On Apr 9, 1:22*pm, Cecil Moore wrote:
Keith Dysart wrote:
On Apr 8, 8:51 am, Cecil Moore wrote:
Roy Lewallen wrote:
Now, I don't know of any way to assign "ownership" to bundles of energy.
One way is to add a unique bit of modulation to each
bundle of wave energy. I am fond of using a TV signal
and observing ghosting on the screen. This, of course,
assumes that the modulation stays with the same component
wave to which it was originally associated.

But as soon as you modulate, you no longer have sinusoidal
steady state.

You know and I know that is a copout diversion to avoid
your having to face the technical facts.

You seem to be the one who knows this. I don't.

Consider the 1 second interval from 4.5 to 5.5 seconds.
In this second 0.016393 joules flow for an average
power of 0.016393 W. But the sum of the imputed power
in the two spectral components is 1 W. Where did the
missing energy go?

Hint: Missing energy is impossible except in your mind.
Just because you are ignorant of where the energy goes
doesn't mean it is missing. It just means that you fail
to understand interference. Have you not read Hecht's
Chapter 9 on "Interference"?

Obviously, interference is present and there is *NO*
missing energy. I have previously listed the possibilities
at least four times so will not bother listing them again.

Between 9.5 and 10.5 seconds, 1.983607 J (average 1.983607 W)
of energy flows. By 'interference', I think you are suggesting
the missing power from 4.5 to 5.5 appears as excess power
between 9.5 and 10.5, thus satisfying your conservation of
energy requirement. But where was the energy stored for
5 seconds until it could be delivered.

Or, more intriguing, between 0 and 1 second, 1.935466 J
(average 1.935466 W) of energy flowed, but the sum of
the powers of the two constituents was only 1 J (average
1 W) in this interval. Where did the extra energy come from?
Was it borrowed from the future? It did not come from
the past since the generator was not yet on.

Just another example of why assigning too much reality
to the imputed powers of the components of superposition
is misleading.

Just another example of ignorance in action. Waves
possess energy that cannot be destroyed. Just because
you cannot track it doesn't mean it cannot be tracked.

That is why I pose the question, hoping for someone to
describe the mechanism that the energy for the flow that
is happening now can be borrowed from the future.

But what happens if the generator is turned off before
the future arrives? Where did the extra energy come from
then?

In other examples, you have suggested inserting a zero length
transmission line to aid analysis. Why not insert a zero length
transmission line with an impedance to produce the desired
reflection?

What would be the characteristic impedance of a length of
transmission that caused a reflection coefficient of 1.0?

Exactly. With the source impedance being zero, you can use
any impedance line you like.

No one has said there is zero energy. Only that there is
zero energy flow. For energy flow, one needs simultaneous
voltage and current.

Vfor/Ifor = Z0, Vfor*Ifor = Pfor = EforxHfor
If an EM wave exists, it is moving at the speed of
light and transferring energy. For Z0 purely resistive,
Vfor cannot exist without Vfor/Z0 = Ifor. Vfor is
always in phase with Ifor.

Assigning too much reality to component signals is
seriously misleading.

Assigning reality to the components of superposition
is seriously misleading???? Can we therefore throw
out the entire principle of superposition?

Well, you can solve these problems in other ways.
Superposition is not required, but it is certainly
convenient. I would not throw it out just because
the constituent powers do not necessarily have
any real meaning. I would just make sure I used
it in ways that did not mislead.

Until one can grasp the simplicity of a transmission line,
moving to the complexity of free space offers nothing but
obfuscation.

It is obvious that you have many things you desire to
hide inside that black transmission line to which we
are not even allowed to attach a directional wattmeter.

Since you are incapable of explaining what happens in
free space for all to see, why should we believe that
you have figured out what is happening inside a
transmission line where everything is hidden from view?

Actually, I have a pretty good grasp of what is happening
in free space, and it is all available to you by extension
from the behaviours of the one dimensional transmission
line. But there is little point in going there until the
transmission line is understood. Three dimensional free
space has much too much wiggle room. And you are an
expert at wiggling.

...Keith