Abstract
Quantum mechanics is the second great watershed of twentieth century physics, and in some ways it involved an even more radical break with galilean orthodoxy than relativity did. But the nature of this second rift is somewhat obscure. That is partly because quantum mechanics has such a radical and unfamiliar form, but it is also partly because the mathematical formalism of quantum mechanics preceded its interpretation to an unusual degree. Physicists were in possession of the mathematical expression of quantum mechanics before they had a good sense of what it said about the world. In fact, to some degree it is still far from clear what that spectacularly successful formalism says about the world.
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Notes
One quite accessible introduction to quantum mechanics is Roger Penrose, The Emperor’s New Mind, chapter 6. Peter Gibbins, Particles and Paradoxes(Cambridge: Cambridge University Press, 1987) is also quite useful, as is David Albert, Quantum Mechanics and Experience(Cambridge, MA: Harvard University Press, 1992). The classic survey for philosophers, both exhaustive and accessible, is Max Jammer, The Philosophy of Quantum Mechanics(New York: John Wiley & Sons, 1974). R.I.G. Hughes, The Structure and Interpretation of Quantum Mechanics(Cambridge, MA: Harvard University Press, 1989) is an introduction for philosophers to the formalism of quantum mechanics. Bernard d’Espagnat, Conceptual Foundations of Quantum Mechanics(Redwood City, CA: Addison-Wesley, 1989) is somewhat more difficult, but a classic survey of the interpretation problems for quantum mechanics.
See especially Jammer, d’Espagnat, and Albert. J. Wheeler and W. Zurek (editors), Quantum Theory and Measurement(Princeton: Princeton University Press, 1983) is a collection of key original papers on the interpretation of quantum mechanics.
Gibbins presents this economically and accessibly.
The Janus-faced nature at least of light, its having both classically wave-like and particle-like features, was in fact long familiar. Various considerations had led Newton to the hypothesis that light should be understood to consist of discrete particles, though other phenomena like interference effects had led nineteenth century physicists to adopt a wave conception of light, as expressed in Maxwell’s field equations.
W. Heisenberg, “The interpretation of kinematic and mechanical relationships according to the quantum theory” in G. Ludwig, Wave Mechanics (Oxford: Pergamon Press, 1968), 168–182. E. Schrödinger, “Quantization as an eigenvalue problem”, in Ludwig, 94-105, and “Über das Verhaltnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen”,Annalen der Physik79, 1926, 734-756. J. von Neumann, Mathematical Foundations of Quantum Mechanics,translated by R. Beyer (Princeton: Princeton University Press, 1955).
The frequency of the light, the width of the slits, and the distance between the slits are all relevant. See Penrose for a discussion of this.
My exposition follows Penrose, who stays a nice distance from the standard formalism.
Let me omit discussion of the normalization of amplitudes and probabilities.
On the ordinary post-galilean understanding of these things.
Though see Albert.
Einstein himself did not agree.
A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-mechanical descriptions of physical reality be considered complete?”, in Wheeler and Zurek, 356–368. Einstein may not have favored quite the traditional ensemble interpretation. See Arthur Fine, The Shaky Game(Chicago: University of Chicago Press, 1986).
There are some non-standard ensemble interpretations which are not ruled out. But they are seriously non-classical.
David Bohm, “The Paradox of Einstein, Rosen, and Podolsky”, in Wheeler and Zurek, 356–368.
David Mermin, “Quantum Mysteries for Anyone”, in J. Cushing and E. McMullin (editors), Philosophical Consequences of Quantum Theory (South Bend, IN: University of Notre Dame Press, 1989), 49–59. Penrose, 284-285.
John S. Bell, “On the Einstein Podolsky Rosen Paradox”, in Wheeler and Zurek, 903–908.
Add them up: Where the questions are dubbed 1,2,3, the answers + and-, and the first device is represented on the left, the possible combinations are (1+,1-), (l+,2-), (l+,3+), (2+,l-), (2+,2-), (2+,3+), (3-,l-), (3-,2-), (3-,3+). There are four agreements and five disagreements.
Aspect, Dalibard, Reger, “Experimental test of Bell’s Inequality using time-varying analyzers”, Physical Review Letters 49, 1982, 460–463. Clauserand Shimony, “Bell’s Theorem: Experimental tests and implications”, Reports on Progress in Physics41, 1978, 1888-1927. M.L.G. Redhead, Incompleteness, Nonlocality, and Realism(Oxford: Oxford University Press, 1987), 108.
