Photon Wave Collapse Experiment (Yeah sure; AJP Sep 2004, Thorn )

[vzn]

hi all I skimmed thru most of this thread. quite
amazing burst of dialogue. I hope to chat with "nite" 1-on-1 in
the future.. nite, why the mysterious anonymity? are you at
a university currently? want to protect your reputation? who is the
mysterious priesthood anyway, wink..

I have been looking at loopholes in QM for close to a decade.
lately I've realized that it will take an extremely brilliant person
to "get past" QM if that will ever happen. this person will have to
have a brilliant grasp of both theory AND experiment. nite is
the closest I've ever seen to this in many,many years.

I admire
marshall/santos work like nite, however they are hardcore
theorists. note that many of einsteins 1905 papers had NO references,
although he seemed to allude to michelson/morley in one. stunning!
einstein was an unadulterated theorist. the EPR paper is the closest
you can see to einstein actually "getting his hands dirty"...

imho nite really strong in-the-know challenge to the thorn et al
experiment (& even classic predecessors like grangier)
is electrifying, I just went over his criticism very carefully
with the original in front of me, and I would like to delve into
that further at some pt

(I see thorn et al circuitry is indeed quite different
from kwiat paper nite cites, and makes me wonder-- there might be
a lot of variation in detector electronics across experiments and yet
its always reported in papers as a "black box".. I share nite's
frustration over this! all the way back to aspects original papers!
I understand space limitations and all that, blah blah blah, but its
the 21st century, and let's throw away those
archaic & useless conventions pre-mass-digital space. how about
writers put up full schematics online, & summaries in journals? could
it be we are only having this conversation because of add'l detail
of more modern papers makes more careful analysis possible?
but.. clearly.. only approaching the minimum required level of detail to
discriminate two virtually identical theories?).

I can/may write much,much more on this topic just off the top of my
head & years of notes & musings & hope to contribute much more
over time here.

meantime I would like to invite everyone to my (almost 4-yr old)
mailing list to
discuss this thread in particular (outside all the other physics forum threads)

http://groups.yahoo.com/group/theory-edge/


next, some pts for nite. (I will nickname "nite" for now)

nite: I am really rooting for you & have been involved in the same
"research project" you are advancing, namely looking for LHV theories
maximally compatible with QM, or a minor revision of QM.
I agree with your critics however
that you should try to expand your criticism. why is it there can be so
much controversy over what should be _conceptually_
very simple experiments? the problem with LHV advocates is that
they cannot point to any EXPERIMENTS that back their position. not at
all! they point to experiments that are designed to reveal NONLOCALITY.

so if nonlocality is bogus, let's TURN THE TABLES. make experiments and
parameters in which LOCALITY is demonstrated even where NONLOCALITY
is expected. I have yet to see marshall/santos ET AL _EVER_ propose
NOVEL EXPERIMENTS designed to reveal the real problem with QM--
this is a feat bell managed that almost nobody has ever topped.

even better, RUN THEM YOURSELF! I hope that a genuine LHV
advocate gets ahold of an experimental apparatus soon! I have
met at least one (more on that later).. why is the LHV crowd so
devoid of any _experimentalist_ supporters?

what is an experiment that would leave QM supporters scratching their
heads? nite, in particular, here are some things that have never been
done:

a) if bell experiments don't demonstrate nonlocality wrt QFT
predictions, then where is the paper that shows that bell made
a mistake in the theoretical prediction? I in fact have found such
a paper that suggests he is getting photon number operators
mixed up or not clear on them-- I think there is good evidence
that bell didnt understand the photon number operator concept
much at all in his writing. (get his book of collected writings
and look for it! where is it?)

it will take me awhile to dig up
this paper (peer reviewed & published in highly reputable journal)
if there is interest, but it is indeed out there. unfortunately it
is only a beginning, it does not rederive the entire bell thm based
on this new perspective. how about YOU write this paper??
of anyone I have ever seen write, you are about the closest
to filling in all the blanks.

b) you say that QM is just subtracting "accidentals". then how
about this: design an experiment that will maximize the
effect of accidentals. QM has very little to say, or maybe nothing,
about quantitative measurements of accidentals, right?
can we create an experiment
that is entirely focused on "accidentals" which QM is somewhat
blind to, or considers them NOISE,
such that we can force a prediction using semiclassical
(glauber et al) theories, for which QM is MUTE in its prediction?

c)

nite, you are giving up too easily here! (but shame on your
critics for not discovering how to do this themself,
and contributing themself to this foremost goal,
not admitting that it is THEIR responsibility also, if they
want to be serious scientists and not just reactive anklebiters, just
as they accuse nite of being!)

I propose something along these lines, you virtually wrote
it up yourself, and I have long, long been
trying to get info on this experiment. Imagine a single
(semi) classical wavefront going thru N detectors. as I
read vanesch post #64, and we are dealing mostly
in this thread with N=2, look at what he says.
he says QM is only talking about these cases:

(a) only detector R clicks
(b) only detector T clicks.
(c) neither click
(d) both click.

now isn't the entire point (as vanesch seems to be writing) QM
applies only to predicting (a),(b) based on _collapse of the wavefn_
and has NOTHING TO SAY about cases
(c),(d)? and isn't it true however that semiclassical theory can give you
predictions about about all FOUR cases? imho, you have fallen
for the sleight of hand yourself without realizing it!
forget about (a),(b) and focus on (c),(d) which QM is indeed
apparently blind to! ie, exactly as einstein asserted.. INCOMPLETE

for those who advocate QM theory here (eg vanesch),
can you predict the following?
given N detectors, what is the possibility of detecting M<N of them
at a time? nite has given an EXACT PREDICTION FOR THIS
on binomial/poisson statistics, which is ENTIRELY CONSISTENT
with semiclassical predictions (see his earlier post..
I will look up the exact # later).

as I understand it, QM can only predict that only ONE of the N
detectors clicks at a time, if the collapse of the wavefunction
is a real physical phenomenon! so the experiments so far are
focused on N=2, but a really nice experiment would look at a
detector bank and show how a single E/M wavefront, as it
moves thru the detector array, creates a "probability wave" of
clicks! ie (contradicting the existing copenhagen dogma/theory)
the sch. wavefn is a real physical entity!

more later

 

[vanesch]

for those who advocate QM theory here (eg vanesch),
can you predict the following?
given N detectors, what is the possibility of detecting M<N of them
at a time? nite has given an EXACT PREDICTION FOR THIS
on binomial/poisson statistics, which is ENTIRELY CONSISTENT
with semiclassical predictions (see his earlier post..
I will look up the exact # later).

as I understand it, QM can only predict that only ONE of the N
detectors clicks at a time, if the collapse of the wavefunction
is a real physical phenomenon! so the experiments so far are
focused on N=2, but a really nice experiment would look at a
detector bank and show how a single E/M wavefront, as it
moves thru the detector array, creates a "probability wave" of
clicks! ie (contradicting the existing copenhagen dogma/theory)
the sch. wavefn is a real physical entity!

