This article presents a novel interpretation of quantum mechanics. It extends the meaning of “measurement” to include all property-indicating facts. Intrinsically, space is undifferentiated: There are no points on which a world of locally instantiated physical properties could be built. Instead, reality is built on facts, in the sense that the properties of things are extrinsic, or supervenient on property-indicating facts. The actual extent to which the world is spatially and temporally differentiated (that is, the extent to which spatiotemporal relations and distinctions are warranted by the facts) is necessarily limited. Notwithstanding that the state vector does nothing but assign probabilities, quantum mechanics affords a complete understanding of the actual world. If there is anything that is incomplete, it is the actual world, but its incompleteness exists only in relation to a conceptual framework that is more detailed than the actual world. Two deep-seated misconceptions are responsible for the interpretational difficulties associated with quantum mechanics: the notion that the spatial and temporal aspects of the world are adequately represented by sets with the cardinality of the real numbers, and the notion of an instantaneous state that evolves in time. The latter is an unwarranted (in fact, incoherent) projection of our apparent “motion in time” into the world of physics. Equally unwarranted, at bottom, is the use of causal concepts. There nevertheless exists a “classical” domain in which language suggestive of nomological necessity may be used. Quantum mechanics not only is strictly consistent with the existence of this domain but also presupposes it in several ways.
REFERENCES
1.
N. David
Mermin
, “What is quantum mechanics trying to tell us?
,” Am. J. Phys.
66
, 753
–767
(1998
).2.
David Bohm, Quantum Theory (Prentice–Hall, Englewood Cliffs, NJ, 1951).
3.
I cannot at this point define what I mean by a “matter of fact about the value of an observable,” except by saying that it is an actual event or state of affairs from which that value can be inferred. The question of how to define “(matter of) fact,” “event,” “state of affairs,” and similar expressions will be addressed below.
4.
Yakir
Aharonov
, Peter G.
Bergmann
, and Joel L.
Lebowitz
, “Time symmetry in the quantum process of measurement
,” Phys. Rev.
134B
, 1410
–1416
(1964
);reprinted in Quantum Theory and Measurement, edited by John Archibald Wheeler and Wojciech Hubert Zurek (Princeton U. P., Princeton, NJ, 1983), pp. 680–686.
5.
Yakir
Aharonov
and Lev
Vaidman
, “Complete description of a quantum system at a given time
,” J. Phys. A
24
, 2315
–2328
(1991
).6.
B.
Reznik
and Y.
Aharonov
, “Time symmetric formulation of quantum mechanics
,” Phys. Rev. A
52
, 2538
–2550
(1995
).7.
Lev
Vaidman
, “Time-symmetrized quantum theory
,” Fortschr. Phys.
46
, 729
–739
(1998
).8.
If the measurement at had yielded the final measurement could not have yielded
9.
This point has been forcefully made by Huw Price, Time’s Arrow & Archimedes’ Point (Oxford U. P., New York, 1996).
10.
Professional soccer players and neuroscientists alike may contest this account, but that is besides the point.
11.
Ulrich
Mohrhoff
“Objectivity, retrocausation, and the experiment of Englert, Scully and Walther
,” Am. J. Phys.
67
, 330
–335
(1999
).12.
Michael A. E.
Dummett
, “Bringing about the past
,” Philos. Rev.
73
, 338
–359
(1964
).13.
Berthold-Georg
Englert
, Marlan O.
Scully
, and Herbert
Walther
, “The duality in matter and light
,” Sci. Am.
271
(6
), 56
–61
(December 1994
).14.
Marlan O.
Scully
, Berthold-Georg
Englert
, and Herbert
Walther
, “Quantum optical tests of complementarity
,” Nature (London)
351
(6322
), 111
–116
(1991
).15.
In this context Mermin considers it possible that my now is two weeks behind or fifteen minutes ahead of his now. This peculiar notion does not bear scrutiny. Temporal relations exist between objective events and/or objective states of affairs, not between nows. The use of “now” in the plural is at best bad English. My experiential now—the special moment at which the world has the technicolor reality it has in my consciousness—is coextensive with my worldline, and so is Mermin’s with his worldline. Every event that I have been or will be aware of has had or will have this miraculous kind of reality. Assigning a temporal relation to the experiential nows of different persons therefore makes as much sense as assigning a temporal relation to two parallel worldlines. If I point at a spot on my worldline and a spot on your worldline and say, “When my now is here, yours is there,” I actually say “When my clock shows your clock shows ” But this is a statement that makes sense only if it concerns the relation between two coordinate systems. As a statement about different times relative to the same coordinate system, it is a self-contradictory statement about synchronized clocks.
