On Dec 30, 2:12*am, Roy Lewallen wrote:
Keith Dysart wrote:
. . .
Notice a key point about this description. It is
completely in terms of charge. There is not a single
mention of EM waves, travelling or otherwise.

Now we expand the experiment by placing a pulse
generator at each end of the line and triggering
them to each generate a 50V one second pulse at
the same time. So after one second a pulse has
completely entered each end of the line and these
pulse are racing towards each other at the speed
of light (in the line). In another second these
pulses will collide at the middle of the line.

What will happen? Recall one of the basics about
charge: like charge repel. So it is no surprise
that these two pulses of charge bounce off each
and head back from where they came. At the center
of the line, for one second the voltage is 100 V
(50 V from each pulse), while the current is
always zero. No charge crossed the mid-point. No
energy crossed the mid-point (how could it if
the current is always zero (i.e. no charge
moves) at the mid-point.

* . . .

That's an interesting and compelling argument. With the conditions you
describe, I don't see how it would be possible to tell whether the waves
reflected from each other or simply passed by without interacting.

But suppose we launch waves of different shapes from the two directions,
say a triangular wave and a rectangular one. Or perhaps make them
asymmetrical in some fashion. It seems to me that then we should be able
to tell which of the two possibilities happened. Being different, you
could argue that the reflection wouldn't be complete. But shouldn't we
expect some distortion of any part of a pulse that was acted upon by the
* other?

I'll put my money on each of the waves arriving at the opposite end
unchanged. What do you predict will happen?

I predict that the pulse arriving at the left end will
have the same voltage, current and energy profile as
the pulse launched at the right end and the pulse
arriving at the right end will be similar to the
one launched at the left.

They will appear exactly AS IF they had passed
through each other.

The difficulty with saying THE pulses passed
through each other arises with the energy. The
energy profile of the pulse arriving at the left
will look exactly like that of the one launched
from the right so it will seem that the energy
travelled all the way down the line for delivery
at the far end. And yet, from the experiment above,
when the pulses arriving from each end have the
same shape, no energy crosses the middle of the
line.

So it would seem that the energy that actually
crosses the middle during the collision is
exacly the amount of energy that is needed to
reconstruct the pulses on each side after the
collision.

If all the energy that is launched at one end
does not travel to the other end, then I am
not comfortable saying that THE pulse travelled
from one end to the other.

But I have no problem saying that the system
behaves AS IF the pulses travelled from one
end to the other.

On the other, it is completely intriguing that
a directional voltmeter could be placed anywhere
on the line and the voltage profile of the two
pulses can be recovered. And this is true even
at the middle of the line where, in the experiment
with identical pulse shapes, no current flows and
no energy crosses. But the shape of the two pulses
can still be recovered.

So in the end I say it is AS IF the voltage and
current pulses pass through each other, but the
energy does not necessarily do so. That way I
am not left with having to account for where the
reflected energy goes when it arrives back at
the source.

...Keith