist it could be), then “1890″ cannot be correct. Jeans was born in 1877 and did not go to Cambridge until 1896.
A better date, in the next century but still in the earliest years of the old quantum theory, would be 1904, the first publication of his book The Dynamical Theory of Gases, which has a lengthy discussion of how kinetic theory fails to account for gases’ specific heats. The nub is on p. 173: “Our theory has, then, led to a result which is in flagrant opposition to experiment.” Jeans’ own attempt at a solution was basically to deny that all the degrees of freedom were in statistical equilibrium. Additional references can be found in R. Hudson (1989), “James Jeans and radiation theory,” Studies in History and Philosophy of Science A vol. 20, pp. 57–76.
UDPATE (9 December 2013): I wrote a letter to the people in charge of revising the Feynman red books, and the incorrect year has been corrected.