Superposition
 

Gene Fuller wrote:
# Is this not written in English?

You have obviously misunderstood what I was trying
to say.

# Just what do you mean by, "superposition of two (or more)
coherent waves as the *cause* of the interference *process*"?

Superposition is necessary for interference to exist.
Superposition is not sufficient for interference to exist.
Superposition and interference are both in the cause and
effect chain of events.

# Are you playing some sort of word game by using *event* and *process*?

No, just responding to Jim Kelley's assertion that interference
is only an end result. Eugene Hecht says the "intricate color
patterns shimmering across an oil slick ... result from ...
the phenomenon of interference." The intricate color patterns
are the *result* of interference.

# Do you have a reference for the rules of that word game?

It's no word game - it's just English as plain as I can make it.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Gene Fuller wrote:
Sorry. I missed it because it is not there. They don't say any such thing.

Yes they do - I distinctly remember reading it.
I will prove it to you as soon as I find my book.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Cecil Moore wrote:
Gene Fuller wrote:
Sorry. I missed it because it is not there. They don't say any such
thing.

Yes they do - I distinctly remember reading it.
I will prove it to you as soon as I find my book.

I'm pretty sure it is in the section which discusses
the irradiance (power density) equation. It says the
total irradiance of two waves of the same magnitude
that are interfering can be up to four times the
irradiance of one wave.
--
73, Cecil http://www.w5dxp.com

Superposition (Antenna Arrays)
 

"Tam/WB2TT" wrote

You know that can't be right, because combining two antennas
gives 3 db gain.
_____________

The vector sum of the EM fields at every point in free space from identical
radiators fed by the same source depends in part on their relative physical
orientations, and their separation in wavelengths (see Kraus' ANTENNAS, 3rd
edition, chapters 5 and 6).

If all radiators in an array generate identical fields relative to each
other, then the peak directivity of an array of two radiators exceeds 3 dB
for radiator spacings of about 0.75 to 1.2 wavelengths (max of about 3.3
dB).

If they are spaced 1/2-wave apart then the peak directivity drops to about
1.9 dB, and at 1/4-wave separation it drops to about 0.5 dB (see Johnson &
Jasik ANTENNA ENGINEERING HANDBOOK, 2nd edition, Figure 3-4).

RF

Superposition (Antenna Arrays)
 

Richard Fry wrote:
The vector sum of the EM fields at every point in free space from
identical radiators fed by the same source depends in part on their
relative physical orientations, and their separation in wavelengths (see
Kraus' ANTENNAS, 3rd edition, chapters 5 and 6).

It's too bad that we cannot see the interference patterns
created by two radiators. Just know that all of the
interference patterns involving visible light that we can
see with our own eyes are also possible at RF frequencies.

Who hasn't been listening to a repeater that almost
completely faded out while stopped at a red light?
Letting the vehicle move a short distance brings it
back to Q5. That old familiar "picket-fencing" that
some of us have experienced is the antenna alternately
moving through zones of destructive and constructive
interference. The same thing can be caused by an
airplane flying over during local TV reception.
--
73, Cecil http://www.w5dxp.com

Superposition (Antenna Arrays)
 

"Cecil Moore" wrote
Who hasn't been listening to a repeater that almost
completely faded out while stopped at a red light?
Letting the vehicle move a short distance brings it
back to Q5. That old familiar "picket-fencing" that
some of us have experienced is the antenna alternately
moving through zones of destructive and constructive
interference. The same thing can be caused by an
airplane flying over during local TV reception.
______________

All true, but those cancellations don't originate in the transmit array.
They are the result of reflections from surfaces in the propagation
environment that arrive at the receive antenna ~180°out of phase with the
direct signal from the transmit array.

RF

Superposition
 

Cecil Moore wrote:
Cecil Moore wrote:
Gene Fuller wrote:
Sorry. I missed it because it is not there. They don't say any such
thing.

Yes they do - I distinctly remember reading it.
I will prove it to you as soon as I find my book.

I'm pretty sure it is in the section which discusses
the irradiance (power density) equation. It says the
total irradiance of two waves of the same magnitude
that are interfering can be up to four times the
irradiance of one wave.

Cecil,

The physical effect is well known and is non-controversial, even on
RRAA. What is at issue is all of the philosophical gibberish that seems
to surround the reality.

The exact words from B&W on page 289 of the 7th edition:

"the intensity varies between a maximum value Imax = 4I1, and a minimum
value Imin = 0"

In the 6th edition the same words are on page 259.

The modern convention is to use "irradiance" instead of "intensity",
since "intensity" can have multiple meanings.

What B&W *don't* say is anything about two 1 watt waves interacting,
waves exhibiting constructive and destructive interference, cause and
effects relationships, or even energy conservation.

All of those are things written by more casual writers, such as Hecht,
Melles-Griot, and the FSU Java dudes. There is nothing wrong with that
type of explanation for simple illustration, but it runs out of gas when
trying to support detailed analysis. One quickly ends up with silliness
such as waves that are launched and then cancel destructively within a
short (but undefined) distance. None of that nonsense occurs if one
simply applies the standard analysis techniques such as used by B&W.

