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Students ask me a few times a year what to read on the foundations of quantum mechanics. This is the answer I give, written out.
Two problems have organized the subject, and a great deal is gained by keeping them apart.
The measurement problem is that the dynamics of the theory is linear, so it assigns superpositions to everything it is applied to — including measuring devices, and including the people who read them — while experiments have single definite outcomes. Something in the standard presentation has to give, and the interesting question is what. Maudlin’s trilemma, below, is the sharpest statement of the options.
Nonlocality is the second, and it is a different kind of problem. Bell proved in 1964 that no theory assigning each system its own local properties can reproduce the correlations quantum mechanics predicts, and the experiments have since been done. This is not something an interpretation solves; it is a constraint every interpretation has to live with. Bohm’s theory answers the measurement problem completely and is flagrantly nonlocal, which is the quickest way to see that the two questions come apart. Running them together is the most common mistake in the popular literature and not unknown in the professional literature.
Underneath the second sits entanglement, which is the phenomenon rather than the problem. Bell nonlocality is something we have learned about entangled states; it is not the same thing as entanglement, and most of what is philosophically interesting about entanglement survives whether or not a given state violates a Bell inequality. It gets a section of its own, and it comes first, because it does so both historically and conceptually.
Nearly everything below is a response to one or the other.
A warning about all of it. The reading list that most philosophers of physics carry around was fixed in the 1990s, and I am one of the people carrying it. It is very good on some things — it is the reason any of us take the measurement problem seriously — and it has a distortion built into its foundations, which is that it treats the physicists who actually created quantum mechanics as having had nothing to say. That is false, and the books that say it are the ones students read first. So this guide is organized by question rather than by author, and where a standard book is unreliable I say so and say why.
Each entry is tagged with what it assumes. No physics means none is needed and none is smuggled in. No prior QM is different and worth distinguishing: the book starts from nothing but still builds the formalism, so you will be manipulating vectors and operators whether or not you have ever taken a physics course. Some QM means one undergraduate course. Serious QM means you have solved problems. Mathematical means functional analysis, or the willingness to acquire it.
David Albert, Quantum Mechanics and Experience (Harvard, 1992) — no prior QM. Still the book that puts the measurement problem at the center and refuses to let you look away from it, and still the best short treatment of Bohm and of GRW in print. Read it first — but do not mistake “assumes no physics” for “easy.” Albert builds the Hilbert space formalism from nothing, and in my experience readers who have never manipulated a vector do not get through it. Then read it critically: it is unreliable as history, it is fully committed to a picture of “the Copenhagen interpretation” that historians have since dismantled (see the next section), its chapter on many worlds gives Albert’s own reading of a view that has been developed enormously since, and it treats quantum mechanics as a statistical algorithm that only makes predictions — which is uncharitable to the many physicists who evidently use it to describe things that nobody is looking at.
Tim Maudlin, “Three measurement problems,” Topoi 14 (1995): 7–15 — some QM. Fifteen pages, and the single most useful thing on this list. Maudlin shows that three claims are jointly inconsistent: the dynamics is linear, the wavefunction is complete, and measurements have outcomes. Every interpretation is then classified by which one it gives up — collapse theories the first, hidden-variable theories the second, Everett the third. If you want a thesis topic, pick a denial and defend it.
Tim Maudlin, Philosophy of Physics: Quantum Theory (Princeton, 2019) — some QM. Much the best written of the modern introductions, and it carries the same distortion as Albert, more confidently. Maudlin’s dismissal of Bohr is not an interpretive disagreement, which would be fine; it is a refusal to engage with a body of scholarship, and it will mislead you about what the historical options were. Read it for the clarity of the positive arguments.
Jeffrey Barrett, The Conceptual Foundations of Quantum Mechanics (Oxford, 2019) — some QM. The closest thing to an actual textbook, and the one I would now assign first to a philosophy student who wants structure: the von Neumann–Dirac formulation built up properly, then collapse, Everett and Bohm, with the history integrated rather than bolted on. Barrett is the leading historian of Everett and it shows.
Peter Lewis, Quantum Ontology (Oxford, 2016) — some QM. Organized by metaphysical question — determinism, locality, what the wavefunction is — rather than by interpretation. Useful as a second book, because it cuts the field along a different axis.
Emily Adlam, Saving Science from Quantum Mechanics: The Epistemology of the Measurement Problem (Oxford, 2025) — serious QM. Not an introduction; it presupposes the landscape. But it is the most interesting recent reframing: Adlam argues the measurement problem is badly posed as a question about ontology and should be posed as one about epistemology — about whether the various proposed solutions leave scientific knowledge able to do what we need it to do. Worth reading late in the project rather than early.
Travis Norsen, Foundations of Quantum Mechanics (Springer, 2017) — some QM. Written as an undergraduate physics course, with over a hundred problems. Sympathetic to Bohm and open about it, but it covers the field. The natural first book for a physics student.
Roderich Tumulka, Foundations of Quantum Mechanics (Springer, 2022) — serious QM. Mathematically careful, even-handed across Copenhagen, GRW, Bohm and Everett, and it goes on to particle creation and relativity. The harder companion to Norsen.
Franck Laloë, Do We Really Understand Quantum Mechanics? 2nd ed. (Cambridge, 2019) — serious QM. The most thorough single survey of formalism-plus-interpretation there is, at 546 pages. A reference more than a read-through.
David Snoke, Interpreting Quantum Mechanics: Modern Foundations (Cambridge, 2024) — serious QM. Unusual in taking quantum field theory seriously as part of the interpretive problem rather than treating non-relativistic QM as the whole story, which is a real defect of the philosophical literature. Snoke argues for a collapse variant; discount accordingly.
Read Schrödinger, who named it. “Discussion of probability relations between separated systems,” Proceedings of the Cambridge Philosophical Society 31 (1935): 555–563 — some QM. Freely available, and the opening pages are readable by an undergraduate. This is where the word enters English, and where the verdict is delivered that entanglement is “not one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.” The 1936 sequel, in volume 32 at 446–452, proves the steering theorem: a distant experimenter can steer the remote system into any ensemble compatible with its reduced state. That is the sharpest early statement of what is strange about entanglement independent of any locality argument, and it is thirty years before Bell. The cat paper of the same year is “Die gegenwärtige Situation in der Quantenmechanik”; the standard English translation is John Trimmer’s, in Proceedings of the American Philosophical Society 124 (1980): 323–338, also free. The cat occupies one paragraph of it and entanglement occupies the serious part.
Entanglement is not Bell nonlocality. Students almost always conflate these, and most introductory treatments let them. The technical fact that separates them is Reinhard Werner’s construction in Physical Review A 40 (1989): 4277–4281, of mixed states that are provably not separable — they cannot be written as a mixture of product states, so they are entangled on the only principled definition — and yet whose statistics for projective measurements are reproduced by an explicit local hidden-variable model, so that they violate no Bell inequality. Entanglement is a structural property of the state; Bell nonlocality is an operational property of a correlation table. The metaphysics is therefore logically prior to, and survives the failure of, any argument from Bell violation. Worth knowing that the Stanford Encyclopedia article on entanglement does not draw this distinction.
The oldest philosophical question about entanglement, and still the best one: does the whole have properties that fail to supervene on the properties of its parts?
Paul Teller, “Relational holism and quantum mechanics,” British Journal for the Philosophy of Science 37 (1986): 71–81 — some QM. Where the question starts. Teller’s proposal is that there are inherent relations between particles that do not supervene on the non-relational properties of the relata.
Richard Healey, “Holism and nonseparability,” Journal of Philosophy 88 (1991): 393–421 — some QM. Establishes the vocabulary everyone now uses, and shows that property holism and spatiotemporal nonseparability come apart.
