The mechanical measurements by a physicist/observer of the spacetime properties of a classical particle consists of (a) identifying which clock detects the existence of the particle in what interval of synchronous time and (b) determining the particle's velocity by measuring its Doppler shift. The first is a counting process in space and time, the second is a counting process in temporal frequency space.

The wave mechanical measurements of the spacetime properties of a
classical electromagnetic (e.m.) field consist of using the expanding
set of recording clocks to form a *phased array* of mutually
receding receivers. This array samples the e.m. field at the
locations of the recording clocks at regular intervals of synchronous
time. The phased array mode involves all clocks at once and thus
provides a record of the magnitude and spatial phase of the
e.m. field. By repeating this procedure at temporal intervals
controlled by the synchronized ticking of the clocks, one obtains a
sampled historical record of the magnitude of the field and its
temporal phase.

Ulrich Gerlach 2001-10-09