Re: The time it takes to emit one photon
- From: "nightlight" <nightlight@xxxxxxxxxxxxxx>
- Date: Fri, 23 Sep 2005 19:56:29 +0000 (UTC)
> DOUBLE-SLIT
>
> This is called interference. If you think this experiment
> can be explained without the notion of photons and their
> quantum-mechanical behavior, I would like to hear your
> explanation.
>
The classical EM field produces the same interference pattern of
intensity variation across the screen. Therefore the interference
pattern alone would be entirely unsurprising to Maxwell. How would you
surprise him? A simple detector which thresholds the classical field
intensity values (of the incident field superposed with the 1/2 hv
vacuum fluctuations per mode) into 1-bit approximation (above
threshold: 1=trigger, below threshold: 0=non-trigger) will give you
exactly the counts that you will observe.
In order to surprise Maxwell with this experiment you would need to
place an array of detectors at the screen and show that triggers of
detectors show subpoissonian trigger statistics (e.g. enhanced mutual
exclusivity of 2 points A and B so that probability P(AB) of coincident
triggers at A and B is smaller than what independent coincident
triggers p(A)*p(B) imply). Otherwise (for poissonian or superpossonian
trigger statistics) he could easily explain the discrete single
triggers as result of simple thresholding of the photocurrents at the
detectors (i.e. they get approximated with 1-bit precision; that is
precisely what pulse analyzer-discriminator, PAD, the electronic
component of a photodetector does; see Bykov papers [1] on the origins
and nature of the photo-detection discreteness).
To see why you need additional exclusivity, consider a simple (but very
close) analogy. Arrange onto a rectangle a list of all cities buying
lottery tickets so that the average ticket sales viewed across the
rectangle form an interference-like pattern, say, matching exactly your
double-slit interference pattern. The probability of a guess is such
that on average n tickets wins per week (a lottery cycle). For any
given week there will be k winners with probability given by Poisson
distribution:
p(k,n) = [n^k/k!] exp(-n) ... (1)
For example, if the odds are tuned so that on everage 1 player wins per
week (n=1) you will have odds of no winners p(k=0,n=1) = 1/e = 36.8%,
odds of exactly 1 winner as p(k=1,1) = 1/e = 36.8% and the odds of more
than 1 winner as p(k>1,1) = 1-2/e = 26.4%. The ratio of single to
multiple wins is 1.4, which doesn't seem very exclusive. But if you
reduce the average number of wins tenfold, hence n=0.1, you will have
the odds of no winners p(k=0,.1) = 1/e^.1 = 90.5%, odds of 1 winner as
p(k=1,.1) = .1/e^.1 = 9.05% and odds of more than 1 winner p(k>1,.1) =
..46 %. The ratio of single to multiple wins is now 19.3, which is quite
like "one particle at a time with inefficient detectors" (the 90.5%
losses). For general n, the odds of a single win/trigger are p(k=1,n) =
n/e^n and of multiple triggers p(k>1,n) = 1 - (1+n)/e^n. The ratio of
multiple to single triggers is then:
R(m/s) = [e^n - (1+n)]/n ... (2)
In the low intensity limit (n->0) this ratio goes as: R(m/s) -> n/2 ->
0, i.e. it approaches the perfect particle like exclusivity, _provided_
you don't count the no-win/trigger cases (as the Glauber's QO
subtraction conventions do with the photo-detections in coincidence
experiments). If you now check the often cited paper [2] Grangier et
al.(GRA), their Fig 2. (p.176), you will see that they use precisely
this property of the ratio of single to multiple triggers in the low
intensity limit as the "proof" of the nonclassical behavior, where for
classical case they use all data, thus R(m+k0/s+k0) -> 1 for their
"classical" case as n->0 (since it is dominated by k0, the no-detection
cases; see also [3] for discussion and errata of GRA paper). The
AJP-2004 paper [4] also uses this same ratio (with the same strawman
"classical" limit of Rc -> 1). Note that GRA & AJP paper use only two
detectors per "screen" and GRA also verifies that the two beams, when
their paths are extended to intersect, do interfere with nearly perfect
visibilty (sharpness). The "non-classical" exclusivity in their setup
corresponds to the double-slit setup detectors placed behind one or the
other slit, which supposedly will detect "almost always" a single
photon, and "almost never" two or more photons (i.e. the R -> 0 as
n->0).
