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The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective
This is a modern classic, a seminal work by one of our foremost philosophers of science, cited by just about every serious thinker who has explored the foundations of quantum mechanics. Jammer is one of a precious few who are equally at home within quantum theory and the larger philosophical tradition. The text is quite accessible, but it is a work of real scholarship, written for scholars and scientists, and will present significant challenges for the layman.
536 pages, Hardcover
First published January 1, 1974
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October 15, 2022
A peculiar feature of quantum mechanics consists in the circumstance that, while its formal mathematical apparatus has been elaborated into a high state of art, its physical interpretation remains, nearly a century later, a matter of much dispute. There is no ambiguity as to what the theory predicts, but, in that it remains counterintuitive to physicists whose experience is drawn from the classical world, nobody is sure just how to resolve the paradoxes in a completely satisfactory way. At the same time, quantum mechanics and its daughter discipline, relativistic quantum field theory, continue to demarcate the frontier of our knowledge of the microscopic world. Therefore its proper interpretation stays as much a pressing concern as ever to those who care about philosophical coherence, and the contentiousness of the debates has not abated. Where should a neophyte look to get his groundings? As always, it would probably be inadvisable to start from the current literature for in physics, just as much as in other scholarly disciplines, the history of the Fragestellung will be determinative of the contours of present-day discussions. The great historian of science Max Jammer feels this way as well. For this reason, he has complemented his meticulous history of the conceptual development of quantum physics (reviewed by us here) with an extensive volume on the history of its philosophical interpretation, subject of the present review.
What one gets, as usual with Jammer, is more in the nature of a thorough literature review than an independent development of the subject from first principles. This suits the author’s intent well, for a diachronic treatment serves to disclose the origin of concepts. From our twenty-first-century vantage point, one will be struck by how little is absolutely new in the physics world! To be sure, reading Jammer alone would not prepare one to participate in current debates on, say, quantum Bayesianism, superdeterminism, the multiverse and what have you. Yet, it is worthwhile to see how much David Bohm owes to Louis de Broglie, for instance – for the crucial ideas of the quantum potential and the pilot wave go back to the latter, about which more in a moment.
After a brief and somewhat stilted sketch of the formalism of quantum mechanics in chapter one, chapter two covers its early reception by Schrödinger, Born and in various hydrodynamical models. An interesting comment to note as an aside: Bohm’s so-called quantum potential is interpretable in a hydrodynamic sense as originating from internal stresses in the fluid [p. 50]. Jammer summarizes [p. 53], all the interpretations in this chapter seek to explain quantum mechanics in terms of a model of some classical system or other or slightly modified versions thereof.
In chapters three and four, Jammer turns to Bohr and Heisenberg and the so-called Copenhagen interpretation. His evaluation in chapter five of the Bohr-Einstein debate serves as an illustration of how Jammer can fall prey to an excessively scholarly tendency and ends up considering in detail results that appear trivial in significance to us, fifty years on. For he aims to cover everything ever said on a subject rather than to give a complete, rounded exposition of it (which means ignoring tangents).
Jammer turns next in chapter six to the important Einstein-Podolsky-Rosen incompleteness argument. We may remark with respect to this argument that Einstein presumes that having a sharply defined position and momentum simultaneously at a given time are elements of physical reality! Though he acknowledges they would have be be measured at different times. The physical reality EPR have in mind is what emerges only in the classical limit – why would one expect it to hold at the microphysical level, short of that limit? Once one recognizes contextuality, EPR ceases to be necessarily paradoxical. Jammer’s concise summary of Bohr’s reply to EPR can be found on p. 196. The impossible counterfactual EPR embrace is that the joint system could be embedded into two mutually contradictory measurement situations at the same time.
Later, in chapters seven and eight, Jammer goes on to treat hidden variables, John von Neumann and the beginnings quantum logic. Re. Bell and Bohm, a helpful clarification of what is new in Bohm over Madelung and de Broglie [p. 281]. In Bohm’s pilot-wave theory, since the initial position cannot be measured by any methods known so far it is a hidden variable [p. 282]. Note the difficulty that Bohm’s quantum potential depends on the absolute value of the wavefunction amplitude and its Laplacian; hence one has to solve the problem via Schrödinger’s equation first then substitute back to integrate the hidden variable – thus, the dynamics becomes self-referential across time in a fashion contrary to what is usual in theoretical physics, in which time evolution is ordinarily governed by an initial-value problem, typical that is of parabolic or hyperbolic rather than of elliptic systems.
