| Interim summary |
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| The real problem | |
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The extrinsic nature of the values of observables — they must be indicated in order to be possessed — appears to entail a vicious regress. A particle's position has a value only if, only when, and only to the extent that a value is indicated (by a detector in the broadest sense of the word). But the same is true of a detector's position. Particle positions presuppose particle detectors, detector positions presuppose detector detectors, and so an ad infinitum. You may recognize this as a version von Neumann's "catastrophe of infinite regression." Somewhere the buck must stop. Some properties must be different, not by arbitrary decree but as a consequence of the principles of quantum mechanics.
QuasiQuasi (detail) by Eric J. Heller. Here we see "a quasicrystal, showing some aspects of crystalline order, but missing crucial long range order we expect of a crystal. That is, with an ordinary crystal we can always move around by multiples of the repeating distances ("lattice constants") and come to a repeated atom or structure; not so in this quasicrystal. It looks like a crystal at first glance, but then stubbornly refuses to yield to our human tendency to search for a pattern. There is no repeating pattern, not ever!"
There is no boundary at which properties cease to be extrinsic and become intrinsic (possessed regardless of measurements). Macroscopic positions, too, are extrinsic. At the same time they are different. They indicate each other's values so abundantly, so persistently, and so sharply that they are fuzzy only in relation to an imaginary background that is more differentiated than the real world. In other words, macroscopic positions are only counterfactually fuzzy. Their fuzziness would reveal itself (through the unpredictability of their measured values) if the regions over which they are "smeared out" were probed. But they never are. (Macroscopic positions, recall, are defined that way.) The distinctions we make between these regions correspond to nothing in the real world. They exist solely in our minds. The buck stops because the spatial differentiation of the world stops: it doesn't go "all the way down." The extrinsic nature of physical observables is a consequence of their fuzziness. If macroscopic positions are only counterfactually fuzzy, then they are also only counterfactually extrinsic. This doesn't make them intrinsic. Even a macroscopic position doesn't exist "by itself." Even the Moon has a position only because of the myriads of "pointer positions" that betoken its whereabouts. We cannot attribute an independent ("free-standing") reality to an individual macroscopic position. But we can attribute independent reality to the totality of macroscopic positions — the macroworld. The macroworld depends on nothing external to itself. Everything else is what it is because of what happens or is the case in the macroworld. The existing values of all observables other than macroscopic positions supervene on value-indicating events in the "lives" or "histories" of macroscopic positions. |
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