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jj October 29th 03 12:18 AM

What Exactly is a Radio Wave?
 
This may at first sound like a stupid question. But after some years
as a radio enthusiast, I don't know what a radio wave is - what it
really is. Supposedly, modern physics does not believe there is such
a thing as "action at a distance". In other words, if you launch a
radio wave and I intercept it, there must be a transfer of "stuff"
between you and me. You can't just say that if I wiggle an electron
at point A, I can cause a wiggle at the same wiggle rate at point B.
I mean you can say it, but it doesn't explain anything.

OK, so the latest science says that electromagnetic energy is really
particle-waves. I guess this means that when I transmit, my antenna
is firing particles in the form of low-energy photons (energy
packets), and that these photons do not really exist anywhere but
exist only as probability waves - until, of course, someone intercepts
the wave. Then, magically, the photons appear at the receiving
antenna, in which they manage to produce oscillating electrons.

So, the best I can ascertain is that radio waves are really
probability waves. I'm not sure that really helps with an intuitive
understanding. Does anyone have a good description for what a radio
wave really is?

- JJ

Tdonaly October 29th 03 12:40 AM

JJ wrote,

So, the best I can ascertain is that radio waves are really
probability waves. I'm not sure that really helps with an intuitive
understanding. Does anyone have a good description for what a radio
wave really is?

- JJ


Yes, go ask your question on sci.physics.electromag and you'll get
some answers, although I can't guarantee they'll be of any use to you.
73,
Tom Donaly, KA6RUH



Roy Lewallen October 29th 03 01:04 AM

A radio wave is an electromagnetic field. On my first day of fields
class, I asked the professor what an electromagnetic field was. His
reply: "An electromagnetic field is a mathematical model that enables us
to explain certain phenomena which we can measure." The professor was
Carl T. A. Johnk. I have in front of me his text, _Engineering
Electromagnetic Fields and Waves_. On page 1, it says, "A field is taken
to mean a mathematical function of space and time."

"Stuff" isn't transferred from one place to another by electromagnetic
fields, but energy most definitely is. Force can be applied through
space from one place to another by means of an electromagnetic field,
and energy can be transferred by means of a field. Since the energy
contained in a field can be calculated, I'll go out on a limb and say
that a radio wave can be regarded as a form of energy, like heat or
falling water. Perhaps a purist or physicist can find grounds to argue
with that statement, it's certainly a valid concept for engineering
purposes.

As far as photons and waves go, be really, really careful in extending
your everyday experience to quantum mechanical objects. Feynman very
nicely illustrates in "Quantum Behavior" in his book _Six Easy Pieces_
that neither particles nor waves is adequate to describe such things:

"Things on a very small scale behave like nothing that you have any
direct experience about. They do not behave like waves, they do not
behave like particles, they do not behave like clouds, or billiard
balls, or weights on springs, or like anything that you have ever seen.
.. . Historically, the electron, for example, was thought to behave like
a particle, and then it was found that in many resepects it behaved like
a wave. So it really behaves like neither. Now we have given up. We say:
'It is like *neither*'"

I highly recommend this book, and other of his writings, if you're
interested in understanding these phenomena on a more basic level.

Roy Lewallen, W7EL

jj wrote:
This may at first sound like a stupid question. But after some years
as a radio enthusiast, I don't know what a radio wave is - what it
really is. Supposedly, modern physics does not believe there is such
a thing as "action at a distance". In other words, if you launch a
radio wave and I intercept it, there must be a transfer of "stuff"
between you and me. You can't just say that if I wiggle an electron
at point A, I can cause a wiggle at the same wiggle rate at point B.
I mean you can say it, but it doesn't explain anything.

OK, so the latest science says that electromagnetic energy is really
particle-waves. I guess this means that when I transmit, my antenna
is firing particles in the form of low-energy photons (energy
packets), and that these photons do not really exist anywhere but
exist only as probability waves - until, of course, someone intercepts
the wave. Then, magically, the photons appear at the receiving
antenna, in which they manage to produce oscillating electrons.

So, the best I can ascertain is that radio waves are really
probability waves. I'm not sure that really helps with an intuitive
understanding. Does anyone have a good description for what a radio
wave really is?

