no way. Prove there is no change in the power delivered by the sources.

Making reference to the case under discussion (Wave#1 produces 50 joules/s at
the receiver when alone, and so does Wave#2 when alone), imagine that the two
waves are generated by two remote transmitters (+antennas) and that you measure
the power of the two superimposed waves on a receiver (+antenna) that you can
move in the space as you like.

If you put your receiver/antenna in a point where the two waves have equal
amplitude and opposite phase, your receiver will measure zero joules/s.

If you instead put your receiver/antenna in a point where the two waves have
equal amplitude and same phase, your receiver will measure 200 joules/s (i.e.
four times the power produced by each wave alone, not just two times).

Finally, if you put your receiver in a point where the two waves have equal
amplitude and a 45 deg. shift (as in the proposed case), your receiver will
measure 171 joules/s (still more than twice the power produced by each wave
alone).

Moving your receiver here and there will obviously cause no change in the power
delivered by the two remote transmitters.

The trick is due to the fact that the two waves interfere each other in
constructive or destructive manner depending on the particular receive point.
So, in the "lucky" points you get some extra power, which is however compensated
for by the power loss occurring at the "unlucky" points.

The original question is deceiving, because it attracts the reader's attention
on just one particular point of the space, where energy can unexplicably appear
to be created or destroyed. But instead considering the power distribution over
the whole space, the mistery disappears.

73

Tony I0JX