I have one very clear advice for all those trying to explain that QM is bogus, and that is: learn it first!

First of all, these experiments don't "show that collapse is a real phenomenon". I for one, don't believe in such a collapse, as many other people (not all) interested in foundational issues. That discussion (about collapse) has nothing at all to do with what we all agree on: the PREDICTIONS OF OUTCOME OF EXPERIMENT of quantum theory.

As to your specific question: is quantum theory not able to predict several coincident detections ? Answer: you must be kidding. Of course it is. For instance, the simultaneous detection of idler and signal photons from a PDC xtal.
There are two ways to see it: one is the "student" way, the other is the "more professional" way.
The student way: PDC xtals generate 2-photon states. Applying two annihilation operators to a 2-photon state gives you the vacuum state which has a finite norm.
The more professional way: PDC xtals have an effective time evolution operator which couples the 1 UV photon -> idler photon + signal photon and the incoming beam (a UV laser) is well described by a coherent state.
Apply the time evolution operator to that incoming beam, and you generate a lot of photon states, but with a surplus (as compared to a coherent state) of two-photon states (= the student case). The rest generates you the non-matched clicks (the 1-photon states that remain).
See, the "professional way" takes into account more "side effects" but the student way has the essential effect already.

But if your aim is to critique QM, all the above should be EVIDENT to you.

As should be evident the answer to your specific question:
If we have an incoming 1-photon state (such as is essentially produced by taking a 2-photon state from a PDC and triggering on the idler), and you give it the possibility to hit (through beamsplitters) several detectors, then there will only be ONE that hits indeed. Of course there could be a slight contamination in the beam of other, multi-photon states (remnants of the original coherent beam, or light leaking in or...), which can give rise to occasional double hits.

How about the following: if you send the signal beam on a hologram, and that image then onto a position-sensitive photodetector, then your N detectors are the N pixels of the position sensitive detector. Each time the idler clicks, at most ONE pixel should be hit. And it should built up the image of the hologram over time. I have vague souvenirs of such an experiment, but I don't know if they looked at the right things. I'll try to look it up.

As to the binomial distribution in the classical case: quantum theory also predicts that, if the incoming beam is a coherent state. You can do a lot of calculations, but there is a neat trick to see it directly:
Coherent states are eigenstates of the annihilation operator:
a |coh> = some number x |coh>

This means that applying an annihilation or not, to a coherent state, doesn't change its photon content, which comes down to saying that the statistics of detecting a photon somewhere is _independent_ of having detected a photon somewhere else or not. Detections are statistically independent, which immediately, as in the classical case, gives rise to the same binomial distributions.

cheers,
Patrick.

 

[nightlight]

Question-a) Given actual DT and DR of their setup, thus DT absorbing mode |T> (hence a_t |T> = |0>, a_t |R> = 0) and DR absorbing mode |R>,...

This is a particularly easy question to answer.

It surely was, especially with the little hint (a_t |R> = 0) added to "help" you (sorry:) decide whether to "plunge into" the head on answer.

Unfortunately, the low-res analysis you provided (shared also by the "quantum prediction" of AJP.8-11 and the typical textbooks they copied it from) does not resolve well enough to distinguish between an absorber (=detector) covering both paths T,R and an absorber covering just path T, or for that matter, an absorber set somewhere else altogether, away from T and R paths. The reason it can't resolve these different absorbers is not because all these cases yield the same outcomes (they obviously don't; e.g. think of different apperture sizes of DT and consider its singles rates) but because the low-res treatment lacks any formal counterpart for the detector size. And the reason for this omission is that the low-res approach assumes one fixed size, an infinite absorber absorbing an infinite plane-wave modes, thus in the low-res it is indeed true that a_t |R> = 0. In our case of (Q-a), though, neither the absorbers nor the EM fields are of this kind.

In order to model the difference, say, of the singles on DT as we change its size or position relative to T and R beams (or similarly for the coincidences of DT and DR), we would need a formalism which does not assume one fixed size, much less infinite, of the absorbers or the infinite modes -- thus the formalism which has the formal counterparts for these parameters (which are the key in discussing matters of non-locality).

As luck would have it, Mandel had already done it in 1966 (cf. [8]) and a simplified form is in his QO textbook [9]. The main simplification in [9] (sect. 12.11) is that [8] considers general multi-time operators while [9] deals only with the single-time operators. For our present questions Q-a,b, though, that doesn't matter (it would matter if we were discussing effects such as the possible [post=533012]polarizer flip-flop effect[/post] I mentioned earlier). In [9], Mandel breaks the problem of the finite absorbers to cases of infinite (12.11.1-4) and finite (12.11.5) EM field modes. The upshot of his analysis is that in the latter case (relevant to our problem Q-a,b), no general relations of the kind a_t |R> = 0 holds for the finite absorbers (his V(r,t), eq 12.11-1) acting on finite modes (his Phi(r,t), eq. 12.11-28), although the Glauber's mode absorption rates are still formally given by the same type of normally-ordered expectation values of localized mode creators & annihilators averaged over localized states. Thus, one can formally look at the (AJP.9) as still being valid, except that now the annihilators a_t and a_r must be considered as localized absorbers acting on localized modes.

