Philosophy of quantum mechanics: interpretations (Copenhagen, Many-Worlds, Bohmian, QBism)

Intuition Beginner

Quantum mechanics is the most successful physical theory ever built. Its predictions match experiments to fourteen decimal places. Transistors, lasers, MRI machines, and atomic clocks all depend on it. Yet after a century of confirmation, what the theory means remains contested.

The puzzle is easiest to see in the double-slit experiment. Send electrons one at a time through two narrow slits. Each electron lands as a single dot on a screen — a particle. But after many electrons, the dots form a wave-like pattern of stripes. The electrons behave as both particles and waves.

Before measurement, a quantum system exists in a "superposition" of all possible states, described by the wave function. When measured, it "collapses" into one definite state. But what counts as a measurement? What causes the collapse? This is the measurement problem.

The Copenhagen interpretation (Bohr, Heisenberg) says: don't ask. The wave function is just a tool for predicting outcomes. Measurement is a primitive concept — it needs no deeper explanation. The theory works; leave it at that.

The Many-Worlds interpretation (Everett, 1957) says: there is no collapse. Every possible outcome happens, each in a separate branch of reality. Every time you measure, the universe splits. You observe one outcome; copies of you observe the others.

David Bohm's pilot-wave theory says particles always have definite positions, guided by the wave function. No collapse, no splitting — but the guiding influence acts instantaneously across any distance, faster than light.

Bell's theorem (1964) proved that no local hidden-variable theory can reproduce quantum predictions. Aspect (1982), Hensen (2015), and the 2022 Nobel Prize confirmed it. Reality is nonlocal: distant systems are correlated in ways no classical picture allows.

Visual Beginner

Picture four interpretations lined up against the same experiment — an electron fired at a detector. Copenhagen: before observation the electron has no definite position; the act of looking forces nature to pick one. Many-Worlds: the electron takes every possible path, and so do you, splitting into branch after branch. Bohmian: the electron always had one definite trajectory, guided by an invisible wave that reaches everywhere at once. QBism: the wave function lives in your head, a catalogue of what you should expect.

Each panel answers the same question — what is the wave function, and what happens when we measure? — with a radically different picture of reality.

Worked example Beginner

A single electron is prepared and sent through a Stern-Gerlach apparatus, which splits its path into "spin-up" and "spin-down" branches. The electron's state is a superposition: equal weights of up and down. A detector sits in each branch.

Under Copenhagen, the moment the electron hits a detector, the wave function collapses. One detector fires; the other does not. The collapse is real but unexplained. Why one branch and not the other? Random — a primitive fact.

Under Many-Worlds, both detectors fire. Each fires in its own branch of reality. Two versions of you, one seeing the top detector flash, one seeing the bottom. The split becomes irreversible once decoherence scrambles the branches.

Under Bohmian mechanics, the electron was always heading to one specific detector. Its position is fixed by the guiding wave, which itself evolves exactly as in standard quantum mechanics. The outcome looks random only because we do not know the initial position.

Under QBism, the wave function is the experimenter's personal belief about where the electron will land. The Born rule tells them how to bet. When a detector fires, the agent updates their beliefs — that is the "collapse".

Check your understanding Beginner

Formal definition Intermediate+

An interpretation of quantum mechanics is a proposal about what the theory is about — what ontology it posits and what dynamics it attributes to the world. The formalism is fixed: a Hilbert space $\mathcal{H}$, a state $|\psi ⟩\in \mathcal{H}$ evolving unitarily via the Schrödinger equation $i\hslash {\partial }_t|\psi (t)⟩=H|\psi (t)⟩$, observables as self-adjoint operators, and the Born rule $p(a)=⟨\psi |P_a|\psi ⟩$ for the probability of outcome $a$. What varies across interpretations is the answer to: what in the world corresponds to $|\psi ⟩$?

$\psi$-ontic vs. $\psi$-epistemic. Following Harrigan-Spekkens ^{[Harrigan Spekkens 2010]}, an interpretation is $\psi$-ontic if two distinct pure states always correspond to distinct ontic states of the world. Many-Worlds, Bohmian mechanics, and GRW are $\psi$-ontic. An interpretation is $\psi$-epistemic if the same ontic state can be compatible with multiple pure states — the wave function represents an agent's information. Copenhagen, QBism, and the Bub-Pitowsky information-theoretic view are $\psi$-epistemic. The distinction matters because $\psi$-epistemic interpretations dissolve the measurement problem by denying that the wave function was ever the kind of thing that had to collapse.