Healey and Henrique Gomes, “Holism and nonseparability in physics,” Stanford Encyclopedia of Philosophy — no physics. Free, and the best entry point on this whole question. Unlike the entanglement article, it keeps holism, nonseparability and Bell violation distinct.
Don Howard, “Holism, separability, and the metaphysical implications of the Bell experiments,” in Cushing and McMullin, eds., Philosophical Consequences of Quantum Theory (Notre Dame, 1989), 224–253 — some QM. The companion to his Einstein paper in the next section. Despite the title, this is a paper about separability.
Michael Esfeld, “Quantum entanglement and a metaphysics of relations,” Studies in History and Philosophy of Modern Physics 35 (2004): 601–617 — some QM. Argues that entangled systems have their state-dependent properties only as relations, with no underlying intrinsic properties needed to ground them. The book-length version is Holism in Philosophy of Mind and Philosophy of Physics (Kluwer, 2001).
Michael Seevinck, “Holism, physical theories and quantum mechanics,” Studies in History and Philosophy of Modern Physics 35 (2004): 693–712 — some QM. Free on the arXiv. Proposes an epistemological criterion for holism — a theory is holistic if global properties cannot in principle be inferred from local operations plus classical communication — and shows quantum mechanics comes out holistic even for unentangled states. A useful shock.
Elizabeth Miller, “Quantum holism,” Philosophy Compass 11 (2016): 507–514, and “Two notions of holism,” Synthese 197 (2020): 4187–4206 — some QM. The first is the best short orientation. The second is the sceptical foil: the quick argument from entangled states to non-supervenient whole-level properties equivocates, and the dispute is better recast as the general reductive-versus-non-reductive dispute in metaphysics. Read it before you commit to a holist thesis.
There has been a good deal of activity here, and much of it is accessible to a student with no physics beyond the formalism of the two-particle singlet state.
The Synthese special issue on the metaphysics of entanglement, volume 197, issue 10 (2020), edited by George Darby, is the single best place to start. Eight papers, and they talk to each other. The lead article is Jenann Ismael and Jonathan Schaffer, “Quantum holism: nonseparability as common ground” (4131–4160), which is free on Schaffer’s website and unusually well written: nonseparability is explained on the model of common-cause explanation, with entangled entities as scattered reflections of a more unified underlying reality. Also in the issue: Healey on a pragmatist view of the metaphysics of entanglement, Wallace on what realistic physics should teach metaphysicians, Miller’s “Two notions” above, and Ney on the macro-object problem.
What kind of relation is entanglement? This is the liveliest current dispute and it is genuinely three-sided. Claudio Calosi and Matteo Morganti, “Interpreting quantum entanglement: steps towards coherentist quantum mechanics,” British Journal for the Philosophy of Science 72 (2021): 865–891, propose coherentism: entangled systems stand in symmetric relations of ontological dependence, which is neither whole-before-parts holism nor relations-without-relata structuralism. Enrico Cinti, Alberto Corti and Marco Sanchioni, “On entanglement as a relation,” European Journal for Philosophy of Science 12 (2022): 10, argue it is an external relation among degrees of freedom, fully determined by mutual information — so the metaphysics should be read off a quantitative entanglement measure. Matías Pasqualini, “Quantum entanglement, internality and dependence,” European Journal for Philosophy of Science 16 (2026): 30, replies that it is internal, on a Finean essence-based analysis rather than a supervenience-on-intrinsics one, and that the internal reading stays neutral between the metaphysical options. Three papers, one argument, all recent: a very good thesis topic.
Isaac Wilhelm, “Intrinsicality and entanglement,” Mind 131 (2022): 35–58 — some QM. Free preprint on PhilSci-Archive. Valuable partly because Wilhelm is not a philosopher of physics: he shows that the Langton–Lewis account of intrinsicality classifies certain properties of entangled particles as intrinsic, while plausible duplication principles reclassify them as extrinsic. A dilemma for Lewis’s program generated from quantum mechanics.
What counts as a part? Matías Pasqualini and Sebastian Fortin, “Towards a tensor product structure-grounded mereology,” Entropy 28 (2026): 627 — mathematical, open access. Whether a state is entangled depends on a choice of tensor factorization, and the space of such factorizations has no canonical meet, so quantum parthood turns out non-extensional and decomposition-relative. This is a problem for anyone who wants entanglement to be a mind-independent relation between antecedently fixed relata, and it has not been absorbed by the metaphysics literature above.
Humeanism. Entanglement is standard-issue evidence against Humean supervenience. Harjit Bhogal and Zee Perry, “What the Humean should say about entanglement,” Noûs 51 (2017): 74–94, is the reply the later debate presupposes; Eddy Keming Chen, “From time asymmetry to quantum entanglement: the Humean unification,” Noûs 56 (2022): 227–255, free on the arXiv, folds the Past Hypothesis and the quantum state into the best system together.
Alyssa Ney, The World in the Wave Function: A Metaphysics for Quantum Physics (Oxford, 2021) — some QM. The fullest recent statement of wave function realism, and entanglement is what drives it: Ney’s argument is that moving to a field on a high-dimensional space lets you recover separability and locality, which she treats as theoretical virtues that the primitive-ontology and structuralist rivals must surrender. David Wallace’s review in Philosophical Review 131 (2022): 528–532, free on his website, is the sharpest response. Ney’s own “Three arguments for wave function realism,” European Journal for Philosophy of Science 13 (2023): 50, is open access, concessive about which arguments actually work, and the better assignment if you want one article rather than a book.
Two recent papers, both open access in Philosophy of Physics, on what is probably the most-hyped and least-examined claim in the area.
Emily Adlam, “How are entanglement entropies related to entropy bounds?” Philosophy of Physics 2 (2024): 9 — serious QM. The only serious philosophical treatment of entanglement entropy I know. Asks whether a universal entropy bound is epistemic or ontological in origin, and argues that area laws favour the epistemic reading.
Rasmus Jaksland, “Spacetime from entanglement: the emergence of metric, gravity, or topology,” Philosophy of Physics 3 (2025): 16 — serious QM. A corrective to the slogan, by someone who had previously argued for a strong version of it. The claim that spacetime emerges from entanglement conflates three different claims — about the bulk metric, about gravitational dynamics, and about topological connectivity — and determination fails for all three, while novelty holds only for the second. A metric emerging from a metric is not emergence. His earlier “Entanglement as the world-making relation,” Synthese 198 (2020): 9661–9693, is the strong version being retracted, and the two make an instructive pair.
There is, as far as I know, no book-length philosophical treatment of entanglement as such — as distinct from books on Bell’s theorem. The nearest is Bokulich and Jaeger, eds., Philosophy of Quantum Information and Entanglement (Cambridge, 2010). That gap is itself worth noticing.
Quantum nonlocality as a precise, quantifiable property of models was born with Bell’s theorem in 1964. The underlying phenomenon of entanglement had been identified thirty years earlier by Schrödinger and by Bohr, and was what Einstein, Podolsky and Rosen were exploiting. More has been established here than anywhere else in the subject: this is the one place where a philosophical dispute produced a theorem, the theorem produced experiments, and the experiments were decisive.
Read Bell himself first. Speakable and Unspeakable in Quantum Mechanics, 2nd ed. (Cambridge, 2004), with an introduction by Alain Aspect — some QM. Bell writes better than almost anyone in the field and the papers are short. Two in particular. “Bertlmann’s socks and the nature of reality” (1981) is his own entirely non-technical explanation of why the correlations cannot be explained the way Bertlmann’s mismatched socks can; it is freely available, and it is the best single thing to hand a student. “La nouvelle cuisine” (1990) is his last and most careful statement, where he defines local beables and gives the light-cone formulation of local causality. If you are going to argue about what Bell proved, argue about that paper and not about a textbook paraphrase of it. Travis Norsen, “John S. Bell’s concept of local causality,” American Journal of Physics 79 (2011): 1261–1275, is a line-by-line reconstruction of it pitched at physics undergraduates.