- JJ



Dave VanHorn October 29th 03 02:03 AM


"Things on a very small scale behave like nothing that you have any
direct experience about. They do not behave like waves, they do not
behave like particles, they do not behave like clouds, or billiard
balls, or weights on springs, or like anything that you have ever seen.


I love that part, and I always picture Ed Norton of the Honeymooners.. :)

I picture it more or less, as sort of a tide in the wheeler foam, changing
the probabilities.

Works for me..



Cecil Moore October 29th 03 03:59 AM

jj wrote:
So, the best I can ascertain is that radio waves are really
probability waves. I'm not sure that really helps with an intuitive
understanding.


Photons behave strangely when you are dealing with one at a time. When
you are dealing with billions of photons, quantum probability predicts their
collective behavior very well. Quoting _QED_, by Feynman: "So now I present to
you the three basic actions, from which all phenomena of light (including radio
waves) and electrons arise:

-Action #1: A photon goes from place to place.
-Action #2: An electron goes from place to place.
-Action #3: An electron emits or absorbs a photon.
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil Moore October 29th 03 04:10 AM

Roy Lewallen wrote:
"Things on a very small scale behave like nothing that you have any
direct experience about. They do not behave like waves, they do not
behave like particles, they do not behave like clouds, or billiard
balls, or weights on springs, or like anything that you have ever seen.
. . Historically, the electron, for example, was thought to behave like
a particle, and then it was found that in many resepects it behaved like
a wave. So it really behaves like neither. Now we have given up. We say:
'It is like *neither*'"


OTOH, quantum physics predicts the outcomes perfectly and has never been
proven wrong so it doesn't matter what we call photons. If you really want
to understand this stuff, you need to read a good book on string theory. May
I suggest _The_Tenth_Dimension_, by Jeremy Bernstein or catch the two NOVAs
that were on tonight.
--
73, Cecil http://www.qsl.net/w5dxp



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Roy Lewallen October 29th 03 05:09 AM

Cecil Moore wrote:
Roy Lewallen wrote:

"Things on a very small scale behave like nothing that you have any
direct experience about. They do not behave like waves, they do not
behave like particles, they do not behave like clouds, or billiard
balls, or weights on springs, or like anything that you have ever
seen. . . Historically, the electron, for example, was thought to
behave like a particle, and then it was found that in many resepects
it behaved like a wave. So it really behaves like neither. Now we have
given up. We say: 'It is like *neither*'"



OTOH, quantum physics predicts the outcomes perfectly and has never been
proven wrong so it doesn't matter what we call photons. If you really want
to understand this stuff, you need to read a good book on string theory.
May
I suggest _The_Tenth_Dimension_, by Jeremy Bernstein or catch the two NOVAs
that were on tonight.


Is that where we'll learn all about virtual photons, the fourth
dimension, and their application to measuring voltage?

Roy Lewallen, W7EL


Peter O. Brackett October 29th 03 07:36 AM

jj:

A round about way of defining a "radio wave" is that it is just
any field function that satisfies a wave equation.

Period, end of story. No one really knows any more than that!

A wave equation is a partial differential equation of theoretical
physics which describes the dynamics of electrical and magnetic
fields. i.e. a wave equation is a simple derivation from Maxwell's
celebrated equations of electrodynamics.

In the beginning of electrodynamics there were only circuit-theoretic
concepts [Kirchoff, Ohm] which sufficed to explain many
electromagnetic phenomena.

Then later wave-theoretic concepts or wave electrodynamics [Maxwell,
Heaviside] were required to explain phenomena that circuit theory could
not explain satisfactorily [radiation, skin effect, proximity effect, etc.].
This is when the concept of radio waves as the solutions to partial
differential wave equations arose.

Then later quantum-theoretic concepts known as quantum
electrodynamics, or QED [Einstein, Dirac, Pauli, Feynman] were
required to explain phenomena that wave-theory could not explain
satisfactorily [photoelectric effect]. This is when the concept of radio
waves as a flow of particles [photons] arose.

QED is completely without intuitive analogic interperation by anything
closely related to regular human experience, like say waves. One just
has to "crank" the formulas [Feynman] and see what comes out.
Regardless, today in the first decade of the 21st century it seems that
the QED theory which is now approximately 60 years old and which
casts the "true" meaning of "radio waves" as a floww of discrete photons,
remains as the only theory that can quantitatively explain exactly all of
electromagnetic phenomena and the interaction of energy with matter.