There is nothing in the low intensity limits in the double-slit (or
their more practical variant, the beam-splitter) experiments which
would surprise Maxwell or Poisson or Laplace (or Pascal and Newton,
even Archimedes) in the slightest. What is happening, the counts being
actually observed, exactly parallels what is happening in the lottery
analogy above. Despite half a century of attempts (since the 1956
Hanbury Brown & Twiss controversy), the Quantum Opticians haven't shown
a single experiment in which the ratios of multiple to single triggers
drops below the classical (poissonian) value RHS of eq. (2) (cf. [4.c]
to see the experimental perfection crowning the half a century of
pursuit of this non-existent effect, the keystone of the Quantum Optics
magic photon dogma -- behind the curtain, the holy of the holies of
Quantum Optics phenomena rests on nothing more but a cheap magic
trick).
It is important to note that the Glauber's QED photo-concidence
predictions (via his filtered-correlation functions Gn() cf. [5])
explicitly _require_ these subtractions (in the QO coincidence
experiments) of no-detections _by definition_ of his Gn(). Check his
primary derivation in his 1964 Les Houches lectures [5] (the sacred
tablets of the QO, and nearly as hard to find nowdays as the tablets of
Moses), in particular his transition from eq. (5.2b) to eq. (5.5),
where he simply drops from the full n-detector+EM field evolution, all
the terms "we" (??) are not "interested in" (why?), such as all
no-detections, 'missing' and 'excess' detections, generally, any count
of photo-absorptions m different than the number of detectors n). These
subtractions/filtering (which are explictly non-local!) at the level of
formalism are operationally mapped to standard Quantum Optics
subtractions/rejections of the counts, such as of no-detections,
unpaired singles, accidental coincidences etc (depending on the number
of detectors and the type of Gn() sought). These terms are dropped not
because they are small, but because "we" are not "interested in" them.
The sleight of hand the Quantum Opticians do when they trot out their
quantum magic show (all their numerous "observed" non-classicalities,
including their "observations" of Bell inequality violations and photon
anticorrelations) to physicists is to extract (non-locally!) Glauber's
Gn() from the actual counts (using the standard QO subtractions, to
match the Glauber's _definition_), then they pretend that these Gn()
functions are what is supposed to happen in the "ideal" case. They
conveniently forget that the "derivation" of the coincidence "counts"
Gn() in [5] is _not a derivation of what counts are supposed to be
observed_ at all (which is predicted by the full dynamics in eq. (5.2b)
in [5]), but merely Glauber's definition of a "signal function" Gn().
The Gn() is indeed practical and useful (in the engineering sense) by
virtue of retaining only the terms with the incident "signal" field
photons being absorbed precisely specified number of times at specified
locations, thus it concentrates and amplifies the effects of the
incident field (through the non-local QO subtractions). By pretending
that these QO subtractions are due some kind of temporary technological
imperfections (instead of being a fundamental step, as it is obvious in
[5] pp. 84-86, in the "derivation" of Gn() and its experimental
reconstruction from the obtained counts), the Quantum Opticians mislead
the physicists in what has been observed, feeding the mass
misperception among physicists on what the genuine empirical facts are.
In his "derivation" of Gn() (which is just a round about, obfuscated
definition of his Gn()), Glauber drops most of the terms from (5.2b)
describing the actual evolution (i.e. what is supposed to happen) of
the n detectors in EM field, for no other reason (such as, say, showing
that the dropped terms are negligible) beyond declaring that "we"
(Quantum Opticians, engineers?) are not "interested in" them. The
Quantum Opticians (especially in popular & pedagogical accounts) start
with the filtered eq. (5.5) in [1], or an equivalent, declare it as
actually describing what is supposed to happen with n detectors,
implying that the dropped terms (which are rarely, if ever nowdays,
mentioned) from the genuine evolution (5.2b) are result of some kind of
present technological imperfection which are not supposed to be there,
once they perfect the detection technology (e.g. the so-called "ideal
detector" which will show "loophole free" B.I. violations).