73,
Gene
W4SZ

Superposition
 

Gene Fuller wrote:
"the intensity varies between a maximum value Imax = 4I1, and a minimum
value Imin = 0"

Yes, that's essentially what I have been saying. The peak
intensity (irradiance) can be double the intensity of
the combined intensity of both superposed waves.

What B&W *don't* say is anything about two 1 watt waves interacting,
waves exhibiting constructive and destructive interference, cause and
effects relationships, or even energy conservation.

Eugene Hecht calls the last term in the irradiance equation
the "interference term". He talks about "total destructive
interference" and "total constructive interference". The sign
of the interference term indicates whether the interference
is destructive (-) or constructive (+).

All of those are things written by more casual writers, such as Hecht,
Melles-Griot, and the FSU Java dudes. There is nothing wrong with that
type of explanation for simple illustration, but it runs out of gas when
trying to support detailed analysis. One quickly ends up with silliness
such as waves that are launched and then cancel destructively within a
short (but undefined) distance. None of that nonsense occurs if one
simply applies the standard analysis techniques such as used by B&W.

Exactly what nonsense are you referring to? Please be specific. It
is difficult to defend myself from assertions of "nonsense" with no
specific allegations.

I gather from the above that wave cancellation due to superposition
is against your religion. Since all impedance discontinuities cause
reflections, exactly how and why do those reflected waves cease to
exist? Please be specific.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Cecil Moore wrote:

If waves are not 'doing things' to other waves, how
are reflected waves eliminated by thin-films on glass?

A reasonable question, for a third grader. It's like asking: if '-2'
is not doing something to '2', then how can the result be zero when
they combine? For the case A + B = 0, B does not change A, and A does
not change B even though their sum happens to be zero. (Certain other
problems arise when you try to algebraically add commodities which
cannot be negative - power for example.)

As I've told you many times, you could keep from becoming confused on
these points if you would work them through from the standpoint of
fields, rather than power. Not doing so is leading to problems in your
understanding of what actually goes on.

Imagine you're floating above the ground between two closely spaced
football field sized capacitor plates. There is one on either side of
you, and they are parallel to each other. Consider now that one of
them becomes highly charged with respect to the other, and to Earth.
(Some source of energy would be required in order for this to happen
and to keep it charged in air.) You would then experience a strong
electric field.

Now imagine the other plate becomes highly charged in magnitude and
polarity equal to the opposite plate. It now produces a field equal
in magnitude and opposite in direction to the other plate. The net
field from your perspective is now zero, but one can imagine that from
a different perspective the total field is much greater with the two
plates being charged. But you'll note that nothing actually happened
to the field from either the first plate or the second plate, yet
between the two plates their effect was canceled. Their ability to do
work on a charged particle is negated. But in the way that many of
your references points out, that ability has moved to different points
in space. Please note that nothing moved that 'ability' there other
than the charge which was applied to the second capacitor plate.

An interference pattern doesn't 'cause' energy to move around, fields
don't move other fields just as waves don't move other waves and
photons don't move other photons.

73, Jim AC6XG

Superposition
 

Jim Kelley wrote:
As I've told you many times, you could keep from becoming confused on
these points if you would work them through from the standpoint of
fields, rather than power.

As you know, I did exactly that in a private email to
you, Jim, and it didn't change anything.

Imagine you're floating above the ground ...

Just last night in a dream, I imagined that I was floating
above ground. Since I can also imagine that I went to the
moon, do you really consider imagination to be a tool of
knowledge?

An interference pattern doesn't 'cause' energy to move around, fields
don't move other fields just as waves don't move other waves and photons
don't move other photons.

Then exactly what "redistributes the photons to regions that
permit constructive interference", as the FSU web page says?
Is it really imagination that accomplishes that magic feat?
If not, exactly how and why and what redistributes (moves)
those photons?

I will be happy to engage you in a step by step mathematical
explanation/discussion of what happens during superposition but
all you have done so far is hand-waving and ad hominem attacks.

Given the power-density equation:

Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

May I assume that from what you have said so far, that P1
and P2 never existed in the first place???? If they never
existed, wouldn't their magnitudes be zero in violation
of every rule of physics concerning reflections????

Jim, you have *NEVER* said what you think causes total
re-reflection of reflected waves (aside from your magical
imagination). Please enlighten us with some math and details
that don't violate the laws of physics.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Cecil Moore wrote:

Then exactly what "redistributes the photons to regions that
permit constructive interference", as the FSU web page says?

I don't think it reasonable to be held responsible to explain what
other people write. It's not a particularly rigorous or precise
treatise, Cecil.

Is it really imagination that accomplishes that magic feat?

How clever. You'll forgive me if I thought it better to ask you to
visualize the concept than for me to try to draw a football field
sized pair of capacitor plates with you between them using ASCII
characters. I suspect most other readers were able to accomplish the
task.

Jim, you have *NEVER* said what you think causes total
re-reflection of reflected waves (aside from your magical
imagination).

