Why is the ExB Poynting vector of each wave no longer
proportional to the energy content? Why does the energy
content of the component waves have to change when they
superpose? Where does that energy change go? Do the
necessary joules disappear and/or appear from thin air?

Joules do not disappear, they just get distributed over the free space in a
non-uniform manner.

In certain regions of the space the two waves add up (apparently creating extra
power), in other regions they cancel out (apparently destroying power). The
integral of total radiated power does not change.

In your example you considered a location where the two waves have a 45 deg.
shift. At another location, where the two waves have a zero deg. shift, you
would observe an even higher apparent power creation. Conversely, at locations
where the two waves have a 180 deg. shift you would observe absence of power.

The principle causing the apparent power creation at your location is the same
principle by which an antenna formed by two stacked dipoles features a gain of
up to 3 dB with respect to a single dipole, and can then deliver up to twice the
power to a receiver placed at the maximum radiation heading (and zero power at a
receiver placed at 90 degrees from that heading). .

That's what I did and the result was 171 joules/sec.
The Poynting vector for each of the two source waves
is 50 joules/sec. Why is the energy content of the
component waves not a meaningful number?

Each wave produces 50 joules/s when alone. When the two waves are superimposed,
each wave produces not only its 50 joules/s but also 35.5 more joules that it
"robs" from other regions of the space. If you would plainly sum the power of
two components (i.e. 50 + 50), you would neglect the fact that coherent waves
necessarily interfere with each other in the space, in constructive or
destructive manner depending on the receiver location.

Summing wave powers could only be done in case of incoherent waves.

No, there is a special equation to be used for summing coherent
waves, i.e. the irradiance equation from optical physics. For
power density:

Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

where 'A' is the angle between the two E-fields.

Please re-read my sentence more carefully. My statement was that summing powers
(that is. Ptotal = P1 + P2) would only be correct for incoherent waves.

For coherent waves, plainly summing powers would generally be incorrect (apart
from one particular phase angle), and one must nstead use the equation you have
shown.

For every second that passes, 50 + 50 = 100 joules has no
physical meaning? Are you saying that an EM wave is not
associated with ExB joules/sec?

see previous remarks.

73

Tony I0JX