Measurement and Metaphysics

It is a prima facie reasonable assumption that if a physical quantity is measurable, then it corresponds to a genuine physical property of the measured system. You can measure a person’s mass because human beings have such a property. You can measure the average mass of a group of people because groups of people have such a collective property. And so on.

Now it would be truly surprising – miraculous, perhaps – if you could determine the average mass of a group of people by making measurements on just one of them. To ascribe such a statistical property to an individual looks like a category mistake. At first glance, protective measurements seem to pull off just such a miracle, determining, for example, the expectation value of position for an ensemble of particles via a measurement performed on one of them. The lesson we are supposed to draw, of course, is that expectation values are not statistical properties at all, despite their name. Rather than being an average over an ensemble of systems, the expectation value of position for a particle is a physical property of the individual system, and the wave function, as the bearer of these properties, is a physical entity (Aharonov, Anandan and Vaidman, 1993).

The protective measurement procedure has been challenged (Uffink, 1999; Gao, 2013; Uffink, 2013), but for present purposes I will assume that protective measurements exist, at least in principle, that are capable of revealing “statistical” properties like expectation values in a single measurement. My aim here is not to challenge the existence of such a physical procedure, but rather to explore the arguments that connect the existence of protective measurements with conclusions concerning the nature of physical reality. What protective measurements are supposed to show is that “epistemological” interpretations of the quantum state are untenable – that the wave function of a system must instead be interpreted “ontologically” (Aharonov, Anandan and Vaidman, 1993: 4617).

But what exactly are the epistemological and ontological interpretations contrasted here? There are at least two distinct possibilities.1 First, the epistemological interpretation could be identified with an empiricist attitude towards quantum mechanics in general – taking the theory as a recipe for generating the probabilities of measurement results. Here the contrast is with scientific realism, construed as the view that quantum mechanics is in some sense a true description of the physical world. However, Dickson (1995) has convincingly argued that protective measurement cannot decide between empiricism and realism about quantum mechanics, since protective measurement is entirely consistent with empiricism.2 Hence I set this construal of the argument aside.

Second, the contrast between the epistemological and ontological interpretations of the wave function could be construed within an overall scientific realist attitude towards quantum mechanics in terms of the distinction between a statistical description and a categorical description of the physical system in question. Under this construal, the ontological interpretation is that the wave function is a description of the properties of a single physical entity, whereas the epistemological interpretation is that the wave function is a description of the distribution of properties over an ensemble of similar physical systems.

Peter J. Lewis

Note: This is an excerpt of the seventh chapter of the anthology Protective Measurement And Quantum Reality (CUP, 2014).

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