gauge transformations must preserve the values of measurable quantities. The assumption of unitarity (often implicit) underlies some of the influential articles that have been published on the subject of gauge choice.

Examples employed here to demonstrate the primacy of potentials – a charged particle in interaction with a constant electric field, and a bound electron subjected to a plane-wave field – represent basic physics problems, unlike the narrow specificity of the Aharonov-Bohm effect. An important feature revealed by these examples is that, although the physical consequences of static or quasistatic-electric (QSE) fields are quite similar to plane-wave effects at the low field intensities that exist in the usual atomic, molecular and optical (AMO) physics processes, at the high field intensities now achievable with laser fields, they can be profoundly different. These differences have yet to be fully appreciated in the AMO literature, leading to misconceptions that persist nearly forty years after the first laboratory observation [@ati] of explicit intense-field effects.

A concept introduced here is that of a hierarchy of physical quantities. Since potentials are primary and fields are secondary, it follows that energies are primary and forces are secondary. This ranking resolves the long-standing mystery about why the Schrödinger 