402 



certain as yet. Thus Ehrenfest ^) could account for the course of 

 tlie specific heat of liydrogen without assuming zero-point energy, 

 whereas Einstein and Stern.") derived from this course a proof for 

 tiie existence of zero-point energy. 



1 will now draw attention to a phenomenon, which, so far as I 

 know, has nev^er been considered in the light of a possible existence 

 of a zero-point energy '), and for which it seems very difficult to 

 account even qualitatively without the assumption of zero-point 

 energy. This phenomenon is the radio-activity. A radio-active atom, 

 jiamely. which has continued to exist unchanged for a long. time, 

 suddenly explodes. So something must have been modified, either in 

 the atom itself, or in its surroundings. If no zero-point energy is 

 assumed, no movement would be present in the atom which follows 

 from the value of the specific heat. Accordingly nothing would 

 change there. With thermal equilibrium, however, the changes in 

 the surroundings 'are determined by the thermal motion ; they seem, 

 therefore, unable to explain the appearance of radio-active phenomena, 

 as they are independent of the temperature. Thus no circumstance 

 governed by chance is found on which the setting in of a radio- 

 active explosion of an atom could depend. 



Matters are different if it is assumed that several particles vibrating 

 with a high frequency are present in the atom. On account of the 

 high frequency they will possess no thermal energy, but only their 

 zero-point energy. So this energy can manifest itself neither by 

 radiation, nor by a contribution to the specific heat. If it is now 

 assumed that the different particles have different frequencies, and 

 that they exhibit different amplitudes (vai-ying from o to v/i) and 

 phases in different atoms of the same kind, a circumstance is given 

 in liieir motion, which renders the setting in by chance of a definite 

 unstable configuration of the particles of the atom possible, and thus 

 leads to a radio-active explosion. Then the energy of the radio-active 

 rays and of the generation of heat might be found from the zero- 

 point energy. A change in jtotential energy might also contribute to 

 this, but so far as we know this might be as well positive as 

 negative, and the supposition would naturally suggest itself that the 



1) P. Ehrenfest, Verh. d. D. pliys. Ges. 1913, S. 451. 



-) Einstein and Stern. Ann. d. Physik IV, 40, 551, 1913. 



•') Note added in the English translation, wlien I was correcting the proofs. As 

 Dr. Keesom was so kind as to point out to me, I was mistaken when I thought 

 that this interpretation of the radio-active phenomena had not been given before. 

 It was aheady given by Planck himself. Vorlesungen über Warmestrahlung, 2'"i 

 ed. p. 140. 