See the papers collected in Cushing and McMullin.
See page 190 of J.S. Bell, “Six possible worlds of quantum mechanics”, Speakable and unspeakable in quantum mechanics (Cambridge: Cambridge University Press, 1987), 181–195.
N. Bohr, “Can Quantum-Mechanical Descriptions of Physical Reality Be Considered Complete?”, in Wheeler and Zurek, 148–151, and “The Quantum Postulate and the Recent Development of Atomic Theory”, Wheeler and Zurek, 87-126. One book by a philosopher on complementarity is Henry Folse, The Philosophy of Niels Bohr(Amsterdam: North-Holland Publishing, 1985).
Jim Joyce suggested this.
Hilary Putnam, “The logic of quantum mechanics”, in Mathematics, Matter, and Method (Cambridge: Cambridge University Press, 1979), 174-197. See Jammer for a survey of such accounts, and Gibbins for a good introduction and some wise discussion.
See Gibbins.
In the end we may not be able to coherently conceive what quantum mechanics tells us about the world, but we shouldn’t give up this soon. This isn’t a sufficiently instructive place to give up, and the strong reading of this approach which might drive us there relies on the questionable notion of a logic of the world and the even more questionable notion of a non-standard logic of the world.
H. Everett III, “‘Relative state’ formulation of quantum mechanics”, in Wheeler and Zurek, 315–323. DeWitt and Graham (editors), The Many-Worlds Interpretation of Quantum Mechanics(Princeton: Princeton University Press, 1973).
There is a related set of views called the “many minds” interpretation, which is due to B. Loewer and D. Albert. See Albert, 112-133. That class goes something like this: Allow the physical world to be always in a superposition. But allow that minds evolve in such a (probabilistic) way that they always register a particular measurement after a measurement interaction. In the simplest version of this scheme, all but one of the many physical alternatives which are superposed in that measurement are mere “mindless husks”, but Albert prefers an alternative in which to each human brain there corresponds an infinity of minds, which register the alternative measurements in the right proportion. This seems to me to give minds or their physical bases an inordinate and implausible significance, much like Wigner’s version of the orthodox von-Neumann style views, which we will soon discuss. And each mind is supposed to be governed by implausibly special probabilistic laws, which somehow ensurethat the development of all the minds corresponding to a particular body will be such that they will end up as a group in the right places and in the right proportions. And of course such a view must deal in implausible infinities of minds for each person, as the only way to avoid perhaps even more implausible mindless hulks. So such views seem implausible.
A. Daneri, A. Loinger, G.M. Prosperi, “Quantum theory of measurement and ergodicity conditions”, Wheeler and Zurek, 657–679.
See Jammer for references and discussion.
Some interpretations, of course, deny that they do consist at least solely of such particles. For instance, see the next interpretive option.
But see Jammer and d’Espagnat.
See page 171 of Nancy Cartwright, “How the Measurement Problem is an Artifact of the Mathematics”, in How the Laws of Physics Lie(Oxford: Oxford University Press, 1983), 163-216. See also d’Espagnat, 196.
Though see Albert.
E.P. Wigner, “Remarks on the Mind-Body Question”, in Wigner, Symmetries and Reflections (Bloomington, IN: Indiana University Press, 1967). See also the earlier article by F. London and E. Bauer, “The theory of observation in quantum mechanics”, in Wheeler and Zurek, 217-259.
Of course, the objective phenomenal colors fail even in this role, because of perceptual relativity arguments. And at least the determinate classical properties would play some causal role, though it would be merely within the realm of the successive classical properties of things.
Perhaps the macro-object only emits its various “components” if it is broken up in some way, and otherwise they don’t exist. Or perhaps it is constituted by the particles plus some other strange sort of thing, which yet could not make it up without them. But all this seems pretty dicey.
Penrose, 348-373.
Richard Healey, The Philosophy of Quantum Mechanics (Cambridge: Cambridge University Press, 1989). D. Dieks, “On some alleged difficulties in the interpretation of quantum mechanics”, Synthese86,1991,77-86.
B. van Fraassen, Quantum Mechanics: An Empiricist View (Oxford: Oxford University Press, 1989).
See Albert, 191-197.
