Time and Lengths Scales for Scientific Theories

As noted in an earlier post, I am in the process of reading (and thoroughly enjoying) N. David Mermin's Boojums All the Way Through. In a couple of his essays Mermin emphasizes the incredible successes of quantum mechanics. He mentions the fact that quantum mechanics was born in 1900 (on December 14, exactly 73 years before I was born!) and that even now (he published one of these essays in 1988, but we'll update it to 2007) there are no signs that quantum mechanics is incorrect. So we've had over 100 years to overthrow the theory, or at least build some solid evidence against it, and nothing has happened. Mermin also points out that the quantum theory was developed to explain atomic processes that have a characteristic length scale of 10^-9 meters or so, but that the theory has been extended to the much smaller length scales of subatomic particles (for this we can use the length scale for weak interactions, something like 10^-17 meters). So quantum mechanics has proven successful over length scales spanning 8 orders of magnitude.

This got me thinking: Is this really all that impressive? How does it stack up to the run that classical physics had? Not very well, it turns out. Classical physics was born, to give a conservative estimate, with the publication of Newton's Principia in 1687. Classical physics was essentially unchallenged until Planck's lecture on December 14, 1900. It wasn't SERIOUSLY challenged until Einstein's "On the Electrodynamics of Moving Bodies" in 1905. That's a span of well over 300 years. As for length scales, classical mechanics was primarily devised to account for the motions of the planets in the solar system. The diameter of the solar system is on the order of 10^16 meters. Of course, Newtonian mechanics also turned out to work pretty well for small objects (let's say on the scale of 1 mm - again a conservative estimate since classical physics surely works quite well at the micrometer scale and even somewhat smaller). This conservative estimate gives us length scales spanning 19 orders of magnitude. So it looks like quantum mechanics has a long way to go before it could be considered as "successful" as classical mechanics according to these measures. But eventually we did concede that classical mechanics was not the final correct theory. Why should we then accept quantum mechanics as the final correct theory?

Now, this is not to say that I think quantum mechanics is wrong in some specific way. It really has looked pretty good so far. But the inductive argument doesn't work - just because it hasn't failed yet doesn't mean it never will. As scientists we should not consider ANY theory to be final, regardless of its level of success (as measured by time, length, or any other means). There is no doubt that quantum mechanics is impressive. The fact that it has challenged some of our basic notions of the nature of physical reality indicates, I think, that it gets at something very deep. But we also should not refuse to question quantum mechanics when the answers it provides are less than satisfying.

There is no doubt that quantum mechanics represents the best theory available right now. We should continue to use it, and to extend it in interesting ways (i.e. quantum field theory, quantum gravity if we can manage it, etc.). But the same was true of classical mechanics long ago when it was being extended in interesting ways by the likes of Lagrange, Maupertuis, and Hamilton. Let us not be guilty of the hubris of Lord Kelvin who declared at the end of the Nineteenth Century that physics was all but finished. Nature may still have some surprises in store for us, and since we cannot know if we will be surprised we must always remain open to the possibility.