The excelent example of this QO sleight of hand is the Ou & Mandel 1988
experimental "demonstration" of the Bell Inequality violations [6], in
particular when they write down their eq. (4), supposedly describing
the QED/QO "prediction" as to what will happen with the 4 counts in the
Bell EPR setup (for PDC source), which is a G2(x1,x2), and they cite
(as their reference [17]) the pair of Glauber's 1963 Phys. Rev. papers
as the source for the equation (the [17] in [6] is the same as parts of
Glauber's lectures [5], minus the key derivation in [5] pp. 84-88).
While the operational interpretation may not be obvious from the
Ou-Mandel's ref [17], due to the absence of the key "derivations", it
is plain in [5] that the Ou-Mandel's eq. (4) _does not_ describe what
is happening with the 4 detector counts in Bell EPR setup, but it
merely means that one can extract such function from the actual counts
by applying the Glauber's subtraction scheme (as applied in his
transition from (5.2b) to (5.5) in [5], where (5.5) implies, as a
special case, Ou-Mandel's eq. (4)). In addition to Glauber's non-local
subtractions implicit in G2() of their eq. (4) in [6], the mere usage
of the particular G2() (referring only to a pair of events on the
opposite sides of Bell EPR setup) discards (also non-locally!) the
triple and quadruple events (requiring G3() and G4() terms, since there
are 4 detectors) as well as the other G2() functions, such as G2()
terms for double detections (+ and -) on the same side of the Bell EPR
setup. These _additional_ defects (failures to model what is happening
on the four detectors) are partially masked out by their use of the
caricature incident EM field state eq. (2) in [6], which contains only
a single PDC pair of D-photons (free field photons), thus it would
yield 0 contributions for G3, G4 and other G2's, even though the number
of pairs in any detectable in any sampling window is Poissonian (being
just a 'sparsed' out Poissonian distribution of the PDC laser pump,
which has Poisonian number of incident D-photons, cf [7]). The "single
pair" of eq. (2) in [6] is not merely a poor caricature of their PDC
source output, but it is an even worse caricature of any QO coincidence
measurements (cf. [8]).
None of these two kinds of data adjustments/rejections, the one from
the original use of G2() in eq. (4), and the others from their use of
particular G2() only (in part via their choice for the input state
eq.(2)), is result of an imperfect detection technology. The imagined
"perfect detectors" which would generate _actual_ counts to match what
their eq. (4) "predicts" is "supposed to happen" on the four detectors,
would need, by definition of G2() and their choices in (4), to perform
not just the Glauber's non-local subtractions (implied in any G2()),
but would need the results database of supplementary experiments (for
accidentals and other rejections) to help each "perfect detector", the
G-detector, decide whether to declare trigger or no-trigger. Except for
subtracting their own local noise (which could be legitimately built
into a detector electronics), all the other subtractions & data
rejections required for G-detector are purely non-local by definition.
In short, there is _no QED prediction_ that the counts collected in a
Bell EPR setup will violate Bell Inequalities. The best you will find
is the 'QO sleight of hand' kind of "proof" shown by Ou & Mandel in
[6], which only weakly pretend to predict what is happening on the four
detectors. Most of what you will see, though, are the QM toy
derivations, which are at best the crude caricatures of the QED
"derivation" in [6] (which in turn is based on [5] for the key eq (4)
in [6] and on the toy input state (2) in [6]). The exactly same bare
factual situation (the double absence of any observed effect and of any
genuine QED prediction of such effect) holds for the double-slit and
beam-splitter experiments (cf. [4.c] for a discussion).
