efficiency loophole in bell tests & "NEP"
V.Z.Nuri
To: physics-research
Subject: efficiency loophole in bell tests & "NEP"
Date: Tue, 27 Aug 2002 17:45:21 -0600
recently Ive been posting here about the efficiency
loophole in bell tests & my convictions that deeper analysis
of it may be the way to a LHV, local hidden variable theory
for QM. I speculated there is some physical law for
the dark noise and efficiency tradeoff phenomenon of
PMTs in general.
I just ran across excellent and great evidence along these lines.
in ref (a), ribordy et al look at characteristics
of APDs relative to single photon experiments. later
in the paper they give an important formula I hadnt noticed
before, and arguably all Bell related experiment researchers
have not noticed it either, starting from Bell himself!!
the formula for "noise equivalent power" of a
detector is, p 2276 of ref (a)
NEP = (h * nu * (2 R) ^ 1/2) / eta
where h is planks constant, nu, R is dark rate in hertz,
eta is detector efficiency, eta->1 at perfect efficiency.
I dont know the origination of this formula. somewhere in
QM?
heres a defn .. also defined as minimum detectable power per
square root bandwidth. given in units of watts per (hertz) ^ 1/2.
http://www.its.bldrdoc.gov/fs-1037/dir-024/_3558.htm
but look at this!! we can easily rearrange this formula
to write
eta * NEP / (2R)^1/2 = h nu
but look at h nu!! that is just the familiar expression
for energy of a photon, E= h nu!! therefore its easy to assume that
we can never detect less than the energy of a single photon!! therefore
eta * NEP / (2R)^1/2 > h nu
or we can write the detector efficiency/dark count tradeoff as
eta / (2R)^1/2 > h nu / NEP
now this is the interesting part. NEP approaches zero as the
noise in one's detector approaches zero. but presumably,
one can never totally get rid of the noise. ribordy measured
NEP = 6e-17 W/(Hz^1/2), an improvement in one order of magnitude
over the lacaita value (a similar prior single photon efficiency study).
basically what this formula is telling us is this. every detector
has a NEP associated with it. once we know the constant k = h nu / NEP,
we have the efficiency/darkcount tradeoff curve & relation (between eta and
dark count) based on above formula, f(eta,R) > k.
this detection tradeoff is intrinsic to quantum mechanics if one
assumes there is always some nonzero NEP!!
** hence, we must rederive the bell equation to take into account
** there is no such thing as a perfect detector via the
** dark noise/efficiency tradeoff formula.
that is on my "to do" list. it doesnt look all that easy to
figure out how to do it yet!! but Im sure it will look trivial
in retrospect once nailed down!! one can now argue that bell (and
subsequent researchers such as CH/SH) failed
to take this key detection property into account in his original
derivation with extremely perplexing consequences!!
it is natural to speculate there is some minimum NEP beyond which
sensitivity in the detector cannot be improved!! NEP > 0 is
natural to assume. note the dark count/efficiency tradeoff is
true for all NEP > 0.
maybe it is also true that NEP > K for some
physical constant K. and it seems like a new, unrecognized
fundamental law of nature or constant, from what I can tell.
how could one measure K? one idea would be to look at single
atom traps and measure the NEP ensuing from photon detection
associated with a single atom.
then arguably NEP can never be lower than the NEP associated
with a single atom. APDs are possibly measuring a mass NEP
property over many atoms. presumably an extremely sensitive APD would
approach the single atom NEP.
I am still scratching my head on the ribordy log linear
dark count probability/efficiency curves from fig (4) of ref (a)..
not sure how it relates to the above formula yet, & ribordy has
informed me (via email) he does not know of a derivation of them. but they
would seem to be closely related to the NEP formula above.
another way of looking at the above formula is that it gives
a fundamental property of "false positives" and "false negatives" per time
for **any** experiment involving photons, but also bell experiments
in particular (where the count rate is crucial and critical to demonstrating
nonlocality).
let false positives, "Fp" per time be R, the dark rate.
let false negatives, "Fn" be 1-eta, where eta is efficiency.
then we have simply
(1-Fn) / (2 Fp/t)^1/2 > h nu / NEP
or another interesting or natural approach might be
Fp' = (dark counts)/t
Fn' = 1/eta^2
then
Fp' * Fn' = NEP / (2 h nu)
this is a fundamental false positive/false negative tradeoff rule
for all photon detection scenarios which shows that as
one decreases, the other increases and vice versa. we can also assume
that Fp'max is nu, with one dark count per wave.
in this form the above formala is quite reminiscent of
the heisenberg uncertainty equation. (it seems quite possible one
can be derived from the other.)
so let Fp' = Fp'' * nu where Fp'' is now a dimensionless quantity
(less than 1) like Fn'. then
Fp'' * Fn' = NEP / (2 h nu^2)
it seems possible to wildly speculate here, based partly on the
resemblance to the E = h nu formula, that maybe something like
NEP > 2 h nu^2
holds where nu is the energy transition frequency of the APD atom
material and the incoming wave frequency is matched to it. (?)
then the formula is simply
Fp'' * Fn' > 1
in any case we have some very significant implications for the
derivation of the bell formula(s) and all nonlocality theory and
experiments to date. I hope to be able to give a new
derivation of the bell formula based on the above false positive/negative
tradeoff formula.
what will be the effect on a bell formula derivation??? what if there is
an amazing situation that all nonlocality of the formalism is a side effect
of failing to take into account the above fundamental
tradeoff formula?? I am really starting to seriously wonder if that
is exactly the case.
also, a nice recent paper that I just found relevant to bell formula
derivations relative to the detector efficiency and sampling problems
is ref (b). however the authors unfortunately found that increased
"dimensions" of measurements were not sufficient to allow significantly
decreased detector efficiencies in bell experiments.
refs
--
(a) Ribordy, G et al, Performance of InGaAs/InP avalanche photodiodes as
gated-mode photon counters, Applied Optics 37, 2272-77 (1998)
(b) A Zoology of Bell inequalities resistant to detector inefficiency
by Serge Massar, Stefano Pironio, Jeremie Roland, Bernard Gisin
http://www.arxiv.org/abs/quant-ph/0205130/
Date: Thu, 29 Aug 2002 14:37:40 -0400
From: ebunn
To: vznuri
Subject: efficiency loophole in bell tests & "NEP"
You submitted the article below to the moderated newsgroup
sci.physics.research. I am unable to accept your article, as the
newsgroup does not accept "overly speculative" postings.
In particular, you are concluding *much* more than is justified from
the relation between NEP and dark rate. All it says is that the noise
goes down as the dark rate goes down.
You are of course free to post your article to another newsgroup such
as sci.physics if you choose.
Ted Bunn
sci.physics.research co-moderator
Spaceman
>You submitted the article below to the moderated newsgroup
>sci.physics.research. I am unable to accept your article, as the
>newsgroup does not accept "overly speculative" postings.
What a joke for "research"
They won't even research a clock,
nevermind anything else.
the research group should be named
relativity.is.correct.so.dont.post thoughts.here.
poor researchers.
they even forgot what research was.
Hey screwball researchers!
Your frellling atomic clock malfunctioned you frelling
mechanically illiterate research morons!
research group?
<LOL>
maybe more like
we.are.brainwashed.physics.
<ROFLOL>
James M Driscoll Jr
Spaceman
http://www.realspaceman.com