nonobservables

Nonobservables are quantities arising in theoretical descriptions that cannot be measured directly in any experiment. They contrast with observables, which are defined by measurement outcomes. Nonobservables are often defined by the theoretical framework—gauge choices, renormalization schemes, or bases—and depend on those conventions rather than on experimental facts.

Examples include the overall phase of a wavefunction and the wavefunction itself, which are not directly observable; only probabilities and relative phases matter. In quantum field theory, off-shell Green's functions, bare masses and couplings, and other scheme- or gauge-dependent quantities are not directly observable; observable content comes from renormalized, on-shell quantities. Potentials in nonrelativistic quantum mechanics are likewise not observables, since different phase-equivalent potentials can produce the same observables. Spectroscopic factors and similar model-dependent structure descriptors can be nonobservables, because different theoretical constructions yield the same cross sections.

Role and interpretation: Nonobservables enable theory construction, renormalization, and phenomenology; they organize calculations and encode assumptions about unmeasured degrees of freedom. Their values must be interpreted within a framework, and their physical meaning arises only when tied to observables. Debates continue about which quantities reflect real physics versus artefacts of representation. They are central to modern physics for connecting experimental results to underlying theories.