You will constantly read that Bell refuted “local realism,” and that we may therefore keep locality by giving up realism. A large part of the literature holds that this is a mistake, and the argument is worth following closely, because it is a case where getting the logic of a theorem right changes the metaphysics.
The case against the phrase: Bell’s theorem is the second half of a two-part argument whose first half is EPR. Given the perfect anticorrelations, locality entails the determinate values — so those values are a conclusion, not a premise, and there is no separate “realism” assumption available to jettison. What is refuted is locality, full stop.
Travis Norsen, “Against ‘realism’,” Foundations of Physics 37 (2007): 311–340 — some QM. Free on the arXiv. Goes through every candidate meaning of “realism” in the phrase — naive realism, scientific realism, counterfactual definiteness, hidden variables, determinism — and shows each fails as a reading of the second premise. Concludes that the phrase should be retired.
Tim Maudlin, “What Bell did,” Journal of Physics A 47 (2014): 424010 — some QM. Free on the arXiv. The sharpest statement of the two-part argument, from the special issue marking fifty years of the theorem.
The other side, in the same issue. Reinhard Werner’s “Comment on ‘What Bell did’” (424011) and Maudlin’s reply (424012); and Marek Żukowski and Časlav Brukner, “Quantum non-locality — it ain’t necessarily so” (424009). Werner and Żukowski–Brukner both hold that every derivation smuggles in a second premise, so that one may keep locality and drop classicality instead; on Werner’s operational definition of locality — local operations do not disturb distant states, only an observer’s conditional probabilities — quantum mechanics comes out perfectly local. Read the exchange rather than either side alone. Much of the disagreement is about whether the EPR step is sound, and much of the rest is about whether “local” should be defined causally, as Bell defined it, or operationally as no-signalling — with each side convinced the other has quietly changed the subject.
Howard Wiseman, “The two Bell’s theorems of John Bell,” J. Phys. A 47 (2014): 424001 — some QM. Free on the arXiv. Distinguishes Bell’s 1964 theorem, which assumes determinism plus parameter independence, from his 1976 theorem, which assumes local causality alone, and argues the two license different conclusions. The most useful diagnosis of why the parties talk past each other.
Bell’s factorizability condition is the conjunction of two logically independent conditions, and a student who does not have this distinction will misread most of the literature. Parameter independence says the probability of an outcome on one wing does not depend on the setting chosen on the far wing. Outcome independence says that, given the settings and the hidden state, the two outcomes are probabilistically independent of each other.
The distinction is diagnostic. Bohm’s theory violates parameter independence; GRW-type collapse theories, and orthodox quantum mechanics as usually read, violate outcome independence. The two sit quite differently with respect to relativity, which is the origin of Shimony’s phrase “peaceful coexistence.” The decomposition is due to Jon Jarrett, “On the physical significance of the locality conditions in the Bell arguments,” Noûs 18 (1984): 569–589, with the now-standard terminology from Abner Shimony. One caveat specialists insist on: parameter independence is not equivalent to no-signalling. Bohmian mechanics violates it and still cannot signal, because the hidden state is not controllable. For the argument that reading Bell through Jarrett’s decomposition distorts him, see Travis Norsen, “Local causality and completeness: Bell vs. Jarrett,” Foundations of Physics 39 (2009): 273–294.
Not that quantum mechanics was spooky. “Spooky action at a distance” is a phrase from a 1947 letter to Born, not a summary of an argument, and Einstein disliked the EPR paper itself — Podolsky drafted it, and Einstein complained to Schrödinger that the main point had been buried by the erudition.
Don Howard, “Einstein on locality and separability,” Studies in History and Philosophy of Science 16 (1985): 171–201 — no physics. Freely available. Separates two principles the popular story fuses. Separability: spatially separated systems each have their own real state, and the joint state is fixed by them — which is what makes it possible to individuate systems at all, and which Einstein took to be a precondition of any field theory. Locality: those states change only through effects propagating subluminally. Howard’s case is that Einstein’s fundamental objection was to giving up separability, and that his later and cleaner versions of the argument make this visible. The dilemma Einstein posed was: either quantum mechanics is incomplete, or separability fails.
Tim Maudlin, Quantum Non-Locality and Relativity 3rd ed. (Wiley-Blackwell, 2011) — some QM. The standard book on the question, and the best thing Maudlin has written. He argues that Bell establishes genuine superluminal causal dependence, then asks with unusual care what relativity actually forbids, taking the candidate prohibitions one at a time: superluminal signalling, superluminal information, superluminal causation, Lorentz invariance of the dynamics. The conclusion is that nonlocality and relativity are in tension but not in contradiction, since what is strictly forbidden is signalling, and quantum correlations deliver none. The third edition adds a chapter on Tumulka’s relativistic flash model, which violates Bell’s inequality without a preferred foliation, and on the Conway–Kochen free will theorem. It teaches the relativity it needs from scratch.
Aspect, Dalibard and Roger, “Experimental test of Bell’s inequalities using time-varying analyzers,” Physical Review Letters 49 (1982): 1804–1807, is the one everybody cites. The loopholes it left were closed in 2015 by three independent experiments — Hensen et al. in Nature 526: 682–686, using electron spins in diamond separated by 1.3 km, and Giustina et al. and Shalm et al., both in Physical Review Letters 115 (250401 and 250402). The 2022 Nobel Prize went to Aspect, Clauser and Zeilinger for this work. Since then, Storz et al., Nature 617 (2023): 265–270, have done a loophole-free test with superconducting circuits, which matters because the systems are massive. The freedom-of-choice loophole has been attacked from the other direction by the cosmic Bell tests, which take their measurement settings from starlight and from high-redshift quasars.
Bell’s inequality is a consequence of classical probability theory, so one might conclude that what its violation shows is that classical probability is false, and that locality survives. This reading is older and better than its current reputation, and I think there is still something in it.
Arthur Fine is the name to know. His “Hidden variables, joint probability, and the Bell inequalities,” Physical Review Letters 48 (1982): 291–295 — some QM — proves that five conditions on a correlation experiment are equivalent: there is a deterministic hidden-variable model; there is a factorizable stochastic model; there is a single joint distribution over all four observables returning the experimental probabilities; there are compatible joint distributions for all pairs and triples, commuting and non-commuting alike; and the Bell inequalities hold. Fine’s own gloss is the provocative part — that hidden variables and the Bell inequalities are “all about” forcing the existence of exactly those joint distributions for non-commuting observables “whose rejection is the very essence of quantum mechanics.” The mathematical companion is “Joint distributions, quantum correlations, and commuting observables,” Journal of Mathematical Physics 23 (1982): 1306–1310, which links the failure of joint distributions to failure of commutativity directly.
This was not a sudden thought. Fine had argued as far back as “Logic, probability, and quantum theory,” Philosophy of Science 35 (1968): 101–111, that quantum mechanics needs neither a non-classical logic nor a non-classical probability theory, only the recognition that its quantities are statistical variables lacking joint distributions — and that the condition for a joint distribution to exist reproduces the standard compatibility conditions. Nor was he alone in 1981–82: Patrick Suppes and Mario Zanotti, “When are probabilistic explanations possible?”, Synthese 48 (1981): 191–199, freely available, prove the three-variable version and the common-cause theorem behind it; and Luigi Accardi and A. Fedullo, “On the statistical meaning of complex numbers in quantum mechanics,” Lettere al Nuovo Cimento 34 (1982): 161–172, also free, give necessary and sufficient conditions for a Kolmogorovian model and point out that their result needs no locality assumption at all, since it applies to a single spin.
