How to Evaluate an Interpretation

An interpretation should be evaluated by its explicit commitments and explanatory performance, not by whether its vocabulary sounds familiar. A modified theory also faces direct empirical tests of its altered predictions. The most useful comparison holds the physical scenario fixed while identifying which premises each account keeps, changes, or leaves primitive.

Required background. Born rule: Translate a specified state and measurement into outcome probabilities.

Begin with a concrete record

Use a two-outcome measurement as a common benchmark:

$$(\alpha|0\rangle+\beta|1\rangle)|R\rangle \longrightarrow \alpha|0,R_0\rangle+\beta|1,R_1\rangle.$$

Ask what this expression represents physically, whether it is the final state, what makes a record definite, and why observers should use $|\alpha|^2,|\beta|^2$. These questions expose differences that labels like “realist” or “orthodox” can conceal.

A proposal may answer by adding configurations, modifying dynamics, accepting relative outcomes, or treating outcomes as primitives. The comparison should record that answer without assuming that one type is automatically legitimate and another illegitimate.

Separate six tests

Empirical adequacy. Does the model reproduce specified experiments with quantified approximations? A broad statement of agreement is weaker than an explicit calculation.

Mathematical definition. Are its states, dynamics, probability laws, and composition rules defined? A metaphor is useful only if it helps interpret such structure.

Ontology and records. What exists, and how do stable detector readings fit it? Extra variables should have a clear role.

Probability. Is the Born rule postulated, represented by a theorem, or connected to expectation through a further principle? A circularity criticism should identify an actual premise.

Locality and relativity. Does “local” mean no-signaling, local field equations, or Bell factorization? Are claimed relativistic extensions actually supplied?

Classical emergence. Does the account explain robust records and approximately classical motion under stated conditions? Decoherence, localization, and single outcomes are distinct requirements.

Compare explanatory costs without inventing a score

Simpler equations can accompany a richer ontology. Definite trajectories can require nonlocal dynamics. A predictive operational theory can leave outcomes primitive. An agent-centered account can avoid absolute states while requiring a theory of intersubjective agreement.

These costs are not measured in one universal unit. A comparison matrix should expose them rather than silently assign weights and announce a winner. The interpretation comparison provides a compact map.

A worked discriminating question

Suppose theory A is exactly unitary and theory B predicts coherence decay $e^{-\Gamma t}$ in an isolated interferometer. A visibility experiment can constrain B’s $\Gamma$ once environmental dephasing is modeled. That is an empirical comparison.

If theories C and D predict identical distributions for every permitted experiment, the same visibility data cannot distinguish their ontologies. One can still compare conceptual clarity or explanatory reach, but should label the argument accordingly.

Common pitfalls

Popularity as proof. A community preference is evidence about practice, not a derivation or discriminating experiment.

Unequal standards. Demanding a complete relativistic theory from one proposal while comparing it with an ideal nonrelativistic version of another distorts the assessment.

One solved example as universality. Reproducing spin correlations does not establish composition, fields, thermodynamics, or cosmology.

Exercises

A new interpretation introduces no equations and claims to solve probability by “information.” What concrete follow-up would make the claim assessable?

Solution

Specify what information means, whose state or uncertainty it describes, the mathematical measure, and the assumptions leading to Born-weighted expectations. Then work through a finite measurement example. A definition and a derivation make the claim testable by reasoning even if it adds no new empirical prediction.

References

• T. Maudlin, “Three measurement problems,” Topoi 14, 7–15 (1995), doi:10.1007/BF00763473.
• M. Schlosshauer, “Decoherence, the measurement problem, and interpretations of quantum mechanics,” Reviews of Modern Physics 76, 1267–1305 (2005), author manuscript.