In this explication, I argue that the confirmation of Einstein’s formula can be understood as support for the general quantum postulate, but that it does not distinguish between specific quantum conjectures. This helps to clarify the claim that we should consider Millikan’s experiment as supporting a general QP rather than the light quanta conjecture.
The quantum postulate gained support from Millikan’s experiments on the photoelectric effect due to the fact that it allowed Einstein to make a very accurate prediction about an experimental result, namely, the linear relationship of slope h/e
between V and ν. Predictive power can be cashed out in a Bayesian framework with a few provisos (Maher, 2004, 72). In general, if evidence E is a logical consequence of hypothesis H on background B, thenP(H|E)> P(H) provided that
0< P(H)<1 and P(E|¬H)<1. In our case, H isQP and E is the expression of the linear relationship between V and ν. That is, E: “In photoelectric effect
experiments, the stopping voltage V and the frequency of incident light ν display a linear relationship.” We have seen how Einstein’s light quanta conjecture, in
conjunction with other assumptions about the absorption of energy in a
photoelectric substance, yields the prediction that 12mv2 =V ·e=hν−p regarding the energy being emitted. This entails the linear relationship between V and ν.
In order to draw the conclusion, we must also consider whether the provisos are satisfied in this case. The first proviso states that our credence in QP must not be either 0 or 1. As I have discussed, we assume that an agent’s credal state is
expressed by a familyC of credence functions, all expressing possible credences in
QP. I argued that such a credal state would contain multiple credence functions, all of which assign value greater than 0 to QP, but distributed largely at the lower end of the spectrum. Thus, the imprecise version satisfies the first proviso. As for the second proviso, which expresses the idea that one should not be sure that the linear
relationship e obtains if QP were not the case, this is also satisfied as there was debate about the nature of the relationship betweenV and ν which was
independent of the status of QP or any alternatives. After Millikan’s experiments, it was reasonable to have a credence very close to 1 for the statement E. It follows that P(QP|E)> P(QP), and QP received support from Millikan’s demonstration of the linear relationship between V and ν.
I now turn to a defence of my identification of the general quantum postulate as the hypothesis receiving support rather than the light quanta conjecture, especially given that Millikan’s experiments are now generally taken to be good evidence for the existence of light quanta. The first reason is simply that it is a more historically accurate reconstruction. After all, Millikan is specifically testing the numerical Equation 3.1 that Einstein provides, and while this may have arisen in part from the light quanta conjecture, I have already argued for the idea that one can consider the equation promising without accepting the underlying physical idea. There is nothing in Millikan’s experimental setup that requires the assumption of light quanta.
More importantly, the support here does not differentiate between alternative explanations of why the linear relationship holds. This is because, if we were to consider the support provided to a general hypothesis about light quanta by the experimental results, we would still have to include a more specific posit such as Equation 3.1 in the background information to derive the specific linear relationship being tested. Given that Equation 3.1 is by no means sure in itself, we would be hiding a crucial piece of information in the background by doing this. Furthermore, we would need to include this equation in the background of any purported account of the behaviour of the energy in order for such an account to be supported by the results. But in that case, the support does not differentiate between the light quanta conjecture and any other account of the mechanisms governing the behaviour of energy. In contrast, Einstein’s equation is excellently supported by the results, since a different postulated expression of the emitted energy would not yield the linear relationship betweenV and ν as a logical result. This is why it is reasonable to consider Millikan’s results as strongly supporting Einstein’s equation, but not necessarily light quanta, and thus makes it reasonable to hold the equation as experimentally well determined, but to pursue different explanations for the result.
4.6
Conclusion
In this chapter, I have argued that a Bayesian framework making use of imprecise credences and modeled on tempered personalism is an appropriate way to
reconstruct the arguments arising from the investigation of quantum conjectures. This stems from the fact that the historical development of quantum theory, which involved seeming inconsistencies and experimental anomalies in different contexts, calls for evaluation of arguments within local frameworks. The addition of imprecise credences allows for a realistic representation of agents’ doxastic states. I showed how we would define background information B in the evaluation of Planck’s quantum conjecture to explicate the support it received in terms of experimental results on blackbody radiation.
I also focused on the significance of Einstein’s correct prediction of the
relationship betweenV and ν, and I argued that the confirmation of this prediction provided support to the general quantum postulate. However, we have also seen that one of the great advances made in Millikan’s experiments was that the reliability of the experiments and the precision of the results enabled him to
determine the value of the parameter h to a very exact degree. This is crucial, as it allowed for these results to be used in a comparative way with other measurements of h through experiments in different domains. The importance of this fact will be the subject of Chapter 6, but I first turn to a discussion of the ability of the quantum postulate to account for previously known phenomena.