The Eigenstate-Eigenvalue Link (EEL). Standard QM says: a system has a definite value $a$ for observable $A$ if and only if its state is an eigenstate of $A$. The EEL is what makes superpositions exotic — a system in $(|a_1⟩+|a_2⟩)/\sqrt{2}$ has no definite $A$-value. Interpretations differ in how they handle the link. Bohmian mechanics keeps position always definite via the hidden configuration, even when the wave function is in superposition; other observables become contextual. Everett relativises definiteness to branches: each branch is an eigenstate of the recorded outcome. Epistemic views treat the EEL as a constraint on an agent's beliefs, not on reality.

The interpretation trilemma. Any interpretation must sacrifice at least one of three commitments: (i) unitary-only evolution of the wave function, (ii) definite single outcomes for every measurement, (iii) the universal validity of quantum mechanics (no special "measurement" cut). GRW sacrifices (i) by modifying the dynamics. Everett sacrifices (ii) by embracing branching. Copenhagen sacrifices (iii) by leaving "measurement" as a primitive. Bohmian mechanics keeps (i) and (ii) but adds particle positions to the ontology, modifying what "the quantum state" describes. The empirical predictions are preserved; what changes is the metaphysics.

Counterexamples to common slips

• "Bell's theorem disproves hidden variables." It disproves local hidden-variable theories satisfying measurement independence. Bohmian mechanics is a hidden-variable theory that survives Bell's theorem by accepting nonlocality. The theorem constrains the structure of hidden-variable theories; it does not abolish them.

• "Decoherence solves the measurement problem." Decoherence (Zurek) explains why interference between macroscopically distinct branches is suppressed — but it does not produce a single outcome. The post-decoherence state is still a superposition; it merely looks classical when traced over the environment. Decoherence is necessary for any interpretation but not sufficient as a solution.

• "QBism is just instrumentalism." QBism is a more specific claim: quantum states are personal degrees of belief governed by the Born rule as a normative constraint. Instrumentalism is the broader view that theories are tools for prediction; QBism accepts this but adds a substantive account of what the tool tracks (an agent's experiences).

Key argument — Bell's theorem and the interpretation trilemma Intermediate+

Bell's 1964 theorem ^{[Bell 1964]} is the cleanest philosophical argument that yields a sharp empirical constraint. It shows that no theory satisfying three plausible premises can reproduce the quantum-mechanical predictions for entangled particles. The argument converts a conceptual dispute (Einstein vs. Bohr on completeness) into an experimental question.

Setup. Two spin-1/2 particles are prepared in the singlet state and separated. Alice measures spin along axis $\vec{a}$; Bob measures along axis $\vec{b}$. Outcomes are $\pm 1$. Quantum mechanics predicts the correlation $E_{\text{QM}}(\vec{a},\vec{b})=-\vec{a}\cdot \vec{b}$.

Premises of a local hidden-variable theory.

• (P1) Realism. Each particle carries definite properties encoded in a hidden variable $\lambda$, prior to and independent of measurement. The outcomes of any possible measurement are determined by $\lambda$ and the measurement setting.

• (P2) Locality. Alice's outcome depends only on her local setting $\vec{a}$ and $\lambda$; Bob's only on $\vec{b}$ and $\lambda$. Formally, $A(\vec{a},\lambda )\in \{+1,-1\}$ and $B(\vec{b},\lambda )\in \{+1,-1\}$, with no $\vec{b}$ dependence in $A$ and no $\vec{a}$ dependence in $B$.

• (P3) Measurement independence. The distribution $\rho (\lambda )$ is statistically independent of the settings $\vec{a},\vec{b}$. The experimenter's choice is not correlated with the hidden variables.

Derivation. Under (P1)–(P3), the joint correlation is

$$E_{\text{LHV}}(\vec{a},\vec{b})=\int A(\vec{a},\lambda )B(\vec{b},\lambda )\rho (\lambda )d\lambda .$$

A short combinatorial argument using $A,B\in \{+1,-1\}$ yields the CHSH inequality

$$|E(\vec{a},\vec{b})-E(\vec{a},{\vec{b}}^{\prime })+E({\vec{a}}^{\prime },\vec{b})+E({\vec{a}}^{\prime },{\vec{b}}^{\prime })|\le 2.$$

Choosing axes at angles of $\pi /4$ apart gives the quantum value $2\sqrt{2}$ — a clear violation.