An interesting high school level introduction and explanation of all of
this is available in the popular book on QED by one of the world's
great teaching physicists. The guy from CalTech who dipped a piece
of the Challenger rocket booster's O-ring in the glass of ice water at
the Challenger space shuttle disaster hearings.

cfr:

Richard Phillips Feynman, QED - The Strange Theory of Light and
Matter, Princeton University Press, Princeton, NJ 1985.
ISBN:0-691-02417-0 [QC793.5P422F48]

From the page 9 of the Introduction to "QED" Feynman says,
"You're not going to be able to understand it... You see my
Physics students don't understand it either. That is because
I don't understand it. Nobody does!"

Good luck with analogies to things we seem to "understand".

--
Peter K1PO
Indialantic By-the-Sea, FL.


"jj" wrote in message
om...
This may at first sound like a stupid question. But after some years
as a radio enthusiast, I don't know what a radio wave is - what it
really is. Supposedly, modern physics does not believe there is such
a thing as "action at a distance". In other words, if you launch a
radio wave and I intercept it, there must be a transfer of "stuff"
between you and me. You can't just say that if I wiggle an electron
at point A, I can cause a wiggle at the same wiggle rate at point B.
I mean you can say it, but it doesn't explain anything.

OK, so the latest science says that electromagnetic energy is really
particle-waves. I guess this means that when I transmit, my antenna
is firing particles in the form of low-energy photons (energy
packets), and that these photons do not really exist anywhere but
exist only as probability waves - until, of course, someone intercepts
the wave. Then, magically, the photons appear at the receiving
antenna, in which they manage to produce oscillating electrons.

So, the best I can ascertain is that radio waves are really
probability waves. I'm not sure that really helps with an intuitive
understanding. Does anyone have a good description for what a radio
wave really is?

- JJ




Tom Bruhns October 29th 03 09:01 AM

Roy Lewallen wrote in message ...
....
(writing about Richard Feynman's books)
I highly recommend this book, and other of his writings, if you're
interested in understanding these phenomena on a more basic level.


I strongly agree. You'll also find some interesting words about it in
the opening pages of the "Antennas" chapter of King, Mimno and Wing's
"Transmission Lines, Antennas and Waveguides."

I would go so far as to say that everything we've summarized about
"radio waves" in all our writings is all just models to explain our
observations. On some level, we don't really know what anything is;
we just have ways to communicate about those things. We have models.
Some of them seem pretty darned good, but perhaps we're just looking
at the actions in one tiny corner of our multi-dimensional universe
and we may find that all our models are woefully inadequate to cover
the big picture. So what? They work for what we're doing right now.
We can deal with the inadequacies when they arise. We can stay
constantly on the lookout for them, and accept them and learn from
them. A couple hundred years ago, Newtonian physics seemed adequate,
and for the time, for what people were observing and designing, it
was. But we've learned more, and refined our models. You should
expect it will continue to happen, as long as curious humans are
around to ponder the problems. In fact, just because our models are
somehow "better" now than they were five years ago, or fifty, or five
hundred, that doesn't necessarily mean that the earlier models are now
worthless. You just need to know their limitations, and apply them
only where the limitations are practically unimportant. We still use
Newtonian physics for a lot of engineering work because it's not worth
the effort to add relativistic terms when we know that they won't be
observable, and other errors will dominate.

Cheers,
Tom

Al - KA5JGV October 29th 03 01:48 PM


"Tom Bruhns" wrote in message
...
On some level, we don't really know what anything is;
we just have ways to communicate about those things. We have models.
Cheers,
Tom


I like that definition, Tom. Instead of struggling with what every tiny
thing is, just model it, apply it to your needs, and life (and radio waves)
goes on.

Al KA5JGV



Alan October 29th 03 02:33 PM

But that's NOT a definition.

Alan
WN4HOG

--
Windsurfing Club: http://www.ibscc.org


"Al - KA5JGV" wrote in
I like that definition, Tom. Instead of struggling with what every tiny
thing is, just model it, apply it to your needs, and life (and radio

waves)
goes on.

