Keith Dysart wrote:

Let's consider your and my bank accounts. If we generated
a net bank account of yours plus mine on a daily basis and
reported the results at the end of the month, even though
perfectly accurate, what relationship would that report
bear to reality.

Let us consider a transmission line....

Keith, that was the best example I have ever seen on how
an over-simplified math model can confound and confuse. As
long as one understands the underlying principles, a
simplification can be useful. But when the simplification
is presented as an example of the laws of physics when it
actually violates the laws of physics, it's time to object.
As a useful shortcut, there's nothing wrong with your standing-
wave analysis. It's the conclusions you draw about the underlying
laws of physics that violate the laws of physics.

EM waves must follow certain laws of physics.

1. Being photonic in nature, they must move at the speed of
light at the VF of whatever medium they are in.

2. The power density of an EM wave is ExH in joules/sec/unit-area.
The voltage and current are the *result* of the E-field and the
H-field. In phasor notation: V dot I = E cross H, e.g. adjusted
for the unit-area of the transmission line.

3. The joules in any volume must be conserved. In a lossless
transmission line, joules that have been put into the transmission
line and have not left the transmission line are still in there.

4. EM waves cannot exist without momentum. The momentum in any
volume must be conserved. If EM waves are confined to a volume,
they are moving at the speed of light and reflecting off the
physical boundaries containing the volume.

Do standing waves meet the definition of EM waves?

1. Standing waves do not move at the speed of light. Therefore,
standing waves are technically not EM waves. Standing waves are
a simplified mathematical construct and have no stand-alone
existence outside of the human mind, i.e. standing waves simply
cannot exist without the underlying forward and rearward
traveling waves.

2. Standing waves contain exactly the sum of the energy components
of the forward and reverse traveling waves. The conservation of
energy principle will not allow anything else.

3. The joules contained in the standing waves are exactly the
number of joules needed to support valid measurements of
forward power and reflected power. These joules are supplied
by the source during the transient power-up state.

4. EM waves cannot stand still in a transmission line. Any EM
energy confined to a transmission line must necessarily be moving
at the speed of light in the medium. In a Z0-matched system, where
no reflected energy is allowed to be incident upon the source, all
EM energy confined to a lossless transmission line and contained
in the standing waves must be reflecting back and forth between
two reflection points (physical impedance discontinuities).

About standing waves:

1. The standing wave voltage is not moving. It is oscillating in
place. It is not an EM wave. It's phasor could just as easily
be rotating in the opposite direction and nothing would change.

2. The standing wave current is not moving. It is oscillating in
place. It is not an EM wave. It's phasor could just as easily
be rotating in the opposite direction and nothing would change.

3. There is no net average energy flow in either direction. Therefore,
the net power is zero. Pfor - Pref = 0 However, the forward joules
passing a point in one second are still there and so are the
reflected joules/sec.

The *only* energy in a transmission line with standing waves is EM
energy. Standing wave energy does NOT meet the definition of EM
energy. Therefore, standing waves may be a useful math model but
that model has a built in technical contradiction when forced
upon reality.

For instance, in a one-second long lossless transmission line with
forward power = 200w and reflected power = 100w, the total energy
contained in that line is 200+100 = 300 joules and the EM wave
nature of those 300 joules has not changed because they are allocated
to the standing waves. They are still moving at the speed of light
in the medium, 200 joules in the forward direction and 100 joules
in the rearward direction.

Here is an EXCEL spread sheet of the transient build-up to steady-
state when the steady-state forward power is 200 watts and the
steady-state reflected power is 100 watts in a one-second long
lossless transmission line.

http://www.w5dxp.com/1secsgat.gif
--
73, Cecil http://www.w5dxp.com