Owen Duffy wrote:

Fine Roy, the maths is easy, but you don't discuss the eligible
quantities.

As I learned the superposition theoram applying to circuit analysis, it
was voltages or currents that could be superposed.

Presumably, for EM fields in space, the electric field strength and
magnetic field strength from multiple source can be superposed to obtain
resultant fields, as well as voltages or currents in any circuit elements
excited by those waves.

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 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.

Is anything above contentious or just plain wrong?

No, I agree entirely, except for

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.

which I don't understand. We lose information when we add or otherwise
operate on two numbers to get one. (Which I think is what you might be
saying.) Given a number which is the sum of two others, we can't tell
from that sum alone what the two original numbers were. The same is
naturally true of superposed or added, if you prefer, waves or fields.
Power has the same problem (among others) -- given even an instantaneous
power, we can't tell without some other information (such as the complex
impedance) what the constituent voltage and current were.

Roy Lewallen, W7EL