360 RADIATION OF ENERGY. 



Einstein 1 has gone much farther than Planck and has proposed the theory th t 

 energy exists in free space, unassociated with matter, in certain definite units 

 these units being the quanta of Planck, now no longer associated with matter' 

 but projected into free space. 



He says: "The undulatory theory of light operating with continuous space 

 functions has served excellently for the representation of pure optical phenomena 

 and will indeed never be replaced by another theory. It is however to be noted 

 that optical observations are concerned with time-mean values, and not with 

 momentary values, and it is conceivable that, in spite of the complete confirma- 

 tion of the theory of diffraction, reflection, refraction, dispersion, etc., by experi- 

 ment, the theory of light operating with continuous space functions leads to a 

 contradiction of experience when one applies it to the phenomena of light pro- 

 duction and light transformation." 



"It appears to me, indeed, that the observations of black radiation, photo- 

 luminescence, the excitation of cathode rays by ultraviolet light and those 

 groups of phenomena which are concerned with the production and transforma- 

 tion of light, can be better understood on the assumption that the energy of light 

 is discontinuously distributed in space. According to this assumption the energy 

 of a ray of light issuing from a point is not distributed continuously over a larger 

 and larger space but consists of an endless number of elements of energy (Energie- 

 quanten) localized in points of space, each one of which moves without being 

 divided and can only be excited or absorbed as a whole." 



This hypothesis of Einstein that energy exists in discrete elementary quanti- 

 ties in free space has been called the light-quantum hypothesis, and may be dis- 

 tinguished by this name from Planck's energy-quantum hypothesis. It differs 

 from Planck's hypothesis in that, in Planck's hypothesis, the energy-quanta 

 exist only in association with matter. Planck 2 himself does not accept the 

 light-quantum hypothesis of Einstein. 



Certain well-known experimental results can, however, conveniently be 

 explained by Einstein's hypothesis. 3 



For instance, Stokes' law that the light given out by a phosphorescent body 

 is as a rule of lower frequency, v 2 , than that, v h of the exciting light, can be 

 explained by supposing that only one quantum goes to excite an oscillator. V* e 

 would then have 



V2 < V\ 



The exceptions to Stokes' law can be explained by assuming that in such 

 or two or more quanta are absorbed by each elementary oscillator. 



1 AnncOen der Physik, Bd. 17, pp. 132-148, 1905; Bd. 20, pp. 199-206, 1906; Bd. 22, 180-19Q 

 Phy&ifodische Zeitsehrift, Jahrg. 10, pp. 185-193, 817-826, 1909. 



2 



der 



Zeitsehrift, Jahrg. 11, pp. 351, 352; 1249, 1250 