16.
A.
Peres
and W. H.
Zurek
, “Is quantum theory universally valid?
,” Am. J. Phys.
50
, 807
–810
(1982
).17.
Where real detectors are concerned, we must distinguish between two kinds of probability: the probability that a detector will respond (no matter which) and the probability that a specific detector will respond given that any one detector will respond. The latter (conditional) probability is the one that quantum mechanics is concerned with. The former (absolute) probability can be measured (for instance, by using similar detector in series), but it cannot be calculated using the quantum formalism (nor, presumably, any other formalism). One can analyze the efficiency of, say, a Geiger counter into the efficiencies of its “component detectors” (the ionization cross sections of the ionizable targets it contains), but the efficiencies of the “elementary detectors” cannot be analyzed any further. The efficiency of a real detector cannot be calculated from “first principles.” And since the efficiency of a real detector is determined by at least one fundamental coupling constant such as the fine structure constant, this also implies that a fundamental coupling constant cannot be calculated; it can only be gleaned from the experimental data.
18.
Michael Redhead, Incompleteness, Nonlocality and Realism (Clarendon, Oxford, 1987), p. 72.
19.
An anonymous referee (of a different paper and a different journal) claims that standard quantum mechanics rejects Redhead’s sufficiency condition but endorses the “eigenstate-eigenvalue link,” according to which an element of reality corresponding to an eigenvalue of an observable exists at time t if and only if the system at t is “in the corresponding eigenstate of this observable.” It is obvious that the PIQM rejects this claim, since it rejects the very notion that quantum states warrant inferences to actualities.
20.
Asher
Peres
, “Can we undo quantum measurements?
,” Phys. Rev. D
22
, 879
–883
(1980
);reprinted in Wheeler and Zurek (Ref. 4), pp. 692–696.
21.
Thus the characterization of a measurement as an “irreversible act of amplification” is inadequate. As long as what is amplified is counterfactuals, the “act of amplification” is reversible. No amount of amplification succeeds in turning a counterfactual into a fact. No matter how many counterfactuals get entangled, they remain counterfactuals. On the other hand, once a property-indicating event or state of affairs has happened or come into existence, it is logically impossible to reverse this. For the relevant fact is not that the needle deflects to the left (which could be reversed by returning the needle to the neutral position); the relevant fact is that at a time t the needle deflects (or points) to the left. This is a timeless truth. If at the time t the needle deflects to the left, then it always has been and always will be true that at the time t the needle deflects to the left.
22.
G.
Lüders
, “Über die Zustandsänderung durch den Messprozess
,” Ann. Phys. (Leipzig)
8
, 322
–328
(1951
).23.
John von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton U. P., Princeton, 1955).
24.
Wojciech Hubert
Zurek
, “Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?
,” Phys. Rev. D
24
, 1516
–1525
(1981
).25.
Wojciech Hubert
Zurek
, “Environment-induced superselection rules
,” Phys. Rev. D
26
, 1862
–1880
(1982
).26.
E.
Joos
and H. D.
Zeh
, “The emergence of classical properties through interaction with the environment
,” Z. Phys. B: Condens. Matter
59
, 223
–243
(1985
).27.
Wojciech Hubert
Zurek
, “Decoherence and the transition from quantum to classical
,” Phys. Today
44
(10
), 36
–44
(1991
).28.
Wojciech
Hubert Zurek
, “Preferred states, predictability, classicality and the environment-induced decoherence
,” Prog. Theor. Phys.
89
, 281
–312
(1993
).29.
Robert B.
Griffiths
, “Consistent histories and the interpretation of quantum mechanics
,” J. Stat. Phys.
36
, 219
–272
(1984
).30.
M. Gell-Mann and J. B. Hartle, “Quantum mechanics in the light of quantum cosmology,” in Complexity, Entropy, and the Physics of Information, edited by W. H. Zurek (Addison–Wesley, Reading, MA, 1990), pp. 425–458.
31.