The algebraic version, which is where this gets sharp. If Fine is right that non-commutativity is what does the work, one would expect a theorem saying so, with no reference to locality or hidden variables. There is one. Consider two algebras of observables, and ask when some state is Bell-correlated across them. The answer is: exactly when neither algebra is commutative.
John Baez, “Bell’s inequality for C*-algebras,” Letters in Mathematical Physics 13 (1987): 135–136 — two pages, and free from his website — proves the easy half: if either algebra is abelian then every state is a limit of convex combinations of product states, and the CHSH inequality holds in every state. He noted the converse as open beyond type I, which is the case quantum field theory needs. G. A. Raggio, “A remark on Bell’s inequality and decomposable normal states,” Letters in Mathematical Physics 15 (1988): 27–29, supplied it: for a tensor product of von Neumann algebras, the inequality holds in all normal states if and only if one of the factors is commutative, if and only if every normal state is decomposable into product states. Guido Bacciagaluppi later gave the C*-algebra version (arXiv 2306.01909), and it is the cleanest statement to hand a student.
For commuting subalgebras of a common algebra rather than a tensor product, the corresponding result is L. J. Landau, “On the violation of Bell’s inequality in quantum theory,” Physics Letters A 120 (1987): 54–56, obtained independently by Stephen Summers and Reinhard Werner: two commuting non-abelian von Neumann algebras admit a state violating Bell’s inequality maximally, at the Tsirelson value. One caution worth passing on, because the literature is not consistent about it: this direction needs a mild independence hypothesis on the pair — the Schlieder property, which says a nonzero element of one algebra times a nonzero element of the other is nonzero. Without it there are counterexamples. In quantum field theory the hypothesis is free, since it holds for strictly spacelike separated regions.
The moral is the one Fine was reaching for, and it is worth making a student prove for themselves: Bell violation is not fundamentally about distance, or signalling, or even about two systems. It is about a pair of algebras neither of which is commutative. Where to read further: Summers, “Bell’s inequalities and algebraic structure” (arXiv funct-an/9701003) is fourteen free pages and the best compact account; his “Yet more ado about nothing: the remarkable relativistic vacuum state” (arXiv 0802.1854) is the readable one. The striking downstream fact is that in essentially any quantum field theory the vacuum is Bell correlated across every pair of spacelike separated regions, with the correlation decaying exponentially in mass times separation, and maximally correlated across complementary wedges.
On quantum probability generally. Guido Bacciagaluppi, “Quantum probability: an introduction,” in Hájek and Hitchcock, eds., The Oxford Handbook of Probability and Philosophy (Oxford, 2016) — some QM — is the survey to start from, and a fuller version is free on PhilSci-Archive; it is organized around precisely the non-existence of joint distributions for incompatible observables. Itamar Pitowsky, “Quantum mechanics as a theory of probability” (2006), free on the arXiv, is the manifesto version of the thesis; his Quantum Probability — Quantum Logic (Springer, 1989) and, more accessibly, “George Boole’s ‘conditions of possible experience’ and the quantum puzzle,” British Journal for the Philosophy of Science 45 (1994): 95–125, show that Bell-type inequalities are instances of Boole’s conditions of possible experience, which makes the geometry vivid. For the operator-algebraic background, Miklós Rédei and Stephen Summers, “Quantum probability theory,” Studies in History and Philosophy of Modern Physics 38 (2007): 390–417, free on the arXiv — demanding, but it supplies exactly what the theorems above presuppose.
The case against. Márton Gömöri and Carl Hoefer, “Classicality and Bell’s theorem,” European Journal for Philosophy of Science 13 (2023): 45 — open access — argue that probabilistic classicality is not an independent premise of the theorem but a corollary of locality together with the standard auxiliary assumptions, so that it cannot be isolated as the culprit in order to rescue locality. Read with Fine, this makes a self-contained unit, and a good one: two defensible readings of the same theorem, and a student who can say why they differ has understood Bell.
It is often said that a particle can be in two places at once. Quantum mechanics does not say this. It says that two systems can behave in ways that are hard to explain by treating them as separate individuals, which is a different and more interesting claim.
Myrvold, Genovese and Shimony, “Bell’s theorem,” in the Stanford Encyclopedia of Philosophy, is free, current and much more careful about all of the above than the older literature — it is explicit that calling Bell violations a refutation of “local realism” is “true but misleading.” Mary Bell and Shan Gao, eds., Quantum Nonlocality and Reality (Cambridge, 2016), is the best place to watch specialists disagree in one volume. Nicolas Gisin, Quantum Chance (Springer, 2014), is about 120 pages by a leading experimentalist and is the most accessible thing here. For the physics, Brunner, Cavalcanti, Pironio, Scarani and Wehner, “Bell nonlocality,” Reviews of Modern Physics 86 (2014): 419–478, free on the arXiv, is the standard review, organized around nonlocality as a resource rather than around the conceptual disputes; Scarani’s book, in the mathematical section below, is the gentler route into the same material.
This is the section the standard reading list does not have, and the reason I wrote this page.
There was no “Copenhagen interpretation” in the sense the textbooks describe — a unified doctrine of wavefunction collapse plus an observer — until the mid-1950s, when Heisenberg largely invented it and it was then taken up by critics who needed a monolith to argue against. Bohr’s own view contains neither collapse nor an observer. This is not a minority revisionist position; it is where the history has been for twenty years. You should know it before you read Albert or Maudlin, not after.
Don Howard, “Who Invented the ‘Copenhagen Interpretation’? A Study in Mythology,” Philosophy of Science 71 (2004): 669–682 — no physics. Thirteen pages, freely available online, and it will change how you read everything else. Start here.
Kristian Camilleri, “Constructing the Myth of the Copenhagen Interpretation,” Perspectives on Science 17 (2009): 26–57 — no physics. The companion piece: how the label got canonized, partly through Cold War exchanges with Soviet critics. Howard and Camilleri disagree about attribution, which is why reading both makes the point better than either alone.
Niels Bohr, the philosophical essays. Atomic Theory and the Description of Nature (1934), Atomic Physics and Human Knowledge (1958), and Essays 1958–1962 on Atomic Physics and Human Knowledge (1963) — no physics, but hard. Reprinted as volumes I–III of The Philosophical Writings of Niels Bohr (Ox Bow Press, 1987), with a fourth volume of supplementary papers edited by Faye and Folse (1998). For anything scholarly, cite the Collected Works (North-Holland, 1972–2008), especially volumes 6 and 7 on the foundations of quantum physics and volume 10 on complementarity beyond physics — the drafts and correspondence there are where the recent scholarship does its work. Bohr is genuinely difficult to read, and some of the difficulty is his fault. Do not let anyone tell you that means there is nothing there.
Slobodan Perović, From Data to Quanta: Niels Bohr’s Vision of Physics (Chicago, 2021) — some QM. The best recent book-length case for Bohr. The argument is that Bohr thought as an experimentalist, building upward from particular experimental arrangements to general hypotheses, and that what looks like vagueness is a method refusing to outrun the phenomena.
Jan Faye and Henry Folse, eds., Niels Bohr and the Philosophy of Physics: Twenty-First-Century Perspectives (Bloomsbury, 2017) — some QM. Sixteen essays, and the best single place to see what serious Bohr scholarship looks like now. Faye’s own Niels Bohr: His Heritage and Legacy (Kluwer, 1991) is the origin of the thesis that Harald Høffding was Bohr’s philosophical teacher — contested, and still the most interesting thing anyone has said about where Bohr’s philosophy came from.
