Reading guide for Tues. 11/17: Norwood Russell Hanson, “Uncertainty” (on JSTOR); Hanson, “On the Symmetry Between Explanation and Prediction” (on JSTOR)
Hanson’s name came up on several occasions while reading Kuhn, and you may notice some points of agreement, especially in the second of these short articles. The two combine to make a single point: the uncertainty of certain sorts of measurements that is built into modern physics means that many of events of which it offers accounts could not have been predicted—even in principle. Below I’ll provide a few notes on each article individually as well as suggestions about how they fit together.
• Hanson seems to intend both articles as an antidote to a way of introducing quantum theory that minimizes its differences from classical physics. The issue, in the case of “Uncertainty,” is Heisenberg’s Uncertainty Principle, which places a limit on the joint precision of the measurements of certain quantities. (Specifically, there is a lower bound on the product of the standard deviations of the measurements of the two quantities, so the if the standard deviation of one is decreased, an indication of increased precision, the standard deviation of the other must increase, and its precision will thus decrease.) Hanson focuses on position and velocity (or momentum), one of the pairs of quantities to which the uncertainty principle applies, but there is a variety of others.
• There is an analogous uncertainty concerning the time when decay processes occur that figures in Hanson’s second article. There is a second crucial connection between Hanson’s points in the two articles: the uncertainties described in the first makes it impossible to do more than ascribe distributions of probability to certain measurements. For example, if a slit experiment is set up so that the momentum of an electron is relatively certain, its position is uncertain. Since a particular electron will hit a screen beyond the slit in a definite position, the uncertainty means that the particular position cannot be predicted. That is, the uncertainty in the position of the electron places limits on our ability to predict the position of the impact.
• The key premise for Hanson’s argument in the second article that explanation and prediction must be distinguished in the case of quantum theory is the role probability has in quantum theory that is different from its role in the statistical mechanics that Boltzman and others used to provide a foundation for thermodynamics in the later 19th century. So think whether you would grant him that premise as well as thinking whether, given it, his conclusion about explanation and prediction follows.
Finally, here are a few notes on some of Hanson’s references in this paper.
• Pierre-Simon Laplace (1749-1827), who Hanson mentions on pp. 354 and 356, was responsible for completing the formulation of Newton’s mechanics in terms of the calculus and giving the theory of planetary motion (celestial mechanics) its classical form. Hanson’s first reference alludes to his statement of classical determinism:
Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes. (A Philosophical Essay on Probabilities, Truscott and Emory, tr., John Wiley & Sons, 1902, p. 4—the original was published in 1814.)
Laplace notes our great distance from such an intelligence (in spite of the successes of celestial mechanics in predicting planetary motion) and goes on
The curve described by a simple molecule of air or varpor is regulated in a manner just as certain as the planetary orbits; the only difference between them is that which comes from our ignorance.
Probability is relative, in part to this ignorance, in part to our knowledge.… (Ibid., p. 6.)
• The expression “pm-mp” that appears on p.355 is closely tied to the Heisenberg Uncertainty Principle. The operators Hanson refers to apply to states of a system to give the value of some quantity, and an expression like “pm” indicates the application of the operator p after the operator m. (That the result is a number rather than a composite operator is a feature of this particular example.) The fact that pm ≠ mp—and this is Hanson’s point—is expressed by saying that these operators do not “commute.”
• The references to “renormalization” and Yang and Lee on p. 356 concern issues that had arisen by the end of the 1950s in accounting for the interactions of elementary particles and that led in the 60s and 70s to the development of the “standard model” of particle interactions, which still works within the general framework of quantum theory.