Mandel emphasized the difference between his first case of infinite modes (where the absorption rates and the photon intensities are roughly interchangeable, almost as freely as in the more elementary analysis) and the second case of finite absorbers and finite modes (where the two are not interchangeable cf. eqs 12.11-30 vs 12.11-40). Pointing to this difference, he warns of the pitfalls (for the low-res analysis relying on naive photon image and photon numbers to deduce detection probabilities) in the precise case we are discussing, where we have localized modes/photons and the localized absorbers, due to the particular distinctions between the photon numbers & intensities (as photon fluxes) and the detector counts & the absorption rates ([9] p 639):

From these considerations it is apparent that the concept of the photon as a localized [approximately, as defined in eq 12.11-30] particle traveling with velocity c can be quite inappropriate and misleading under some circumstances, even though it works in other cases.

To obtain the classicality of the coincidence rates via (AJP.9) in the case (Q-a), where we have the localized detectors DT and DR, as given in the actual experiment, and on the actual input state |Psi.1> = (|T> + |R>)/sqrt(2), as explained by Mandel in [8],[9], we need to use generalized absorbers for the a_t and a_r. To get these absorbers, we will go back to their origin as "absorbers" (whose counts G2(DT,DR) in numerator of AJP.9 "correlates") in the Glauber's perturbative treatment ([4] Lect's iv,v) and augment them there in accordance with the finite interaction volumes given by DT and DR.

The interaction Hamiltonian for the absorber+EM field in dipole approximation is H_i = Sum(j){q_j(t) E(r,t)} (cf [4] eq 4.1, ignoring constants), where q_j are dipole moments of j-th electron in the absorber and E is the incident Electric field operator. To obtain the time evolution of the field-detector system Glauber uses interaction picture, where the combined state |Psi> = |Psi_em> |Psi_a> (where subscripts em refers to EM field and 'a' to absorber) evolves as: i d|Psi>/dt = H_i |Psi> (note that here the state evolves via the interaction H_i only, while the EM field operators, including those in H_i, evolve via the free field Hamiltonian H_f, thus via Maxwell equations). In the 1st order perturbation he obtains for the ionization rates (or the electron transition "probabilities" which already include his subtraction conventions): <i|E(-)E(+)|i>, where |i> is the incident field state and the E=E(+)+E(-) (positive & negative frequency decomposition of Electric field operator in the H_i). He identifies (E+) as 'photon' annihilation operator (and (E-) as creation), thus in our earlier notation we can write this as <i|(a+)(a)|i>. The multiple absorbers ([4] lect 5) yield in n-th order perturbation the regular Glauber "correlation" functions Gn() (shown as G2() in numerator of AJP.9), with his subtractions already built into their definition.

Those derivation did not assume any localization of the absorbers, thus any restrictions on the H_i interaction. In our case of localized detectors, we need to limit the effect of the H_i to the space region of the detector. We can do this by attaching a factor with H_i which is 0 outside of the detector and 1 inside. In his analysis [8] & [9] of space limited detectors, Mandel had also introduced this factor as U(r,V) where U=0 if r outside of volume V and 1 if r is inside V (cf. [9], p 633). With that factor included (which will follow E of H_i throughout derivations in [4]), the interaction part evolution operator U_i (cf. [4] eq 4.3 for single detector and 5.2 for n detectors) remains unchanged from the earlier analysis inside V and becomes identity outside V (in interaction picture). In Schrodinger picture the latter becomes free evolution of field states |Psi> outside the volume V(DT) of the detector DT, and the absorption described via 'limited' annihilator A_t(V) inside the detector volume V(DT). The Glauber's Gn() functions remains formally same as before, except for the replacements of the 'unlimited' operators a_t and a_t(+) with the 'limited' operators A_t(V) and A_t(+,V).

Thus we can now interpret the (AJP.9), when applied to the actual limited space detectors DT and DR used in the experiment, as containing the 'limited' versions of the operators, simply labeled as a_t and a_r (with the understanding that, e.g. a_t includes the volume parameter, which defines its action as identity outside the volume and absorption inside V).

Now we arrive to the critical question: how does this 'limited' a_t act on the space limited state |R> (this is precisely the type of case that Mandel warned about when using the naive photon number reasoning in predicting detection rates)? Since the region R is outside the volume V(DT), in Schrodinger picture the state |R> will evolve via the free field equations, as it did before its "interaction" with the 'limited' absorber a_t. Therefore a_t |R> = |R>. As you already noticed, this implies (we can call it, I guess, our joint conclusion) that QED prediction is g2>=1 for the space limited detectors DT and DR and the input state Psi.1> = (|T>+|R>)/sqrt(2) of this experiment.



--- Ref

[8] L. Mandel "Configuration-Space Photon Number Operators in Quantum Optics"
Phys. Rev 144, 1071-1077 (1966)

[9] L. Mandel, E. Wolf "Optical Coherence and Quantum Optics"
Cambridge Univ. Press., Cambridge (1995)

 

[vanesch]

Therefore a_t |R> = |R>.

That's silly. You know the solution for that, don't you ? An eigenstate of an annihilation operator: it is a coherent state. So you just showed that |R> is a coherent state :-)

cheers,
Patrick.

 

[seratend]

as I read vanesch post #64, and we are dealing mostly
in this thread with N=2, look at what he says.
he says QM is only talking about these cases:

(a) only detector R clicks
(b) only detector T clicks.
(c) neither click
(d) both click.

now isn't the entire point (as vanesch seems to be writing) QM
applies only to predicting (a),(b) based on _collapse of the wavefn_
and has NOTHING TO SAY about cases
(c),(d)? and isn't it true however that semiclassical theory can give you
predictions about about all FOUR cases? imho, you have fallen
for the sleight of hand yourself without realizing it!
forget about (a),(b) and focus on (c),(d) which QM is indeed
apparently blind to! ie, exactly as einstein asserted.. INCOMPLETE

It seems that you have some problems with probability in general and the meaning of random variables and observables. Let take a basic example:
If in a classical probability problem you choose, for example 2 random variables X and (-X), where X has only two values {-1,+1}, do you think that case (c) and (d) are possible for these 2 random variables?
If you think it is impossible, does that mean that Kolgomorov probability is incomplete or blind?
Do you really understand what is, mathematically, the sample space of an observable?

Seratend.