Another nice point in Jammer’s exposition: explanation of how Bohm’s theory gets around von Neumann’s non-existence proof [p. 286]. Jammer has previously covered in some detail Grete Hermann’s critique of the implicit presuppositions underlying von Neumann’s argument. Chapter eight goes into fairly extensive detail on further work on quantum logic, or logics one should say in the parlance (somewhat oxymoronically, for logic is or ought to be by design universal): very abstract, some unevenness in the exposition in that Jammer chooses occasionally to spell out in detail the proofs of some propositions in alternate quantum logics while elsewhere his account of a derivation may be cursory.
As one might expect given the central importance of quantum mechanics to modern physics, it has attracted quite a lot of interpretive work from numerous points of view and one can appreciate that Jammer has had the patience to wade through the original literature and pick out the connecting thread. For instance, his remark that
Gleason’s theorem simplified the axiomatics of quantum mechanics since it showed that quantum mechanical probabilities can always be calculated by means of the density matrix….Through Gleason’s work it became clear that von Neumann’s result concerning the impossibility of hidden variables does not hinge on postulate iv that is, on the additivity assumption for the expectation values of any operators, even if they do not commute. It now became clear that in Hilbert spaces of at least three dimensions it suffices to postulate such an additivity for commuting operators alone in order to exclude the possibility of dispersion-free states. [p. 297]
Another interesting topic would be Jauch and Piron’s reformulation of von Neumann’s proof to avoid all objections of circular reasoning and to make it independent of the additivity assumption [pp. 300-302]. Others whom Jammer mentions include Ludwig, Wigner, Bunge, Popper and Bub.
Lastly in the final section of chapter eleven, a succinct coverage of Everett’s many-worlds interpretation (which may be something of a misnomer; Everett himself refers to his theory as the relative wave function in his original dissertation submitted to Princeton University under John Wheeler’s direction in 1958 – in the modern approach, alternate branches of the relative wave function, all of which live in the same encompassing Hilbert space, become distinct from one another via the mechanism of decoherence, so there is some justification to speaking of them as so many different worlds).
To close: dependable but not very exciting, impartial, having been written in 1974 misses decoherence and consistent histories. Throughout one will notice how a perusal of Jammer may be good for finding out what everyone in the past, including minor physicists, thought about an issue in the interpretation of quantum mechanics, but not for settling it definitively. Yet it lies in the nature of research that one has to canvass the views of a good number of authorities on a given subject before one will be in a position to assemble a synthetic understanding of it for oneself, and only from the latter can anything original spring that could serve as the inception of a contribution of one’s own. So, by all means read Jammer but do not get one’s hopes up! He is not going to tell one the answer or even point one in the right direction. At best, he will alert one to possibly obscure work in the literature to which one can turn to follow up on a potential insight.
What one gets, as usual with Jammer, is more in the nature of a thorough literature review than an independent development of the subject from first principles. This suits the author’s intent well, for a diachronic treatment serves to disclose the origin of concepts. From our twenty-first-century vantage point, one will be struck by how little is absolutely new in the physics world! To be sure, reading Jammer alone would not prepare one to participate in current debates on, say, quantum Bayesianism, superdeterminism, the multiverse and what have you. Yet, it is worthwhile to see how much David Bohm owes to Louis de Broglie, for instance – for the crucial ideas of the quantum potential and the pilot wave go back to the latter, about which more in a moment.
After a brief and somewhat stilted sketch of the formalism of quantum mechanics in chapter one, chapter two covers its early reception by Schrödinger, Born and in various hydrodynamical models. An interesting comment to note as an aside: Bohm’s so-called quantum potential is interpretable in a hydrodynamic sense as originating from internal stresses in the fluid [p. 50]. Jammer summarizes [p. 53], all the interpretations in this chapter seek to explain quantum mechanics in terms of a model of some classical system or other or slightly modified versions thereof.
In chapters three and four, Jammer turns to Bohr and Heisenberg and the so-called Copenhagen interpretation. His evaluation in chapter five of the Bohr-Einstein debate serves as an illustration of how Jammer can fall prey to an excessively scholarly tendency and ends up considering in detail results that appear trivial in significance to us, fifty years on. For he aims to cover everything ever said on a subject rather than to give a complete, rounded exposition of it (which means ignoring tangents).