Physicists, such as Gerard 't Hooft (cf. [9]), exploring the next
fundamental layer of physical laws, which he (similarly to another
great physicist too far ahead of his time, Stephen Wolfram) suspects
are based on local, discrete cellular automata dynamics, has to divert
his creative efforts to puzzle out how to fit in the fake pieces which
just don't fit, the allegedly observed (by Quantum Opticians) non-local
QM phenomena, which have in fact never been observed. It is a great
waste of time and creativity for physics. Our grandchildren will laugh
at us for getting bamboozled for this many decades by a small mutual
back-patting society of pretentious 'engineers' with a gift of gab
(such as Glauber, Mandel) and an unquestionable talent for slick magic
tricks and showmanship (Clauser, Aspect, Grangier, Chio,...).
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. P. Grangier, G. Roger, and A. Aspect
"Experimental evidence for a photon anticorrelation effect on a
beam splitter: A new light on single-photon interferences"
Europhys. Lett. 1, 173-179 (1986).
http://kh.bu.edu/qcl/pdf/grangiep19867a0e0f09.pdf
3. P.N. Kaloyerou
"The GRA Beam-Splitter Experiment and Wave-Particle Duality of
Light"
quant-ph/0503201 http://arxiv.org/abs/quant-ph/0503201
4. 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).
a) http://marcus.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf
b) Experiment Home Page: http://marcus.whitman.edu/~beckmk/QM/
c) On how it cheats:
http://www.physicsforums.com/showthread.php?t=71297
5. R. J. Glauber "Optical coherence and photon statistics"
in Quantum Optics and Electronics (1964 Les Houches Lectures)
ed. C. de Witt-Morett, A. Blandin, and C. Cohen-Tannoudji
(Gordon and Breach, New York, 1965), pp. 63-185.
For discussion & objections see:
http://www.physicsforums.com/showpost.php?p=529314&postcount=16
http://www.physicsforums.com/showpost.php?p=535516&postcount=61
http://www.physicsforums.com/showpost.php?p=538215&postcount=73
6. Z.Y. Ou, L. Mandel
"Violation of Bell's Inequality and Classical Probability in
a Two-Photon Correlation Experiment"
Phys. Rev. Lett. 61(1) pp 50-53 (1988).
http://prola.aps.org/abstract/PRL/v61/i1/p50_1
http://puhep1.princeton.edu/~mcdonald/examples/QM/ou_prl_61_50_88.pdf
For more discussion on this see sci.physics.research post:
http://groups.google.com/group/sci.physics.research/msg/5d5dec33366d0bd9
7. T. S. Larchuk, M. C. Teich, and B. E. A. Saleh
"Statistics of Entangled-Photon Coincidences in Parametric
Downconversion"
Ann. N. Y. Acad. Sci. 755, 680-686 (1995)
http://people.bu.edu/teich/pdfs/ANYAS-755-680-1995.pdf
A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich
"Coherence Properties of Entangled Light Beams Generated by
Parametric Down-Conversion: Theory and Experiment"
Phys. Rev. A 53, 4360-4371 (1996).
http://people.bu.edu/teich/pdfs/PRA-53-4360-1996.pdf
Additional M.C. Teich's papers of interest:
http://people.bu.edu/teich/cv.html#TECHNICAL
8. Earlier sci.physics.research posts on use of "single photons" in QO
coincidence experiments:
http://groups.google.com/group/sci.physics.research/msg/5d07857496608a75
http://groups.google.com/group/sci.physics.research/msg/7764006d43d65061
9. G. 't Hooft "Determinism beneath Quantum Mechanics"
quant-ph/0212095 http://cul.arxiv.org/abs/quant-ph/0212095
"Quantum Gravity as a Dissipative Deterministic System"
gr-qc/9903084 http://cul.arxiv.org/abs/gr-qc/9903084
"Quantummechanical behaviour in a deterministic model"
quant-ph/9612018 http://cul.arxiv.org/abs/quant-ph/9612018
M. Blasone, P. Jizba, H. Kleinert
"'t Hooft's quantum determinism -- path integral viewpoint"
quant-ph/0504047 http://cul.arxiv.org/abs/quant-ph/0504047
Hans-Thomas Elze
"Determinism and a supersymmetric classical model of quantum fields"
hep-th/0503069 http://cul.arxiv.org/abs/hep-th/0503069
{ Sept 22, 2005, 00:05 EST }
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