I read my reply to Abineri's question (about the energy in nodes) and I did
not like it. Here is a more clear version.
Let me rephrase his question to show a puzzling situation. Suppose we have
two parallel laser beams whose temporary coherence is nearly PERFECT. The
first beam travels along the x axis passing a beam splitter positioned at
45 degrees. The second beam, after being reflected from a mirror, and from
the beam splitter, is superimposed on the first one. The phase relation
between the beams is controlled by a retarding glass plate (thickness
between zero to lambda/4) to make sure they are out of phase. The beams are
polarized in the same plane and an additional layer of glass is provided (to
compensate a glass plate of the splitter, as in Michelson's interferometer).
In principle, this arrangement would create two electromagnetic waves which
are out of phase everywhere after the beam splitter. It would be a very long
"antinode" (no energy there). Actually there would be two such antinodes,
one pointing to the right and one pointing down.
The beam splitter is controlled by nature and energy must be conserved. How
can this be satisfied? My prediction is that the beam splitter will lose its
semitransparency. Beam #1 will be totally reflected down and beam #2 will
be totally reflected toward the wall. The destructive interference will be
prevented in that way. The beam going down (100% #1) and the beam going to
the right (100% #2) will remain out of phase. Does this make any sense?
I suppose a similar situation can be created with sound waves (two phase-
correlated speakers at the entrance of a long pipe). The reflected sound
can be suppressed, for example, by making the pipe very long. Will the
pipe's entrance become a strong reflector when two beams are "forbidden
to enter" into it at the same time? Each beam will be individually accepted
(to act on a small micophone inside) but the combination of two beams will
be rejected. Do you think this will really happen?