Interpretation Comparison Matrix
Interpretations differ along several independent axes: what the state represents, what counts as an outcome, how probability is understood, and whether the dynamics changes. The tables below compare representative versions rather than assigning each family one immutable doctrine. Follow the individual articles before attributing a precise position to an author.
Required background. Born rule: Translate a specified state and measurement into outcome probabilities.
States and outcomes
Section titled “States and outcomes”| Account | State and physical description | Account of a record |
|---|---|---|
| Textbook collapse | Predictive state, with differing ontological readings | A primitive measurement selects an outcome |
| Copenhagen family | Context-dependent descriptions; no single doctrine | Classically described experimental record |
| Operationalism | Equivalence class of preparations or prediction tool | Outcomes enter the operational description |
| Everett | Universal unitary state; emergent branches | Definite record relative to a branch |
| Pilot wave | Wavefunction plus actual configuration | One occupied apparatus configuration |
| Objective collapse | Stochastic state plus specified matter ontology | Physical localization and amplification |
| QBism | Personal expectations of an agent | Experience resulting from an intervention |
| Relational QM | State and facts relative to systems | Event relative to an interacting system |
| Consistent histories | State plus a consistent history framework | Probabilistic record within that framework |
| Modal interpretations | State plus selected actual properties | A definite-valued apparatus property |
| Ensemble interpretations | Statistics of similar preparations | Individual records may remain primitive |
| Transactional | Offer/confirmation structures, variant-dependent | Actualized emitter–absorber transaction |
The same operational density operator can play different explanatory roles. Conversely, proposals using different words may make identical predictions in a stated domain.
“Hidden variables” is not a synonym for every realist ontology. Bohmian configurations, collapse matter densities, and an Everettian universal state are different kinds of physical structure. Realism and ontology explains why the proposed entities and their laws matter more than a broad philosophical label.
Dynamics, probability, and empirical scope
Section titled “Dynamics, probability, and empirical scope”| Account | Probability input or explanation | Predictive scope and main cost |
|---|---|---|
| Textbook collapse | Born postulate | Measurement boundary remains primitive |
| Everett | Born weights plus a decision, symmetry, or other bridge | Standard predictions require an account of Born weights; branch emergence and meaning of expectation need explanation |
| Pilot wave | Equilibrium or typicality measure | Standard quantum statistics in equilibrium; nonlocal guiding structure; extensions need specification |
| Objective collapse | Physical stochastic law | Parameter-dependent departures, heating and localization costs |
| QBism | Personal probabilities constrained by Born rule | Agent and shared-world interpretation |
| Relational QM | Born rule applied relationally | Cross-perspective consistency needs explicit rules |
| Consistent histories | History probabilities in consistent families | Framework choice and incompatible descriptions |
| Modal family | Property weights and possible transition rules | Definite-property selection and stability |
| Ensemble family | Preparation statistics | Individual ontology often unspecified |
The same numerical Born rule can be postulated, interpreted as objective stochastic chances, connected to equilibrium or typicality, or supported by rationality and symmetry arguments. These are different explanatory tasks; agreement on probabilities does not establish agreement on their meaning or justification. The probability chapter compares the assumptions and conclusions of these accounts.
Empirical distinctions require a specified state space, dynamics, preparation, and measurement model. Equilibrium pilot-wave formulations can reproduce standard quantum statistics in their stated domain; proposed nonequilibrium extensions need a separate predictive analysis. Objective collapse models change the dynamics and can yield parameter-dependent departures, whereas a purely interpretive re-description can retain the same predictions. An informal account without quantitative laws is not yet an experimental competitor.
Programs organized by causal assumptions
Section titled “Programs organized by causal assumptions”Retrocausal approaches can permit hidden variables to depend on future settings or boundary conditions. Superdeterministic approaches relax measurement independence through a different causal account. Neither label alone supplies a complete state space, dynamics, or Born-rule derivation.
A setting-dependent measure identifies a change to Bell assumptions. It does not tell us whether the dependence arises from a common past, future boundary data, or an arbitrary fit.
Relativistic scope
Section titled “Relativistic scope”Relativistic compatibility is a separate comparison axis. Distinguish a nonrelativistic formulation from an extension for specified relativistic systems, and ask whether that extension uses preferred structures, what covariance it establishes, and whether interacting-field dynamics is actually supplied. A family label does not settle these questions. Compare models in the same domain rather than crediting one with an extension while judging another only by its nonrelativistic version.
Bell’s theorem states the locality assumptions behind its obstruction; Bell’s essays in Speakable and Unspeakable in Quantum Mechanics provide further conceptual context. No-signaling of observed probabilities alone establishes neither Bell-local factorization nor a complete relativistic formulation.
How to use the comparison
Section titled “How to use the comparison”Keep the experimental domain fixed. “Empirically equivalent” must name which preparations, transformations, measurements, and parameter regimes are included. The evaluation guide supplies concrete tests of mathematical clarity and explanatory scope.
For one concrete scenario, identify each account’s physical state, record, probability rule, and applicable dynamics. Then separate disagreements in predictions from disagreements in explanatory commitments. The individual articles explain where versions within each family differ.
Exercises
Section titled “Exercises”Why should a column labeled “local: yes/no” be replaced by more precise questions?
Solution
No-signaling, Bell-local factorization, local interactions, separability, and Lorentz covariance are different properties. A theory can satisfy some and fail others. One binary label conceals the exact assumption being compared.
References
Section titled “References”- J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd ed., Cambridge University Press (2004), publisher.
- M. S. Leifer, “Is the quantum state real? An extended review of -ontology theorems,” Quanta 3, 67–155 (2014), author manuscript.
- M. Schlosshauer, “Decoherence, the measurement problem, and interpretations of quantum mechanics,” Reviews of Modern Physics 76, 1267–1305 (2005), author manuscript.