Jim Kelley wrote:

Jim, you have a habit of erecting strawmen somewhat like:
"I don't care what you say, the sun will rise tomorrow." For that
reason, I'm going to trim the parts of your posting with which I
agree and have never disagreed.

You take too great a liberty with the name Eugene Hecht. Among the
things which won't be found in any of Dr. Hecht's texts is a minus sign
in front of number expressing an irradiance.

Sure wish you would read the book before making such statements.

On the contrary, here's equation (9.16) representing total destructive
interference.

Imin = I1 + I2 - 2*SQRT(I1*I2) = 0

The third term is indeed a minus sign in front of a number expressing
irradiance. However, total average irradiance cannot be less than zero.
And for the record, I have never said total average power could be less
than zero but, like Hecht, I treat destructive interference energy as a
negative term and constructive interference energy as a positive term.

Dr. Stephen Best, VE9SRB, did the same thing for his "Wave Mechanics
of Transmission Lines, Part 3:" QEX article, Nov/Dec 2001. He said:

"When the voltages V1 and V2 are exactly 180 deg out of phase, the
total power can be determined as follows:"

"PFtotal = P1 + P2 - 2*SQRT(P1)*SQRT(P2)"

so if you don't like negative power terms, you should confront both
Eugene Hecht and Dr. Best.

Nor will we find a
negative scalar quantity accompanied by the claim that the negative sign
indicates a change in direction, as you have done.

On the contrary, in equation 9.16 above, according to Hecht, the
interference term is negative indicating "total destructive
interference", his words, not mine. Here's Hecht's quote from _Optics_.

“The principle of
conservation of energy makes it clear that if there is constructive
interference at one point, the ‘extra’ energy at that location must have
come from somewhere else. There must therefore be destructive
interference somewhere else."

Sorry, but a negative interference term denotes destructive
interference. A positive interference term denotes constructive
interference. In a transmission line with only two directions,
if destructive interference occurs in one direction, then
constructive interference must occur in the only other direction
in order to satisfy the conservation of energy principle.

A wave cancellation event in a transmission line implies an equal
constructive interference event in the opposite direction. Anything
else violates the laws of physics.

Similarly, power and irradiance do not
physically propagate and they do not physically interact.

On the contrary, they do physically interact for coherent waves as can
be inferred by the interference equations. Please reference Chapter 9
in _Optics_, by Hecht. The mathematical interaction of power and
irradiance is a *result* of superposition of coherent EM waves. That's
where the interference equations involving irradiance come from.

JC Maxwell and others observed that it is
electric and magnetic fields which propagate, interact with matter, and
add algebraically and vectorially.

And contain power equal to ExH. EM waves cannot exist without energy.
If EM waves interact, their energy components interact. Destructive
and constructive interference cannot occur without energy components
which follow the laws of physics.

Of course the interference equation accurately expresses power and
irradiance.

That is some progress on your part so there's hope. What you need to
realize is that those interference equations define what happens to
the energy at a match point in a transmission line. Dr. Best kicked
this discussion off by his QEX article. He just didn't realize that
the equations he published were virtually identical to the classical
optical interference equations.
--
73, Cecil http://www.qsl.net/w5dxp


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