Empirical verdict. Aspect (1982), Hensen et al. (2015), and the 2022 Nobel Prize experiments confirm the violation with overwhelming statistical significance. At least one premise must fail.

Who pays which price. Bohmian mechanics keeps (P1), rejects (P2): the guiding wave is explicitly nonlocal. Everett keeps locality in the sense of no superluminal signalling, but rejects the single-outcome assumption needed to set up the correlation. Superdeterminism (Hossenfelder, 't Hooft) keeps locality and realism, rejects (P3): the hidden variables and the settings share common causes in the past. No interpretation is forced by the data alone; each pays a price, and the disagreement is about which price is tolerable.

Exercises Intermediate+

Copenhagen, Many-Worlds, and Bohmian mechanics in depth Master

The Copenhagen interpretation is not a single view but a family. Bohr's version centres on complementarity: wave and particle descriptions are mutually exclusive but both necessary for a complete account. Heisenberg stressed potentiality versus actuality — quantum systems harbour possibilities that measurement actualises. Wheeler's later "participatory universe" made the observer partly constitutive of reality. What unites the family is instrumentalism: the wave function is a tool for prediction, not a representation of a mind-independent state. Bell's "Against 'measurement'" (1990) ^{[Bell 1990]} is the canonical critique — a fundamental theory should not have "measurement" as an undefined primitive. The vagueness of where the quantum-classical cut falls is the standing complaint.

The Many-Worlds interpretation (Everett 1957) ^{[Everett 1957]} denies collapse. The universal wave function evolves unitarily; every outcome in a superposition is realised in a separate branch. DeWitt's "many-worlds" branding made the view famous; Everett's own "relative state" formulation is more cautious and is closer to the contemporary Saunders-Wallace programme. Decoherence (Zurek) ^{[Zurek 2003]} explains why branches do not interfere: environmental coupling rapidly suppresses cross-branch coherence. The appearance of collapse is recovered.

The standing problem is probability. If all outcomes happen, what does it mean to assign probability $1/2$ to one branch? The Deutsch-Wallace decision-theoretic programme derives the Born rule from axioms of rational preference in a multiverse ^{[Wallace 2012]}. Saunders and Wallace apply "Ockham's razor" to ontology (one universal wave function) rather than to universes. Carroll has become a vocal contemporary defender. Critics (Maudlin, Kent) charge that approximate branching cannot ground definite outcomes and that the probability derivation is circular. The Saunders-Wallace reply reframes the dispute: the Born rule is a constraint on rational agents embedded in a branching structure, not a frequency claim about world-counts.

Bohmian mechanics (de Broglie 1927, Bohm 1952) ^{[Bohm 1952]} adds particle positions to the wave function. Particles always have definite trajectories, guided by the wave function via the "quantum potential". The theory is explicitly nonlocal: the velocity of each particle depends instantaneously on every other particle's position, however distant. Bell championed the theory as the strongest hidden-variable model and as proof that "hidden variables" are consistent with QM. Its empirical predictions match standard QM exactly when the initial distribution satisfies quantum equilibrium (the Born rule). Valentini's subquantum H-theorem explains how equilibrium is approached. The main cost is a fundamental tension with relativity, since the dynamics picks out a preferred foliation of spacetime. Dürr, Goldstein, and Zanghì have developed the contemporary "primitive ontology" programme.

Maudlin's diagnostic in Quantum Non-Locality and Relativity ^{[Maudlin 2011]} sharpens the interpretive choice. The Bell experiments rule out local realism. Any interpretation must accept one of three options: many-worlds (no single outcome), Bohmian (explicit nonlocality), or collapse (modified dynamics). Each pays a price; the dispute is about which price is acceptable, not about whether a price must be paid. No interpretation is currently empirically distinguishable from QM-as-standardly-used, so the choice is partly metaphysical and partly aesthetic.

