Gosh Cecil... In a lossless line if you put in 100 joules, at the rate
of 100 joules per second, and get 200 joules back, I predict that in
less than 30 seconds (30 doublings) there will be a titanic explosion
exceeding all the Hydrogen bombs on the planet... Do the math!

OK, tongue out of cheek...
Assume that we put a 1 second squirt at the rate of 100 Joules per
second, into the input end of the line, it is an open line at the far
end, and yank the input end of the line out of the transmitter at
exactly 1 second... Now we have a lossless line with a wave going
forward and a reflected wave coming back... Do you still claim 200
joules?

We are going to do this in quarters (25% of time, 25% of 100 joules and
25% of line length)
Start pushing energy into the line at T=0 and jump ahead to T = .25
second... The is 25 joules total in the .00 to .25 line section and 0
joules in the other 3 sections... At T=.50 there are 25 joules in each
of the first two .25 sections and nothing in the last two .25
sections... Total 50 joules... The next two time periods is more of
the same so let's jump to T=1.00
The line is now just 'full', with 4 'quarters' of energy having been
inserted into the line, at that instant the leading edge of the wave
reaches 1.00 of line (.25 x 4) and reflects off the open terminal,
folding back and going towards the input... The total power in the
line is 100 joules at T= 1.00.... No surprise there...
At 1.25 seconds we have a quarter of the wave reflected back and
re-reaching the .75 line point (25 joules in that quarter) laid over
top of the quarter of the wave front still going outwards in the .75 to
1.00 section (25 joules in that quarter).
So at T = 1.25 in that 0.75 to 1.00 portion of line we have 50 joules
of energy (first quarter coming back plus second quarter still going
out, passing each other... )
In the .50 to .75 line we have 25 joules of energy...
In the .25 to .50 line we have 25 joules of energy...
In the .00 to .25 line we have 0 joules of energy...

At T = 1.50 we have a wave going out in the .50 to .75 section and also
in the .75 to 1.00 section... And reflected wave coming back in both
those sections for 50 watts in each quarter section... The .00 to .25,
and .25 to .50 sections are empty... For a total of 100 joules...

T=1.75 and 2.00 is just more of the same... 4 quarters of 25 joules
each lined up a row with 4 quarters of 0 joules each... Chasing each
other up and down the line, folding back and passing each other at each
..25 time period... A given quarter line section can have 0 joules, 25
joules or 50 joules, present at the instantaneous T of any given time
block..

In a lossless line this power will slosh back and forth forever...
Never having more than 50 joules in any quarter section of line and
certainly not doubling to 200 joules... If you have ever held a slinky
toy between your hands and watched the wave bouncing from hand to hand,
you have seen what happens in the 1 second of line section...

BTW, this can be visualized by cutting 4 paper strips 3" long and
marking them as 25 joules each and pushing them onto your 1 foot ruler
(or ugly 250 mm stick) one at a time and just like box cars on a train
see what they do...

Awww righty, now lets leave the transmitter on the line instead of
yanking it... Sort of like non coitus interruptus...
At T=1.00 nothing is happening as far as the transmitter knows... The
line is still taking power like a hungry calf taking milk from a cow...

At T = 1.25 we have put 125 joules into the line... The line section
..75 to 1.00 is doubled up with 25 joules going and 25 joules coming...
At T = 1.50 we have put in 150 joules... Line sections 3 and 4 are
doubled up to 50 joules each and line sections 1 and 2 have 25 joules
each on board...
At t = 1.75 sections 2,3,4 are doubled up and only section one has 25
joules currently on board...
At T = 2.00 we have 50 joules in each quarter section of line for a
total of 200 joules, and Cecil is fat and happy... Thinks he has been
vindicated...

But wait! There's more... These Ginsu knifes will slice and dice and
uuunhhh, - oops, wrong topic...
Well, as a thought experiment there is nothing to inhibit me from
pumping another 100 joules into the line in the T = 2.00 to 3.00 time
block, and again in the 3.00 to 4.00 time block, ad infinitum until we
come to the Big Bang... So Cecil, why doesn't this happen? You can't
have it both ways, a theoretical thought experiment of putting energy
into a lossless line and at T = 2.00 suddenly revert to some mumble
jumbo about the energy going away at the same rate it is entering, or
the transmitter absorbing the reflected wave (those bottles gonna
vaporize on the first long dah)... There is nothing in our theoretical
world to differentiate T = 2 from any T = n + 1... Inquiring minds,
and all that...

But let me suddenly play spoiler here... After 2 seconds, the reflected
returning slug of energy present in each quarter line section is 180
degrees out of phase with the out going energy slug in each respective
section... The two slugs vectorally neutralize each other... No energy
present in that quarter section at any given T... So for each .25 T
after T = 2.00 you are merely replacing the energy that has been
neutralized by the returning wave.... Remember, energy can neither be
created nor destroyed... So, where did the energy go?

denny / k8do