# Rynasiewicz, Robert: *On 'The[?] So-Called Correspondence Principle'*

Both the textbook tradition and vast segment of the secondary historical literature speaks as though there is such a thing em The Correspondence Principle, which (i) was first articulated explicitly by Bohr (1917) in Part I. of “On the Quantum Theory of Line Spectra,” (QTLS) (ii) guided the subsequent development of the “old” quantum theory up through Heisenberg’s 1925 “ Umdeutung” paper, and (iii) remained embodied in some fashion or other in the subsequent “new” quantum mechanics. The question remains, though, whether much of this assessment derives primarily from Bohr’s post-1925 propaganda concerning interpretation of the new mechanics.

In QTLS, Bohr articulated three principles for guiding the construction of the quantum theory, (or more specifically the treatment of the relation between radiation and material systems). The first, implicit in his seminal 1913 work establishing the Bohr model, addresses the frequencies of emitted and absorbed radiation. The second, sought a guide to determining the probabilities of transitions (Einstein’s A and B coefficients), and thus predicting the intensity of the radiation. The third addressed the problem of handling polarization. One question that naturally arises is whether these are instances of a truly principled general rule (as suggested by Bohr’s subsequent introduction in 1920 of the title “the correspondence principle” ) or instead are logically independent, albeit analogously motived moves for extending the quantum theory. The ultimate irony, though, is that, no matter what, the dialectic of Heisenberg’s “Umdeutung” paper proceeds from the observation that the unobservability of various quantities appearing in the quantum theory would be tolerable if “the formal rules which are used in the quantum theory . . .were internally consistent and applicable to a clearly defined range of quantum mechanical problems.” This suggests that Heisenberg saw his matrix mechanics as principled replacement for a previous patchwork of ad hoc maneuvers. The paradox, then, is how Bohr could have (cogently and without equivocation) understood matrix mechanics (and the new quantum mechanics in general) to embody and vindicate “the” correspondence principle. One comes to suspect that, to the extent that the content of “the” correspondence principle can be articulated, that content must be seen to evolve hand in hand with the evolution of the quantum theory.

My talk will review the role of “the” correspondence principle in QTLS, then survey its subsequent use, elaboration, and “extensions” in the years leading up to 1925, and finally explore the paradox raised by the reconciliation of “the” correspondence principle with the dialectic of the Umdeutung paper.