Objective collapse, consistent histories, modal interpretations Master

Objective collapse theories modify the Schrödinger equation to produce real, physical collapse. The GRW theory (Ghirardi-Rimini-Weber 1986) ^{[GRW 1986]} gives each particle a small probability per unit time of spontaneously localising; for macroscopic objects with $10^{23}$ particles, collapse is effectively instantaneous. The continuous spontaneous localisation (CSL) model refines this into a stochastic field equation. Penrose proposes that gravity induces collapse: a superposition becomes unstable once the mass-energy difference is large enough to curve spacetime meaningfully. The attractions are an objective single outcome and a definite ontology (mass-density in GRW; a "flash" ontology on Bell's reading). The theory is falsifiable: it predicts small deviations from standard QM at mesoscopic scales. Tumulka has constructed relativistic versions of GRW.

The standing worry is energy non-conservation: the collapse mechanism injects a small amount of energy on each localisation event. Defenders reply that the effect is far too small to be observed and is the price of having a real physical collapse. Pearle's CSL and Diósi's gravity-inspired model address related concerns. The interpretive benefit is that the measurement problem is solved rather than dissolved: collapse is a dynamical process in the theory, not an external postulate. The cost is that the theory is no longer pure quantum mechanics — it makes predictions that differ at scales not yet probed.

Consistent histories (Griffiths, Omnes, Gell-Mann-Hartle) applies the rules of quantum mechanics to closed systems, including the universe as a whole. A "history" is a sequence of events at different times. Sets of histories that satisfy a decoherence condition can be assigned classical probabilities; sets that fail the condition cannot be combined. The framework recovers quasi-classical reality without collapse. The central difficulty is the set-selection problem: many decoherent history sets exist, and the framework does not say which corresponds to "what really happens". Wojciek Zurek's quantum Darwinism addresses a piece of this: the environment acts as a witness, redundantly encoding pointer-state information so that multiple observers agree on classical properties.

Modal interpretations (van Fraassen, Vermaas, Dieks) propose that a system has definite values for some observables — those picked out by its state via a specified rule — even when not all observables have definite values. The eigenstate-eigenvalue link is relaxed: definiteness extends beyond eigenstates. Bub and Clifton develop lattice-theoretic versions that pick out the value-definite properties algebraically. The interpretations sit between Bohmian mechanics (which always makes position definite) and Many-Worlds (which makes everything branch-relative). Their main challenge is stability: the set of definite properties can change discontinuously under smooth evolution, which strains the metaphysics. Dickson has explored the relationship between modal interpretations and determinism.

QBism, relational QM, and quantum information Master

QBism (Fuchs, Mermin, Schack) ^{[Fuchs Mermin Schack 2014]} reads the wave function as an agent's personal probability assignment, governed by the Born rule as a normative constraint on quantum bets — analogous to the Dutch book argument for ordinary probability theory. "Quantum states do not exist" in the mind-independent sense; they live in the agent's head. Measurement is the agent's interaction with the world; outcomes are the agent's experiences. Mermin's "I-thou" framing radicalises this: the world is made of experiences, and the quantum state codifies my beliefs about your future experiences. QBism dissolves the measurement problem at the cost of an explicitly first-person metaphysics.

Critics charge that QBism makes reality too private — if quantum states are agent-relative, what grounds the intersubjective agreement that experiments seem to deliver? Defenders reply that agreement is recovered through shared evidence and the Born rule's normative force: any rational agent observing the same data is constrained to assign the same probabilities. The debate between subjectivist and realist readings of QBism remains live. Healey's pragmatist interpretation is an allied view: quantum theory is a tool for prediction, not a description of a mind-independent reality. The Caves-Fuchs-Schack programme treats quantum probabilities as personal in the strict Bayesian sense, with the Born rule emerging as a consequence of consistency constraints on an agent's beliefs.

Relational quantum mechanics (Rovelli 1996) ^{[Rovelli 1996]} holds that a system has no absolute state — only states relative to other systems. The partial-trace operation that extracts a subsystem's state is not a mathematical convenience but a reflection of a deep relationalism: the "state of $S$" is always "the state of $S$ relative to some other system $O$". Different observers can assign different states to the same system, and all are correct. The view has affinities with QBism but is realist in spirit: the relational structure is mind-independent. Critics ask what the world is made of if not states; Rovelli answers that it is made of relations, not relata. Laudisa presses the question of how dynamical laws apply across relational transitions.