 

[vanesch]

Now we arrive to the critical question: how does this 'limited' a_t act on the space limited state |R> (this is precisely the type of case that Mandel warned about when using the naive photon number reasoning in predicting detection rates)? Since the region R is outside the volume V(DT), in Schrodinger picture the state |R> will evolve via the free field equations, as it did before its "interaction" with the 'limited' absorber a_t. Therefore a_t |R> = |R>. As you already noticed, this implies (we can call it, I guess, our joint conclusion) that QED prediction is g2>=1 for the space limited detectors DT and DR and the input state Psi.1> = (|T>+|R>)/sqrt(2) of this experiment.

In order to illustrate a bit further your confusion here, let us consider one of those infinite absorbers you like, which are absorbing perfectly IR photons, and are completely transparant to, say, UV photons. This is in fact the best possible definition associated to the annihilators of the plane wave basis. (you still didn't understand that you can change basis, and that that is all that matters here).
So, with this absorber, which absorbs ONE fock space mode, namely certain IR photons exactly along the z-axis, corresponds perfectly a_IRmode, and our detector DOES NOT absorb UV photons.
So, applying the same reasoning, a_IRmode |UV state> = |UV state>, right.
Well, that's wrong. a_IRmode |UVstate> = 0.
Because now we are with the orthodox creation and annihilation operators.

I can tell you that you are digging something up you don't understand yourself: what Mandel is addressing is those cases where you have such tiny detectors, so close to one another, that you cannot have modes which are solutions to the EM field, hitting fully, or missing fully, the tiny detectors. But from the moment they have a size of several wavelengths, and are zillions of wavelengths apart, this doesn't matter ; for all purposes you can approximate the modes by the plane wave modes, in spatial wave packets. This is tedious, complicates matters, and doesn't change the result. It only leads to confusion. You are again talking about plate tectonics to show that planets are not point particles and that Newtonian theory doesn't predict Kepler orbits.
One thing is sure: your conclusion that for a finite detector, a_detector|other stuff>= |other stuff> is obviously plain wrong, because it means that ALL other stuff is a coherent beam of a certain intensity!
You've been digging in plate tectonics because you've read somewhere that someone said that the mass distribution within a planet has gravitational effects (which is true, tiny effects are due to that), and you came to the conclusion that this means that planets go in square orbits.

cheers,
Patrick.

 

[nightlight]

That's silly. You know the solution for that, don't you ? An eigenstate of an annihilation operator: it is a coherent state. So you just showed that |R> is a coherent state :-)

The limited volume operator a_t isn't the same thing as the annihilation operator. Additionally, for Mandel's case two (of limited volume modes, such as |R>) most analogies with regular algebra of a,a+ doesn't work, and many usual implications dont' follow. Check the cited sections in ref [9], where I quoted Mandel's warning.

(I've seen not long ago another paper which aimed to establish different QO measurement theory, where the "single photon" Fock states appear statistically as coherent states, which agrees with my conclusion as well.)

-- EDIT

Ok, I found that paper (quant-ph/0307089), and indeed Fock state in their model produces Poissonian photo-count distribution (which is an entirely different claim than claiming Fock state has Poissonian photon distribution, as you tried to interpret it, illustrating thus perfectly the very warning by Mandel, I cited):

M. C. de Oliveira, S. S. Mizrahi, V. V. Dodonov
"A consistent quantum model for continuous photodetection processes"

Abstract

We are modifying some aspects of the continuous photodetection theory, proposed by Srinivas and Davies [Optica Acta 28, 981 (1981)], which describes the non-unitary evolution of a quantum field state subjected to a continuous photocount measurement. In order to remedy inconsistencies that appear in their approach, we redefine the `annihilation' and `creation' operators that enter in the photocount superoperators. We show that this new approach not only still satisfies all the requirements for a consistent photocount theory according to Srinivas and Davies precepts, but also avoids some weird result appearing when previous definitions are used.

CONCLUSION

Summarizing, in this paper we proposed modifications
in the SD photocount theory in order satisfy all the precepts,
as proposed by Srinivas and Davies for a consistent
theory. Our central assumption was the choice of
the exponential phase operators E− and E+ as real ‘annihilation’
and ‘creation’ operators in the photocounting
process, instead of a and a†. The introduction of those
operators in the continuous photocount theory, besides
eliminating inconsistencies, leads to new interesting results
related to the counting statistics. A remarkable
result, which is responsible for all the physical consistency
of the model, is that in this new form an infinitesimal
photocount operation JE really takes out one photon
from the field, if the vacuum state is not present. Consequently,
the photocounting probability distribution for
a Fock field state is Poissonian, evidencing again the direct
correspondence of number of counted photons and
number of photons taken from the field.
We also have investigated the evolution of the field
state when photons are counted, but with no readout,
leading to the pre-selected state. The mean photon number
change shows now (in contrast to the exponential
law obtained for the amplitude damping model) a nonexponential
law, which only depends on the condition
that photons are present in the field, independently of
their mean number.
An advantage of the proposed model is its mathematical
consistence. Since many of its predictions, especially
those related to multiphoton events, are significantly different
from the predictions of the SD theory, it can be
verified experimentally. One of the first questions which
could be answered is: whether the decrease of number of
photons in the cavity due to their continuous counting
always obeys the exponential law (61) (i.e., the rate of
change is proportional to the instantaneous mean number
of photons), or nonexponential dependences can be also observed (for example, in the case of detectors with
large dead times)? ...

.

 

[vanesch]

The limited volume operator a_t isn't the same thing as the annihilation operator. Additionally, for Mandel's case two (of limited volume modes, such as |R>) most analogies with regular algebra of a,a+ doesn't work, and many usual implications dont' follow.

I think you'll agree that you can write a_detector (your "limited volume" modes) as an algebraic combination of the a_{planewave}, right ? Or not ?
Note that all operators are writable in a_{planewave} and a^dagger_planewave.
So some expression is possible. Please do.

Say I have a detector that has 1cm^2 absorption surface for 500nm photons, is placed in the XY plane {points {0,0,0}, {0,1,0},{1,1,0} and {1,0,0}}.
It doesn't absorb anything else.

Can you write me, according to Mandel, what a_{squaredetector 500nm} is, as a function of the plane wave annihilation operators ?

cheers,
Patrick.

 

[vanesch]

I think you'll agree that you can write a_detector (your "limited volume" modes) as an algebraic combination of the a_{planewave}, right ? Or not ?
Note that all operators are writable in a_{planewave} and a^dagger_planewave.
So some expression is possible. Please do.

