Re: The time it takes to emit one photon

> Now, gradually turn down the intensity of the light source up
> to the point when just one photon per second is emitted. You
> are now having Feynman's two-slit experiment. It's explanation
> requires quantum mechanics.

You are misinformed on the empirical facts of this type of experiment.
Low intensity makes no difference in the correlations of the counts or
their classicality (the only thing that changes are photocurrent
intensities). What photo-detectors will show you is exactly what is
predicted by Maxwell ED plus the model of square law detectors (which
are perfectly semi-classical devices i.e. they don't require "photons"
or the 2nd quantized EM field for the explanation of their behavior,
cf. [1]). There is no experiment to date which has shown that the
probability of "trigger" (which is, after all, a mere convention based
on arbitrarily chosen cutoff in the intensity of the photocurrents,
defining the 1-bit approximation of the photocurrent intensity i.e. the
"trigger", cf. [1]) at location A is affected in any way by the
"trigger" or "non-trigger" at some space-like location B. (The only
experiments, such as [2], which make such claims, blatantly cheat.)

The experimental failure to show any trigger exclusivity
(anticorrelations) at points A and B does not contradict QED
predictions. It only contradicts the naive single marble-photon imagery
from the popular and pedagogical QM literature (cf. [6] on limitations
of this imagery & language). Even if you allow for the buckshot
"theory" of detection (where each Dirac photon/ D-photon, the free
field quanta, produces a trigger with some fixed probability, cf. [1]),
the QED model of actual sources, such as PDC pairs, will show you that
the finite pulses (in space and time) will have Poissonian or
super-Poissonian (such as Gaussian) distribution of D-photon counts on
each detector. The two Poissonian processes at A and B have only the
common average counts (which are proportional to incident light
intensity). The individual counts (or photocurrent intensities) in each
try, for a given incident intensity (which fixes the Poissonian
average), are entirely independent.

Note also that a "single" D-photon that you are apparently imagining,
has infinite space-time extent, and thus it has no empirical connection
or operational mapping onto the double-slit or beam-splitter setups and
coincidence counts (cf. [3]). For any given field sampling time window
dT, the most accurate (the sharpest) measurement of energy (minimum dE)
is obtained for coherent states, and these have infinite number of
D-photons (superposed with Poissonian amplitude weights; any space-time
finite field configuration has similar 'infinite number of D-photons'
property). The PDC sources used to "demonstrate" the so-called
"non-classical" effects generate precisely this type of Poissonian
D-photon pairs distributions (for short enough time windows, wider
otherwise) since the pump (say, a perfectly stable laser) is at best a
Poissonian (i.e. coherent light) source and the PDC interaction
Hamiltonian randomly converts some of these incident photons into the
pairs (hence the pairs, being just a randomly 'sparsed' Poissonian
distribution, are in a Poissonian distribution themselves). Within the
buckshot "theory" of detection (the natural counterpart of the naive
marble-photon imagery), some random finite number of photo-electrons
are ejected/scattered by the infinite number of incident D-photons as a
Poissonian (stochastic, generally) point process on each cathode. The
only constraint that ties the two Poissonian point processes at the two
detectors A and B are the Poissonian averages. Beyond that, the
individual counts are entirely the result of interactions of the local
cathode with the locally incident EM field (cf. [1]). The single pair
(or any fixed number of pairs) of photons, which is the underlying
misleading imagery in the popular expositions, doesn't operationally
map onto the QO coincidence experiments.

Although it has been a "holy grail" of Quantum Opticians since the
1950s Hanbury Brown and Twiss "shock" (cf. [4],[6]) to show the
_genuine_ (nonclassical) trigger exclusivity (antibunching,
subpoissonian counts etc), the best they can show off with, as of the
last year, are the cheap magic tricks such as [2], or ever more
creative euphemisms (the only aspect of this hopeless pursuit which has
advanced at all since 1950s) to state the bare, unpleasant fact that
'no genuine anticorrelation was observed' (cf. [5]).


References:

1. V. Bykov "Photons, photocounts and laser detection of weak optical
signals"
Ann. Fond. L. de Broglie, V 26, n. spec. 1, 115-134 (2001)
http://www.ensmp.fr/aflb/AFLB-26j/aflb26jp115.htm

For more detailed account see their paper:

V P Bykov, A V Gerasimov, V O Turin
"Coulomb disintegration of weak electron fluxes and the photocounts"
Physics-Uspekhi 38 (8) 911-921 (1995)
http://ufn.ioc.ac.ru/abstracts/abst958.html#d

2. J.J. Thorn, M.S. Neel, V.W. Donato, G.S. Bergreen, R.E. Davies, M.
Beck
"Observing the quantum behavior of light in an undergraduate
laboratory"
Am. J. Phys., Vol. 72, No. 9, 1210-1219 (2004).
Paper: http://marcus.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf
Experiment Home Page: http://marcus.whitman.edu/~beckmk/QM/
On how it cheats:
http://www.physicsforums.com/showthread.php?t=71297

3. Earlier sci.physics.research message on the extent of "single
photon":

http://groups.google.com/group/sci.physics.research/msg/5d07857496608a75

4. Earlier sci.physics.research message on HB&T controversy:

http://groups.google.com/group/sci.physics.research/msg/748a0293fffe2872

5. R.Y. Chiao, P.G. Kwiat
"Heisenberg's Introduction of the `Collapse of the Wavepacket' into
Quantum Mechanics"
quant-ph/0201036 http://cul.arxiv.org/abs/quant-ph/0201036

6. D. N. Klyshko "Quantum Optics: quantum, classical and metaphysical
aspects"
Physics-Uspekhi 37 (11) 1097-1123 (1994)
http://eprint.ufn.ru/article.jsp?particle=122
http://ufn.ioc.ac.ru/ufn94/ufn94_11/ufn4bc.dvi
http://ufn.ioc.ac.ru/ufn94/ufn94_11/ufn4bc.tgz
http://ufn.ioc.ac.ru/ufn94/ufn94_11/Russian/r9411b.pdf (in Russian)

{ 9:24 PM, Sept 19, 2005 }

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