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tarigwaemir asks in the Kuhn 20 thread whether the quantum revolution is really a revolution,* seeing as we still use classical mechanics as "a valid approximation for certain frames of reference." Kuhn would emphatically say yes it's a revolution (and so would I, though my poor knowledge of physics makes my "yes" less impressive than his). In Structure Kuhn directly addresses our continued use of Newtonian mechanics, though in regard to the difference between classical physics and relativity, not between classical physics and quantum physics. Kuhn says flatly, "Einstein's theory can be accepted only with the recognition that Newton's was wrong." He argues against the contention that Newton's Laws can be seen as a correct, but limited, application of Einstein's, or that our limited use of Newton's Laws somehow means those laws remain in effect.** Kuhn's argument runs from pp 98-103 of the second edition. I'm only giving you the tail end, where he's arguing against the idea that Newton's Laws can be derived from Einstein's theory as a special case of it. ("<<" means "way way way way less than," and I'm guessing that "(v/c)2 << 1" is a way to limit velocity to being way way way way less than the speed of light. I apologize if I'm wrong.)Can Newtonian dynamics really be derived from relativistic dynamics? What would such a derivation look like? Imagine a set of statements, E1, E2... En, which together embody the laws of relativity theory. These statements contain variables and parameters representing spatial position, time, rest mass, etc. From them, together with the apparatus of logic and mathematics, is deducible a whole set of further statements including some that can be checked by observation. To prove the adequacy of Newtonian dynamics as a special case, we must add to the Ei's additional statements, like (v/c)2 << 1, restricting the range of the parameters and variables. This enlarged set of statements is then manipulated to yield a new set, N1, N2... Nm, which is identical in form with Newton's laws of motions, the law of gravity, and so on. Apparently Newtonian dynamics has been derived from Einsteinian, subject to a few limiting conditions.
Yet the derivation is spurious, at least to this point. Though the Ni's are a special case of the laws of relativistic mechanics, they are not Newton's Laws. Or at least they are not unless those laws are reinterpreted in a way that would have been impossible until after Einstein's work. The variables and parameters that in the Einsteinian Ei's represented spatial position, time, mass, etc., still occur in the Ni's; and they there still represent Einsteinian space, time, and mass. But the physical referents of these Einsteinian concepts are by no means identical with those of the Newtonian concepts that bear the same name. (Newtonian mass is conserved; Einsteinian is convertible with energy. Only at low relative velocities may the two be measured in the same way, and even then they must not be conceived to be the same.) Unless we change the definitions of the variables in the Ni's, the statements we have derived are not Newtonian. If we do change them, we cannot properly be said to have derived Newton's laws, at least not in any sense of "derive" now generally recognized. Our argument has, of course, explained why Newton's Laws ever seemed to work. In doing so it has justified, say, an automobile driver in acting as though he lived in a Newtonian universe. An argument of the same type is used to justify teaching earth-centered astronomy to surveyors. But the argument has still not done what it purported to do. It has not, that is, shown Newton's Laws to be a limiting case of Einstein's. For in the passage to the limit it is not only the forms of the laws that have changed. Simultaneously we have had to alter the fundamental structural elements of which the universe to which they apply is composed.
*The quantum example in "What Are Scientific Revolutions?" somewhat obscures its revolutionary character by not alluding to the many changes wrought by the quantum but instead focusing on the vocabulary shift from "resonator" to "oscillator" that accompanied the recognition that the resonator's energy levels were discontinuous rather than continuous.
**My analogy on the Kuhn 20 thread was to say that our continued use of Newtonian mechanics was like our continued use of the words "sunrise" and "sunset," which have a real and irreplaceable function (at least not replaceable in any way that I can see) but whose existence hardly makes the Copernican Revolution less revolutionary or means that Ptolemaic/Aristotelian cosmology are still partially in effect.
