Einstein's Light Quantum Hypothesis

Ueber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, Annalen der Physik 17 (1905), 132-148

As is well known, Einstein published 5 important papers in 1905, and the famous "light quantum hypothesis" was proposed in one of them. As you can see from its title, Einstein presented his view (modestly) as a heuristic device, but he thought this view was revolutionary. This paper begins as follows:

A profound formal difference exists between the theoretical concepts that physicists have formed about gases and other poderable bodies, and Maxwell's theory of electromagnetic processes in so-called empty space. While we consider the state of a body to be completely determined by the positions and velocities of an indeed very large yet finite number of atoms and electrons, we make use of continuous spatial functions to determine the electromagnetic state of a volume of space, so that a finite number of quantities cannot be considered as sufficient for the complete determination of the electromagnetic state of space.

But the theory of light "leads to contradictions when applied to the phenomena of emission and transformation of light", Einstein claims; and he suggests an alternative way for treating light.

... it seems to me that the observations of "black-body radiation", photoluminescence, production of cathode rays by ultraviolet light, abd other related phenomena associated with the emission or transformation of light appear more readily understood if one assumes that the energy of light is discontinuously distributed in space. According to the assumption considered here, in the propagation of a light ray emitted from a point source, the energy is not distributed continuously over ever-increasing volumes of space, but consists of a finite number of energy quanta localized at points of space that move without dividing, and can be absorbed or generated only as complete units.

After this introductory remark, 9 sections follow. The main line of argument is reconstructed and elaborated by Dr. Tomonaga in Chapter 2 of his textbook, and the reader is referred to that. It should be noted that Einstein is closely following Boltzmann's line for treating entropy, probability, and energy fluctuations in thermal equilibrium. By limiting his consideration to one extreme case (an analogue of what is called "canonical ensemble" in statistical mechanics), the case where Wien's Law holds (i.e. where the frequency is large), Einstein extends the Boltzmannian statistical method to radiation and light. And he comes to an equation which "shows that the entropy of monochromatic radiation of sufficiently low density varies with the volume according to the same law as the entropy of an ideal gas or a dilute solution" (Section 4); this is nothing but another application of the method used in his paper on the Brownian Motion (see Einstein on Brownian Motion).

But what is the significance of this? Einstein states this clearly in Section 6. "From this we further conclude that monochromatic radiation of low density (within the range of validity of Wien's radiation formula) behaves thermodynamically as if it consisted of mutually independent energy quanta of magnitude Rß?/N". "Monochromatic radiation" means radiation with single color, represented by a single line in a spectrum; and it may be identified with "proper oscillation" in Planck's problem. Thus Einstein has shown that Wien's law indirectly supports his quantum hypothesis, and he extended Planck's hypothesis one step further.

Discussions of photoelectric effect and ionization by ultraviolet light come in the last two sections. I will quote only a passage on photoelectric effect.

According to the view that the incident light consists of energy quanta ..., the production of cathode rays by light can be conceived in the following way. The body's surface layer is penetrated by energy quanta whose energy is converted at least partially into kinetic energy of the electrons. The simplest conception is that a light quantum transfers its entire energy to a single electron; ...
The kinetic energy of such electrons is

[P is the work the electron performs in order to leave the body]

References

Einstein, A. (1905) "On a Heuristic Point of View concerning the Production and Transformation of Light" (English translation of the 1905 paper), in Einstein's Miraculous Year (ed. by John Stachel), Princeton University Press, 1998.

Tomonaga, S. (1969)

Soshichi Uchii