Re: Two-slit experiment
- From: "Ron Baker, Pluralitas!" <stoshu@xxxxxxxxxxxxxxxx>
- Date: Sat, 02 Sep 2006 03:51:22 GMT
"Timo A. Nieminen" <timo@xxxxxxxxxxxxxxxxx> wrote in message
news:Pine.WNT.4.64.0608302155230.276@xxxxxxxxxxxx
On Fri, 25 Aug 2006, Ron Baker, Pluralitas! wrote:
"Timo A. Nieminen" <timo@xxxxxxxxxxxxxxxxx> wrote:
On Thu, 24 Aug 2006, Ron Baker, Pluralitas! wrote:
There is nothing intrinsic in the EM field that makes
the energy of photons in the first Balmer line be what it
is. It is determined by the mass and charge of the electron
and proton of the hydrogen atom which make a resonant
system.
The ultimate test would be a bound system of a proton and a particle of
charge -e and mass other than m_e. Isotopic effects and E=hf working for
ions, neutral atoms, etc, are enough to convince me that E=hf isn't in
the
details of atoms, but you might like stronger proof.
Maybe I'm missing something but it seems to me that
atoms with higher atomic number are analogous to your
hypothetical. e.g. helium with atomic number 2 gives
a whole different set of spectral lines.
Yes, the energy levels are different, and the energy differences between
them and thus the line spectra are different, but E=hf still works. I feel
this shows that E=hf is not a result of the details of interaction between
electron and nucleus, because the details are different in the two cases.
Yes I can see that. I see that as the "quantumization" I was talking
about.
And in a bound system (I'm thinking black body here)
E for any mode has discrete
quantized levels nhf. In an unbound system E and f are
continuously variable. What is interesting is that when
you put energy into the EM field, even in the unbound
case, it acts as a unit, a quantum. And it interacts
with massive charged particals as a quantum. I don't see
that necessarily implies that a quantum can only be completely
absorbed or created in an interaction with matter. The
arguments I have seen to contrary seem metaphysical.
OK, the electron has the same mass and charge in all such cases, so the
same relationship between energy and frequency is perhaps plausible -
that's why I wrote you might like stronger proof. Exotic "atoms" composed
of a nucleus and perhaps an anti-proton could be just the trick. I don't
know if such have been experimentally studied, but it might be worth
checking (electron-positron "atoms" have been, iirc, but that doesn't get
away from the original mass/charge thing).
I accept that E = hf will always apply. The h doesn't come from
the mass or charge of the electron. The discrete allowed levels
of E come from the mass and charge of the entities involved.
Yes, exactly. That's why you have one set of maths (the Maxwell
equations)
to describe fields and another (creation and annihilation operators) to
describe photons. The rules for which rules to use when are not
arbitrary - always Maxwell for the fields, a+/a- for photons.
:) I still find that dissatisfying. (But who the hell am I. ;)
It still seems like a bifurcated model to me.
I will agree that the rules are not arbitrary in the sense
that one could flip a coin in choosing which to use.
But I find the bifurcated model disquieting.
You're certainly not the first to do so.
:) Yes, I know.
But consider: is this _really_ any worse than having two different
entities in classical physics: matter and fields? Fields and quantised
excitations thereof may well be less bifurcated.
Rather my objection is that it seems that even when
some people talk about fields and quantized excitations
thereof they sometime still jump to refering to the 'photon'
and refering to it as if it were _point particle_.
It's not that photons sometimes act as waves, requiring Maxwell, and
sometimes as particles
But that is often just what is said.
Yes. Especially in treatments that graft de Broglie matter waves onto
classical particles. Perhaps a useful handwaving explanation, but it can
cause trouble later down the track.
Also, I don't believe there are things of spatial extent appearing and
disappearing simultaneously or otherwise. There is a set of modes of the
field, which don't change unless the geometry/boundary conditions
change,
and occupation numbers of each mode (how many photons in each mode). n
changes but the modes don't. [Warning: I don't do QED; this might be
wrong, misleading, or both!]
Hmm. I'm inclined to honor your disclaimer but what you said
seems schizophrenic. You subscribe to the quantum leap, to
photons instantaneously appearing and disappearing but
you say the field, which has spatial extent, doesn't change.
How can the field not change? You say the mode changes.
Instantaneously? The mode is separate from the field?
Where is the mode?
The _classical_ EM field is the high-photon-number average behaviour. At
this point, plane waves etc are really troublesome, since the value of the
wavefunction for a single-photon plane wave mode is zero (well, the photon
can be _anywhere_, so the probability of finding it at a particular
location is zero). So consider modes in a resonator. If the expectation
value of the number of photons in the mode is n, and n>>1, then the
classical field is n*single_photon_wavefunction. If n changes, the single
photon wavefunction doesn't change, but the classical field will. Note
that both the wavefunction and the classical field are solutions of the
Maxwell equations: n times one solution is still a solution.
The classical field is a combination of the quantum mode and the number of
quanta in that mode. Unless the boundary conditions change, the modes stay
the same, and quantumly, the number of quanta in the modes changes.
Classically, E and H change, but to be in the classical limit, n is always
very large, so classically, the change is smooth.
Iirc, Jackson has some interesting stuff about the angular momentum of
classical multipole fields vs the small photon number angular momentum of
the equivalent modes.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
--
rb
.
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