246 THEORIES AXD MODELS 



However it may be with the two points noted above, we must 

 come in the end to a third and crucial question. Is the demonstrated 

 lieuristic power of quantum mechanics something due to, or achieved 

 in spite of, the highly formal construction of that theory? So posed, 

 the question is not only heretical but superficially absurd. Has not 

 everybody heard of the "mathematical difficulty" presented by Dirac's 

 quantimi mechanics that, in Noyes' words, 



. . . turned out not to be a difficulty, but a brilliant success for the 

 theory, since such "positive electrons" [postulated to resolve the dif- 

 ficulty] were soon discovered. . . . Thus the mathematical require- 

 ments of relativistic and quantum mechanical structure led to a phys- 

 ical prediction which was experimentally verified. 



Fewer perhaps have heard that the physical prediction thus drawn 

 from "mathematical requirements" was (1) regarded, by such emi- 

 nent theorists as Pauli, as an absurd defect of Dirac's theory, and 

 (2) completely unknown to Anderson, who made the actual experi- 

 mental discovery of the positron. A somewhat similar claim, that the 

 discovery of electron diffraction was uniquely the fruit of de Broglie's 

 original theory of matter waves, is similarly misleading. De Broglie's 

 highly formal theory was indeed a mathematically elegant correlation 

 of many data already known, but Born feels able to write that de 

 Broglie 



. . . studied the consequences for plane waves and indicated the 

 interpretation of Bohr's quantum conditions with the help of standing 

 waves. But what did he predict? As far as I know, nothing. 



In fact, it was only after Elsasser had seen the suggestive maxima and 

 minima in some of Davisson's electron-scattering curves that the de 

 Broglie wave model was taken literally enough to produce the theo- 

 retical prediction of that electron diffraction presently established ex- 

 perimentally by Davisson and Germer and by Thomson. 



Noyes suggests that the methodology of modern physics is charac- 

 terized by its "emphasis on the mathematical structure of the theory" 

 rather than on predictions drawn from models of its "inferred enti- 

 ties." But I would think tiiat no emphasis on mathematical structure 

 as such will yield physical predictions of genuine no\'elties. Further- 

 more, and absolutely conclusive in my opinion, there is the clear 

 •evidence afforded by the quantum physicists' whole terminology. In 



