7 The macroworld

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.”

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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.