Abstract
A scientific theory offers models for the phenomena in its domain; these models involve theoretical quantities of various sorts, and a model’s structure is the set of relations it imposes on these quantities. There is an important, indeed fundamental, demand in scientific practice that those quantities be clearly and feasibly related to measurement procedures. The scientific episodes examined include Galileo’s measurement of the force of the vacuum, Atwood’s machine designed to measure Newtonian theoretical quantities, Michelson and Morley on Fresnel’s hypothesis for light aberration, and time-of-flight measurement in quantum mechanics. The fundamental demand for empirical grounding is then given a precise formulation following this scrutiny of crucial junctures where the role of theory in measurement came clearly to light.
Research for this paper was supported by NSF grant SES-1026183. A short version of this paper was presented at the Philosophy of Science Association Conference 2010 with the title “Modeling and Measurement: The Criterion of Empirical Grounding.”
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Notes
- 1.
Cf. Hanson (1958, 100–102). If g is the acceleration due to gravity, the weight of body m with mass m is mg. The unbalanced force on this body is the difference between the weight and the upward pull F, which is equal and opposite to the upward pull on M. But the unbalanced force on a body equals its mass times its acceleration — which is equal but opposite for the two bodies. So we can solve the equations to yield (M − m)/(M + m) = a/g. Both a and g can be determined by clock and ruler measurements, in principle. Given the result, an easy calculation leads to the mass ratio M/m.
- 2.
- 3.
For discussion of this exciting experimental episode, see Suppe (1993, 191–193).
- 4.
Examining this episode I will again draw on an early account by Adolf Grünbaum (1957, 713–715) who was in close touch with the pioneering foundational work of Henry Margenau.
- 5.
This is an example discussed by Heisenberg himself (1930, 20).
- 6.
For comparison, here is another procedure, discussed by Margenau, in which the operations themselves are as nearly simultaneous as we please: a gamma ray microscope is used to obtain a definite position number from an electron and simultaneously, by using waves of suitable greater length as well, a definite momentum number. (Margenau 1950, 376–377, 1958; discussed in Grünbaum, loc. cit.)
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This point is not trading on the fact that position and momentum are continuous parameters and therefore have no eigenvalues. For this point holds for discretized versions of these observables (or any pair of discrete conjugate observables) and appropriately coarse discretizations.
- 8.
While Margenau and Park’s analyses are illuminating, I do not agree to the conclusion they advocate, which presupposes that every physical operation which can be designed to yield numbers in some systematic fashion defines a physical quantity, independent of the theory.
- 9.
In the following sense: if at time t=0 the particle has a state represented by a wave function with compact support (−s, +s) then the initial Born probability for outcomes of momentum measurements equals the Born probability of measurements of (mass . position at t)/t in the limit for t → ∞. See Park and Margenau (1968, 240–242) for the calculation.
- 10.
This point is crucial also for other, similar puzzles that have been offered for the understanding of measurement in quantum theory. Specifically, the correlations in an entangled state of several particles — as in the Einstein-Podolski-Rosen example — have been called upon to design putative measurements yielding simultaneous values for conjugate observables (e.g. Park and Margenau 1968, 245). These designs are disqualified provided we insist that the measurement must be made by means of a procedure whose validity does not depend on the initial state of the measured object; see van Fraassen (1974, 301–303; 1991, 220–221).
- 11.
It would be no use to cavil at the inclusion of a “paper and pencil operation” in arriving at the outcome value — that is almost a universal characteristic of procedures recognized as measurements. Just think of how Eratosthenes measured the size of the earth, for example.
- 12.
Park and Margenau (1968) leave open the possibility of saying that there is an observable that is being measured, just not one represented in the theoretical models. But once again the criterion requires that a procedure offered as performing measurements must not be one that just happens to apply properly only to a restricted form of initial states that have very special configurations. In fact, Park and Margenau include a proof (concerning what they name “A-type measurements”) that this criterion will be violated for any imagined joint measurement of observables represented by non-commuting observables.
- 13.
Pages 121–122 of his Philosophy of mathematics and natural science (NY: Atheneum 1963; first published in German as Philosophie der Mathematik und Naturwissenschaft in 1927) While Weyl does not mention any, there are clear connections to Schlick’s demand for “unique coordination” which had been further explored by Reichenbach (1920/1965, Ch. IV; see specifically p. 43).
- 14.
This point has often appeared in the scientific and philosophical literature as demands to “operationalize” theoretical concepts, sometimes in polemics against rival theoretical approaches to a common domain — e.g., between advocates of the atomic theory and those advocating energetics, or between behaviorist and cognitive psychology. Such demands fell into disrepute among philosophers because they typically included the presumption that perfectly theory-neutral evidence could be had, or even that theoretical concepts could be reduced to operational ones. But at heart, and however imperfectly, those demands reflect norms operative in scientific practice.
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van Fraassen, B.C. (2014). The Criterion of Empirical Grounding in the Sciences. In: Gonzalez, W.J. (eds) Bas van Fraassen’s Approach to Representation and Models in Science. Synthese Library, vol 368. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7838-2_4
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