Nancy Cartwright has proposed another interpretive direction, which retains classical positions for particles outside of measurement. See Cartwright. Bohm“s view is deterministic. Cartwright”s alternative is not. Particles possess determinate positions but merely classical probabilities for transitions to various successive states. The primary problem with this is that we are not yet in possession of the sketch of such a view, which will require more than a little modification of traditional quantum mechanics. There may be probabilistic elements in a relativistic version of Bohm’s view, as we will soon see, but it seems that Cartwright anticipates that transition probabilities play a role even in non-relativistic quantum mechanics. It is hard to see how such an account could deal with EPR-type correlations without invoking the same sorts of troubling resources which Bohm-style accounts deploy. Also like the Bohm-style accounts, it may fail to give proper respect to the uncertainty relations. So because it has no obvious advantages over the Bohm-style accounts, and hasn’t been developed, I will not explicitly discuss it in what follows.
L. de Broglie, “Sur la possibilitè de relier les phènomènes d’interfèrence et de diffraction á la theorie des quanta de lumiere”, Comptes Rendus 183, 1926,447–448.
David Bohm, “A suggested interpretation of the quantum theory in terms of’ hidden’ variables, I and II“, in Wheeler and Zurek, 369–396. See also the papers collected in Bell, Speakable and unspeakable in quantum mechanics,and Albert, 134-179.
See Jammer, 32. “In the treatment of a macromechanical system the vibrations, which undoubtedly have real existence in three-dimensional space, are most conveniently computed in terms of normal coordinates in the 3n-dimensional space of Lagrangian mechanics.”
Bohm, “A suggested interpretation of the quantum theory in terms of ‘hidden’ variables II”, appendix. Bell, “Beables for quantum field theory”, Speakable and unspeakable in quantum mechanics,173-180.
See for instance Fine, The Shaky Game.
Unlike constitution, it seems, it would need to be.
There’s another possible advantage of the Bohm account which should be noted. At least its simple, pre-relativistic form involves merely deterministic powers, and they may also represent an advantage. This may seem a misguided worry, since irreducibly probabilistic powers are expressible in C. But while that represents my best judgment about what is coherently conceivable, resistance to that feature of C would not be unreasonable: I didn’t provide any story about the realization of our thought of such powers. And perhaps our initial conception of probabilistic powers was of powers which were not irreduciblyso. Perhaps, in our partial ignorance, we conceived of powers of things which we didn’t take as irreducible and basic, but rather to reflect just exactly what little we knew, to ignore deterministic inner detail unknown to us in our ignorance. Perhaps the first sort of probabilities we conceived were mere epistemic probabilities, probabilities given our evidence that things would be such and so rather than probabilities in the world itself. And perhaps we came to the later conception of irreducibly probabilistic powers merely by mouthing the word “irreducible” in the direction of powers we conceived initially to be reducible. So perhaps thought of irreducible causal powers does not really have coherent basic content. If so, it may be that Bohm’s account in it least its simple pre-relativistic form scores some advantage over the views we will discuss in the next section.
See Lawrence Sklar, “Saving the Noumena”, Philosophy and Spacetime Physics, 49–72, for a nice articulation of the difficulty here.
G.C. Ghirardi, A. Rimini, and T. Weber, “Unified dynamics for microscopic and macroscopic systems”, Physical Review 1986, D34:470. J.S. Bell, “Are there quantum jumps?”, in Speakable and unspeakable in quantum mechanics,201-212. Abner Shimony, “Our Worldview and Microphysics”, in Cushing and McMullin, 25-37. Albert, 92-111.
See for instance Albert, 97.
See for instance Shimony, 35-36, and Albert, 97-111.
In the reference just cited.
“Dynamical models for the state-vector reduction: do they ensure that measurements have outcomes?”, Foundations of Physics Letters4:116.
In the reference just cited.
Bell, “Are there quantum jumps?”.
R.P. Feynman, QED(Princeton: Princeton University Press, 1985) is a wonderfully lucid and accessible introduction. See also Harvey Brown and Rom Harre (editors), Philosophical Foundations of Quantum Field Theory(Oxford: Oxford University Press, 1988).
Michael Green, “Superstrings”, Scientific American 255, 1986, 48–60, and “Unification of ferees and particles in superstring theories”, Nature314,1985,409-414.
R. Penrose and W. Rindler, Spinors and Space-Time(Cambridge: Cambridge University Press, 1984).
We might hope to appeal to merely possible or potential chiral relations here, but that probably defeats the reductive intentions which lie behind the pursuit of spinors and twistors.
One easily accessible reference is “Gravity Quantized?”, Scientific American270:9, September 1992,18-20.
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Mendola, J. (1997). Classical Experience and Quantum Mechanics. In: Human Thought. Philosophical Studies Series, vol 70. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5660-8_18
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