Where does gauge collide?

A local redundancy in how a physical field is described: many different choices of the underlying potential give exactly the same observable physics, and the freedom to switch between those choices is the gauge. Weyl introduced the idea in his 1918 Gravitation und Elektrizität, coining the term (Eichinvarianz, from the calibration of a measuring standard), then recast it for quantum electromagnetism in his 1929 Elektron und Gravitation; Yang and Mills generalised it to non-commuting symmetries in their 1954 Conservation of isotopic spin and isotopic gauge invariance, which underpins the modern standard model. Here the referent is a symmetry of the mathematics, not a thing you hold or read. It is unrelated to a measuring instrument or to the variability of a measuring process, apart from the metering word Weyl borrowed.[1][2][3]

Unit

A choice of the redundant potential, one representative for each class of physically equivalent descriptions

Recovery means

Not applicable

Measured by

Not directly measurable: only gauge-invariant quantities are observable, so a gauge is fixed by convention (a gauge condition) to remove the freedom

The portion of observed measurement variation that comes from the measuring system itself rather than from real differences between the items measured, split into repeatability (the same operator and instrument repeating a reading) and reproducibility (different operators or setups reading the same item). The label comes from automotive quality practice; Montgomery and Runger's 1993 Gauge capability and designed experiments, Part I set out the designed-experiment methods now standard for estimating it. Here the referent is a statistical quantity, a variance attributed to the act of measuring, not the instrument itself and not a symmetry of a theory.[4]

Unit

A variance, or its share of total variation, attributed to the measuring process, in the measured quantity's squared units

Recovery means

Not applicable

Measured by

Estimated from a designed study where several operators measure the same parts repeatedly, partitioning variation into repeatability and reproducibility (for example by ANOVA)