In fact, I have repeatedly explained it to you. Ad naseum. And so
have many other people on this group.

Please enlighten us with some math and details
that don't violate the laws of physics.

Texts like Born and Wolf and Jackson say it much more elegantly than I
ever could. There's a pretty good picture of it (albeit pitifully
notated) on your web site.

73, ac6xg

Superposition
 

Cecil Moore wrote:
Gene Fuller wrote:
"the intensity varies between a maximum value Imax = 4I1, and a
minimum value Imin = 0"

Yes, that's essentially what I have been saying. The peak
intensity (irradiance) can be double the intensity of
the combined intensity of both superposed waves.

What B&W *don't* say is anything about two 1 watt waves interacting,
waves exhibiting constructive and destructive interference, cause and
effects relationships, or even energy conservation.

Eugene Hecht calls the last term in the irradiance equation
the "interference term". He talks about "total destructive
interference" and "total constructive interference". The sign
of the interference term indicates whether the interference
is destructive (-) or constructive (+).

All of those are things written by more casual writers, such as Hecht,
Melles-Griot, and the FSU Java dudes. There is nothing wrong with that
type of explanation for simple illustration, but it runs out of gas
when trying to support detailed analysis. One quickly ends up with
silliness such as waves that are launched and then cancel
destructively within a short (but undefined) distance. None of that
nonsense occurs if one simply applies the standard analysis techniques
such as used by B&W.

Exactly what nonsense are you referring to? Please be specific. It
is difficult to defend myself from assertions of "nonsense" with no
specific allegations.

I gather from the above that wave cancellation due to superposition
is against your religion. Since all impedance discontinuities cause
reflections, exactly how and why do those reflected waves cease to
exist? Please be specific.

Cecil,

Waves are useful. However, they are not living objects. They have no
will to survive. There is nothing in the standard E&M science based on
Maxwell's laws that requires waves to be "canceled" if they no longer
exist. There is no conservation law of wave-ality.

If the proper equations are set up and the proper boundary conditions
are applied (not always easy to do), then waves will exist where they
are needed to describe the physical reality and they will not exist
where they are not needed.

There is no need to worry about waves that don't exist.

As for the "nonsense", we had this discussion a few times, including a
couple of months ago. I don't feel like finding the exact messages, but
the gist was something like:

"Wave 4 and wave 5 return toward the source from a match point, but they
are opposite phase and therefore cancel after a short journey."

If you don't recognize that exchange, let's just drop it.

73,
Gene
W4SZ

Superposition
 

Gene Fuller wrote:
Cecil Moore wrote:

Cecil,

Waves are useful. However, they are not living objects. They have no
will to survive. There is nothing in the standard E&M science based on
Maxwell's laws that requires waves to be "canceled" if they no longer
exist. There is no conservation law of wave-ality.

If the proper equations are set up and the proper boundary conditions
are applied (not always easy to do), then waves will exist where they
are needed to describe the physical reality and they will not exist
where they are not needed.

There is no need to worry about waves that don't exist.

As for the "nonsense", we had this discussion a few times, including a
couple of months ago. I don't feel like finding the exact messages, but
the gist was something like:

"Wave 4 and wave 5 return toward the source from a match point, but they
are opposite phase and therefore cancel after a short journey."

If you don't recognize that exchange, let's just drop it.

73,
Gene
W4SZ

Hi Gene,

Yes. The short journey was described by the term "dt". According to
Cecil, that is the amount of time after energy is reflected and before
it 'turns around and goes the other way as it is required to do by the
law of conservation of energy'. You may recall that it is forced to
go the other way 'because there are only two directions in a
transmission line'.

73, ac6xg

Superposition
 

On Tue, 20 Nov 2007 14:37:41 -0800, Jim Kelley
wrote:

The short journey was described by the term "dt".

Ah, suffering the dt's.

As Ed McMahon would prompt Johnny:
"Just how short was that journey?"

My guess it will either be too short to do the job, or much too large
to be true.

This thread should be called:
"Supposition"
or
"Imposition"
or
"Superstition"

73's
Richard Clark, KB7QHC

Superposition
 

Cecil Moore wrote:

Given the power-density equation:

Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

May I assume that from what you have said so far, that P1
and P2 never existed in the first place????

Being an under defined problem, it's difficult to know. But it is
certainly possible that P1, or P2, or both never existed.
Particularly the latter, if the fields happen to be co-located in
space and are at every point equal in magnitude and opposite in phase.

If they never
existed, wouldn't their magnitudes be zero in violation
of every rule of physics concerning reflections????

I assure that no 'physics violations' are implied or intended by
anything I post with my name, callsign, and email address attached to
it. It would not...um.....reflect well. ;-)

73, Jim AC6XG

Superposition
 

Jim Kelley wrote:
Jim, you have *NEVER* said what you think causes total
re-reflection of reflected waves (aside from your magical
imagination).

In fact, I have repeatedly explained it to you. Ad naseum. And so have
many other people on this group.

Nope, you never have - you just say you have hoping
nobody will notice that you have never done anything
except wave your hands.