Henrik Zinkernagel, “Niels Bohr on the wave function and the classical/quantum divide,” Studies in History and Philosophy of Modern Physics 53 (2016): 9–19 — some QM. Freely available. Reconstructs Bohr’s response to the measurement problem from correspondence, and argues the classical and the quantum stand in a relation of mutual dependence rather than reduction.
Kristian Camilleri and Maximilian Schlosshauer, “Niels Bohr as philosopher of experiment,” Studies in History and Philosophy of Modern Physics 49 (2015): 73–83 — some QM. Freely available. Answers the standard objection that decoherence refutes Bohr’s doctrine of classical concepts, by showing the doctrine was epistemological rather than dynamical all along.
Jeffrey Bub, “There is no quantum world” (arXiv 2512.18400) — some QM. Fifteen pages, free, and the most interesting recent attempt to state Bohr’s position in terms a modern reader can actually evaluate. Bub takes Bohr’s notorious remark as a thesis rather than an embarrassment, and reads “classical” as meaning Boolean: the move to quantum mechanics replaces a single Boolean algebra of propositions with a family of intertwined Boolean frames that cannot be embedded in any one of them — which is exactly what Gleason and Kochen and Specker establish. So “there is no quantum world” becomes a structural claim about the impossibility of a global assignment of truth values, rather than instrumentalism or an appeal to observers, and the Heisenberg cut comes out movable: nothing is permanently divided into a classical part and a quantum part. The measurement problem is then not solved but deflated, as a consequence of non-Booleanity rather than a defect to be repaired. Bub also retracts a position he held for thirty years, which is worth watching someone do. Forthcoming in Faye and Johansson, eds., How to Understand Quantum Mechanics.
Guido Bacciagaluppi and Antony Valentini, Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference (Cambridge, 2009) — serious QM. The full text is free on the arXiv (quant-ph/0609184), including a complete English translation of the 1927 proceedings. Read the primary documents and discover that the conference settled nothing, that de Broglie presented pilot-wave theory for many-body systems, and that the story of Copenhagen’s triumph at Solvay was written later.
Guido Bacciagaluppi and Elise Crull, The Einstein Paradox: The Debate on Nonlocality and Incompleteness in 1935 (Cambridge, 2024) — serious QM. The same treatment applied to EPR: the paper, Bohr’s reply, Schrödinger on separated systems, previously untranslated material by Heisenberg and by Grete Hermann, and the correspondence. Since so much of the received picture of Bohr rests on caricatures of his 1935 reply, this belongs next to Howard.
Olival Freire Jr., The Quantum Dissidents (Springer, 2015) — no physics. Why foundations work was disreputable for forty years and how it stopped being so. Explains, better than anything else, why the myth went unchallenged for so long.
Two books to read with resistance. Mara Beller’s Quantum Dialogue (Chicago, 1999) and Adam Becker’s What Is Real? (Basic, 2018) are both well written, both correct that the received account was manufactured, and both then install a replacement myth in which Bohr is a villain who silenced dissent. The archival evidence does not support it. Bohr would happily have renegotiated the philosophical questions into all eternity; that was his besetting vice, not his refusal. Becker in particular is what most students arrive having read, and Freire covers the same ground with archives instead of heroes.
Freire et al., eds., The Oxford Handbook of the History of Quantum Interpretations (Oxford, 2022). Fifty-one chapters, deliberately light on technicalities. Howard on the Copenhagen interpretation, Anja Skaar Jacobsen on Copenhagen and Bohr, and Osnaghi on Bohr’s epistemological lesson are the ones to start with.
There is more on this site under Niels Bohr.
Albert has a chapter on many worlds; it is his own reconstruction of a view that has been rebuilt from the ground up since. Do not form your opinion of Everett from it.
David Wallace, The Emergent Multiverse (Oxford, 2012) — serious QM. Still the definitive statement, and not an introduction: 548 pages, and it assumes you have had a quantum mechanics course. The three problems it addresses are what branching worlds are (decoherence does the work), what probability could mean when everything happens, and what follows. Whatever you conclude, the field’s terms of debate are now set here.
Simon Saunders, Jonathan Barrett, Adrian Kent and David Wallace, eds., Many Worlds? (Oxford, 2010) — serious QM. Proponents and critics in the same volume, which is rarer than it should be. Saunders’ long introduction is accessible on its own; Kent’s and Albert’s contributions are the sharpest objections in print. Many of the individual chapters are on the arXiv.
Lev Vaidman, “Many-worlds interpretation of quantum mechanics,” Stanford Encyclopedia of Philosophy — some QM. Free, current, and revised often; the fastest way to see the present state of the argument. Simon Saunders, “Branch-counting in the Everett interpretation of quantum mechanics,” Proceedings of the Royal Society A 477 (2021), is where the probability problem now stands.
Sean Carroll, Something Deeply Hidden (Dutton, 2019) — no physics. An advocacy book, and admits it. Useful as the Everettian case put attractively; useless as a map of the field.
Jean Bricmont, Making Sense of Quantum Mechanics (Springer, 2016) — some QM. Polemical and pedagogically excellent, with the clearest account I know of what Bell’s theorem does and does not establish — a point on which the popular literature is almost uniformly wrong.
Detlef Dürr and Dustin Lazarovici, Understanding Quantum Mechanics (Springer, 2020) — some QM. Short, and presents Bohm, GRW and Everett as the three realist options. The best recent undergraduate entry on this side.
Detlef Dürr and Stefan Teufel, Bohmian Mechanics (Springer, 2009) and Dürr, Goldstein and Zanghì, Quantum Physics Without Quantum Philosophy (Springer, 2012) — mathematical. The rigorous statements, including the quantum equilibrium argument that answers the question of where the Born rule comes from.
Daumer, Dürr, Goldstein and Zanghì, “Naive realism about operators,” Erkenntnis 45 (1996): 379–397 — some QM, free on the arXiv. Read this early, because it corrects the thing most students believe about Bohm’s theory: that it supplies hidden values for every quantity. It supplies one, position, and treats the operators as bookkeeping for what apparatus interactions produce. The mathematical section below says why the usual gloss on Kochen–Specker encourages the error.
Worth noticing about this school: their task is scientific rather than philosophical. The interesting question is whether Bohmian mechanics extends to the physics we actually have — to quantum field theory, and to relativity. Wallace argues it does not; that is a live and tractable dispute, and a good thesis subject.
Something has changed here since Albert wrote, and the philosophical literature has been slow to notice: GRW-type theories make predictions that differ from quantum mechanics, and people are now measuring them. Collapse is an experimental program.
GianCarlo Ghirardi, Sneaking a Look at God’s Cards rev. ed. (Princeton, 2007) — no physics. Book-length exposition by one of GRW’s authors.
Angelo Bassi, Mauro Dorato and Hendrik Ulbricht, “Collapse models: a theoretical, experimental and philosophical review,” Entropy 25 (2023): 645 — some QM. Open access, and unusual in treating the ontology question — matter density, flashes, wavefunction realism — alongside the experimental bounds. The place to start.
Bassi, Lochan, Satin, Singh and Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Reviews of Modern Physics 85 (2013): 471–527 — serious QM. The standard technical review. For current experimental status see Carlesso et al., Nature Physics 18 (2022): 243–250.
Albert and Maudlin between them leave out most of what is actually being argued about now.