I looked at the Mandel paper Phys. Rev. 144, of 1966 and in fact that's exactly what he does (and what I'd had more or less in mind).

Ok, look at equation, say (32) in that paper. For our correlation function of detection of two photons, we'd have a linear combination (integrals) of terms of the kind: <A_i1(x1,t1) dagger A_i2 (x2,t2) dagger, A_i2 (x2,t2) A_i1(x1,t1) >

So this is a sum of products of two "A-dagger" operators, and two "A-operators".

Now, if you look at equation (1), you see that an A-operator is written as a linear combination of TRUE PLANE WAVE ANNIHILATION operators, and by conjugation, A - dagger is a linear combination of true plane wave creation operators.

Substituting, you will thus find that we have a linear combination of terms which take on the form:

< adagger_s a_dagger_r a_r a_s >

And my story goes again: in each term, we have two annihilation operators, acting on a 1-photon state, which will always give you 0.

But as I said, this is hopelessly complicating the issue, because given the size of the detectors (huge compared to the wavelength), in equation (2) you ESSENTIALLY PICK OUT plane wave annihilators, combined in a wave packet, as I told you. And as our detectors are hugely distant the relations (23) and (24) come close to my "low resolution" treatment.

Kepler orbits.

cheers,
Patrick.

 

[nightlight]

I looked at the Mandel paper Phys. Rev. 144, of 1966 and in fact that's exactly what he does (and what I'd had more or less in mind).

Ok, look at equation, say (32) in that paper. For our correlation function of detection of two photons, we'd have a linear combination (integrals) of terms of the kind: <A_i1(x1,t1) dagger A_i2 (x2,t2) dagger, A_i2 (x2,t2) A_i1(x1,t1) >

So this is a sum of products of two "A-dagger" operators, and two "A-operators".
...

That paper covers only the Mandel's first case, which is the finite detector with infinite space modes. The second case, when modes and detectors are finite is only in the sect 12.11.5 of [9], and that is the case of interest. Physically, in the infinite mode case, the detector does interact with all modes and the detection behavior is approximately similar to ordinary infinite detector case.

The [8] is not directly relevant for the problem discussed, except that it was the paper which recognized the problem (which you denied to exist at all). He introduced there only the limited size detector model and the notation which [9], sect 12.11.5 develops further for the case we are discussing (which is: what happens when the actual DT detector, which is limited, is detecting field in state |R>). Unfortunately, in 12.11.5, he pursues entirely different objectives (analogies with particle wave functions his Phi and Psi, and their difference, eqs. (30) vs (40)).

Thus, to obtain the properties of interest of the correlation functions, it turns out it was more convenient to go back to Glauber's model [4] and obtain formally the limited-space Gn()'s by directly limiting the interaction volume of the H_i and replaying his derivation of Gn()'s with this limitation carried along, as I sketched earlier. It can probably be replicated with Mandel's quantum detection model in [9], chapter 14 (that's left as an excercise for the reader).

The conclusion is also physically perfectly satisfactory since, forgetting the detector and all the QM baggage that goes along, just put an atom (Glauber's model for his "ideal" detector) at DT place and prepare narrow beam, mode |R>, as the EM field state. Its evolution will be entirely unaffected by the presence of the atom (or of the entire detector DT cathode, if you wish), as you can easily verify by experiment.

--- Edit:

I don't doubt that you also realize, without having to do any experiment, it is exactly what will hapen. Then, the subsequent superposition of this |R> with |T>, which is also localized in its own region, doesn't change anything with the EM fields in region R (other than normalization constant if your convention is to keep the total energy fixed). The superposition in this case (with the spacelike interval between T and R at the time of detection) merely means that EM fields at T and R have a common phase, their oscillations are synchronized (with at most some delay), thus should you deflect them and bring them back to a common detector you will observe interference.

The presence of such synchronization surely doesn't somehow allow some kind of magic effect by the T branch of EM interacting with DT, to make any difference at all in the spacelike region R (in any experiment performed in R region on the R EM branch). The only pseudo-magic that can happen is if you perform the experiments on R in sync with the experiments on T, then you will obtain various forms of synchronized efects, such as beats in the results, of these two sets of experiments.

 

[vanesch]

The [8] is not directly relevant for the problem discussed, except that it was the paper which recognized the problem (which you denied to exist at all).

There was nothing to deny, you are, as usual, overcomplicating the issue. Now that [8], which "showed" according to you, that a_det |other mode> = |other mode> doesn't hold, and that my very good approximation of a_det1 and a_det2 as annihilation operators which are to be brought in relationship with essentially orthogonal modes comes out, you say that it isn't relevant, and that I have to switch to its "simplified student treatment" [9].
And there again, you are going to play the "finite space mode" game, which is just a narrow wavepacket of plane wave modes, because, again, the sizes involved are so huge as compared to the wavelengths that it doesn't matter.

But go on, complicate the issue, in the end I'll have to give up because you'll point out that I didn't take into account the gravitational attraction of the moon in my toy model.

I will tell you that it won't work, with finite modes either, and that is because the finite modes involved here (beam goes to the left, and beam goes to the right), will be written as superpositions of plane waves which are 1) all very close to one another in k-space, for one beam, and 2) very remote from each other for the left beam and the right beam.
So these "finite beams" use orthogonal modes. And as there is no overlap in the used modes, everything still holds. No big deal.

cheers,
Patrick.

 

[nightlight]

There was nothing to deny, you are, as usual, overcomplicating the issue.

Of course, you denied there was any difference that mode sizes and detectors size make, when you said:

This is also simple to answer. ANY single-photon mode, with any detector setup, will give 0.

As you now realize (or will realize, when you had time to think it through), using the finite mode sizes and finite detector sizes makes big difference in the results. Among other things, instead of g2=0 you get g2>=1.

Now that [8], which "showed" according to you, that a_det |other mode> = |other mode> doesn't hold,

Which no one claimed to hold under the assumptions in [8], either.

you say that it isn't relevant, and that I have to switch to its "simplified student treatment" [9].

That was already done in my initial post on [8], [9]. Except for the multiple-time results, the paper [8] is three decades older than [9], too. That's about as many decades as there were in the failed attempts, euphemisms aside, to demonstrate Bell inequalities violation. Not a single one worked. And there is no theoretical reason from QED to believe any will ever work.