What happens to the external reflected wave energy
at the moment the internal reflected wave arrives?

If you don't want to duplicate your effort please
re-post your previous posting on the subject. If
you don't respond, it will be obvious that there
was no previous posting.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Jim Kelley wrote:
But it is
certainly possible that P1, or P2, or both never existed. Particularly
the latter, if the fields happen to be co-located in space and are at
every point equal in magnitude and opposite in phase.

You cannot have it both ways, Jim. Either the reflections
existed or they they never existed. Please tell us why
and how a physical impedance discontinuity with a reflection
coefficient of 0.707 avoids causing reflections (in violation
of the laws of physics).
--
73, Cecil http://www.w5dxp.com

Superposition
 

Cecil Moore wrote:

You cannot have it both ways, Jim. Either the reflections
existed or they they never existed.

You want people to believe that the behavior of an antireflective
coating is, first light reflects from it, and then it's cancelled -
before anybody see's it. That's trying to have it both ways.

You're of course entitled to believe whatever you like. But you
really owe it to people to include a disclaimer when you proselytize
about it here.

End of commentary.

73, ac6xg

Superposition
 

Jim Kelley wrote:
You want people to believe that the behavior of an antireflective
coating is, first light reflects from it, and then it's cancelled -
before anybody see's it. That's trying to have it both ways.

No, that is obviously what happens, Jim. Since it happens
at the speed of light, our eyes just cannot see it. But
for the instant of time it takes the light wave to travel
the 1/2WL round trip through the thin-film and back, there
exists a reflection from the thin-film. The laws of physics
will not allow anything else.

It's a lot easier to detect at RF frequencies where 1/4WL
takes some time for the RF wave to travel. For instance,
1/4WL at 4 MHz is 61.5 feet. It takes RF a measurable
length of time to travel that distance and for that length
of time during the transient state, a reflection exists
which is canceled if a Z0-match is achieved. That's just
simple physics. Here is an example:

XMTR---50 ohm T-line---+---1/4WL 291.4 ohm T-line---50 ohm load

Rho at the impedance discontinuity is 0.707. For the length
of time it takes the first reflection to arrive back from
the load at point '+', 1/2 of the forward power is reflected
back toward the source. That's a reflected wave that is
subsequently canceled. Exactly what causes the cancellation
of that reflected wave? You have *never* answered that
question.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Gene Fuller wrote:
Waves are useful. However, they are not living objects. They have no
will to survive. There is nothing in the standard E&M science based on
Maxwell's laws that requires waves to be "canceled" if they no longer
exist. There is no conservation law of wave-ality.

All EM waves must obey the conservation of energy and
conservation of momentum principles. It is not a will
to survive - it is simply the laws of physics.

Here is an example for you to explain. The source is
a signal generator equipped with an ideal circulator
and a load resistor:

Steady-state #1: Rho at '+' equals 0.7143. Load equals
300 ohms.

100w SGCL--50 ohm feedline--+--1/2WL 300 ohm feedline--300 ohm load
Pfor1=100w-- Pfor2=49w--
--Pref1=51w --Pref2=0w

Pref1 is an 51w EM wave whose energy and momentum must be
conserved.

Steady-state #2: Rho at '+' equals 0.7143. Load is switched
to 50 ohms.

100w SGCL--50 ohm feedline--+--1/2WL 300 ohm feedline--50 ohm load
Pfor1=100w-- Pfor2=204W--
--Pref1=0w --Pref2=104w

*Note that Rho has NOT changed!*

The only question that you need to answer is during the
process that changes Pref1 from 51 joules/sec in the direction
of the source to 0 joules/sec (canceled), *exactly* what happens
to the energy and momentum? Please be specific.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Jim Kelley wrote:
Yes. The short journey was described by the term "dt". According to
Cecil, that is the amount of time after energy is reflected and before
it 'turns around and goes the other way as it is required to do by the
law of conservation of energy'. You may recall that it is forced to go
the other way 'because there are only two directions in a transmission
line'.

So you don't even accept differential calculus? :-)
Jim, you have never answered the tough questions so I
will keep asking. I just posted an example with one
question that should be easy for you to answer.

In the example, what happens to the energy and momentum
in Pref1 when the load is switched from 300 ohms to 50
ohms? It's a simple question. Please be specific in your
answer.
--
73, Cecil http://www.w5dxp.com

Superposition
 

On Wed, 21 Nov 2007 14:00:39 GMT, Cecil Moore
wrote:

What is the momentum of 50.95 W?

momentum? Please be specific.
ditto. :-)

Superposition
 

Cecil Moore wrote:
Gene Fuller wrote:
Waves are useful. However, they are not living objects. They have no
will to survive. There is nothing in the standard E&M science based on
Maxwell's laws that requires waves to be "canceled" if they no longer
exist. There is no conservation law of wave-ality.

All EM waves must obey the conservation of energy and
conservation of momentum principles. It is not a will
to survive - it is simply the laws of physics.

Here is an example for you to explain. The source is
a signal generator equipped with an ideal circulator
and a load resistor:

Steady-state #1: Rho at '+' equals 0.7143. Load equals
300 ohms.

