Re: Two-slit experiment
- From: "Ron Baker, Pluralitas!" <stoshu@xxxxxxxxxxxxxxxx>
- Date: Tue, 08 Aug 2006 02:37:25 GMT
"Timo Nieminen" <timo@xxxxxxxxxxxxxxxxx> wrote in message
news:Pine.LNX.4.50.0608071102480.22654-100000@xxxxxxxxxxxx
On Sun, 6 Aug 2006, Ron Baker, Pluralitas! wrote:
"Timo A. Nieminen" <timo@xxxxxxxxxxxxxxxxx> wrote:
On Sun, 6 Aug 2006, Ron Baker, Pluralitas! wrote:
"Timo A. Nieminen" <timo@xxxxxxxxxxxxxxxxx> wrote:[cut]
On Fri, 4 Aug 2006, Ron Baker, Pluralitas! wrote:
Consider typical fluorescence. I was originally thinking about
free-free
inelastic scattering by electrons in plasmas, but the mechanism
isn't
important.
I disagree.
Radiation is absorbed, radiation is re-emitted (but with less
energy).
A plasma is whole different kettle of fish. A plasma is a large
chaotic
system. You can't track an individual electron or photon in a plasma.
If you direct photons at a sufficiently large volume of plasma, yes
the
photons will be absorbed (eventually) and likely be converted to heat
but you can't say that each photon is either totally absorbed or not
affected by each collision.
A plasma can be quite nicely modelled by assuming interaction between
single photons and single electrons or single atoms. For a plasma in
LTE
(local thermodynamic equilibrium), it's the simplest way, since then
the
plasma affects the EM wave passing through it, but the EM wave doesn't
significantly affect the plasma. But this is somewhat of a digression.
The point is that energy is removed from/added to the field in chunks
of
delta_E = h delta_f.
There is nothing quantized there. delta_E is continuously variable.
Yes, delta_E = h delta_f is continuously variable. The point is that E=hf
is removed from the monochromatic field of frequency f,
Why? Why do you say that?
You seem to be saying that a photon can never lose
just part of its energy.
and (E-delta_E) is
added to a monochromatic field of frequency (f-delta_f).
I worded it quite badly, I see. My apologies. Energy is removed/added
to/from the _total_ field in chunks of delta_E = h delta_f, while
removed/added from/to spectral components of the total field in chunks of
E=hf.
What is this? What is that supposed to mean? Seems
like some strange accounting. The 'spectral components'
exchange energy in quantized amounts but when you
total quantized amounts it is a continuously variable
amount?
Can you reference published accepted theory that describes that?
Would you like to illustrate that with an example?
[cut, yes, I agree]
And delta_E = h delta_f is not what you said in objecting
to the OP. Are you withdrawing that objection?
If memory serves, the original objection was to "electron" = "wavefunction
of electron".
No need to rely on memory. It is recorded.
Nightlight said:
The exchange is quantized only for bound electrons, not for
free electrons. In the case of bound or spatially constrained
electrons, the available frequencies for the electron matter
field are discrete for the same reason that the frequencies
of constrained guitar wires are discrete. The discrete
spectrum is a property of the solutions of those types
of PDEs with those boundary conditions.
To which you replied:
"No, that's a different story. If, in a free-free process, why is the
change in frequency given by E=hf?"
But now later you have said that it is delta_E = h delta_f
and that that is continously variable.
This works very well when modelling a plasma. I should add that in my
experience - at optical frequencies - the free electrons don't interact
much with the radiation; if at RF, one's experience will be very
different, but at RF the classical limit works very well.
Low frequencies: photon energy << typical energy of matter, classical
model works very well. This can be explained either by (a) light and
matter really are classical, or (b) the discreteness of the energy
exchange between field and matter is so small that we can see it.
High frequencies: photon energy >> typical energy of matter, need
quantum
model. In this case, a semi-classical ballistic particle model often
works
very well. This can be explained either by (a) light is made of little
billiard balls, or (b) the wavelenght is so short that we can use the
vanishingly small wavelength limit (ie, the particle limit).