Quantum information reframes foundational questions in terms of information flow. The EPR paper (1935) argued that quantum entanglement implies the theory is incomplete — that there must be "elements of reality" missing from the description. Bohr's reply defended complementarity and wholism. Bell's theorem converted this conceptual worry into an experimental question, settled against local hidden variables. Schrödinger called entanglement "the characteristic trait of quantum mechanics". The subsequent rise of quantum information theory (qubits, teleportation, superdense coding, BB84 cryptography, Ekert's entanglement-based protocol) gave the field a new vocabulary. Zeilinger has proposed information as a foundational principle.

Deutsch's work on quantum computing, Shor's algorithm, and the 2019 Google quantum-supremacy experiment (Arute et al.) made the practical stakes of foundational questions tangible. Decoherence and classical emergence are studied through Zurek's einselection programme; Caslav Brukner and Zeilinger have pushed the experimental boundary by interfering large molecules such as C60 buckyballs (Arndt et al.). The classical-quantum transition is no longer a fixed line but a moving experimental frontier. The Kochen-Specker theorem and the Mermin-Peres magic square show that contextuality — the dependence of a measurement outcome on the full experimental context — is the resource powering quantum advantage.

Spacetime, quantum field theory, and quantum gravity Master

Spacetime from entanglement. A recent research programme treats spacetime as emergent from quantum entanglement. Van Raamsdonk's 2010 argument shows that the connectivity of spacetime in AdS/CFT corresponds to the entanglement structure of the boundary field theory. The ER=EPR conjecture (Maldacena-Susskind) proposes that entangled particles are connected by microscopic wormholes (Einstein-Rosen bridges). The Ryu-Takayanagi formula relates the area of a boundary region in the bulk to the entanglement entropy of the corresponding boundary region. If spacetime is built from entanglement, the interpretation of quantum mechanics becomes inseparable from the philosophy of spacetime — connecting this unit forward to 20.03.03 pending.

Time and quantum cosmology. The Wheeler-DeWitt equation — the "wave function of the universe" — has no time parameter. The problem of time asks how the familiar passage of time emerges from a timeless fundamental equation. The Page-Wootters mechanism proposes that time is a pattern in correlations between subsystems; the universe as a whole is timeless, but interior observers see temporal change. Quantum cosmology forces a choice: do we apply quantum mechanics to the universe as a whole (and accept the loss of an external observer), or is QM inherently about subsystems measured from outside?

Philosophy of quantum field theory. Wallace's "In Defence of Naiveté" argues that the Lagrangian QFT used by working physicists is conceptually unproblematic, despite Haag's theorem and the inequivalent representations of algebraic QFT. Doreen Fraser presses the algebraic case, arguing that the particle concept is observer-dependent (the Unruh effect) and that the Malament theorem shows there is no well-defined particle concept in curved spacetime. Spontaneous symmetry breaking, the Higgs mechanism, and renormalisation group flow raise their own philosophical questions about reduction and emergence. See 33.05.02 pending for the philosophy of QFT proper.

Philosophy of quantum gravity. The attempt to unify quantum mechanics with general relativity raises foundational questions of its own. Butterfield, Crowther, Rickles, and Huggett have written on the conceptual structure of string theory, loop quantum gravity (Rovelli, Smolin, Ashtekar), and the problem of what spacetime is at the Planck scale. The Bekenstein bound, black-hole thermodynamics, and the information-loss paradox (Hawking 1976) all turn on interpretive questions about quantum information. See 20.03.03 pending and 28.04.04 pending for the philosophy of spacetime and quantum gravity in more detail.

Connections Master

• Measurement problem 20.03.01 is the direct prerequisite. The four interpretations developed here are direct responses to the trilemma formulated there: Copenhagen rejects universal validity, GRW rejects unitary-only evolution, Everett rejects single outcomes, Bohmian adds hidden variables. The hook is bidirectional: 20.03.01 already declares a proposed hook to 20.03.02 as the natural interpretive extension.

• Spacetime philosophy 20.03.03 pending (pending, proposed successor) takes up the spacetime side of the questions raised here — emergent spacetime, the problem of time, the ER=EPR programme. The proposed hook out from this unit reflects that QM philosophy connects to broader issues of space, time, and reality.

• Consciousness 20.06.01 (pending) connects via the Wigner-von Neumann strand of Copenhagen where consciousness triggers collapse. Most interpretations reject this, but the historical and conceptual link remains.

• Scientific realism 20.07.01 (pending) — multiple QM interpretations are the canonical case of empirically equivalent rivals making incompatible ontological claims. The realism debate uses QM as its primary test case.