Roland
Omnès
, “Consistent interpretations of quantum mechanics
,” Rev. Mod. Phys.
64
, 339
–382
(1992
).32.
Fay
Dowker
and Adrian
Kent
, “On the consistent histories approach to quantum mechanics
,” J. Stat. Phys.
82
, 1575
–1646
(1996
).33.
N.
Gisin
and I. C.
Percival
, “The quantum-state diffusion model applied to open systems
,” J. Phys. A
25
, 5677
–5691
(1992
).34.
L.
Diósi
, N.
Gisin
, J. J.
Halliwell
, and I. C.
Percival
, “Decoherent histories and quantum state diffusion
,” Phys. Rev. Lett.
74
, 203
–207
(1994
).35.
Ian C.
Percival
, “Primary state diffusion
,” Proc. R. Soc. London, Ser. A
447
, 189
–209
(1994
).36.
G. C.
Ghirardi
, A.
Rimini
, and T.
Weber
, “Unified dynamics for microscopic and macroscopic systems
,” Phys. Rev. D
34
, 470
–491
(1986
).37.
Philip
Pearle
, “Combining stochastic dynamical state-vector reduction with spontaneous localization
,” Phys. Rev. A
39
, 2277
–2289
(1989
).38.
Philip Pearle, “True collapse and false collapse,” in Quantum Classical Correspondence, edited by Da Hsuan Feng and Bei Lok Hu (International Press, Cambridge, MA, 1997), pp. 51–68.
39.
Jorge Luis Borges, “The Garden of Forking Paths,” Ficciones (Everyman’s Library, Knopf/Random House, New York, 1993).
40.
Abner
Shimony
, “Metaphysical problems in the foundations of quantum mechanics
,” Int. Philos. Q.
18
, 3
–17
(1978
).41.
Abner Shimony, “Conceptual Foundations of Quantum Mechanics,” in The New Physics, edited by Paul Davies (Cambridge U. P., Cambridge, 1989), pp. 373–395.
42.
Werner Heisenberg, Physics and Philosophy (Harper and Row, New York, 1958), Chap. 3.
43.
Karl R. Popper, Quantum Theory and the Schism in Physics, edited by W. W. Bartley III (Rowan & Littlefield, Totowa, NJ, 1982).
44.
The “collapse” of an inference basis is necessarily unpredictable: if it could be predicted, the inference basis would remain unchanged.
45.
Thomas Nagel, The View from Nowhere (Oxford U. P., New York, 1986).
46.
Alfred North Whitehead, Process and Reality: An Essay in Cosmology (Macmillan, New York, 1960).
47.
It is often said that the “motion” of the now or the “flow” of time are purely subjective (Ref. 11, Sec. V). I would not go so far. I prefer to think that objective reality encompasses more than “objective” science can handle. Science knows nothing of the singular and the individual. It deals with classes and types and the patterns or regularities that define membership in a class. It deals with greylags but not with the greylag goose Martina. It deals with lawfulness but not with what instantiates the lawfulness. It deals with the laws of physics but not with what it is that obeys the laws of physics. It classifies fundamental particles but keeps mum on what a fundamental particle intrinsically is. From this it does not follow that, objectively, there is no such thing as a fundamental particle. By the same token, from the fact that physics can deal only with the quantitative features of time, it does not follow that the qualitative features of time are not objective.
48.
“…there is no interpolating wave function giving the ‘state of the system’ between measurements”—
Asher
Peres
, “What is a state vector?
,” Am. J. Phys.
52
, 644
–650
(1984
).49.
Bernard d’Espagnat, Conceptual Foundations of Quantum Mechanics, 2nd ed. (Benjamin, Reading, MA, 1976), p. 251.
50.
Niels Bohr, Essays 1958–62 on Atomic Physics and Human Knowledge (Wiley, New York, 1963), p. 3.
51.
Niels Bohr, Atomic Theory and the Description of Nature (Cambridge U. P., Cambridge, 1934).
52.
Abraham Pais, ‘Subtle is the Lord…’: The Science and the Life of Albert Einstein (Clarendon, Oxford, 1982).
53.
Another way to see this is to recall from Ref. 17 that no theoretical account can be given of the efficiency of a real detector—its likelihood to click when the corresponding Born probability is 1. A fortiori, no theoretical account can be given of why or when a detector is certain to click. It never is.
54.