For frequencies in the middle, typically optical frequencies, a purely
classical model can work well (especially when the interaction with
matter
is off-resonance - most "classical" optics), sometimes a simple
semi-classical model can work well (my experience with plasmas), and
sometimes you need the full treatment.
The complete incompatibility between (a) and (a) above is IMO a very,
very
good reason for the field + photon model, where the field is
essentially
the wavefunction for the photon, and the photon is the E=hf of
adding/removing energy to/from the field.
Does delta_E = h delta_f fit into your view?
As above. For a monochromatic field, E=hf. For a non-monochromatic field,
for the total field, delta_E = h delta_f, while for any spectral
component, E=hf, with delta_E = E1 - E2 = h (f1 - f2) = h delta_f.
But you are assuming populations again, right?
It doesn't work for a single photon, does it?
What are the spectral components of a non-monochromatic
single photon? Which one loses hf? How does
one calculate or measure the delta_f?
The directivity of emission, as seen by where the energy is detected is
also a very good reason. An atom changes state by E, another atom some
distance away gains that energy, although classically, the emission -
from
an emitter the size of an atom - _cannot_ be that directional.
Wouldn't that be what is called the 'collapse of the wave function'?
Some call it that. If the "collapse" is the instantaneous collapse of
energy over an extended volume to the small volume of a detector, this is
problematic - an instantaneous process is only instantaneous in a small
subset of coordinate systems. This is why I lean towards Schroedingerism.
But whatever you call it, it's a fundamental failure of classical EM
theory.
Yup.
EM field is quantised in the sense that energy goes into it or comes
out
of it in multiples of hf.
Always? No exceptions? Even in free-free?
The low energy cases can't be measured experimentally,
What do you mean 'low energy cases'?
Energies where single photons can't be detected with available technology,
eg RF.
OK. Understood.
the high energy cases work very well, but "always E=hf, no exceptions"
unifies the two
But you said delta_E = h delta_f above.
As above. Basically, the incoming and outgoing photon are different
photons, each with energy E=hf.
As I asked above, what is your basis for saying that?
very well. Also, the blackbody spectrum, even emitted by matter with
continua of energy states available suggests it works very well.
I don't believe it is required. I think it is true that Planck himself
did
not conclude that.
If all matter has such quantisation, then it isn't required. We now know
far more than Planck did about electronic states in matter, both discrete
and quantised. I wouldn't say that all matter is (electromagnetically
speaking) harmonic oscillators with energy and frequency related by E=hf.
Consider, specifically, conduction electrons - resonant frequency = 0,
Brehmsstrahlung, anything where boundary conditions don't result in a
discrete energy spectrum for the electron.
Perhaps there are exceptions, so far unobservable, or at least
unobserved.
I think that the model is already complex enough, and works well enough
for modelling observations, I'd hesitate to add exceptions without good
evidence.
Ever hear of Compton scattering?
Yes. And it supports E=hf very well. E_in = h f_in, E_out = h f_out.
It doesn't support it. It doesn't disallow it, but it doesn't
support it. It supports E_in = h (f_in - f_out) just
as well. Do you have a counter argument?
'quantization' is often mentioned in decribing the
non-continuous, allowed energy levels of a bound electron.
Seems to me these are different concepts and the
distinction should be made clear.
Yes. I'd call them "discrete", not "quantised", although perhaps
energy
"level" is sufficient.
What do mean 'perhaps energy "level" is sufficient'?
That "level" implies "discrete" already. But it never hurts to be
unambiguous and explicitly say "discrete".
What nouns are you applying those adjectives to?
Energy states of an electron. "Discrete" being the adjective, "level"
being shorthand for "energy state of an electron" or "discrete energy
state of an electron", depending on usage.
What I should have written earlier on this point: "discrete" is not the
same as "quantised". "Discrete" means that (under suitable conditions)
the electron can only have certain discrete energies. "Quantised" means
that you have 0 electrons, 1 electron, 2 electron, etc, and nothing
in-between.
Photonic energy states are not usually discrete (exception: lossless
resonator).
OK.
--
rb
.
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