• Quantum gravity 28.04.04 pending (pending) is referenced in the master section on emergent spacetime and AdS/CFT. The interpretation of QM becomes entangled with the interpretation of spacetime at the Planck scale.

• Philosophy of QFT 33.05.02 pending (pending) extends the interpretive questions from non-relativistic QM to quantum field theory, where the particle concept becomes observer-dependent and Haag's theorem complicates the formalism.

Cross-domain to epistemology 20.01.01: QBism invokes first-person epistemic notions of belief, evidence, and Bayesian rationality that connect directly to the epistemology tradition. Cross-domain to phil-of-mind 20.06.01: the consciousness-causes-collapse hypothesis and the "participatory universe" view import phil-of-mind commitments into phil-of-physics.

Historical and philosophical context Master

The foundational period (1925–1935) established quantum mechanics in two parallel formalisms: Heisenberg's matrix mechanics and Schrödinger's wave mechanics, shown equivalent by von Neumann (1932). Bohr's Como lecture (1927) introduced complementarity as the official "Copenhagen" line, defended through decades of debate with Einstein at the Solvay Conferences (1927, 1930). The EPR paper (1935) ^{[EPR 1935]} argued that quantum mechanics must be incomplete if locality and certain "elements of reality" are granted; Bohr's reply defended complementarity and wholism. Schrödinger's cat paper (1935) made the macroscopic-superposition problem vivid. The exchange did not settle anything; it established the form of the dispute.

The 1950s broke the Copenhagen monopoly. Bohm's 1952 papers revived de Broglie's 1927 pilot-wave theory in fully developed form, proving hidden-variable theories were viable. Everett's 1957 thesis proposed the relative-state formulation, later popularised as "many-worlds" by DeWitt in the 1970s. Both developments showed that the Copenhagen insistence on a classical-quantum cut was not forced by the formalism.

Bell's 1964 theorem ^{[Bell 1964]} is the watershed. Bell showed the EPR-Bohr dispute could be made empirically tractable: a particular kind of correlation predicted by QM was unavailable to any local hidden-variable theory. Kochen and Specker (1967) added the contextuality theorem, ruling out noncontextual value assignments in dimension 3 and above. Aspect's experiments (1981, 1982) confirmed the Bell-violation predictions; the loophole-free experiments of Hensen et al. (2015) and others settled the empirical question. The 2022 Nobel Prize (Aspect, Clauser, Zeilinger) ratified the result publicly.

The decoherence programme began with Zeh (1970) and was developed by Zurek through the 1980s and 1990s. Joos-Zeh and later Schlosshauer's textbook consolidated the framework. GRW (1986) initiated the objective-collapse programme; Pearle's CSL and Tumulka's relativistic refinements followed. The contemporary Everettian programme (Saunders, Wallace, Greaves, Carroll) integrates decoherence and decision theory; the contemporary QBist programme (Fuchs, Mermin, Schack) reframes quantum states as personal beliefs. Rovelli's relational QM (1996) opened a separate information-theoretic thread.

The 21st century has seen the information-theoretic turn. Quantum computing (Deutsch, Shor), quantum cryptography (BB84, Ekert), and quantum supremacy experiments (Arute et al. 2019) made foundational questions practically consequential. The AdS/CFT correspondence and the ER=EPR programme have linked entanglement to spacetime geometry. The phil-of-physics literature is now a mature subfield, centred in Studies in History and Philosophy of Modern Physics, Foundations of Physics, and British Journal for the Philosophy of Science, with the Philsci-Archive at Pittsburgh hosting an open-access preprint collection.

Bibliography Master

1. Bell, J. S. — "On the Einstein-Podolsky-Rosen paradox", Physics 1, 195–200 (1964).

2. Bell, J. S. — Speakable and Unspeakable in Quantum Mechanics, 2nd ed. (Cambridge University Press, 2004).

3. Bell, J. S. — "Against 'measurement'", Physics World 3 (8), 33–40 (1990).

4. Everett, H. — "'Relative state' formulation of quantum mechanics", Rev. Mod. Phys. 29, 454–462 (1957).

5. Bohm, D. — "A suggested interpretation of the quantum theory in terms of 'hidden' variables", Phys. Rev. 85, 166–179, 180–193 (1952).

6. Einstein, A., Podolsky, B. & Rosen, N. — "Can quantum-mechanical description of physical reality be considered complete?", Phys. Rev. 47, 777–780 (1935).