100w SGCL--50 ohm feedline--+--1/2WL 300 ohm feedline--300 ohm load
Pfor1=100w-- Pfor2=49w--
--Pref1=51w --Pref2=0w

Pref1 is an 51w EM wave whose energy and momentum must be
conserved.

Steady-state #2: Rho at '+' equals 0.7143. Load is switched
to 50 ohms.

100w SGCL--50 ohm feedline--+--1/2WL 300 ohm feedline--50 ohm load
Pfor1=100w-- Pfor2=204W--
--Pref1=0w --Pref2=104w

*Note that Rho has NOT changed!*

The only question that you need to answer is during the
process that changes Pref1 from 51 joules/sec in the direction
of the source to 0 joules/sec (canceled), *exactly* what happens
to the energy and momentum? Please be specific.


Cecil,

Nice try.

Combining "steady state" with "switched" and "during the process that
changes" makes a very messy problem for an analytical solution.

You first.

And you won't get any closer to the correct solution through all of your
handwaving arguments either.

73,
Gene
W4SZ

Superposition
 

Richard Clark wrote:
On Wed, 21 Nov 2007 14:00:39 GMT, Cecil Moore
wrote:

What is the momentum of 50.95 W?

momentum? Please be specific.
ditto. :-)

If 50.95 watts is the Poynting vector, actually
watts/unit-area, then the momentum is 50.95/c^2.
Please reference pages 56,57 of "Optics", by Hecht,
4th edition.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Gene Fuller wrote:
Cecil Moore wrote:
Gene Fuller wrote:
Waves are useful. However, they are not living objects. They have no
will to survive. There is nothing in the standard E&M science based
on Maxwell's laws that requires waves to be "canceled" if they no
longer exist. There is no conservation law of wave-ality.

All EM waves must obey the conservation of energy and
conservation of momentum principles. It is not a will
to survive - it is simply the laws of physics.

Here is an example for you to explain. The source is
a signal generator equipped with an ideal circulator
and a load resistor:

Steady-state #1: Rho at '+' equals 0.7143. Load equals
300 ohms.

100w SGCL--50 ohm feedline--+--1/2WL 300 ohm feedline--300 ohm load
Pfor1=100w-- Pfor2=49w--
--Pref1=51w --Pref2=0w

Pref1 is an 51w EM wave whose energy and momentum must be
conserved.

Steady-state #2: Rho at '+' equals 0.7143. Load is switched
to 50 ohms.

100w SGCL--50 ohm feedline--+--1/2WL 300 ohm feedline--50 ohm load
Pfor1=100w-- Pfor2=204W--
--Pref1=0w --Pref2=104w

*Note that Rho has NOT changed!*

The only question that you need to answer is during the
process that changes Pref1 from 51 joules/sec in the direction
of the source to 0 joules/sec (canceled), *exactly* what happens
to the energy and momentum? Please be specific.

You first.

Cop out. Why am I not surprised that you, yet once again, refuse
to answer the question? Could it be because you would immediately
be proven wrong? Do you really believe that diversions are a tool
of technical knowledge?

The original 51 joule/sec reflected wave toward the source interacts
with the newly reflected wave from the load and is partially
canceled which through constructive interference, delivers more
forward power toward the load, which results in an increase in the
energy in the reflected wave from the load, which results in more
wave cancellation at '+', etc. until steady-state #2 is reached.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Cecil Moore wrote:
Richard Clark wrote:
On Wed, 21 Nov 2007 14:00:39 GMT, Cecil Moore
wrote:

What is the momentum of 50.95 W?

momentum? Please be specific.
ditto. :-)

If 50.95 watts is the Poynting vector, actually
watts/unit-area, then the momentum is 50.95/c^2.
Please reference pages 56,57 of "Optics", by Hecht,
4th edition.

50.95 divided by the speed of light squared? So, for all
practical purposes - if that's right - it's zero. Why not
just say so?
73,
Tom Donaly, KA6RUH

Superposition
 

Cecil Moore wrote:


Cop out. Why am I not surprised that you, yet once again, refuse
to answer the question? Could it be because you would immediately
be proven wrong? Do you really believe that diversions are a tool
of technical knowledge?

The original 51 joule/sec reflected wave toward the source interacts
with the newly reflected wave from the load and is partially
canceled which through constructive interference, delivers more
forward power toward the load, which results in an increase in the
energy in the reflected wave from the load, which results in more
wave cancellation at '+', etc. until steady-state #2 is reached.

Blah, Blah, Blah. Totally useless drivel. Let's see some real numbers.
Then we can discuss cop out.

You might also check your favorite reference to try to figure out what
conservation of energy really means. Then you would realize that even a
full solution to your idealized problem would demonstrate absolutely
nothing with respect to conservation of energy.

73,
Gene
W4SZ

Superposition
 

Tom Donaly wrote:
Cecil Moore wrote:
Richard Clark wrote:
On Wed, 21 Nov 2007 14:00:39 GMT, Cecil Moore
wrote:

What is the momentum of 50.95 W?

momentum? Please be specific.
ditto. :-)

If 50.95 watts is the Poynting vector, actually
watts/unit-area, then the momentum is 50.95/c^2.
Please reference pages 56,57 of "Optics", by Hecht,
4th edition.

