Inventing a new theory of nature requires, as Feynman [1] said, ‘imagination in a terrible strait–jacket’. Unlike the artist who need not obey constraints, as scientists we are not free to imagine whatever we want—the new theory must obey a ‘correspondence principle’. It must, obviously, give different predictions from those of the old theory for some phenomena, but at the same time it must agree with the old theory in all the places in which the old theory was already experimentally verified. For all those experiments the new theory must give numerical results that are very similar to those of the old theory; the only acceptable difference must be smaller than the precision of the measurements that seemed to confirm the old theory.
Insofar as the numerical predictions of a theory are concerned, the correspondence principle is fairly obvious and straightforward. However, theories are not only mathematical devices for making numerical predictions—they contain concepts that tell us a story of what the nature of physical reality is and, as Feynman also noted, even in situations when the numerical predictions of two theories are almost identical, the concepts they involve may be completely different. Indeed, it is a fundamental conceptual difference between, say, mass being an absolute constant or mass changing with the speed even when the speed is so low that the change of mass is negligible.
The Classical Limit of Quantum Optics: Not what it seems at first sight
2013
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