And there again, you are going to play the "finite space mode" game, which is just a narrow wavepacket of plane wave modes, because, again, the sizes involved are so huge as compared to the wavelengths that it doesn't matter.

It matters because it affects what detection rates you will get. With the DT and DR setup they had, with their state |Psi.1>, the infinite mode treatment is absurd, it gives absurd result (which they could "confirm" experimentally only by dropping almost all the triple coincidences through their timing trick).

But go on, complicate the issue, in the end I'll have to give up because you'll point out that I didn't take into account the gravitational attraction of the moon in my toy model.

It does make big difference whether the mode |R> overlaps detector DT or not. The infinite mode treatment simply doesn't apply. The finite modes complicate matter only mathematically. But the infinite modes complicate matters conceptually and logically, since you get tangled in the web of absurd results, for which your "simple" solution is to imagine splitting universes (how often?), and finally declaring that the whole universe, along with all its innumerable MWI replicas, is a figment of your mind (solipsism to which you fell on as your last defense in the previous discussion).

And now you complain that I am complicating matters by insisting, what ought to be obvious, that the detectors DR and DT and the modes |T> and |R> are restricted in size and that this restriction makes difference in correlations compared to infinite detectors and modes. You make an example of pot calling snow black.


I will tell you that it won't work, with finite modes either, and that is because the finite modes involved here (beam goes to the left, and beam goes to the right), will be written as superpositions of plane waves which are 1) all very close to one another in k-space, for one beam, and 2) very remote from each other for the left beam and the right beam.

You can't have infinite extent of |R> transverally either. Which means you will nead many transversal components to build a narrow beam |R>. Plus, you need to have a very large box, so that the periodicity of the expansion doesn't leave nonzero parts in the region DT.

So these "finite beams" use orthogonal modes. And as there is no overlap in the used modes, everything still holds. No big deal.

No it doesn't hold, not with finite detectors (which you apparently forgot again), with spatial limitation of DR and DT.

--- Edit

I think the discussion of the last several messages has been running in circles. Again, thanks for the good challenge, and we'll be at again in some other thread.

 

[vzn]

hi guys. yes I think I now see an experiment that could
prove that QM is incomplete based on nite's arguments & the replies
of his critics. so far
even nite does not seem to be aware of this possibility.

lets look at a PDC "ring" of correlated photons emitted
from a crystal illuminated by a laser, a photo of this can
be seen in the kwiat et al paper that nite cited here.

existing QM experiments tend to be focused on looking
at only two branches or detection locations of this emission.

lets just look at multiple "branches" (to borrow charged manyworld
terminology, but only at nite's lead) with N>2. unfortunately
this would translate into very expensive experiments
because good photodetectors tend to cost $5K or more each. but
maybe it could be shown with cheaper detectors. (and in fact
imho, the experimenters are going somewhat
in the wrong direction, at least wrt these types of
experiments, by trying to get the most expensive
detectors possible, translating into low N..)

QM experiments are oriented around "signal" and "idler" photons.
but this is a misnomer in the sense that both branches are fully
physically equivalent/symmetric. there is no physical distinction.
it is just an N=2 detector experiment. both branches are equivalent.

according to the predictions of QM, if I have say N=3 detectors
and NOT assigning any particular detector as "signal vs idler"
(as is natural in the symmetry of the physics),
the following events are mutually exclusive:

detector 1 clicks only.
detector 2 clicks only.
detector 3 clicks only.

IN CONTRAST the prediction of semiclassical theory is that you will always
get a meaningful, nonrandom distribution of
coincident clicks in any of the detectors.
nite quotes this result in post #16 on this thread where he talks about
the binomial vs poisson statistics. (possibly due to a paper of glauber,
based on semiclassical theory, I would like nite to clarify where that
came from.. also I wish nite would describe in short what a "glauber detector" is...)

and yes, I have pointed out in the past & vanesch notes--
an experiment using
a CCD camera (array) would be natural to use (N very large) &
might be able to show this effect across detectors.
however one would have
to get "flat" planar wavefronts hitting the front of the array, which is
difficult because optics always makes them spherical. however some kind
of collimator might be possible.

vanesch replies that QM makes the prediction about
coincident poisson/binomial statistics in multiple detectors. how about
giving me a reference on that? or let's see the derivation! this after
he denies that it talks about coincident clicks! I don't see it.

let us call this "noncoincident vs coincident" clicks to try to contrast
QM vs semiclassical.

semiclassical states (as I crudely understand it..if not just call
it "vzn-classical"),
there will be NO WAY to narrow the time window such that all events
are mutually exclusive as QM predicts. however if we LIMIT OUR SAMPLE
of incoming data
(either in the electronics or post experimental data selection)
only to events in which we don't have coincident events, then we get
EXACTLY the QM predictions.
in other words, QM makes no INCORRECT predictions, but it is
INCOMPLETE; semiclassical theory is more COMPLETE because it makes
the same predictions as QM for noncoincident events, but also can
talk meaningfully about COINCIDENT events, which QM is mute on.

QM is mute on COINCIDENT events because they are simply nonexistent
by the "collapse of the wavefn", which is the semantical shorthand
which refers to the projection operation in the mathematical formalism
(ie collapse of wavefn is in the theory, and its effect is that QM cannot
speak about coincident events) & also its model of the probability spaces
(yes that's what I am saying seratend)..

actually I am being generous to QM, as vanesch replied,
if QM DENIES there can be anything other than random coincident
events, as he has stated & interpreted ("statistically independent"),
then it must be INCORRECT and I have
given an experiment above to prove it. (yes vanesch I would be
interested in your "vague souvenirs" of this experiment)

acc to nite, semiclassical can speak naturally on the case N>2 detectors,
whereas QM has no such prediction

actually, let me revise this experiment to be as open as possible.
I propose an experiment that
just tries to work with an N very large, and then GRAPH the distribution
over time, not ASSUMING any particular distribution (poisson or binomial
or whatever) and then showing how well it fits to a binomial or poisson
distribution.. can anyone show me that in the literature anywhere??
wouldnt it be a nice experiment scheme that would
tend to discriminate semiclassical from QM type theories, without
any experimenter/experimental bias? its one I've proposed a long time
ago & wanted to carry out myself..

ps guys it is true that I am not a specialist in the QM formalism. please
do not crucify me on this

ps nite, you complain about physics corrupting the mind of physics
students. I am one of those students. I am all ears..
when are you going to teach me? or would you rather spear at the infidels
or priesthood some more? after about 4 yrs I have lined up group of
N>200 "detectors" waiting for your "signal".. please reply to my email
wink

 

[vanesch]

So these "finite beams" use orthogonal modes. And as there is no overlap in the used modes, everything still holds. No big deal.