50.95 divided by the speed of light squared? So, for all
practical purposes - if that's right - it's zero. Why not
just say so?

The percentage difference between zero and that momentum
is infinite. And whatever value it is must be conserved.
Sweeping it under the rug in violation of the laws of
physics is just not acceptable.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Gene Fuller wrote:
Cecil Moore wrote:
Cop out. Why am I not surprised that you, yet once again, refuse
to answer the question? Could it be because you would immediately
be proven wrong? Do you really believe that diversions are a tool
of technical knowledge?

The original 51 joule/sec reflected wave toward the source interacts
with the newly reflected wave from the load and is partially
canceled which through constructive interference, delivers more
forward power toward the load, which results in an increase in the
energy in the reflected wave from the load, which results in more
wave cancellation at '+', etc. until steady-state #2 is reached.

Blah, Blah, Blah. Totally useless drivel. Let's see some real numbers.
Then we can discuss cop out.

In the words of the biggest cop out artist I know, "You first".
I've already posted the numbers for the graphic at:
http://www.w5dxp.com/thinfilm.gif

Instead of responding, you tucked tail and ran.

You might also check your favorite reference to try to figure out what
conservation of energy really means. Then you would realize that even a
full solution to your idealized problem would demonstrate absolutely
nothing with respect to conservation of energy.

That's exactly the problem. Lots of people pay lip service to
the conservation of energy principle without realizing they
advocate violation of it.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Cecil Moore wrote:
Tom Donaly wrote:
Cecil Moore wrote:
Richard Clark wrote:
On Wed, 21 Nov 2007 14:00:39 GMT, Cecil Moore
wrote:

What is the momentum of 50.95 W?

momentum? Please be specific.
ditto. :-)

If 50.95 watts is the Poynting vector, actually
watts/unit-area, then the momentum is 50.95/c^2.
Please reference pages 56,57 of "Optics", by Hecht,
4th edition.

50.95 divided by the speed of light squared? So, for all
practical purposes - if that's right - it's zero. Why not
just say so?

The percentage difference between zero and that momentum
is infinite. And whatever value it is must be conserved.
Sweeping it under the rug in violation of the laws of
physics is just not acceptable.

Actually, you're writing about momentum density. Momentum is
conserved, but momentum density isn't, any more than energy
density, or any other kind of density, with the possible
exception of the bone density in the heads of some people.
As for any finite number being an infinite percentage above
zero, I think you should take that up with the next mathematician
you meet. Mathematicians need to laugh once in a while, too.
73,
Tom Donaly, KA6RUH

Superposition
 

On Wed, 21 Nov 2007 16:50:49 -0600, Cecil Moore
wrote:

Richard Clark wrote:
On Wed, 21 Nov 2007 14:00:39 GMT, Cecil Moore
wrote:

What is the momentum of 50.95 W?

momentum? Please be specific.
ditto. :-)

If 50.95 watts is the Poynting vector, actually
watts/unit-area, then the momentum is 50.95/c^2.

Hmmm, basic math demands that momentum be in units of rather more
prosaic terms, namely
kg·m/s

If we carry out the math of your own answer, it renders units in your
terms to:
(watts/m²)/(m/s)²
or
((kg·m²/s³)/m²)/(m/s)²
or
kg/(s·m²)

Perhaps I fumbled the product of powers, but it looks like you could
have as easily just divided by pi and still come out to the same
effect of "proving" a balance to conserve your dignity. ;-)

With momentum like this, Lyndon LaRouche would have been elected
president in 1991.

Superposition
 

On Thu, 22 Nov 2007 00:48:02 -0500, "AI4QJ" wrote:


"Richard Clark" wrote in message
.. .
On Wed, 21 Nov 2007 16:50:49 -0600, Cecil Moore
wrote:

Richard Clark wrote:
On Wed, 21 Nov 2007 14:00:39 GMT, Cecil Moore
wrote:

What is the momentum of 50.95 W?

momentum? Please be specific.
ditto. :-)

If 50.95 watts is the Poynting vector, actually
watts/unit-area, then the momentum is 50.95/c^2.

Hmmm, basic math demands that momentum be in units of rather more
prosaic terms, namely
kg·m/s

If we carry out the math of your own answer, it renders units in your
terms to:
(watts/m²)/(m/s)²
or
((kg·m²/s³)/m²)/(m/s)²
or
kg/(s·m²)

Perhaps I fumbled the product of powers, but it looks like you could
have as easily just divided by pi and still come out to the same
effect of "proving" a balance to conserve your dignity. ;-)

With momentum like this, Lyndon LaRouche would have been elected
president in 1991.

I think you never got a chance to take the basic courses in quantum
mechanics Richard. If you did, you would understand this. As it is, you seem
close to understanding it without having such a background which is really
curious. I think you would learn it quite easily.

