Re: a question about conservation and photons
- From: "Sue..." <suzysewnshow@xxxxxxxxxxxx>
- Date: 30 Oct 2005 20:17:50 -0800
Ken S. Tucker wrote:
> FrediFizzx wrote:
> > "Tom Roberts" <tjroberts@xxxxxxxxxx> wrote in message
> > news:El79f.4043$8W.766@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> > | bz wrote:
> > | > The laws of conservation should(must), of course, apply at all
> > times,
> > | > during the emission, propagation and absorbtion of a photon.
> > |
> > | Reading "light pulse" for "photon", in classical electrodynamics there
> > | is no problem -- the fields carry energy and momentum, and the
> > | appropriate integrals over all of space are constant (i.e. total
> > energy
> > | and momentum are exactly conserved). I believe this can be shown as a
> > | general theorem using Maxwell's equations, without making detailed
> > | computations for any specific physical situation.
> > |
> > | So I assume your question is one of the few instances around here that
> > | is truly in the context of quantum field theory (which I will take as
> > | QED). This means that the quantum nature of photons becomes important.
> > |
> > | In QED the comparable integrals over all of space make no sense. For
> > | instance, the "number of photons present" is not a good quantum
> > number,
> > | and you cannot count them (in general, such as this discussion).
> > | Remember, too, that in the configuration-space representation one must
> > | integrate over all possible times for each and every vertex, and then
> > | (anti-)symmetrize over all (Fermions)Bosons. This, too, makes the
> > notion
> > | of "the configuration of the system at a given instant in time"
> > | meaningless. Remember the usual dictum to discuss only MEASURABLE
> > | quantities, and you'll realize you cannot measure the "configuration
> > of
> > | the system" as would be necessary for this classical notion to apply.
> > |
> > | So just as in GR, but for a VERY different reason, the theory has only
> > | LOCAL conservation of energy and momentum. In QED this is expressed in
> > | the 4-d Dirac Delta function at every vertex that requires total
> > | 4-momentum to be conserved.
> >
> > All true.
> >
> > | > This would seem to join widely separated (by time and/or distance)
> > items
> > | > together into a 'system'.
> > |
> > | It's not really possible to do that, at least usefully. To be useful
> > | such a "system" must have definite quantities "at a given instant in
> > | time", and QED does not really permit that (see above).
> > |
> > | Just think about it -- you don't really know precisely "when" a given
> > | detector detects a photon, because Heisenberg's uncertainty principle
> > | applies. Ditto for a source's emission. Ditto for "where" a "given"
> > | photon is "located" at a given time (words in quotes are PUNs and are
> > | not really well defined -- a consequence of attempting to discuss
> > | unmeasurable quantities).
> >
> > Well, I think the above paragraph has a bit of a nonsense factor to it.
> > There are certainly unmeasurable quantities in the classical realm also
> > that are in fact discussed. Uncertainty is a natural phenomenon of even
> > classical wave mechanics.
> >
> > | > For instance, the question of where does the doppler shift occur?
> > Can it be
> > | > answered or can we at least be sure that the question is
> > meaningless?
> > |
> > | It occurs between source and detector. Remember the usual dictum to
> > | discuss only MEASURABLE quantities, and you'll realize you don't need
> > to
> > | worry about the more detailed questions you attempt to ask.
> >
> > Sure... part of the "shut up and calculate" mentality. However, some of
> > us *do* wonder and worry about such things. Should the failure of
> > Newton's calculus be an obstacle to wondering about what really happens
> > in the microscopic world? Or should we try to get a better handle on
> > exactly why it fails? I don't think it is impossible. If it were
> > impossible, we wouldn't have so may people working on string theory.
> > ;-) For me, it is simply due to relativistic effects and the concept
> > that spacetime is actually being defined at this level. Point-like
> > objects are also "extended" objects. Spacetime is "goofy" at this level
> > wrt Newton's calculus. ;-)
> >
> > | > I don't imagine that I am the first to ask such questions.
> > | > Where should I look for answers? What do I need to know to
> > understand where
> > | > this may go?
> > |
> > | Try:
> > |
> > | Feynman, _QED_. This is a nonmathematical introduction to QED.
> >
> > A very good example of how to get around the problems associated with
> > the failure of Newtonian mechanics in the microscopic realm. A must
> > read for anyone interested that has not read it. But it still can leave
> > a person wondering. Which is a good thing.
> >
> > FrediFizzx
>
> Hi Fred and all...
>
> I think Freddi nailed her! The differential calculus
> must give way to the incremental (quantum like cal.)
> in the microscopic realm, an indefinitely
> differentiable continuum died with atomism but of
> course applies in engineering in Macroworld.
> We've inherited that engineering and attempted
> to subsume macroscopic approximations into the
> microscopic, with no ((NONE)) success.
Earth to Ken... Earth to Ken....
<< A method based on the utilization of the relationships
between oscillator strengths and densities from one side
and photoelectric absorption coefficients on the other,
developed by Parratt and Hempstead,36 did ***not*** succeed
initially in providing satisfactory results due mainly
to the lack of good experimental values of the absorption
coefficients and also, to my belief, to the lack of
reliable experimental and theoretical atomic scattering
factors.
Cromer67 used self-consistent field relativistic
Dirac-Slater wave functions to calculate accurate
oscillator strengths for elements 10 through 98. He
calculated then the dispersion terms by using Parratt
and Hempstead's36 solution of equation (26) and summing
over the different absorption edges. The imaginary terms
were also computed for the same elements from equation (29).
The values of the parameters n used by Cromer,67 Dauben
and Templeton28 and other authors were taken from the
discussion by Parratt and Hempstead,36 as n = 11/4 for
the 1s1/2 edge, n = 7/3 for the 2s1/2 edge and n = 5/2
for all other edges. >>
http://www.iucr.org/iucr-top/comm/cteach/pamphlets/8/node6.html#SECTION00060000000000000000
<<Fig. 3-1. Total photon cross section in carbon, as a function of
energy, showing the contributions of different processes: t, atomic
photo-effect (electron ejection, photon absorption); , coherent
scattering (Rayleigh scattering-atom neither ionized nor excited);
, incoherent scattering (Compton scattering off an electron); , pair
production, nuclear field; , pair production, electron field; ,
photonuclear absorption (nuclear absorption, usually followed by
emission of a neutron or other particle). (From Ref. 3; figure courtesy
of J. H. Hubbell.)>>
http://xdb.lbl.gov/Section3/Sec_3-1.html
Sue...
>
> Example, does water consist of particles?
> Regards
> Ken S. Tucker
.
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