Foundations Glossary

Foundations terminology often compresses several assumptions into one word. This glossary gives a working meaning and points to the full explanation. When a paper uses a term differently, its explicit definition takes precedence over an inferred everyday meaning.

States, reality, and explanation

Beable. A variable a theory treats as part of what physically exists, rather than only as an outcome-prediction device. A beable need not be an observable operator. See ontology.

Completeness. Adequacy of a specified theoretical state description for a stated purpose. EPR completeness is a particular criterion and should not be equated with every modern notion. See EPR.

Epistemic state. A state interpreted as encoding knowledge, information, or credence. This broad usage is not identical to the technical ontological-model definition of ψ-epistemicity.

Hidden variable. An additional variable in a model of preparations and outcomes. It need not imply determinism; response probabilities may remain stochastic. See local hidden variables.

Instrumentalism. An approach treating the formalism primarily as a means of organizing and predicting observations. It is not itself a modified dynamical law. See operationalism.

Ontology. The entities and structures taken to constitute physical reality. Distinguish an ontology from a calculational representation.

ψ-ontic and ψ-epistemic. In a ψ-ontic model, every pair of distinct pure quantum states has disjoint ontic-state distributions in the relevant measure-theoretic sense. A ψ-epistemic model permits nonzero overlap for at least one such pair. These are technical classifications, not synonyms for “real” and “unreal.” See ontological models.

Locality and correlations

Bell locality or factorizability. The conditional joint response factorizes as $p(a,b\mid x,y,\lambda)=p(a\mid x,\lambda)p(b\mid y,\lambda)$. The completeness and causal interpretation of $\lambda$ matter. See Bell theorem.

Local causality. A causal screening-off condition expressed using an adequate specification of relevant prior variables. In a Bell setting it motivates factorization. Together with measurement independence, factorization implies operational no-signaling; the observable marginal equalities alone do not imply factorization.

Measurement independence. The setting pair is statistically independent of the relevant hidden variables: $\mu(\lambda\mid x,y)=\mu(\lambda)$. It is a probabilistic premise, not a complete philosophical theory of free will.

Outcome independence. Given settings and $\lambda$, one party’s response probability is independent of the other outcome. Together with parameter independence it yields factorization.

Parameter independence. Given $\lambda$, a party’s response probability does not depend on the remote setting. With a measurement-independent hidden-variable distribution, this conditional property implies no-signaling after averaging over $\lambda$; the converse need not hold. Parameter independence alone does not guarantee the observable marginal equalities when that distribution depends on settings.

No-signaling. Observable local marginals do not depend on remote setting choices. It permits nonlocal Bell correlations. See No-Signaling.

Separability. In quantum information, a state is a mixture of product states. In metaphysical discussions, “separability” can instead concern whether a whole is fixed by intrinsic properties of its parts. State which meaning is intended.

Superdeterminism. A family of approaches permitting correlations between settings and hidden variables that violate measurement independence. The label alone supplies neither a predictive model nor an explanation of the correlation. See Superdeterministic Approaches.

Measurement and classical records

Branch. An approximately autonomous component of a decohering quantum description in Everettian accounts. Branches depend on a physical coarse-graining and are not generally an exact countable set with equal weights.

Collapse. Either a conditional state-update rule or a physical stochastic localization process. These meanings differ empirically and conceptually. See Collapse as Postulate and Objective Collapse.

Decoherence. Suppression of locally observable coherence through correlations with inaccessible degrees of freedom. It does not alone imply selection of one global outcome.

Einselection. Environment-induced selection of states or observables robust under a specified interaction. See Environment-Induced Superselection.

Pointer state. A state approximately stable under the relevant system–environment monitoring interaction. Stability is dynamical and approximate, not a universal preferred basis.

Macrorealism. A family of assumptions about definite macroscopic properties and their measurement, often including noninvasive measurability. See Leggett–Garg.

Contexts and models

Context. A specified compatible measurement arrangement, or a set of operational procedures in a defined scenario. The meaning differs between sharp-observable and generalized contextuality frameworks.

Noncontextuality. Independence of a representation from irrelevant context, with irrelevance fixed by the theorem or operational equivalence relation.

Contextuality. Failure of the applicable noncontextual model. It is not merely any dependence of a measurement on its apparatus. See Contextuality.

References

• Bell, John S., Speakable and Unspeakable in Quantum Mechanics, second edition, Cambridge University Press, 2004 — locality, beables, and interpretive distinctions. Publisher.
• Harrigan, Nicholas, and Robert W. Spekkens, “Einstein, incompleteness, and the epistemic view of quantum states,” Foundations of Physics 40, 125–157 (2010). Paper.
• Spekkens, Robert W., “Contextuality for preparations, transformations, and unsharp measurements,” Physical Review A 71, 052108 (2005). Paper.