Owen Duffy wrote:
For avoidance of doubt, power is not a quantity to be superposed, though
presumably if it can be deconstructed to voltage or current or electric
field strength or magnetic field strength (though that may require
additional information), then those components may be superposed.

The single bit of additional information required is the phase
angle between the voltages (or currents or fields). Optical
physicists deduce the relative phase angle by the ratio of
intensity (power density) in the bright rings vs the dark rings.
We hams can deduce the relative phase angle by the ratio of
forward power (density) to reflected power (density). Our task
as hams looking at a one-dimensional transmission line is much
easier than the task of optical physicists looking at visible
light in three-dimensional space. Our transmitted CW signals are
coherent and collinear in a transmission line, something that
optical physicists can only dream of.

The resultant fields at a point though seem to not necessarily contain
sufficient information to infer the existence of a wave, just one wave,
or any specific number of waves, so the superposed resultant at a single
point is by itself of somewhat limited use. This one way process where
the resultant doesn't characterise the sources other than at the point
seems to support the existence of the source waves independently of each
other, and that there is no merging of the waves.

That is the case in a majority of examples. But in the case
of two coherent collinear waves superposed in a one-dimensional
transmission line where the resultant is the same at every point,
we can safely assert that those two waves have ceased to have an
existence independent of each other. The idea of two waves
canceling all up and down the transmission line yet continuing
their separate existences until their combined zero energy level
is dissipated (or not) is a pipe dream. If ExB = 0, the energy
in those canceled waves went the other direction a long time ago
and those waves have ceased to exist in their original direction
of travel, i.e. they have interacted and canceled.

When two waves combine to a zero energy level, the pre-existing
energy in those two waves is "redistributed in the direction
of constructive interference". In a one-dimensional transmission
line, there are only two possible directions. If waves superpose
to zero energy in one direction, their energy components are
"redistributed" in the only other direction possible. If the energy
ceases to flow in the reverse direction, then it must flow in the
forward direction. That's why Pforward = Psource + Preflected.
Anything else would violate the conservation of energy principle.
--
73, Cecil http://www.w5dxp.com