No it doesn't hold, not with finite detectors (which you apparently forgot again), with spatial limitation of DR and DT.

I still remain with my initial claim, that no matter how you combine, in wave packets, plane wave modes into finite-size beams, and their corresponding plane wave annihilation operators and creation operators in "finite volume" number operators, that the expectation value:

< 1-photon state | A+(1) A+(2) A(2) A(1) | 1-photon state>

is ALWAYS 0.

For always the same reasons: these "finiteness" just combines the "infinite plane wave" quantities (number operators, 1-photon states) LINEARLY together, in what I've been calling spatial wave packets, and in the end you become a huge linear combination of terms which CAN be expressed in the "plane wave" quantities (by bringing all these weighting functions and their integrals outside the in-product). ALL these terms take on the form:

<plane wave 1 photon state | a+(r) a+(s) a(t) a(u) | plane wave 1 photon state>
with a(r), a(s), a(t) and a(u) the plane wave mode annihilation operators.

And now we're home, because we have TWO ANNIHILATION operators acting on a single photon state, GIVING 0.

All these terms are 0, no matter how you combine them in linear superpositions.

What is however uselessly complicating the issue is that such considerations could be important if the distances and sizes involved were of the order of the wavelength. However, when they are of the order of mm or even cm, there is no point at all not to work directly with the idealized plane wave situation directly.

Nevertheless, you didn't show an explicit calculation yourself, reducing your quantities to plane waves and plane wave creators and annihilators, that you obtained 1 for this quantity, and not 0. You always said that the calculation that was presented didn't take this, or that, into account, but you never presented a clear calculation yourself, for 1cm^2 detectors, at 1 m distance apart, with light of 650 nm, that you had another result. You only claimed that we COULDN'T do certain things.

I still want to see you derive a kind of A_detector and a finite 1-photon mode, as expressed in plane wave quantities so that there's no discussion, so that you have A_detector |finite 1-photon mode> = |finite 1-photon mode>.

cheers,
Patrick.

 

[vanesch]

lets look at a PDC "ring" of correlated photons emitted
from a crystal illuminated by a laser, a photo of this can
be seen in the kwiat et al paper that nite cited here.

End of the game already: there is no ring of correlated photons.
Depending on the angular conditions, let us assume that we placed ourselves (in order to come as close as possible to what you think is happening) in the lambda -> 2 lambda + 2 lambda condition, then there are many 2-photon states that are emitted, and because of the cylindrical symmetry of the setup, these two "arms" of the 2-photon states can take any orientation ; however, within one "pair", they are oppositely aligned. So you have many independent "pairs".
There's no special correlation between different pairs.

existing QM experiments tend to be focused on looking
at only two branches or detection locations of this emission.

That's because it is in that way that there is some hope of "catching the two arms of the same pair".

lets just look at multiple "branches" (to borrow charged manyworld
terminology, but only at nite's lead) with N>2. unfortunately
this would translate into very expensive experiments
because good photodetectors tend to cost $5K or more each. but
maybe it could be shown with cheaper detectors. (and in fact
imho, the experimenters are going somewhat
in the wrong direction, at least wrt these types of
experiments, by trying to get the most expensive
detectors possible, translating into low N..)

I just build a 128-branch neutron detector, for a total worth of about $800000,- so this is probably not the argument :-)

QM experiments are oriented around "signal" and "idler" photons.
but this is a misnomer in the sense that both branches are fully
physically equivalent/symmetric. there is no physical distinction.
it is just an N=2 detector experiment. both branches are equivalent.

Let's change the names then in "signal1" and "signal2" :-)

Problem solved ?

according to the predictions of QM, if I have say N=3 detectors
and NOT assigning any particular detector as "signal vs idler"
(as is natural in the symmetry of the physics),
the following events are mutually exclusive:

detector 1 clicks only.
detector 2 clicks only.
detector 3 clicks only.

Absolutely not. If these detectors are not specifically aligned to see the "two arms of the 2-photon pairs", they will detect independently different pairs. The "arrival sequence" of these independent pairs is determined by the pump beam ; but if it is a coherent laser beam, then these pairs can be thought of to be generated Poisson like. As each detector will see one arm of an arbitrary pair, it will click in independent Poisson series. As in classical optics.

IN CONTRAST the prediction of semiclassical theory is that you will always
get a meaningful, nonrandom distribution of
coincident clicks in any of the detectors.

No, classical theory will also predict independent Poisson clicks.

and yes, I have pointed out in the past & vanesch notes--
an experiment using
a CCD camera (array) would be natural to use (N very large) &
might be able to show this effect across detectors.

Good luck with the time resolution of a CCD camera :-))) (about a few ms ?)

vanesch replies that QM makes the prediction about
coincident poisson/binomial statistics in multiple detectors. how about
giving me a reference on that? or let's see the derivation! this after
he denies that it talks about coincident clicks! I don't see it.

He must be real stupid. In fact, depending on the incoming state of the field, the predictions change ! If it is a 1-photon state you can only detect 1 photon, and suddenly if it is a coherent beam containing a superposition of all number of photon states, it can be binomially distributed. How strange...
As if the time of orbit around the sun of a planet depended on its distance to the sun and the sun's mass! Crazy. Never ever the same results.

semiclassical states (as I crudely understand it..if not just call
it "vzn-classical"),
there will be NO WAY to narrow the time window such that all events
are mutually exclusive as QM predicts. however if we LIMIT OUR SAMPLE
of incoming data
(either in the electronics or post experimental data selection)
only to events in which we don't have coincident events, then we get
EXACTLY the QM predictions.
in other words, QM makes no INCORRECT predictions, but it is
INCOMPLETE; semiclassical theory is more COMPLETE because it makes
the same predictions as QM for noncoincident events, but also can
talk meaningfully about COINCIDENT events, which QM is mute on.

