The International Second (SI) is defined in terms of a resonant frequency of cesium imagined at 0 K, differing from any
measurable resonant frequency by an offset calculated from a chosen wave function. As proved in prior work, the choice
of wave function cannot be determined by measured data but requires a reach beyond anything measurable or calculable,
thereby bringing incalculablility, along with an element of free choice, into the definition and the realization of the second.
A clock that realizes the second contains a variable-frequency oscillator controlled by a measurement model running
in a computational process, and the chosen wave function is embodied in the measurement model. Embedded in a computational
process, the measurement model, with its dependence on the chosen wave function, acts as an active agent,
responding to incalculable detections by calculating numbers that adjust the oscillator.
Because the choice of realization of a proper clock influences the measured numbers that give evidence of spacetime
curvature, the chosen wave function for cesium clocks affects spacetime curvature, inviting exploration of offsets of
imagined proper clocks from measurable frequencies in interesting situations, such as stellar interiors.