"Henri Wilson" HW@.... wrote in message
...
On Fri, 08 Jun 2007 05:57:23 -0700, George Dishman

wrote:

It seems this went missing.

"Henri Wilson" HW@.... wrote in message
. ..
On Mon, 4 Jun 2007 22:44:06 +0100, "George Dishman"


Can you not get it into your head that Fourier
analysis is based on pure maths and applies to
_all_ arbitrary waveforms. It is nothing more
than the repeated application of a simple
identity.

If you are thinking of a monochromatic beam,

Why would I be thinking of a monochromatic beam
when I clearly said "_all_ arbitrary waveforms"?

You said you had used Fourier Transforms but it
looks as though you have no idea what they are at
all. An FT takes any arbitrary waveform and tells
you the amplitudes and phases of a series of sine
waves which, if added, reproduce the waveform.
In terms of light, it tells you what set of
monochromatic beams need to be mixed to create
the total.

I'm thoroughly aware of what a Fourier series can produce George.

Apparently not.

It basically says that any periodic function can be expressed as a series
of
terms containing multiples of the fundamental frequency.

The function doesn't need to be periodic, consider
the sum of two monochromatic components at 1Hz and
sqrt(2) Hz.

Any curve can be broken down into separate single frequency components.

That's better.

However
if it is not periodic, then there is no point in trying....because you
will get
a different answer every time you repeat the experiment.

Garbage.

I fail to see any connection between Fourier analysis and my theory of
light
rays.

That doesn't surprise me, but I've told you the link
many times. Here it is again: Take a monochromatic
source and modulate it with a rectangular wave. That
produces 'pulses' of the source or equivalently a
carrier and sidebands. You can separate the sidebands
from the carrier with a grating (c.f. terabit WDM).
If the pulses are to travel at c+v, the same Doppler
shift must apply to each of the component frequencies
as applies to the discrete pulses hence the Doppler
equation must be the same as that for the pulsar that
we worked out some time ago.

the observed wavelength IS also
the individual photon wavelengh.

Yes, that is what I have been saying all along and
which you denied in the past.

...not for monochromatic light.

Yes, even for monochromatic light. You started
with that and switched to white later. Anyway
as yyou said above "Any curve can be broken down
into separate single frequency components." so
what applies to one applies to the other.

If the latter is VDoppler or ADoppler shifted,
so is the whole beam.

Again, that is what I have been telling you.

But George, the bunching effect doesn't have to be in the same proportion.

Yes it does Henry - you said you were "thoroughly
aware of what a Fourier series can produce" so you
should already know that.

The brightness can change by much more than the wavelength.

It doesn't matter if individual photons move wrt others in the beam.

That's less clear. Obviously it can only happen
in ballistic theory but the effect would be that
sometimes overlapping photons add constructively
but sometimes destructively.

I say this is purely a numbers effect.... Do you thnk there is
interference
between individual photons making up a beam?

As I say, that's much more complex and since it
only applies in ballistic theory, I would have to
guess, but consider two photons in a laser beam
that partially overlap. If they are moving at
slightly different speeds, they will drift between
constructive and destructive interference as they
propagate until they move far enough to cease to
overlap.

In fact it is quite possibly their random phase distribution that
accounts
for Huygen's Principle.

No, the principle works for an individual photon.
Again bear in mind that individual photons are
deflected from a grating at the same angle as the
macroscopic waves.

Well, there are many ways that can be interpreted.

Not really, it is a simple fact that the probability
of single photon landing at some point on a screen
depends on its frequency (or wavelength).

maths well enough to see the unavoidable
connection.

I understand the maths perfectly well George. I also know that what you
are
saying is not relevant to my model.

It is relevant since it defines how light is
observed to behave.

Only in diffraction phenomena....
It doesn't tell us anything about light in transit.

It tells you the Doppler equation for monochromatic
light.

Not possible Henry - how do you make a pure
sine wave out of components at a different
frequency? I'll give you a hint - it isn't
possible.

Of course it isn't.
I never said it was.

Yes you did, you said an RF CW signal was actually
amplitude modulated white light. The frequencies in
white light are many orders higher than RF.

I said this COULD BE done. An RF signal can be made by modulating white
light.

********. Get your brain in gear Henry, think
about the Fourier transform of modulated light
and that of a CW signal.

Diffraction angle should be independent of the arrival phases of
individual
photons. Can you not see the possible link between phase randomicity and
reinforcement?

I can't see how you think that can explain why
each _individual_ photon is diffracted by the
angle.

Single photons form the same diffraction pattern that a beam of them
would.

