Jim Kelley wrote:

Cecil Moore wrote:
True negative power just doesn't exist.
Negative energy would violate the conservation of
energy principle.

Correct. Therefore 2*sqrt(P1*P2)cos(180) is impossible as well as
ridiculous.

That's the interference term, Jim. Hecht, Born, and Wolf
all agree that the interference term can be negative.
Suggest you take a refresher course and alleviate the
ignorance you are displaying for everyone to observe.

Remember that P1 and P2 are Poynting vectors, i.e. power
densities and the negative sign simply denotes the
decrease in power density due to destructive interference.
The negative destructive interference subtracts from the
P1+P2 power and the result of that subtraction can *never*
be negative. The interference term has NO separate existence
aside from the existence of the power density components of
P1 and P2.

Please tell Hecht, Born, and Wolf that they are ridiculous.

2SQRT(I1*I2)cos(A)

That's the third term in equation (15) page 259, 4th
edition of "Principles of Optics".

If cos(A) is 180 degrees, the interference term becomes
negative and subtracts from the I1+I2 sum.

Born and Wolf continue, "... and minima of intensity

Imin = I1 + I2 - 2*SQRT(I1*I2)"

Exactly the same equations appear in "Optics", by Hecht,
4th edition, page 388.

"Imin = I1 + I2 - 2*SQRT(I1*I2)"

Note that I is intensity or irradiance, the dimensions
of which are watts/unit-area, exactly the same dimensions
as the Poynting vectors, P1 and P2 above.

In "Fields and Waves in Modern Radio", Ramo and Whinnery
subtract Poynting vectors that are 180 degrees out of
phase to obtain the net Poynting vector?

Since true negative power is impossible, the negative
power result of a square root process is discarded
as an artifact.

But what is TRUE negative power, and how does it differ from other
types of negative power? :-)

The sign on a power term denotes a decrease in power level
but never to a negative level. Thus, reflected power subtracts
from the forward power to obtain power delivered to the load.
Destructive interference power subtracts from average power
to allow for constructive interference power. In no case does
the net power go negative.
--
73, Cecil, w5dxp.com