CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL 

 LABORATORY, HARVARD UNIVERSITY. 



PLANCK'S RADIATION FORMULA AND THE CLASSICAL 



ELECTRODYNAMICS. 



By David L. Webster. 

 Presented by G. W. Pierce. Received, December 1, 1914. 



Introduction. As Poincare : has pointed out, Planck's formula 

 for black body radiation, or any other formula giving only a finite 

 amount of energy per unit volume in the radiation field, involves the 

 assumption of some discontinuities in the process of absorption and 

 emission. Thus Planck assumes that while an oscillator may absorb 

 energy continuously, it may radiate only when the energy is an 

 integral multiple of h v, and that if it does then radiate, all its energy 

 is radiated at once. 



This assumption, being inconsistent with the classical electrodyna- 

 mics, involves the abandonment of the explanations that the classical 

 system gives of many phenomena. Its explanation of inertia, for 

 example, depends directly on the theorem that every part of an ac- 

 celerated electron will radiate electric forces proportional to its accel- 

 eration, and that these forces, acting on other parts of the electron, 

 produce the force of inertia, proportional and opposite to the acceler- 

 ation. This explanation must be abandoned if we make Planck's 

 assumptions, which deny the existence of these forces in most cases. 



Likewise, according to the retarded potential theorem, the classical 

 explanations of all phenomena of the propagation of light through 

 matter may be put entirely on the basis of continuous re-radiation 

 from vibrating electrons, whose energy in many cases never reaches 

 the value h i>, because the amplitude of a forced vibration is so small 

 unless the frequency is near that of resonance. Although light phe- 

 nomena other than scattering are not ordinarily treated in this way, 

 any method derived from the classical field equations must necessarily 

 be equivalent to any other, and any assumptions that make one of 

 these methods give wrong results must necessarily do the same for all. 

 Therefore, if Planck's assumptions are true, all such explanations must 

 be abandoned, and we must create a whole new theory of optics. 



1 Journal de Physique, (5) 2, p. 1 (1912). 