Exactly what I said above Henry. You do like to
waste time, don't you.

I'm suggesting that a photon's so called 'wave function' is none other
than
the phase of its 'intrinsic oscillation' at the time of arrival.

Use my 'traveling oboe' model again George.

Yes so Henry.

There are two possibilities.
If it does as you say then the only way to check is to determine the
doppler
shift of the white light that makes up each pulse......not easy...

Not at all, and this is where you don't know how
to use the maths. You can take a monochromatic
beam and apply sine wave amplitude modulation.
That produces sidebands which can be separated
from the carrier by reflecting the modulated
beam from a grating.

Just as I said....

No, what you said several times was "There are NO
sidebands!". Do I need to dig up the quotes?

YOU said the grating would be sensitive to only the beam wavelength and
NOT the
modulation wavelength.

Exactly. If you modulate frequency fc with fm, you
get three components at fc-fm, fc and fc+fm and
when you shine that on a grating you see three
reflected lines

Have you changed your mind.

No, but you have. You previously said there were
NO sidebands (your emphasis) and now you agree not
only that there _are_ sidebands but they can be
separated from the carrier with a grating.

See the papers on terabit
WDM for the spectrum showing the sidebands and
the specification of a grating designed for this
purpose or see if you can find what part Fujitsu
or Alcatel used.

Each of the three resulting beams is itself
monochromatic at fc-fm, fc and fc+fm respectively.

How can you prove that?

I showed you the equation several times and you can
see from the links on WDM that the industry uses
gratings to confirm the performance of terabit
systems by examinimg the sidebands.

Above you said:

the observed wavelength IS also
the individual photon wavelengh.

which is correct, so the photons in the lower sideband
all have a frequency of fc-fm.

That doesn't follow at all.

You said above:

the observed wavelength IS also
the individual photon wavelengh.

and later:

Single photons form the same diffraction pattern
that a beam of them would.

so I'm not saying anything you haven't already
agreed.

You can confirm that by considering what you would
see if you took the extracted sideband of a WDM
channel carrying a single sine wave, shone it on
an echelle and then turned the brightness down
until you saw single photons on a PM tube.

Don't speculate on what MIGHT happen George....

I don't need to, WDM developers test systems by
looking at the spectrum, single photon detection
is a common experiment and heterodyning is used
for very accurate Doppler measurement including
photon counting detectors. It's all done on a
regular basis but there's no fuss at they are all
just mundane tools.

Now if you emit that waveform from an accelerated
source, your Doppler equation applies to each of
the three beams separately. If you then recombine
them by the reverse method and detect it with a
photodiode, you get back the modulation. The
'bunching' of the waves in the modulation is
defined by the Doppler shift formula that was
applied to the three monochromatic beams so there
is a direct mathematical link between individual
photon Doppler and the pulse bunching formula. If
you want the sine waves in the modulation to move
at c+v, the photons must have the Doppler shift
corresponding to the bunching formula so they must
be fully compressible.

George, this conclusion is based on too many assumptions.

No assumptions, just a series of steps all of
which are well known.

I understand what you are saying but I don't accept a word of it. It is
pure
speculation. However I agree that investigation of side band diffraction
might
be able to tell us something interesting about the nature of photons.

Not really, if you modulate a fine line with a
clean sine wave, you get three monochromatic lines.
Extract any one and it is no different to any other
monochromatic source.

If it does not, then my claim that pulsar velocites are a lot smaller
than
they
appear is correct.

We have analysed the pulsars and we derived results
from observations. It's one of the few areas where
we were able to work through and reach agreement.
The mathematical link from considering the effect
on sidebands tells us that photon Doppler must be
the same as macroscopic bunching formula.

George, why do you always jump to outrageous conclusions when other
possible
explanations are obvious?

Because I studied maths to a level that lets me
use it to reach such conclusions while you still
think these aspects are unconnected.

That doesn't conflict with any of the observations
or experiments and is directly derivable from
ballistic theory, it only disagrees with your
'concept' of photon being like springs.

No,

You seen all the maths above, and you claimed you
were familiar with Fourier so you shouldn't even
need me pointing it out.

....
Give some thought to the terabit WDM spectrum and
perhaps you will start to follow. At some point I
expect you to say "wait a minute, that's impossible"
for one specific reason and when you do I'll know
you've grasped the implications. In fact that aspect
is not only possible but the basis of the technology,
but I'm sure you'l argue it can't happen nonetheless.

I understand this is a relatively new technique.

It is a new application but the techniques fundamentally
the same as the earliest telephone trunk connections
where many conversations were sent down a single cable
using frequency division multiplexing.

George