Modal interpretations, and why they matter more than their current reputation suggests. Before 1995 “the modal interpretation” meant one of two things. Bas van Fraassen, who originated the approach and gave it its name, split the state description in two: a dynamical state that evolves unitarily and says only what may be the case, and a value state saying what actually is the case, with no rule taking you from the first to the second (Quantum Mechanics: An Empiricist View, Oxford, 1991, chapter 9 — some QM). Simon Kochen in 1985 and Dennis Dieks shortly after supplied the missing rule: take the biorthogonal decomposition of the state of a composite system, which is generically unique, and let the terms appearing in it fix which properties are definite — equivalently, diagonalize the reduced density matrix. No collapse, no observer, and the definite properties are a function of the state alone. Rob Clifton, “Independently motivating the Kochen–Dieks modal interpretation,” British Journal for the Philosophy of Science 46 (1995): 33–57, is the best statement of the case for it.
Then Jeffrey Bub and Rob Clifton showed that Kochen–Dieks is one species in a whole genus. “A uniqueness theorem for ‘no collapse’ interpretations of quantum mechanics,” Studies in History and Philosophy of Modern Physics 27 (1996): 181–219 — mathematical — proves that given a state and a choice of preferred observable, there is a unique maximal sublattice of propositions that can be assigned determinate truth values consistently with the Born probabilities. One free parameter, and everything else is forced. The simplified proof, with Sheldon Goldstein, is “Revised proof of the uniqueness theorem,” same journal, 31 (2000): 95–98, free on the arXiv; Goldstein had noticed that an auxiliary assumption in the original could simply be dropped, so the theorem is more general than first advertised. Read the 2000 paper first — it is four pages.
What makes this worth a student’s time is what the parameter does. Fix the preferred observable once and for all at the fundamental level and you get Bohm’s theory, with position in configuration space as the choice. Let the state fix it and you get Kochen–Dieks. And let it be fixed by the experimental context — by which classically described apparatus happens to be in place — and you get something that looks a great deal like Bohr. That last case is the interesting one: complementarity stops being a slogan and becomes a value of a parameter in a theorem, with the shifting of the preferred observable from one experimental arrangement to the next doing exactly the work Bohr wanted contexts to do. Bub develops the reading at length in Interpreting the Quantum World, in the mathematical section below. For the Bohr case specifically, Hans Halvorson and Rob Clifton, “Reconsidering Bohr’s reply to EPR,” in Placek and Butterfield, eds., Non-locality and Modality (Kluwer, 2002), 3–18, free on the arXiv and PhilSci-Archive, reconstructs the reply so that the elements of reality are the properties invariant under the symmetries preserving a measurement context. Fair warning: the Stanford Encyclopedia treats Bohr-as-modal-interpretation as Bub’s reconstruction rather than as straight exegesis, and van Fraassen’s review of Bub (Foundations of Physics 28, 1998, free on his website) argues the uniqueness is relative to the program rather than absolute. Both are worth reading against the claim.
Why the program stalled, which is instructive. The specific Kochen–Dieks rule ran into theorems, not merely objections. Guido Bacciagaluppi, “A Kochen–Specker theorem in the modal interpretation,” International Journal of Theoretical Physics 34 (1995): 1205–1216, shows that applying the rule to every factorization of the Hilbert space and demanding consistency yields a contradiction, so a preferred factorization has to be posited. Clifton’s own “The properties of modal interpretations,” BJPS 47 (1996): 371–398, presses the failure of property composition — the value assigned to a property of a subsystem need not match the value assigned to the corresponding property of the whole. And Wayne Myrvold, “Modal interpretations and relativity,” Foundations of Physics 32 (2002): 1773–1784, proves in considerable generality that no modal interpretation can be seriously Lorentz invariant at the fundamental level. The book-length assessment is Pieter Vermaas, A Philosopher’s Understanding of Quantum Mechanics: Possibilities and Impossibilities of a Modal Interpretation (Cambridge, 1999) — mathematical, and the “Impossibilities” in the title is not decoration. A research program with a clean formal statement, a beautiful uniqueness theorem, and a documented set of reasons for its decline is an unusually good thing for a student to study.
And what became of it. The relativity problem above is the hinge. If definite properties cannot be assigned absolutely across a foliation, relativize them to a perspective — which is what Joseph Berkovitz and Meir Hemmo proposed in “A new modal interpretation in terms of relational properties,” in Demopoulos and Pitowsky, eds., Physical Theory and its Interpretation (Springer, 2006), and what Gyula Bene and Dennis Dieks had already built in “A perspectival version of the modal interpretation of quantum mechanics and the origin of macroscopic behavior,” Foundations of Physics 32 (2002): 645–671. So the relational turn described next has a forgotten ancestor, and in part it is a repair strategy for the modal program rather than an independent invention. Dieks makes the claim himself, and in the open, in “Perspectival quantum realism,” Foundations of Physics 52 (2022): 95 — open access, and the best single thing to assign here: every single-world no-collapse interpretation that uses decoherence or diagonalization to pick out definite quantities, he argues, leads naturally to a relational picture. Mauro Dorato, “Bohr meets Rovelli,” Quantum Studies 7 (2020): 233–245, free on the arXiv, runs the other connection, from Bohr through dispositions to Rovelli. Olimpia Lombardi and Juan Sebastián Ardenghi, “How different interpretations of quantum mechanics can enrich each other,” Foundations of Physics 52 (2022): 64, is devoted to the relation between the two programs. And Bas van Fraassen, “Rovelli’s world,” Foundations of Physics 40 (2010): 390–417, is the originator of the modal interpretation assessing relational quantum mechanics at length, which is as good a way into the comparison as exists.
The survey is Olimpia Lombardi and Dennis Dieks, “Modal interpretations of quantum mechanics,” Stanford Encyclopedia of Philosophy, free and substantially revised in 2025 — though note that Dieks is both an author of the entry and the originator of one of the interpretations it surveys, so its optimism about the program’s health is not a neutral verdict. Much of the primary material is collected in one place in Quantum Entanglements: Selected Papers of Rob Clifton (Oxford, 2004), whose first part is the modal papers and whose chapter 12 is the Bohr reply.
Relational quantum mechanics. Rovelli’s proposal is that quantum states are relative to systems, not absolute — there are no facts simpliciter, only facts for something. Start with Carlo Rovelli, “Relational quantum mechanics,” International Journal of Theoretical Physics 35 (1996): 1637–1678 — some QM. The Stanford Encyclopedia entry is by Rovelli himself, which you should know while reading it. Then Andrea Di Biagio and Carlo Rovelli, “Stable facts, relative facts,” Foundations of Physics 51 (2021), and Emily Adlam and Carlo Rovelli, “Information is physical: cross-perspective links in relational quantum mechanics,” Philosophy of Physics 1 (2023) — where the view is amended to restore enough absoluteness for science to function, which is either a repair or a concession depending on your sympathies. Helgoland (2021) is the popular version and is advocacy.
QBism. What if the point of the quantum revolution is that physics should stop trying to say how things are? The view forces you to think hard about what a probability claim asserts about the world, and about objectivity and the aims of science. Bell would have called this a romantic interpretation, and he did not mean it kindly. Hans Christian von Baeyer, QBism: The Future of Quantum Physics (Harvard, 2016) is the only book-length introduction — no physics. Richard Healey’s Stanford Encyclopedia entry on Quantum-Bayesian and pragmatist views is the reliable survey.
Pragmatism. Richard Healey, The Quantum Revolution in Philosophy (Oxford, 2017) — some QM. Quantum theory as authoritative advice about claims stated in non-quantum language rather than as a description of the world. Shares features with Bohr, with Rovelli and with QBism, and is more carefully argued than any of them.
Wavefunction realism. The wavefunction is a real thing, living in a very high-dimensional space. Developed by Alyssa Ney and defended by Carroll; the anthology is Ney and Albert, eds., The Wave Function (Oxford, 2013), and Ney’s own book is discussed in the entanglement section above, since entanglement is what motivates the view. I have argued against it in print, in “To be a realist about quantum theory” — see publications.