Jammer turns next in chapter six to the important Einstein-Podolsky-Rosen incompleteness argument. We may remark with respect to this argument that Einstein presumes that having a sharply defined position and momentum simultaneously at a given time are elements of physical reality! Though he acknowledges they would have be be measured at different times. The physical reality EPR have in mind is what emerges only in the classical limit – why would one expect it to hold at the microphysical level, short of that limit? Once one recognizes contextuality, EPR ceases to be necessarily paradoxical. Jammer’s concise summary of Bohr’s reply to EPR can be found on p. 196. The impossible counterfactual EPR embrace is that the joint system could be embedded into two mutually contradictory measurement situations at the same time.
Later, in chapters seven and eight, Jammer goes on to treat hidden variables, John von Neumann and the beginnings quantum logic. Re. Bell and Bohm, a helpful clarification of what is new in Bohm over Madelung and de Broglie [p. 281]. In Bohm’s pilot-wave theory, since the initial position cannot be measured by any methods known so far it is a hidden variable [p. 282]. Note the difficulty that Bohm’s quantum potential depends on the absolute value of the wavefunction amplitude and its Laplacian; hence one has to solve the problem via Schrödinger’s equation first then substitute back to integrate the hidden variable – thus, the dynamics becomes self-referential across time in a fashion contrary to what is usual in theoretical physics, in which time evolution is ordinarily governed by an initial-value problem, typical that is of parabolic or hyperbolic rather than of elliptic systems.
Another nice point in Jammer’s exposition: explanation of how Bohm’s theory gets around von Neumann’s non-existence proof [p. 286]. Jammer has previously covered in some detail Grete Hermann’s critique of the implicit presuppositions underlying von Neumann’s argument. Chapter eight goes into fairly extensive detail on further work on quantum logic, or logics one should say in the parlance (somewhat oxymoronically, for logic is or ought to be by design universal): very abstract, some unevenness in the exposition in that Jammer chooses occasionally to spell out in detail the proofs of some propositions in alternate quantum logics while elsewhere his account of a derivation may be cursory.
As one might expect given the central importance of quantum mechanics to modern physics, it has attracted quite a lot of interpretive work from numerous points of view and one can appreciate that Jammer has had the patience to wade through the original literature and pick out the connecting thread. For instance, his remark that
Gleason’s theorem simplified the axiomatics of quantum mechanics since it showed that quantum mechanical probabilities can always be calculated by means of the density matrix….Through Gleason’s work it became clear that von Neumann’s result concerning the impossibility of hidden variables does not hinge on postulate iv that is, on the additivity assumption for the expectation values of any operators, even if they do not commute. It now became clear that in Hilbert spaces of at least three dimensions it suffices to postulate such an additivity for commuting operators alone in order to exclude the possibility of dispersion-free states. [p. 297]
Another interesting topic would be Jauch and Piron’s reformulation of von Neumann’s proof to avoid all objections of circular reasoning and to make it independent of the additivity assumption [pp. 300-302]. Others whom Jammer mentions include Ludwig, Wigner, Bunge, Popper and Bub.
Lastly in the final section of chapter eleven, a succinct coverage of Everett’s many-worlds interpretation (which may be something of a misnomer; Everett himself refers to his theory as the relative wave function in his original dissertation submitted to Princeton University under John Wheeler’s direction in 1958 – in the modern approach, alternate branches of the relative wave function, all of which live in the same encompassing Hilbert space, become distinct from one another via the mechanism of decoherence, so there is some justification to speaking of them as so many different worlds).
To close: dependable but not very exciting, impartial, having been written in 1974 misses decoherence and consistent histories. Throughout one will notice how a perusal of Jammer may be good for finding out what everyone in the past, including minor physicists, thought about an issue in the interpretation of quantum mechanics, but not for settling it definitively. Yet it lies in the nature of research that one has to canvass the views of a good number of authorities on a given subject before one will be in a position to assemble a synthetic understanding of it for oneself, and only from the latter can anything original spring that could serve as the inception of a contribution of one’s own. So, by all means read Jammer but do not get one’s hopes up! He is not going to tell one the answer or even point one in the right direction. At best, he will alert one to possibly obscure work in the literature to which one can turn to follow up on a potential insight.
December 9, 2020
Unnecessarily filled with equations. Anyway, good for those who are interested. Also filled with some historical stories of the people.
Displaying 1 - 2 of 2 reviews