Where does measurement collide?

In quantum mechanics, measurement is the interaction that turns a system's superposition of possibilities into one definite recorded outcome, with the probability of each outcome fixed by the state that held before the interaction. Von Neumann's 1932 Mathematische Grundlagen der Quantenmechanik formalised this as a separate process, the projection of the state onto the observed eigenstate, sitting alongside the smooth, reversible evolution the equations otherwise describe, and the gap between the two is what came to be called the measurement problem. Zurek's 2003 Decoherence, einselection, and the quantum origins of the classical gave the modern account of how interaction with a surrounding environment selects the definite outcomes we actually see. Here the referent is a physical event that fixes the value of a property in a system, not a way of classifying numbers assigned to survey answers, and not a laboratory procedure for reporting a quantity with its uncertainty.[1][2]

Unit

A single outcome: a definite value of an observable such as spin or position

Recovery means

Not applicable

Measured by

Realised by coupling the system to an apparatus whose pointer records one eigenvalue, with outcome frequencies following the Born rule

In psychology and the social sciences, measurement is the assignment of numbers to observations according to a rule, and Stevens's 1946 On the theory of scales of measurement sorted those rules into four kinds: nominal (labels), ordinal (ranks), interval (equal steps), and ratio (equal steps with a true zero). Which arithmetic and which statistics are defensible depends on which of the four a variable belongs to, so the classification governs how questionnaire and behavioural data may be analysed. The referent here is a scheme for how numerals stand for things, not a physical event that fixes a property inside an atom, and not the metrological procedure of pinning down a quantity value together with how far off it might be.[3]

Unit

A number assigned to an observation under a nominal, ordinal, interval, or ratio rule

Recovery means

Not applicable

Measured by

Established by stating the assignment rule and the transformations it permits, then applying it to responses or observations

In metrology, the science of measurement, measurement is the process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity, reported together with a stated uncertainty. The International Bureau of Weights and Measures set out this operational definition in its International vocabulary of metrology (VIM, 2012), building on the companion Guide to the expression of uncertainty in measurement (GUM, 2008), which standardised how the doubt around a result is quantified and reported. The discipline itself is old, running back through national standards bodies to the 1875 Metre Convention, though this exact operational wording is a modern codification. Here the referent is a repeatable procedure that yields a number and its uncertainty for a physical quantity, not a scheme for classifying survey scores, and not the interaction that decides an atom's state.[4][5]

Unit

A quantity value in a defined unit, paired with its stated measurement uncertainty

Recovery means

Not applicable

Measured by

Obtained by comparison against a calibrated standard, with uncertainty evaluated and reported following the GUM