On Sat, 17 Nov 2007 21:46:30 -0500, "Stefan Wolfe"
wrote:

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

Hi Dan,

Now let's return to this equation.

It is drawn from the classic optics formula for finding the Intensity
of radiation at a point in space that is illuminated by two sources.
The intensity is a function of illuminators and their relative (at
that point) phase.

Phase can also be thought of as distance (which returns us to the
point in space). As each path has a different length; then relative
phase, their difference in length, is simplified by casting out all
full cycles to leave only the remnant, or partial cycle. Of course,
keeping count of the complete angular distances can be preserved,
nothing will change in the result.

A is a single value (as a point in space is 1D) and is expressed as
that relative phase. A, thus in the world of all possible variations,
can be any single value between 0 and 2·Pi radians. It follows that
the cosine operation then renders a single value between +1 and -1.

If you were to integrate this over some portion of time, or for all
time; then it wouldn't change the answer one iota. The intensity of
interference at a fixed spot in space from fixed illuminators does not
change with time.

If you were to integrate this over some portion of space, or for all
space; then you would come up with different solutions. Across all
space the intensity would become the sum of the two sources'
illumination.

There is no necessity of changing cos(A) to -sin(A) + C at all. There
is no issue of unknown constants, the original intensities do not
disappear.

However, Integration does not resurrect Cecil's sucker punch. There
is no missing power (energy, calories, what-have-you) as the question
was tailored to an illusion that too many bought into.

Lest we go 'round the mulberry bush on that again, please respond to
my critique posted some time ago if you fault IT.

73's
Richard Clark, KB7QHC