Wigner’s friend, revived. Daniela Frauchiger and Renato Renner, “Quantum theory cannot consistently describe the use of itself,” Nature Communications 9 (2018): 3711 — open access — and Bong et al., “A strong no-go theorem on the Wigner’s friend paradox,” Nature Physics 16 (2020): 1199–1205. Serious QM. These results put real pressure on any view that makes facts observer-relative, which is why the relational and QBist literature has spent the last several years responding to them. Currently the liveliest corner of the subject.
An electron not in an eigenstate of spin-x has no determinate spin-x value. Everyone agrees on that much; it follows from the eigenstate–eigenvalue link. The question is what it means. Does the world contain an object that has a determinable property without any of its determinates — genuine indeterminacy out in the world, not in us — or does the electron simply lack the property altogether, the way the British Museum lacks a house number? Analytic metaphysicians have been arguing about this hard since 2019, mostly in metaphysics journals rather than philosophy-of-physics ones, which is why a student working from the standard reading list will never hear of it.
Where it starts. George Darby, “Quantum mechanics and metaphysical indeterminacy,” Australasian Journal of Philosophy 88 (2010): 227–245, and Bradford Skow, “Deep metaphysical indeterminacy,” Philosophical Quarterly 60 (2010): 851–858 — some QM, and Skow is free from his MIT page. Both argue that the then-standard account of metaphysical indeterminacy cannot handle quantum cases. On that account — due to Barnes and Williams — indeterminacy is not a feature of any first-order state of affairs; it consists in its being unsettled which of several fully precise ways the world might be is the actual one. The trouble is Kochen–Specker: contextuality means there is no suitable space of global precisifications to be unsettled between. Skow’s name for quantum cases, “deep” indeterminacy, has stuck. Note that this is the Kochen–Specker theorem doing metaphysical work, which is a good advertisement for the mathematical section below.
The proposal that revived the debate. Jessica Wilson’s determinable-based account locates indeterminacy at the object level instead: a state of affairs is indeterminate when an object has a determinable property without having any unique determinate of it (“A determinable-based account of metaphysical indeterminacy,” Inquiry 56 (2013): 359–385). No precisifications are needed, so the Darby–Skow objection does not arise, and classical logic and bivalence survive intact. Claudio Calosi and Wilson applied it to quantum mechanics in “Quantum metaphysical indeterminacy,” Philosophical Studies 176 (2019): 2599–2627 — some QM — distinguishing three sources of indeterminacy: superposition, incompatible observables, and entanglement. The sequel, “Quantum indeterminacy and the double-slit experiment,” Philosophical Studies 178 (2021): 3291–3317, is freely available and is the one to read first: a superposition of position states is a position state, determinable without a unique determinate, and the interference pattern follows without anything going through both slits and without revising logic.
The opposition. David Glick, “Against quantum indeterminacy,” Thought 6 (2017): 204–213 — free — presses the sparse view: a system with no eigenvalue lacks the determinable too, not just the determinate. He also argues that superpositions cannot play the determinable role, since their amplitudes give them weightings foreign to the determinable–determinate relation. Maria Nørgaard, “Quantum indeterminacy: a matter of degree?”, European Journal for Philosophy of Science 15 (2025): 13, open access, separates gradedness from indeterminacy and argues that treating quantum properties as intrinsically graded gets you out without committing to worldly indeterminacy. Tushar Menon, “On algebraic naturalism and metaphysical indeterminacy in quantum mechanics,” Studies in History and Philosophy of Science 105 (2024): 1–16, deflates from the algebraic side.
Where it has got to. Cristian Mariani, “The determinacy problem in quantum mechanics,” Foundations of Physics 54 (2024): 73 — open access — does the most useful thing anyone has done here, which is to separate the determinacy problem from the measurement problem and state it as three jointly inconsistent claims:
Each way of rejecting one maps onto a research programme — high dimensional realism, primitive ontology, and quantum indeterminacy respectively. This is the Maudlin trilemma’s counterpart for indeterminacy, and it does the same work of turning a muddle into a choice.
The rest of the recent wave sorts by interpretation, and all of it is free. David Glick and Baptiste Le Bihan, “Metaphysical indeterminacy in Everettian quantum mechanics,” European Journal for Philosophy of Science 14 (2024): 3, argues that none of the proposed Everettian sources of indeterminacy delivers it without extra metaphysical assumptions. Andrea Oldofredi, “Unexpected quantum indeterminacy,” same journal, 14 (2024): 15, has the best result in the group: pilot wave theories, supposedly the clean-ontology escape route, generate a distinctive modal indeterminacy of their own, so ontological clarity and indeterminacy turn out not to be exclusive. Patrick Fraser and Michael Miller, “From classical to quantum indeterminacy, and back,” Philosophy of Science 92 (2025): 1245–1255, is ten pages and teaches the crucial distinction: classical indeterminacy is shallow, since hidden variables resolve it, while Kochen–Specker makes the quantum case deep.
Two items connect this section to the two before it. Claudio Calosi and Cristian Mariani, “Quantum relational indeterminacy,” Studies in History and Philosophy of Modern Physics 71 (2020): 158–169, open access, argues that relational quantum mechanics and metaphysical indeterminacy support each other, and that relational quantum mechanics delivers indeterminacy that is fundamental rather than derivative. Calosi’s “Quantum modal indeterminacy,” Studies in History and Philosophy of Science 95 (2022): 177–184, also open access, runs the account inside a modal interpretation, where the split between dynamical state and value state is exactly a split between what is determinable and what is determinate. If the modal interpretation section above interested you, read that one.
Where to start, and what is missing. Claudio Calosi and Cristian Mariani, “Quantum indeterminacy,” Philosophy Compass 16 (2021): e12731, is the survey, it is free, and it is organized the way a student needs — is there quantum indeterminacy, what would it be, and how does it interact with each interpretation. Wilson’s Stanford Encyclopedia entry on determinables and determinates has a section on the quantum application, though she is a principal in the debate rather than a neutral surveyor. There is no encyclopedia entry on the topic itself. Alessandro Torza, Indeterminacy in the World (Cambridge Elements, 2023), is the nearest thing to a book.
And a gap worth pointing out to anyone looking for a thesis topic: none of this literature engages Bohr. The connection is sitting there unmade — complementarity enters the debate through the incompatible-observables source of indeterminacy, but never under Bohr’s name, and a framework in which a preferred observable fixes what is determinate is precisely what the Bohr reading of the uniqueness theorem provides. Someone should write that paper.
None of the introductory books above will tell you about the Kochen–Specker theorem, or Gleason’s theorem, or what a quantum logic is, or why anyone cares about C*-algebras. This is a real gap, and for a student with mathematical ability it is where the unclaimed problems are.
R. I. G. Hughes, The Structure and Interpretation of Quantum Mechanics (Harvard, 1989) — mathematical. Dated on interpretation — it predates everything in the Everett section above — and still not replaced for what it does: it builds the Hilbert space formalism from nothing, proves Gleason’s theorem in an appendix, works through Kochen and Specker, and devotes a chapter to quantum logic, all at a level a philosophy undergraduate can follow. Nothing published since does all four.
Klaas Landsman, Foundations of Quantum Theory: From Classical Concepts to Operator Algebras (Springer, 2017) — mathematical. Open access, 861 pages, and the modern reference: symmetry theorems, C*-algebras, the hidden-variable no-go results, classical limits, spontaneous symmetry breaking, and a closing chapter on topos theory. Assign yourself chapters, not the book. Landsman’s project is to take Bohr’s doctrine of classical concepts as a mathematical constraint rather than a slogan, which makes it the natural sequel to the Bohr section above.