Al KA5JGV





Cecil Moore October 29th 03 02:38 PM

Roy Lewallen wrote:
Cecil Moore wrote:

Roy Lewallen wrote:

"Things on a very small scale behave like nothing that you have any
direct experience about. They do not behave like waves, they do not
behave like particles, they do not behave like clouds, or billiard
balls, or weights on springs, or like anything that you have ever
seen. . . Historically, the electron, for example, was thought to
behave like a particle, and then it was found that in many resepects
it behaved like a wave. So it really behaves like neither. Now we
have given up. We say: 'It is like *neither*'"


OTOH, quantum physics predicts the outcomes perfectly and has never been
proven wrong so it doesn't matter what we call photons. If you really
want to understand this stuff, you need to read a good book on string
theory. May I suggest _The_Tenth_Dimension_, by Jeremy Bernstein or
catch the two NOVAs that were on tonight.


Is that where we'll learn all about virtual photons, the fourth
dimension, and their application to measuring voltage?


Yes, six of the dimensions are thought to support the fabric of space,
the æther, if you will. String theory has yielded a unified field theory
including massless gravitons.

The point is that just because photons do not behave like pure waves
or pure particles, doesn't mean they are useless. It just means that
we don't yet have a one word handle to describe their true nature.
--
73, Cecil http://www.qsl.net/w5dxp



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Cecil Moore October 29th 03 03:11 PM

Alan wrote:
But that's NOT a definition.


From the IEEE Dictionary: "radio wave - An electromagnetic
wave of radio frequency."
--
73, Cecil http://www.qsl.net/w5dxp



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Lionel Carter October 29th 03 05:18 PM

I've been expecting one of the gurus in the ng would be saying Real Radio
Hams build their own theories.

Lionel Carter


"W7TI" wrote in message
...
On 28 Oct 2003 16:18:17 -0800, (jj) wrote:

Does anyone have a good description for what a radio
wave really is?


__________________________________________________ _______

The short answer is "no". Many people confuse the measurement of things
with having an understanding of them.

Scientists are very good at measuring things; less good at understanding
what they measure. For example, gravity is measurable down to a gnat's
eyelash, but nobody knows what it really "is".

--
Bill, W7TI




Alan October 29th 03 05:22 PM

Sounds good to me. Thanks!
Alan
WN4HOG

--
Windsurfing Club: http://www.ibscc.org


"Cecil Moore" wrote in message
...
Alan wrote:
But that's NOT a definition.


From the IEEE Dictionary: "radio wave - An electromagnetic
wave of radio frequency."
--
73, Cecil http://www.qsl.net/w5dxp



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Richard Clark October 29th 03 05:49 PM

On Wed, 29 Oct 2003 17:18:39 -0000, "Lionel Carter"
wrote:

I've been expecting one of the gurus in the ng would be saying Real Radio
Hams build their own theories.

Lionel Carter


Hi Lionel,

Some of the "explanations" couched in Quantum nonsense have
accomplished that end none the less.

73's
Richard Clark, KB7QHC

Yuri Blanarovich October 29th 03 06:03 PM


From the page 9 of the Introduction to "QED" Feynman says,
"You're not going to be able to understand it... You see my
Physics students don't understand it either. That is because
I don't understand it. Nobody does!"

Good luck with analogies to things we seem to "understand".

--
Peter K1PO
Indialantic By-the-Sea, FL.


Makes me feel better :-)
but....

I just picked up "Advanced Electromagnetism and Vacuum Physics" by Patrick
Cornille (Advanced Electromagnetic Systems, France) published by World
Scientific Publishing Co. 2003 while browsing Strand Book Store in NYC (sale
$32) and the following Preface introduction caught my interest:

