Re: How did that field get quantized, exactly...
- From: srp@xxxxxxxxxxxx
- Date: 10 Feb 2007 20:08:03 -0800
On 10 fév, 22:36, "Edward Green" <spamspamsp...@xxxxxxxxxxx> wrote:
On Feb 10, 8:26 pm, s...@xxxxxxxxxxxx wrote:
On 10 fév, 17:55, "Edward Green" <spamspamsp...@xxxxxxxxxxx> wrote:
I'm trying to understand, on a simpletons' level, how the EM field
might wind up quantized so that its incremental excitations show the
characteristic E = hv .
Quantized fields are not hard to understand: violin strings do it,
hydrogenic atoms do it; they say in Boston even beans do it. Ok. But
these fields are spatially confined (except for the pythagorean output
of the beans, which goes over into the continuum spectrum).
But what "confines" the EM field? Although cavity radiation figures
in the history of the thing, as far as I know the energy relation
given applies to free radiation in vacuum: and the size of the cavity
doesn't enter in to it. And of course the spectrum of excitations
doesn't suggest a particle in a box, but an harmonic oscillator -- of
a spring constant k = ... hmm...
Ok... spring constant doesn't really seem to work, since it involves
"m"! But something analogous to an harmonic osciallator. So are we
to think of the EM field as springy thing, which vibrates when
plucked? But it doesn't have a natural frequency -- it can vibrate at
_any_ frequency: the only concession it seems to demand is that the
apparent elastic constant adjusts itself with frequency to make the
energy ladder scale appropriately.
Why would this be so? And for that matter, why doesn't size matter?
Well... it does in the sense that lower energy vibrations demand
greater wavelength.
Hmm... maybe it turns out to act like a wave in a box after all... a
certain number of wavelengths of a standing wave of a given frequency
fit inside a box much larger than the wavelength. And then it will
turn out ... magically or inevitably ... that the effective springness
of the field depends only on the wavelength/frequency, and not on the
number of nodes included. So we get our HO spectrum, and can ignore
the size of the box: at least if we don't ask why it doesn't matter
why in general only a non-integral number of wavelengths fit, or in
general there really is not box anyway...
What do you think?
No... I don't like it that much, either. But maybe something can be
made of it.
Have you had a look at LC oscillators ?
Interesting idea. Thanks.
Maybe one could think of the interplay of magnetic and electric fields
in vacuum as a kind of LC oscillator -- one that's done away with the
circuit elements,
and the resistance.
and just kept the fields.
Absolutely.
Presently, this is apparently what gave Maxwell the final direction
for
dealing with EM enrergy in vacuum. Mentionned somewhere in Sears,
Zemansky and Young and some other source I can't think of right now.
I found that the LC relation allows dealing with localized discrete
quanta of EM energy (photons)
André Michaud
.
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