Asher Peres, Quantum Theory: Concepts and Methods (Kluwer, 1993) — serious QM. The best bridge from a standard quantum mechanics course to the no-go literature. Chapter 7 on contextuality contains Peres’s own economical proof of Kochen–Specker.
Michael Redhead, Incompleteness, Nonlocality and Realism (Oxford, 1987) — mathematical. 191 pages, no padding. The taxonomy of locality conditions that the subsequent literature runs on was substantially fixed here.
Jeffrey Bub, Interpreting the Quantum World (Cambridge, 1997) — mathematical. Underrated, and the book I would most like students to know about. It is the book-length development of the uniqueness theorem discussed under modal interpretations above: one free parameter, and Bohm, Kochen–Dieks and Bohr all fall out as values of it. What the book adds to the theorem is the argument, worked out at length, that the interpretations form a structured space rather than a list, and that choosing one is choosing a determinate observable and nothing else. Worth noticing that Bohr is already inside the theorem in 1997, so the recent reconsideration above is a change of register rather than a conversion. Bananaworld (Oxford, 2016) is the same author making the information-theoretic case, with the algebra quarantined in marked sections at the ends of chapters.
Budroni, Cabello, Gühne, Kleinmann and Larsson, “Kochen–Specker contextuality,” Reviews of Modern Physics 94 (2022): 045007 — serious QM. Free on the arXiv (2102.13036). There is no monograph on contextuality; this is it.
A warning about how that theorem gets stated. You will constantly read that Kochen–Specker rules out non-contextual hidden variables. The phrase is accurate and its implicature is false. It suggests that contextual hidden variables are a going concern — that there is a theory over there which does assign values to all the quantities, only contextually. There is not, and there cannot be, because that is what the theorem forbids. Notice what a context is: a maximal set of compatible observables. So a contextual assignment gives an observable a value only relative to a context that contains it, and an observable incompatible with the context gets no value at all. Measure position, and momentum is not assigned some other, context-relative value. It is assigned nothing. There is no such thing as the value of momentum in a position measurement, and a theory that assigns values this way is therefore not a hidden-variable theory for all the quantities. It is a hidden-variable theory for some of them, and silent about the rest.
So what is a contextual hidden-variable theory? The best sense I can make of the notion is that it is a selection of beable subalgebras in Bub and Clifton’s sense: you choose which quantities are determinate, and the rest do not have values at all. That is not a hedged version of a hidden-variable theory. It is a different thing wearing the name, and the modal interpretation section above is where it actually belongs.
The mistake does real damage in the case of Bohm’s theory, which is described almost universally as a hidden-variable theory in the sense of supplying values for every quantity. It does not. It treats position as real and everything else — momentum included — as fictional: an artefact of an interaction with an apparatus, not a pre-existing property being revealed. See Daumer, Dürr, Goldstein and Zanghì, “Naive realism about operators,” Erkenntnis 45 (1996): 379–397 — some QM, free on the arXiv (quant-ph/9601013). Short, and the best cure there is for the habit of treating self-adjoint operators as though they named properties.
Valerio Scarani, Bell Nonlocality (Oxford, 2019) — mathematical. Open access, with exercises. Bell’s theorem done properly, then device-independent certification — self-testing, randomness, key distribution. The best answer to a student who asks what nonlocality is actually good for.
Laura Ruetsche, Interpreting Quantum Theories (Oxford, 2011) — mathematical. What happens to all of this in quantum field theory and quantum statistical mechanics, where unitarily inequivalent representations make the question of what the theory even says much harder. Read after Landsman’s early chapters.
On quantum logic. Beltrametti and Cassinelli, The Logic of Quantum Mechanics (1981, reissued by Cambridge) is the comprehensive reference; Dalla Chiara, Giuntini and Greechie, Reasoning in Quantum Theory (Kluwer, 2004) is the one written by logicians for logicians and the better choice if you are coming from a logic course; Varadarajan, Geometry of Quantum Theory (2nd ed., Springer, 1985) proves Gleason’s theorem and treats Wigner’s, and is graduate mathematics.
If your mathematics is not yet up to this, see the separate note on mathematics for philosophy.
A perennial question, and a good one for a student with logic training. In an infamous paper, Hilary Putnam argued that quantum mechanics requires a revision of logic (“Is logic empirical?”, 1968). Look at the replies on Google Scholar and you will find not only that many people argued against it but that Putnam eventually decided it was misguided. My own view is that the current consensus is right: nothing in quantum mechanics bears directly on the laws of classical logic. But the consensus has not always been that, and the question has recently reopened — see Saul Kripke, “The question of logic,” Mind 133 (2023), and Timothy Williamson, “Alternative logics and applied mathematics,” Philosophical Issues 28 (2018).
Tim Maudlin has written on this twice, and the later piece is the better one. “The tale of quantum logic” (2005) is the well-known polemic. “The labyrinth of quantum logic,” in Conant and Chakraborty, eds., Engaging Putnam (De Gruyter, 2022), 183–206, follows Putnam’s whole forty-year trajectory — from holding that a revision of classical logic would dissolve both the measurement problem and the two-slit phenomena, to abandoning quantum logic altogether in favour of theories using ordinary logic and probability. The moral Maudlin draws is general, and is the reason to assign it: trying to solve a physical problem by revising the mathematics or the logic is a strategy that tends not to work, and Putnam’s own change of mind is the best evidence for that.
Peter Gibbins, Particles and Paradoxes: The Limits of Quantum Logic (Cambridge, 1987) — mathematical. The formal subject without the drama, and much the best book on quantum logic for a philosopher: 181 pages, scrupulous about which claims are theorems and which are interpretation, and unusual in taking the technical literature and the philosophical dispute equally seriously. Long out of print and not much cited any more, which is a pity.
There are genuine technical questions here that nobody has answered: how quantum logic relates to substructural logics such as linear and relevance logic, and whether the frequently noticed parallels between quantum mechanics and intuitionistic logic can be made into a rigorous correspondence.
Physics students will meet decoherence and be told it solves the measurement problem. It does not, and the reason why is worth understanding precisely: decoherence explains why interference becomes unobservable, which is not the same as explaining why there is one outcome rather than many.
Maximilian Schlosshauer, “Quantum decoherence,” Physics Reports 831 (2019): 1–57 — serious QM. The current standard review, and it supersedes his own excellent book (Decoherence and the Quantum-to-Classical Transition, Springer, 2007) on experimental matters. Joos, Zeh et al., Decoherence and the Appearance of a Classical World 2nd ed. (Springer, 2003), is the harder reference.
The genre does not reward philosophical rigor, but a philosopher can learn a great deal from it, and the good ones are very good.
Nick Herbert, Quantum Reality (Anchor, 1985). Still the best written, and its taxonomy of “eight realities” is a genuine contribution. Dated, obviously.
Jim Baggott, Quantum Reality (Oxford, 2020). The direct successor to Herbert, confusingly sharing a title with it, and the most even-handed of the current crop.
Anil Ananthaswamy, Through Two Doors at Once (Dutton, 2018). The most neutral. Uses the double-slit experiment and its modern descendants as a thread through every interpretation, giving each a fair hearing.
Philip Ball, Beyond Weird (Chicago, 2018). The best prose, and historically careful, though the information-theoretic framing is a thesis rather than a neutral frame.
Tanya Bub and Jeffrey Bub, Totally Random (Princeton, 2018). An actual comic — hand-drawn, 250-odd pages — and it contains the clearest proof of Bell’s theorem I have seen given without mathematics. The main narrative sits below the level of a thesis student, but the endnotes carry real content and are where the value is.
Jim Baggott and John Heilbron, Quantum Drama (Oxford, 2024). The history done by people who read the sources. The corrective to Becker.
Carroll, Rovelli’s Helgoland and Becker are all position papers in popular dress. Read them as such.