Making sense of the theoretical formalism of quantum mechanics calls for a judicious choice on our part. We need to identify that substructure of the theory’s total structure to which independent reality can be attributed. Since observables have values only if, only when, and only to the extent that they are measured, this cannot be the so-called microworld, nor any part thereof. The microworld is what it is because of what happens or is the case in the macroworld, rather than the other way round, as we are wont to think. Since we also reject the (simple-minded) reification of mathematical symbols, this leaves us with the macroworld as the only structure to which independent reality can be attributed. But it also leaves us with the task of providing a rigorous definition of the macroworld.
A preliminary definition: by a classically predictable position we shall mean a position that can be predicted on the basis of (i) a classical law of motion and (ii) all relevant value-indicating events.
The possibility of obtaining evidence of the departure of an object O from its classically predictable position calls for detectors whose position probability distributions are narrower than O’s — detectors that can probe the region over which O’s fuzzy position extends. For objects with sufficiently sharp positions, such detectors do not exist. For the objects commonly and loosely referred to as “macroscopic,” the probability of obtaining evidence of departures from their classically predictable motion will thus be low. Hence among these objects, there will be many of which the following is true: every one of their indicated positions is consistent with every prediction that can be made on the basis of previously indicated properties and a classical law of motion. These are the objects that truly deserve the label macroscopic. To permit a macroscopic object — for instance, the proverbial pointer needle — to indicate the value of measurable physical quantity, one exception has to be made: its position may change unpredictably if and when it serves to indicate a physical property or value.
With this we are in position to define the macroworld unambiguously as the totality of relative positions between macroscopic objects. Let’s shorten this to “macroscopic positions.” By definition, macroscopic positions never evince their fuzziness (in the only way they could, through departures from classically predicted values). Macroscopic objects therefore follow trajectories that are only counterfactually fuzzy: their positions are fuzzy only in relation to an imaginary background that is more differentiated spacewise than is the actual world. This is what makes it legitimate to attribute to the macroworld a reality independent of anything external to it — such as the consciousness of an observer. (Consciousness has been invoked to explain the so-called collapse of the wave function.[1–7] While this offers a gratuitous solution to a pseudo-problem, which arises from the mistaken belief that wave functions evolve, it obfuscate the real interpretational challenges, such as demonstrating the legitimacy of attributing independent reality to the macroworld, and this not merely “for all practical purposes” but strictly.)
And this in turn allows us to state in unambiguous terms the manner in which measurement outcomes are indicated: they are indicated by departures of macroscopic positions from their respective classical laws of motion.
But cannot the information provided by an outcome-indicating position be lost? A position that has departed from a classical law of motion once, to indicate a measurement outcome, may do so again, and may thereby cease to indicate this outcome. This, however, does not mean that no record of the outcome persists. For the positions of macroscopic objects are abundantly monitored. Suppose that at a later time t2 a macroscopic position loses information about an outcome, which it acquired at an earlier time t1. Since in the interim a large number of macroscopic positions have acquired information about this position, and hence about the outcome that was indicated by it, a record of the outcome nevertheless persists.
None of this means that macroscopic positions are exempted from our conclusion that to be is to be measured. Where macroscopic positions are concerned, this conclusion is not false but irrelevant. While even the Moon has a position only because of the myriad of “pointer positions” that betoken its whereabouts, macroscopic positions indicate each other’s values so abundantly, so persistently, and so sharply that they are only counterfactually fuzzy. This is what makes it possible (and perfectly legitimate) to think of the positions of macroscopic objects as forming a self-contained system — the macroworld — and to attribute to this system a reality that depends on nothing external to it.
The crucial role played by the incomplete spatiotemporal differentiation of the physical world in defining the macroworld and in demonstrating the legitimacy of attributing to it an independent reality deserves to be stressed. The fact that “to be is to be measured” 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. Somewhere the buck must stop. Some properties must be different, and macroscopic positions are different. They are different in that they 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 buck stops because the spatial differentiation of the world stops: it doesn’t go “all the way down.”
1. [↑] Goswami, A. (1995). The Self–Aware Universe, Tarcher.
2. [↑] London, F., and Bauer, E. (1939). The theory of observation in quantum mechanics. Reprinted in Wheeler, J.A., and Zurek, W.H. (1983), Quantum Theory and Measurement, Princeton University Press, pp. 217–259.
3. [↑] Squires, E. (1990). Conscious Mind in the Physical World, Adam Hilger.
4. [↑] Stapp, H.P. (2001). Quantum theory and the role of mind in nature. Foundations of Physics 31, 1465–1499.
5. [↑] Rosenblum, B., and Kuttner, F. (2008). Quantum Enigma, Oxford University Press.
6. [↑] von Neumann, J. (1955). Mathematical Foundations of Quantum Mechanics, Princeton University Press.
7. [↑] Wigner, E.P. (1961). Remarks on the mind–body question. In Good, I.J., The Scientist Speculates, Heinemann, pp. 284–302.