378 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



future states of the system of the world. Applying the same 

 method to some other objects of its knowledge, it has suc- 

 ceeded in referring to general laws observed phenomena 

 and in foreseeing those which given circumstances ought to 

 produce." * 



It seems safe to say that some such view as this was held 

 by most scientists prior to the discoveries which eventuated 

 in the quantum theory. The recent interest in indeterminacy 

 in nature can therefore be traced to those scientific dis- 

 coveries which suddenly threw this whole conception into 

 confusion. In outline, these facts were approximately as 

 follows: In the attempt to apply the general functional 

 equation stating the relation between two states of a given 

 system to very small particles such as electrons, certain 

 obstacles appeared. According to the Heisenberg principle, 

 the two values — position and velocity — which indicate the 

 state of a particle at a time cannot both be determined with 

 a high degree of accuracy. Since the particle is very small, 

 a very short wave must be used to determine its position. 

 But a radiation of short wave length has a high momentum, 

 since wave length and momentum are in inverse ratio to 

 one another. Consequently, the electron when struck by 

 this wave will be pushed from its position, and its motion 

 changed. If this difficulty is avoided by using a radiation 

 of long wave length, the momentum is decreased and there 

 is less recoil, but now it is no longer possible to tell precisely 

 where the electron is. Hence there arises an interdependence 

 in the measurement of the position and velocity. If A x 

 be used to express the possible error in fixing position, and 

 A v to express the possible error in fixing velocity, this 

 interdependence may be formulated, 



Ax-At) > h/m 



where h is Planck's constant (magnitude 6.55 X 10~ 27 erg- 

 seconds) and m is the mass of the particle. Since m functions 

 in the denominator of the fraction, the indeterminacy for 



1 Philosophical Essay on Probabilities (New York: Wiley, 1902), p. 4. 



