A Final Illustration of the Ways in Which One Can Fail

In order to motivate the reader to think about her intuitions concerning ad hocness, I introduced the example of Planck’s constant in chapter 1, section II. I will return to it here, as I think that this example helps underscore the differences, discussed in the first section of this chapter, between the introduction of a hypothesis and the acceptance of one, as well as the difference between discarding a non-core component of a theory and discarding a core one.

Planck’s Constant: At the beginning of the 20th century, scientists were committed to either Rayleigh-Jeans statistical-mechanical theory of blackbody radiation or to Wien’s thermodynamical theory, or to some combination of both. There arose disconfirming evidence for both: shorter wavelengths did not produce the infinite amount of energy predicted by Rayleigh-Jeans and the observed emissions from longer wavelengths were not in accord with Wien’s theory. In order to reconcile theories of blackbody radiation with the disconfirming evidence, Planck postulated a constant, which ended up limiting the wavelengths possible.

Both Rayleigh-Jeans and Wien’s theories contained a presupposition that there could be no minimum unit: so, for example, Rayleigh-Jeans theory presupposed that there could be no minimum wavelength for the electromagnetic radiation being emitted by a body. And both, as was noted, encountered major disconfirming evidence in one part of the spectrum or another. Planck successfully solved this blackbody problem by

introducing a constant, h, which enabled him to reconcile what had been postulated about electromagnetic energy with the observed data concerning the intensity of the radiation emitted by a blackbody at certain wavelengths. Yet, this constant, in that it limits the energy being emitted to discrete amounts proportional to the frequencies, leads to the implication that energy itself is quantized and that energy cannot be emitted at every possible wavelength but, instead, only at certain wavelengths.

It has been claimed that Planck’s explanation was not considered by Planck himself to really be an explanation of the phenomena but, rather, a mathematical formula that coincided with the observed phenomena.3233 Suppose this is the case, and that Planck did not treat h as anything more than a mathematical ‘fix’ to the blackbody problem and, so, did not accept the consequence that electromagnetic energy is

quantized. In this case, Planck introduced the hypothesis of h but did not accept it as part of his theory of energy.

On this reading of the Planck example, Planck didn’t accept the hypothesis when he introduced h. This makes its situation very different from Ptolemy’s because Ptolemy accepted the eccentric hypothesis in order to reconcile his theory with the sun’s anomaly. Merely introducing some hypothesis, as Planck did, without committing oneself or one’s theory to the consequences of that hypothesis, is not the sort of act where the charge of ad hocness is appropriate. He was simply using the hypothesis as a placeholder, so that scientists could get accurate results when estimating blackbody radiation at specific frequencies – something that was difficult to do, previously.

Accepting the hypothesis to reconcile one’s theory with the disconfirming evidence is one criterion for ad hocness. And, according to the reading of the Planck

32

See, e.g., Thomas Kuhn.

Kuhn, Thomas. Blackbody Theory and the Quantum Discontinuity 1894-1912. Chicago: Chicago University Press, 1978.

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The way that Planck introduces his constant, h, is quite suggestive of this reading of Planck’s actions. When discussing stationary energy distributions and how to determine them, Planck says: “after the stationary energy distribution is thus determined using a constant, h, […]” (Planck 82) The reason why this quote is suggestive is because Planck speaks of h as a constant, not the constant, and because he speaks of it only as a constant, not as the more fundamental number which it has come to be understood.

example just discussed, it did not fulfill this criterion. However, many people have thought that Planck did something ad hoc in the Planck example. In keeping with their intuitions, let us suppose that Planck really did accept the h hypothesis in order to reconcile blackbody radiation theory with the evidence. Would this have been a hypothesis acceptance where the charge of ad hocness could apply? In order to answer this question, we first need to make sure that this example fulfills the other criteria for ad hocness. There is disconfirming evidence: the actual blackbody radiation curve, that peaks at a certain, middle frequency and vanishes to zero on both the very short and the very long frequencies. Neither the Rayeigh-Jeans theory nor Wien’s theory predicted this particular curve. Next, we need to determine what theory Planck held, so that we may determine what constitutes the core of the theory.

It is not clear as to whether Planck held Wien’s view or Rayleigh-Jeans’s, or both, or neither. However, suppose he was committed to Rayleigh-Jeans, which held that blackbody radiation consisted in standing waves. This would have been held against a background that included, among other things, Maxwell’s wave equation. Part of the core of Planck’s theory, then, is that electromagnetic energy is wave-like in nature – hence, the standing waves of blackbody radiation. Is some part of the theory’s core going to be discarded, in this example? Yes. The modified theory includes the claim that electromagnetic energy is quantized. This replaces the central claim just discussed. So, Planck’s modified theory replaces the previous theory/theories of blackbody radiation. So, again, this example fails a criterion for ad hocness. Discarding a part of the core of a

theory is the same as taking option A, whereas the charge of ad hocness can be appropriate only when the scientist takes option B.34