Fritz London and Edmond Bauer, “The theory of observation in quantum mechanics,” in Wheeler and Zurek (Ref. 4), pp. 217–259.
55.
Don N.
Page
, “Sensible quantum mechanics: Are probabilities only in the mind?
,” Int. J. Mod. Phys. D
5
, 583
–596
(1996
).56.
Henry Pierce Stapp, Mind, Matter, and Quantum Mechanics (Springer, Berlin, 1993).
57.
Michael Lockwood, Mind, Brain and the Quantum (Basil Blackwell, Oxford, 1989).
58.
David Z. Albert, Quantum Mechanics and Experience (Harvard U. P., Cambridge, MA, 1992).
59.
Because these conditions can be stated in classical language, causal terms do have a domain of application. More about this in Sec. X.
60.
See Carl Friedrich von Weizsäcker, The Unity of Nature (Farrar, Straus, Giroux, New York, 1980), Sec. IV.4.
61.
B.
Misra
and E. C. G.
Sudarshan
, “The Zeno’s paradox in quantum theory
,” J. Math. Phys.
18
, 756
–763
(1977
).62.
C. B.
Chiu
and E. C. G.
Sudarshan
, “Time evolution of unstable states and a resolution of Zeno’s paradox
,” Phys. Rev. D
16
, 520
–529
(1977
).63.
Asher
Peres
, “Zeno paradox in quantum theory
,” Am. J. Phys.
48
, 931
–932
(1980
).64.
N. David
Mermin
, “Is the Moon there when nobody looks? Reality and the quantum theory
,” Phys. Today
38
(4
), 38
–47
(1985
).65.
Departures from the classically predicted positions are necessarily random, or unpredictable. A predictable departure would reveal a classical law not previously taken into account; it would not be a departure from the classically predicted position.
66.
“…even when phenomena transcend the scope of classical physical theories, the account of the experimental arrangement… must be given in plain language, suitably supplemented by technical physical terminology. This is a clear logical demand, since the very word ‘experiment’ refers to a situation where we can tell others what we have done and what we have learned.”—Niels Bohr, Atomic Physics and Human Knowledge (Wiley, New York, 1958), p. 72.
67.
If the boundary of a detector D is manifestly fuzzy, there are detectors with smaller sensitive regions, so D cannot be among the ultimate detectors.
68.
Albert
Einstein
, Boris
Podolsky
, and Nathan
Rosen
, “Can quantum-mechanical description of physical reality be considered complete?
,” Phys. Rev.
47
, 777
–780
(1935
);reprinted in Wheeler and Zurek (Ref. 4), pp. 138–141.
69.
Albert Einstein, in Albert Einstein: Philosopher-Scientist, edited by P. A. Schilpp (Open Court, La Salle, IL, 1970), p. 85.
70.
The denial of nomological necessity in physics (sometimes referred to as “causal nihilism”) does not entail that our self-perception as causal agents is a delusion. See
Ulrich
Mohrhoff
, “Interactionism, energy conservation, and the violation of physical laws
,” Phys. Essays
10
, 651
–665
(1997
);Ulrich
Mohrhoff
, “The physics of interactionism
,” J. Cons. Stud.
6
(8/9
), 165
–184
(1999
).71.
“I think it is safe to say that no one understands quantum mechanics… . Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?’ because you will go ‘down the drain’ into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that,”—Richard P. Feynman, The Character of Physical Law (MIT, Cambridge, MA, 1967), p. 129.
72.
David K. Lewis, Philosophical Papers, Volume II (Oxford U. P., New York, 1986), p. x.
73.
Reference 58, p. 126.
74.
For a summary see, for instance, Ref. 18, pp. 49–51;
Barry
Loewer
, “Copenhagen versus Bohmian interpretations of quantum theory
,” Br. J. Philos. Sci.
49
, 317
–328
(1998
).75.
See, for instance,
Rudolf
Peierls
, “In defence of ‘measurement
,’ ” Phys. World
4
(1
), 19
–20
(1991
).76.
Henry
Pierce Stapp
, “The Copenhagen interpretation
,” Am. J. Phys.
40
, 1098
–1116
(1972
).77.
N. David
Mermin
, “What’s wrong with this sustaining myth?
,” Phys. Today
49
(3
), 11
–13
(1996
).78.
Reference 18, p. 48.
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