7. Schrödinger, E. — "Die gegenwärtige Situation in der Quantenmechanik", Naturwissenschaften 23, 807–812, 823–828, 844–849 (1935).

8. von Neumann, J. — Mathematical Foundations of Quantum Mechanics (Princeton University Press, 1955; orig. Springer, 1932).

9. Wheeler, J. A. & Zurek, W. H. (eds.) — Quantum Theory and Measurement (Princeton University Press, 1983).

10. Kochen, S. & Specker, E. P. — "The problem of hidden variables in quantum mechanics", J. Math. Mech. 17, 59–87 (1967).

11. Ghirardi, G. C., Rimini, A. & Weber, T. — "Unified dynamics for microscopic and macroscopic systems", Phys. Rev. D 34, 470–491 (1986).

12. Pearle, P. — "Combining stochastic dynamical state-vector reduction with spontaneous localization", Phys. Rev. A 39, 2277–2289 (1989).

13. Penrose, R. — "On gravity's role in quantum state reduction", Gen. Rel. Grav. 28, 581–600 (1996).

14. Tumulka, R. — "A relativistic version of the Ghirardi-Rimini-Weber model", J. Stat. Phys. 125, 821–840 (2006).

15. Aspect, A., Dalibard, J. & Roger, G. — "Experimental test of Bell's inequalities using time-varying analyzers", Phys. Rev. Lett. 49, 1804–1807 (1982).

16. Hensen, B. et al. — "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres", Nature 526, 682–686 (2015).

17. Zurek, W. H. — "Decoherence, einselection, and the quantum origins of the classical", Rev. Mod. Phys. 75, 715–775 (2003).

18. Fuchs, C. A., Mermin, N. D. & Schack, R. — "An introduction to QBism with an application to the locality of quantum mechanics", Am. J. Phys. 82, 749–754 (2014).

19. Rovelli, C. — "Relational quantum mechanics", Int. J. Theor. Phys. 35, 1637–1678 (1996).

20. Maldacena, J. & Susskind, L. — "Cool horizons for entangled black holes", Fortschr. Phys. 61, 781–811 (2013).

21. Van Raamsdonk, M. — "Building up spacetime with quantum entanglement", Gen. Rel. Grav. 42, 2323–2329 (2010).

22. Albert, D. Z. — Quantum Mechanics and Experience (Harvard University Press, 1992).

23. Wallace, D. — The Emergent Multiverse: Quantum Theory according to the Everett Interpretation (Oxford University Press, 2012).

24. Maudlin, T. — Quantum Non-Locality and Relativity, 3rd ed. (Wiley-Blackwell, 2011).

25. Maudlin, T. — Philosophy of Physics: Quantum Theory (Princeton University Press, 2019).

26. Bub, J. — Interpreting the Quantum World (Cambridge University Press, 1997).

27. Saunders, S., Barrett, J., Kent, A. & Wallace, D. (eds.) — Many Worlds? Everett, Quantum Theory, and Reality (Oxford University Press, 2010).

28. Dürr, D., Goldstein, S. & Zanghì, N. — Quantum Physics Without Quantum Philosophy (Springer, 2013).

29. Schlosshauer, M. — Decoherence and the Quantum-to-Classical Transition (Springer, 2007).

30. Griffiths, R. B. — Consistent Quantum Theory (Cambridge University Press, 2002).

31. Harrigan, N. & Spekkens, R. W. — "Einstein, incompleteness, and the epistemic view of quantum states", Found. Phys. 40, 125–157 (2010).

32. Healey, R. — The Quantum Revolution in Philosophy (Oxford University Press, 2017).

33. Deutsch, D. — "Quantum theory, the Church-Turing principle and the universal quantum computer", Proc. R. Soc. A 400, 97–117 (1985).

34. Arute, F. et al. — "Quantum supremacy using a programmable superconducting processor", Nature 574, 505–510 (2019).

35. Wallace, D. — "In defence of naiveté: The conceptual status of Lagrangian quantum field theory", Synthese 151, 33–80 (2006).

36. Butterfield, J. & Earman, J. (eds.) — Philosophy of Physics (Elsevier, 2007).

37. Crowell, K. — What is Quantum Gravity? (Cambridge University Press, 2022).

38. Rickles, D. — A Brief History of the Philosophy of Time (Oxford University Press, 2018).