Hi Dan,

You might be right, you might be wrong, but you don't really know
yourself, do you?

I did take QM, and I did learn it quite easily. However, this has
nothing to do with Momentum beyond what was already revealed above. If
you've found no math errors (and that could go either way, favoring
either me or Cecil - or we are both wrong), then what's your point?

Momentum is also "Radiation Pressure," a topic I've brought to this
forum in the past. Radiation Pressure has a very Newtonian result
that easily manifests itself in exactly the prosaic terms I posed
above. The computation may be tedious (and bordering well beyond
trivial), but it certainly isn't difficult. Do you care to offer a
solution? :-)

73's
Richard Clark, KB7QHC

Superposition
 

Tom Donaly wrote:
Actually, you're writing about momentum density. Momentum is
conserved, but momentum density isn't, ...

The momentum density may certainly change with area just
as the energy density may change with area. But in either
case, the total energy and total momentum are conserved.

As for any finite number being an infinite percentage above
zero, I think you should take that up with the next mathematician
you meet.

The equation for any percentage change from zero is
100(X-0)/0 Plug any value of X into that equation and
see what you get.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Richard Clark wrote:
kg/(s·m²)

One needs to multiply by the area under consideration
to obtain the total momentum which is conserved.

It's the same as multiplying the Poynting vector
by the area under consideration to obtain the
total energy.
--
73, Cecil http://www.w5dxp.com

Superposition
 

AI4QJ wrote:
If you are considering adding structural supports for your transmission line
it is zero. If you want to understand the physics it is not zero. Photons
have mass (not rest mass but mass), light has pressure that has been
measured and it has momentum.

Quoting Maxwell in 1873: "In a medium in which waves are
propagated, there is a pressure in the direction normal
to the waves, and numerically equal to the energy in a
unit of volume."
--
73, Cecil http://www.w5dxp.com

Superposition
 

Gene Fuller wrote:
Let's see some real numbers.

The numbers are trivial. What is important is the concept.
In the experiment, the Pref1 wave disappears between
steady-state #1 and steady-state #2. Here's the question
that you and others have refused to answer.

When an EM wave disappears in its original direction of
travel, what happens to its energy?
--
73, Cecil http://www.w5dxp.com

Superposition
 

On Thu, 22 Nov 2007 05:20:10 -0600, Cecil Moore
were Cecil's dignity was not conserved, wrote:
If we carry out the math of your own answer, it renders units in your
terms to:
(watts/m²)/(m/s)²
or
((kg·m²/s³)/m²)/(m/s)²
or
kg/(s·m²)

One needs to multiply by the area under consideration
to obtain the total momentum which is conserved.

Which, of course, yields:
kg/s
which is not momentum, but oddly enough the units one might use in
describing how fast his bath tub was filling with photons. :-)

Oh well, third time's a charm! Keep fumbling with the conservation of
dignity, and eventually you might bumble into a job with Anderson
Consulting doing Enron's books.

Superposition
 

50.95 divided by the speed of light squared? So, for all
practical purposes - if that's right - it's zero. Why not
just say so?

That depends entirely on the units you're using.

If you measure the velocity of C in typical human-scale units (e.g.
metres per second) then C^2 is, indeed, a numerically-large value, and
50.95/C^2 is numerically small (and will be in units of
watts seconds-squared over metres-squared).

If, on the other hand, you measure velocities on another scale, things
look very different. Specifically, let's use a scale which represents
each velocity as a fraction of the maximum possible velocity... let's
call this unit of velocity "skedaddles". Measured this way, C is
precisely 1.0 skedaddle, C^2 is precisely 1.0 skedaddle squared, and
50.95/C^2 equals 50.95 (watts per square skedaddle).

Same result... only the units of measurement are different. Neither
result is zero. "Numerically small" is not equivalent to "zero for
all practical purposes".

(obLinguistic: "skedaddle" is a somewhat quirky American term of
uncertain heritage, which means "leave in a hurry, scram, escape", and
seems a reasonable term for a scale of zerch up to as-fast-as-
possible. I believe that the equivalent British term was defined as
"runawayrunaway" by King Arthur, as cited in "Monty Python and the
Holy Grail").

--
Dave Platt AE6EO
Friends of Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

Superposition
 

Cecil Moore wrote:
Gene Fuller wrote:
Let's see some real numbers.

The numbers are trivial. What is important is the concept.
In the experiment, the Pref1 wave disappears between
steady-state #1 and steady-state #2. Here's the question
that you and others have refused to answer.

When an EM wave disappears in its original direction of
travel, what happens to its energy?

OK, but first let's set the ground rules.

The ONLY thing under discussion here is our disagreement about the
canceling waves heading back toward the source from the match point. You
claim those waves must exist and then cancel over a short distance (I
believe you reduced the distance to 'dx' or something similar.) I claim
those waves never exist at all and therefore don't need to be canceled.

If you have anything else in mind, then enjoy your solo activity,
whatever that might be.

So just what "trivial" numbers are required?

