CONTEMPORARY ADVANCES IN PHYSICS 17 1 



which the momentum p, the velocity u, the kinetic energy K, the 

 mass m are related to one another as in Newtonian mechanics — 

 properties which are practically those of electrons except when these 

 are moving much more rapidly than any involved in these experiments: 



p = mil, K = y^mu^. (15) 



Use Ui and Un to denote tangential and normal components of speed; 

 use primes to designate the values which things have in the second 

 medium (nickel). Starting from equation (5), we continue: 



sin djsm 9' ^ N = M'jM = u'/u; 



iV2 _ 1 = (m'2 _ ^^2)1^^2 = (^z _ x)/K. (16) 



The quantity {K' — K) is the gain in kinetic energy which the electron 

 wins on passing into the nickel ; and this gain, as I have said, is positive; 

 hence by equation (16) the index of refraction must be greater than 

 unity. This is in agreement with the result of Davisson and Germer; 

 the agreement, in fact, appears to be quantitative.'* 



It is always pleasant to get an agreement; but note how we got this 

 one. We got it by dropping the assumption that the speed of the 

 corpuscles and the speed of the waves must be the same. Or rather, 

 by not making that assumption. For though the fact of experience 

 is always the same — the swerving of the electron-stream toward the 

 normal as it enters the nickel — it is interpreted by the two theories in 

 opposite ways; the waves are slowed down, but the corpuscles are 

 speeded up, in passing from the vacuum to the metal. Even if wave- 

 speed and corpuscle-speed were the same in empty space, they could 

 not be the same in any other medium. 



This is more serious than it may appear at first. It amounts in 

 effect to saying that a beam of free negative electricity has two dif- 

 ferent speeds; one when we visualize it as a jet of particles, another 

 quite different when we visualize it as a train of waves. 



But is not one of these "the right one" and the other "a wrong one," 

 and can we not settle between them by measuring the actual time 

 which the electricity takes to pass a measured distance? Let us 

 examine this possibility. We shall find that after all it is not so easy 

 to evade the ambiguity in such a fashion. 



Phase-Speed and Group-Speed 



Suppose an endless train of perfect monochromatic sine-waves 



marching along through space. For definiteness, think again of sound- 



^ There is a remarkably interesting correlation between these results and the new 

 statistical theory of the electron-gas inside the metal (cf. my article in the October 

 1929 number of this Journal, pp. 710-716). 