"The electromagnetic theory is the most important theory in physics, first
because the electromagnetic force is the only force that can be easily
manipulated by man with wellknown applications, secondly an extension of this
theory in the future may explain all the fundamental forces known to day in
nature.
A large volume of literature has appeared since the latter days of World war
II, written by researchers expanding the basic principles of electromagnetic
theory and applying Maxwell's equations to many important practical problems.
However, it is my opinion that the electromagnetic theory is not complete and
fully understood. A simple example proven these claims is given in this book
when the Helmholtz theorem is analyzed. We proved from a mathematical point of
view that Maxwell's equations are not complete since a scalar polarization must
be taken into account in the equations.
It is worth insisting that Maxwell, when he formulated out his theory, was
mainly guided by the experimental work performed by the physicists of his time.
He tried to give an hydrodynamics understanding of his theory, which is still
favored by certain physicists. Even today, Maxwell's equations are given as
granted, their validity being justified by experiments. Actually, there is no
demonstration of Maxwell's equations from first principles since the mechanical
approach used by Maxwell was rapidly abandoned in favor of a novel
nonmechanical entity: the electromagnetic field. While the Maxwell's equations
can obviously be obtained from a variational principle where they are derived
from an action appropriately chosen in order to recover them. In spite of the
success of the Maxwell theory in our present technology, we believe that the
last word on Maxwell's equations has not been said yet. The reason is that
Maxwell's equations raise a number of fundamental questions which have not been
answered in a satisfactory manner to date:
- One of these questions deals with the existence of a medium sustaining
transverse electromagnetic waves.
- Another question concerns the fact that Maxwell's equations are not Galilean
invariant.
- The question of covariance is also strongly related to the electromagnetic
induction phenomena, which is difficult to understand within the framework of
the special relativity theory.
- The discrete nature of the electric charge, where no physical concept has
been proposed to explain its quantization, remains one of the deepest mysteries
of physics.
- There is also the reason why the Lorentz force does not come from the
Maxwell's equations, but is additional to them. The reader is reminded that
classical electrodynamics demands a connection between the Maxwell's equations
and the Lorentz force.
In view of a prevalent trend towards a hydrodynamic description of matter and
radiation, we propose in this book another hydrodynamic wave model for the
existence and the propagation of matter and radiation in the vacuum where
equations of electrodynamics can be derived from simple fundamental principles.
We shall answer the above questions. " etc.

Hoping to find answers to some of the puzzling questions relating to antennas
and propagation, I am looking forward to time when I can immerse myself deeply
into this new stuff (and get more confused?)

Maybe this will intrigue some of youze guyz and help in sheding some light on
our neandertal brains?

73 Yuri, K3BU

Dave VanHorn October 29th 03 08:05 PM

I just picked up "Advanced Electromagnetism and Vacuum Physics" by Patrick
Cornille (Advanced Electromagnetic Systems, France) published by World
Scientific Publishing Co. 2003 while browsing Strand Book Store in NYC

(sale
$32) and the following Preface introduction caught my interest:


Good deal. Amazon wants $96 new, and $91 used. (VERY gently, I hope!)



Yuri Blanarovich October 29th 03 08:44 PM


I just picked up "Advanced Electromagnetism and Vacuum Physics" by Patrick
Cornille (Advanced Electromagnetic Systems, France) published by World
Scientific Publishing Co. 2003 while browsing Strand Book Store in NYC

(sale
$32) and the following Preface introduction caught my interest:


Good deal. Amazon wants $96 new, and $91 used. (VERY gently, I hope!)


There was one more left on the shelf as I remember. If anyone wants, I might be
able to check it out at this "World's Largest Used Bookstore". I giured it was
worth for the third I wanted to read in the book :-)

Yuri


jj October 29th 03 11:53 PM

I guess for now I will accept that a radio wave is a force field (or
energy field, if you like), and leave it at that (still seems to imply
action-at-a-distance). When I was in school, if this question were
asked, the professor would right down Maxwell's Equations on the
blackboard and state that they explain everything. I suppose that's
about as good as anything.

Thanks for the responses.

JJ

Peter O. Brackett October 30th 03 08:45 AM

jj:

[snip]
I guess for now I will accept that a radio wave is a force field (or
energy field, if you like), and leave it at that (still seems to imply
action-at-a-distance).

:
:
Thanks for the responses.

JJ

[snip]

There is a phenomena associated with Quantum ElectroDynamics or QED
known as "entaglement" which really does involve instantaneous action at a
distance.

Entanglement was/is the most controversial part of quantum theory and it's
predicted
existence comprised the main "objection" that Einstein had to QED. In
recent years
"entanglement" has been experimentally verified in several ways at several
different
authoratative laboratories by leading Physics researchers around the world.

Entanglement of quantum particles is a facinating part of the whole field
of quantum
mechanics. There is a recent popular book on the subject of entanglement
which outlines
the delightful history of the controversy and the study of how quantum
particles can
become "entangled" and can then exert instantaneous [faster than light]
force at a distance
and helps to clarify the subject for lay folks. The book develops some
basic "understanding"
of QED but it needs a "little" bit of tolerance for maths.

cfr:

Amir D. Aczel, "Entanglement - The Greatest Mystery in Physics", Four Walls
Eight Windows, New York, 2001. ISBN: 1-568-58-232-3 [QC174.12.A29]

Aczel's book is not strictly a Science or Physics book but is more of a
popular
account of the subject. Aczel has personally known many of the famous
protaganists of quantum theory on a personal basis and the book includes
photos
of him together with some of the world famous physicists at their homes,
where
he visited and got their views/contributions on the subject.