First, it is not clear how one make an instant transition from a 50 ohm
environment to a 300 ohm environment. Do you just connect a 50 ohm coax
to a 300 ohm coax? Or do you prefer to connect a 50 ohm twin-lead to a
300 ohm twin-lead? (Good luck with either of these.) If you want to
connect a 50 ohm coax to a 300 ohm twin-lead then you are going to need
some sort of transition device.

Oops! Where is the match point now? Ordinarily we would not really care
very much about such things, but you have stated that important things
are happening within the "dx" zone. It is a safe bet that the Z0
transition is not abrupt either. The "trivial" numbers just got a bit
more complicated.

Let's look at the conservation of energy part. You like to use the
Poynting vector, so we can stick with that. The first thing to note is
that the Poynting vector is E x H, not V x I. Perhaps only a minor bump
in the road, but the transition from E to V and H to I is not quite so
trivial at discontinuities such as the "match point".

But let's muddle ahead in any case. The integral form of the Poynting
theorem goes like the following.

* Define a test volume with a closed surface. There is no particular
size required, although infinite and zero don't work well for practical
reasons.

* Calculate the Poynting vector at all points on the closed surface.

* Integrate the 'normal' component of the Poynting vector over the
entire surface. This integral then represents the net electromagnetic
energy flowing into (or out of) the test volume. I believe this is what
you would consider the energy carried by the waves of interest. Note
that all waves are combined together; they are not treated separately.

* The Poynting theorem says that the net energy flow must be balanced by
the change in electromagnetic energy content within the test volume and
the work done by the fields on any charges within the test volume.

* Note that a change in field strength within the test volume is tied to
the change in electromagnetic energy content. Any charges within the
test volume can be accelerated. Remember, this sort of match point
cannot exist in free space, so there are charges in the region of interest.


This sort of description and the associated derivations can be found in
any ordinary E&M textbook.


You might notice that the Poynting theorem, i.e. conservation of energy
law for EM, says nothing about the sanctity of waves or about the
conservation of energy in waves. It does not say that the integral of
the Poynting vector over the test volume surface must be zero.

Even more importantly for this discussion, the Poynting theorem does not
help at all with your assertion that important things are happening in
the 'dx' zone. If you make the test volume size smaller than your 'dx'
then you run into trouble with the finite size of the transition region
described above. If you make the test volume large enough to contain the
'dx', then all of the purported interesting stuff happens inside. Again,
the Poynting theorem tells nothing.


If you want to believe in the conservation of waves, go right ahead.
Just don't expect conservation of energy to support your case.
Mathematically it cannot.


73,
Gene
W4SZ

Superposition
 

On Thu, 22 Nov 2007 07:34:14 -0800, Richard Clark
wrote:

On Thu, 22 Nov 2007 05:20:10 -0600, Cecil Moore
were Cecil's dignity was not conserved, wrote:
If we carry out the math of your own answer, it renders units in your
terms to:
(watts/m²)/(m/s)²
or
((kg·m²/s³)/m²)/(m/s)²
or
kg/(s·m²)

One needs to multiply by the area under consideration
to obtain the total momentum which is conserved.

Which, of course, yields:
kg/s
which is not momentum, but oddly enough the units one might use in
describing how fast his bath tub was filling with photons. :-)

Oh well, third time's a charm! Keep fumbling with the conservation of
dignity, and eventually you might bumble into a job with Anderson
Consulting doing Enron's books.

Hi All,

Well, no point in waiting for another rationalization when I am
perfectly capable of filling that in for Cec' (and more entertaining
than him when I do).

Let's see if I can pull together a good old-boy drawl and a scrub of
the boot toe in the dirt:
"One needs to multiply by the volume under consideration
to obtain the total momentum which is conserved!"

Umm, yes, if your Xeroxed authors need that much help in you
describing what they must have meant, but didn't say, then throwing in
previously undisclosed terms might do the trick.

However, looking aside from this obvious self-serving manipulation of
the books (Anderson would be proud, in a perverted sense) it then
gives us a third dimension of meters (the one you will have suckered
into the equation) which is also a time specification (and this would
then be called not Momentum, but Impulse, which does carry the same
units but is the Integration over time).

"Yes! Of course! This is called the Conservation of Impulse!
It is EXACTLY what my references meant to say...."

And then we return to an observation I made earlier about:
The short journey was described by the term "dt".

Ah, suffering the dt's.

As Ed McMahon would prompt Johnny:
"Just how short was that journey?"

My guess it will either be too short to do the job, or much too large
to be true.
and we had been left holding the bag once again with asking how big dt
is? Which, of course, also flummoxed Cecil (his having not yet had
the epiphany of what his references "meant to say" but left unsaid).
Some might begin to wonder how they earned a salary in the career of
teaching.

And to whip a dead horse, I also said:
This thread should be called:
"Supposition"
or
"Imposition"
or
"Superstition"

To the group,

Sorry for having unleashed yet another law of conservation that will
undoubtedly yield 100s of postings of "proofs" that in and of
themselves will actually contain no intellectual nourishment.

Next week:
"The Conservation of Radiation Buoyancy"

73's
Richard Clark, KB7QHC