Today we see the photoelectric effect as one of the simplest pieces of empirical evidence that leads to quantum physics. The historical development of the subject, however, seems to have involved much more complicated and indirect evidence such as the blackbody radiation curve.

In textbooks and laboratory manuals, a fact about the photoelectric effect that is often presented prominently is that the stopping voltage is independent of the intensity of the light. This fact is easy to explain with the photon model. One also often sees in textbooks statements that according to "the classical theory," the stopping voltage should have increased with the intensity of the light.

However, it is not at all obvious to me that any such classical theory can be constructed. Specifically, I doubt that one can construct a classical model that makes the following predictions: (P1) the photoelectric effect occurs with solid metals, (P2) there is a finite stopping voltage, and (P3) this stopping voltage increases with the intensity of the light. Note that if the model doesn't predict P1 and P2, then we can't even meaningfully ask whether it predicts P3.

What was the actual historical situation? I can imagine at least five scenarios.

(a) The photoelectric effect in a solid metal cathode was a total Kuhnian anomaly. Physicists trained within the classical paradigm would not have seen any promising lines of attack, and would have been unable to construct even a partially successful model. Therefore they ignored it and worked on other problems.

(b) There was some actual classical model that was published or publicly discussed, which predicted P1-P3.

(c) People built and discussed models that gave predictions similar to P1-P3 in the case of a free electron, or perhaps a gaseous cathode. The models just couldn't be extended to a solid metal cathode.

(d) Textbook authors who refer to "the classical model" are using sloppy language or have not studied the actual history; there is actually some model that predicts P1-P3, but it's not a purely classical model. It's some kind of hybrid such as the Bohr-Kramers-Slater theory.

(f) Looking through the history section of the WP article on the photoelectric effect, it seems that textbook presentations may be giving a misleading impression of the historical sequence. It seems that the evidence prior to 1905 was mostly very crude and qualitative. Because of the paucity of quantitative data, there may have been little motivation to embark on serious model-building.

Can anyone clarify what actually happened?

Einstein's 1905 paper has the following (translation by D. Ter Haar?) on this topic:

As far as I can see, our ideas are not in contradiction to the properties of the photoelectric action observed by Mr. Lenard. [Under the quantum hypothesis] the velocity distribution of the electrons ... will be independent of the intensity of the incident light ...

He does not follow up by claiming that such an observation would contradict the classical theory. Einstein references Lenard's 1902 paper, which showed that the stopping potential increased with the frequency of the light but was independent of intensity.

Briefly, here is the reason why it's not obvious to me that any classical model can produce P1-P3. I'm not claiming that I'm right -- I'm just trying to explain why I have doubts about the existence of any such model. In a classical model of a solid metal cathode, the conduction electrons are a classical gas with a Maxwellian velocity distribution. Visible light has a wavelength much longer than the mean separation between electrons, and therefore all it really does is heat the cathode. Regardless of temperature, the Maxwellian distribution has a high-velocity tail whose energy is greater than the work function, so electrons are emitted from the surface at some rate. There is no sharp cutoff to this tail, and therefore there is no well-defined stopping voltage.


It is likely that there was no "classical theory of photoeffect" or even a draft of it before 1905, all actual references are to Hertz and Lenard, who were doing experiments. Lenard's experiments were qualitative and wide open to interpretation, more precise experiments with gas were only performed in 1908 by Langevin and Bloch, and with metals in 1914 by Millikan. Statistical mechanics in general, and the equipartition theorem in particular, required to treat the electron gas classically were under suspicion until Lorentz's 1908 Rome lecture. Planck, and even Jeans and Lorentz, had doubts about the universality of the equipartition theorem.

Einstein and Lorentz corresponded about light quanta in 1909, and neither one of them mentions any classical theory of photoeffect. This would be particularly strange of Lorentz, who just worked out the classical theory of blackbody radiation in painstaking detail, and sharply criticized "point-like quantities of energy or at least energy quantities concentrated in very small spaces", that Einstein seemed to postulate. Nor was it clear that discretization of energy was necessarily non-classical, even Einstein distanced himself from "point-like light quanta" and offered a description of them as "singularities that are surrounded by a vector field whose strength decreases with increasing distance. The field energy is then related somehow to the number of these singularities." See Kox's Hendrik Antoon Lorentz’s struggle with quantum theory.

Similar substitution happened with blackbody radiation, it did not become clear that classical theory leads to "ultraviolet catastrophe" until Lorentz's 1908 lecture, which doesn't stop textbooks from citing it as Planck's motivation in 1890s. According to Kuhn's source study Planck too was under the impression that he was doing classical physics until 1906. After 1908 even Lorentz admitted that "only with the help of the hypothesis of energy elements one can arrive at the correct radiation-law", so there was little point at constructing a classical theory of photoeffect after that, except for textbook purposes. The focus shifted from purely classical approach to identifying the source of "discontinuity": was it in the matter, in its interaction with electromagnetic field, or in the field itself? And later to reconciling Maxwell's waves with Planck's quanta, or even getting rid of waves altogether, as Duane suggested in connection with X ray diffraction.


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