THE EVOLUTION OF SCIENTIFIC THEORIES 257 



Performing the experiment, Foucault found the image on the right; 

 and he, and practically all his contemporaries, considered it proved 

 that light is a wave and not a particle. Today, however, a new spe- 

 cies of particle theory is very much alive. We credit a third possi- 

 bility unknown to Arago: both wave and particle concepts may be 

 required to render full account of the phenomena of light. Failing to 

 supply proof, this excellently conceived experiment thus failed to 

 supply even a final disproof. The whole conception of "the crucial 

 experiment" is indeed subject to major complications, of which we 

 now examine three. 



Situations of deadlock. Within the always finite range of experi- 

 mental error, two theories may be equally concordant with all ac- 

 cessible facts. Imagine, for example, that a theory of special rela- 

 tivity had been proposed long before the discovery of nuclear phe- 

 nomena and the invention of devices for producing high voltages. 

 Now according to classical mechanics a particle with rest mass (m) 

 and charge (e) which has fallen through a potential drop (V) will 

 be expected to have a velocity (v) given by the equation: 



In relativistic mechanics the equation becomes: 



1 



eV = ^ mv' 



l_(t;2/c2) 



The second equation reduces to the first in the limiting case of veloc- 

 ities small in comparison with that of light (c)—i.e., when d<<c, 

 1 — (v^/c^) =z 1. And so, until extremely high velocity bodies are 



obtained, no crucial experiment will distinguish between these for- 

 mulas—or between the many other such paired formulas, equally 

 concordant within experimental error, derivable from the two theo- 

 ries. If this is everywhere the case, no experiment can break the dead- 

 lock between the two. One may perhaps object that this quite arti- 

 ficial example never actually occurred. But consider that, even widi 

 the immense experimental resources of 20th-century physics, after 

 the passage of half a century, we are still unable to devise an 

 experiment sensitive enough to discriminate between the general 

 relativity theories proposed by Einstein and by others. 



Such conditions of deadlock occur even when only purely quali- 