Facinating stuff...

--
Peter K1PO
Indialantic By-the-Sea, FL



Peter O. Brackett October 30th 03 09:06 AM

Yuri:

[snip]
Maybe this will intrigue some of youze guyz and help in sheding some

light on
our neandertal brains?

73 Yuri, K3BU

[snip]

Maxwell's Equations?

No thanks...

Maxwell is soooo pase.

I prefer to use the equations of quantum electrodynamics when computing the
lengths of the wire loops for my twenty meter quad antennas!

I get better accuracy and more gain that way.

:-)

--
Peter K1PO
Indialantic By-by-the-Sea, FL.



Thierry October 30th 03 02:48 PM

Hi,

Here is an excellent website with explanations, full of animations:
http://users.telenet.be/educypedia/e...ics/javarf.htm

My webiste also contain an explanation but it is written in French in
section devoted to quantum physics.

73's

Thierry
ON4SKY, LX3SKY
http://www.astrosurf.com/lombry


"jj" wrote in message
om...
This may at first sound like a stupid question. But after some years
as a radio enthusiast, I don't know what a radio wave is - what it
really is. Supposedly, modern physics does not believe there is such
a thing as "action at a distance". In other words, if you launch a
radio wave and I intercept it, there must be a transfer of "stuff"
between you and me. You can't just say that if I wiggle an electron
at point A, I can cause a wiggle at the same wiggle rate at point B.
I mean you can say it, but it doesn't explain anything.

OK, so the latest science says that electromagnetic energy is really
particle-waves. I guess this means that when I transmit, my antenna
is firing particles in the form of low-energy photons (energy
packets), and that these photons do not really exist anywhere but
exist only as probability waves - until, of course, someone intercepts
the wave. Then, magically, the photons appear at the receiving
antenna, in which they manage to produce oscillating electrons.

So, the best I can ascertain is that radio waves are really
probability waves. I'm not sure that really helps with an intuitive
understanding. Does anyone have a good description for what a radio
wave really is?

- JJ




Ed Price October 31st 03 07:37 PM


"W7TI" wrote in message
...
On 28 Oct 2003 16:18:17 -0800, (jj) wrote:

Does anyone have a good description for what a radio
wave really is?


__________________________________________________ _______

The short answer is "no". Many people confuse the measurement of things
with having an understanding of them.

Scientists are very good at measuring things; less good at understanding
what they measure. For example, gravity is measurable down to a gnat's
eyelash, but nobody knows what it really "is".

--
Bill, W7TI


It would be more accurate to say that we can measure gravity's effect, not
that we can measure gravity itself. Same for an electromagnetic field. We
have great models for predicting the effects; some models are so good we
call them Laws.

Beyond that, before you know exactly what a field is, do you really know
what ANYTHING really is? How about a copper wire? What really is copper?
Will you find the answer if you can look smaller & smaller? Will you
eventually disturb the observation just by observing? How do we know
anything?

Questions like this are best treated with beer.

Ed
wb6wsn


Peter O. Brackett October 31st 03 09:01 PM

Ed:

[snip]
Questions like this are best treated with beer.

Ed
wb6wsn

[snip]

I prefer to treat those questions with Don Julio tequilla "on the rocks".
After a couple of Don Julio's *I* understand everything!

--
Peter K1PO
Indialantic By-the-Sea, FL



Roger Halstead November 3rd 03 12:14 AM

On Thu, 30 Oct 2003 15:48:01 +0100, "Thierry" Thierry, see
http://www.astrosurf.com/lombry/ wrote:

Hi,

Here is an excellent website with explanations, full of animations:
http://users.telenet.be/educypedia/e...ics/javarf.htm

My webiste also contain an explanation but it is written in French in
section devoted to quantum physics.


I thought all quantum physics was written in "Greek"

Roger Halstead (K8RI EN73 & ARRL Life Member)
www.rogerhalstead.com
N833R World's oldest Debonair? (S# CD-2)




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