In the previous section, I emphasized the different quantum conjectures in use in various domains of application. We have seen that these conjectures differed quite widely in terms of the scientists’ intended scope, as well as their physical
underpinnings. Planck’s conjecture was one about the behaviour of radiation in its interaction with ‘resonators’; Einstein hypothesized the existence of physical quanta of light, as well as suggesting that the energy of an oscillator as a model of solid matter could be quantized; Bohr’s conjecture was used to determine the stable states of his atomic model of hydrogen. Despite these differences, it is clear that there was some common idea that linked all of these applications. I submit that the core assumption that we can infer from all of the quantum conjectures can be articulated in the following way: “There is a universal, nonzero parameter h with the dimensions of action that can be used to impose a quantization condition on quantities that were previously considered to be continuous, in such a way that reduces to the specific conjectures in each of the domains.” Each of the more specific claims about radiation or physical systems can be seen as a particular instance of quantization. I claim that scientists were implicitly seeking to find support for the general postulate, as evidenced by their attempts to find more ways
to apply the idea to different systems despite disagreements or ambivalence about the underlying physical mechanisms causing the quantized behaviour.
Such ambivalence can be observed in several contexts. I have already discussed the varying ways in which we might understand Planck’s quantum conjecture. It was not clear whether the quantization was meant to apply to the physical
resonators modeling a blackbody, or merely in a mathematical description of phase space when calculating the entropy. Lorentz, for instance, said,
[W]e cannot say that the mechanism of the phenomena has been
unveiled [by Planck’s theory], and it must be admitted that it is difficult to see the reason for this partition of energy by finite portions, which are not even equal to each other, but vary from one resonator to the other. (Lorentz 1909, quoted in Jammer 1966, 24)
Even Planck’s assumption of resonators was not meant to be a literal description of the physical system; instead, he was relying on Kirchhoff’s law which states that the radiation in blackbodies is dependent purely on temperature and not on their specific material. Whether this was an appropriate model or not, the fact that quantization was a crucial feature for the recovery of the distribution law for
blackbody radiation emerged quite clearly. Subsequent applications of quantization can be seen as ways that scientists were exploring the possibility of a general postulate that would still recover the distribution law.
We should also consider the fact that Einstein was likely not as committed to the existence of physical light quanta as one might have assumed. Although in the first part of his 1905 paper Einstein phrases the underlying assumption as one about light quanta, his primary argument is about the behaviour of monochromatic low-density radiation. Consider what Einstein writes to Lorentz in 1909: “As far as the light quanta are concerned, it seems that I did not express myself clearly. For I am not at all of the opinion that light has to be thought of as being composed of mutually independent quanta localized in relatively small spaces” (Einstein 1909/1995, p. 123). This might seem quite surprising, but it likely reflects his recognition of the fact that Maxwell’s equations for electromagnetic radiation were extremely well confirmed in certain domains. Indeed, at the start of the paper, Einstein says that “The wave theory of light which operates with continuous functions in space has been excellently justified for the representation of purely optical phenomena and it is unlikely ever to be replaced by another theory” (Einstein, 1905, 91). Thus, even though he called his 1905 paper “revolutionary,” what he was committed to was the
idea that a new concept of quantization would have to be incorporated in some domain of description of the behaviour of light, and not necessarily to the physical existence of the light quanta. This attitude is displayed in the final section of his (1909), where he sketches a possible interpretation of the meaning of light quanta in which the energy of the electromagnetic field is localized in singular points, and the fields associated with each point superpose in such a way as to recover the wave description of the field. However, he goes on to say, “I am sure it need not be particularly emphasized that no importance should be attached to such a picture as long as it has not led to an exact theory” (Einstein, 1909/1989, p. 394).13
Similar considerations are true for Bohr’s use of quantization. Despite his discussion’s use of mechanical concepts such as the angular momentum of an electron, he says that “there obviously can be no question of a mechanical
foundation of the calculations given in this paper” (Bohr, 1913, p. 15), indicating that such links between the quantum conjecture and any physical accounts are speculative at best. Bohr himself did not claim that his use of quantization explained anything in a deep sense in his atomic model.
I am by no means trying to give what might ordinarily be described as an explanation; nothing has been said here about how or why the radiation is emitted. (Bohr, 1922, p. 13)
This is particularly apt given that Bohr never accepted Einstein’s light quanta explanation. Instead, Bohr seems to treat his quantum conjecture as simply another application of a general idea of quantization in the progression towards a theory that includes the notion in a precise way.