It is well known that any theory that doesn't predict pink flying elephants is incomplete. Proof: consider a pink flying elephant. Try to describe it with the theory. QED.

QM is mute on COINCIDENT events because they are simply nonexistent
by the "collapse of the wavefn", which is the semantical shorthand
which refers to the projection operation in the mathematical formalism
(ie collapse of wavefn is in the theory, and its effect is that QM cannot
speak about coincident events) & also its model of the probability spaces
(yes that's what I am saying seratend)..

QM predicts coincident events in certain cases, and it predicts absense of coincidence in others. It predicts absense of detection of 2 photons in 1-photon states, and it predicts coincidence of detection of 2 photons in 2-photon states. And... it can even predict 3 coincidences if the incoming state contains a 3-photon component. More: if we have 4-photon states as incoming state, QM predicts the simultaneity of 4 photon detections.

Exercise: what incoming state is needed for QM to predict the coincidence of 5 photons ... ?



Answer: ... a 5-photon state :-)

After this deep philosophical debate, it is useful to point out that coherent light is a superposition of ALL n-photon states.

actually I am being generous to QM, as vanesch replied,
if QM DENIES there can be anything other than random coincident
events, as he has stated & interpreted ("statistically independent"),
then it must be INCORRECT and I have
given an experiment above to prove it.

And if QM doesn't deny it, then it could be correct.
It is statistically independent if the incoming state is a coherent state.

ps guys it is true that I am not a specialist in the QM formalism. please
do not crucify me on this

ps nite, you complain about physics corrupting the mind of physics
students. I am one of those students. I am all ears..
when are you going to teach me? or would you rather spear at the infidels
or priesthood some more? after about 4 yrs I have lined up group of
N>200 "detectors" waiting for your "signal".. please reply to my email
wink

What is amazing is that for over 4 years, you have been working to disprove a theory of which you don't understand a iota ?
Others complete a PhD on the subject in such a lapse of time...

Hey, I think I'll start a group to disprove the existence of irregular Spanish verbs. Although I don't speak much spanish, that shouldn't be a problem :-))

You're right, you'll need some fresh input to find a guy or a gall that will get you guys beyond QM

At least, nightlight knows some QM. His problem is more that he has read much more than he has understood, and knows miriads of references and derivations which are sophisticated and of which he only understood half, but which can serve at first to "show you that you didn't consider the question deep enough". That means that he can send you from paper to paper, from consideration to consideration, without an end, and it gives the impression of a senior scientist that knows what he's talking about. But it has an advantage: up to a point, it obliges the other also to read through that stuff, which can be hard, and in doing so, I learn also a lot.

cheers,
Patrick.

 

[vzn]

ok look vanesch I am going to wave a white flag
momentarily, but challenge you to be a little
more proactive than a reactive kneejerking anklebiter.
how about you come up with an experiment, please
describe it for me. you say in your last post it is possible.

(Im sure I am aware of some useful/relevant
refs you haven't heard
of either, like nite, but you're such an intense/bitter/thankless
"anticrank", at the moment I doubt its worth my time.)

anyway, anyone else here other than vanesch with an open mind,
consider this writeup on the significance of nite's
"glauber detectors"
http://groups.yahoo.com/group/qm2/message/9870


for vanesch: ok, let me learn a little qm from you. assuming you
believe in the concept of educating here & are not just a posturing
poseur on the idea. (if you feel you
have nothing to teach or for me to learn, then how about saving
me the trouble, & not replying? & I will listen to someone else)

in your earlier posts you describe how to measure
anticorrelated pairs, basically via the classic grangier
et al experiment which nite started this thread critiqing in the
undergraduate experiment.

earlier you denied that measurement of the collapse of the wavefn
is possible, but seem to misunderstand.. THAT IS EXACTLY THE
POINT OF THESE EXPERIMENTS.

so, (you say this is possible in your last post)
I propose to you, describe to me an experiment that will
will show anticorrelation (in the sense of mutual exclusion demanded
by the projection postulate, informally referred to as "collapse of wavefn") between multiple detectors for N>2.

I mean, suppose I have 3 detectors. describe to me an
experiment in which I can send lightwaves thru the apparatus
& detect only 1 of the 3 clicking at all-- never 2, never 3.
next please generalize to N>3.

 

[vanesch]

for vanesch: ok, let me learn a little qm from you. assuming you
believe in the concept of educating here & are not just a posturing
poseur on the idea. (if you feel you
have nothing to teach or for me to learn, then how about saving
me the trouble, & not replying? & I will listen to someone else)

Education is a certain form of communication. You need a sender, and a receiver. If either the sender or the receiver is broken, it cannot take place.

So I will take your second option, and watch you listen to someone else.

cheers,
patrick.

 

[nightlight]

I still remain with my initial claim, that no matter how you combine, in wave packets, plane wave modes into finite-size beams, and their corresponding plane wave annihilation operators and creation operators in "finite volume" number operators, that the expectation value:

< 1-photon state | A+(1) A+(2) A(2) A(1) | 1-photon state>

is ALWAYS 0.

The problem is that the Gn() doesn't correspond to coincidence rates for most of the 'plane waves' you stick into the formula. It has relatively narrow range of validity due to numerous approximations used in deducing it as a coincidence counting expression (dipole approximation, interaction cross sections, limited EM intensites, retaining only E+ based precisely on frequency range assumptions, misc. wavelength assumptions, ... etc, cf [4] 78-88, just note all the invocations of the assumption that (a >> b) holds for various quantities a and b).

Therefore, using the plane wave expansions, especially for these cases of finite detectors and finite modes, you start producing terms which, while mathematically legitimate, have no relation with the coincidence rate for such plane wave. Thus, your calculation has ceased to be a modelling of the coincidence rate for the experiment.

The questions Q-a and b are asking you to use QED/QO via AJP.9 to model the actual experiment and show that it does model this experiment and yields g2=0. I said it doesn't. Your expansion applied in AJP.9 for our finite modes & finite detectors, as actually layed out, ceases to model the experiment right upfront, by using G2() beyond the range of its applicability as a model of any photocounts, much less their coincidences.

There are many ways in physics you can reach absurd or contradictory conclusion by that kind of procedures -- of formally rewriting the parameters into mathematically equivalent sums, then applying the basic formula term by term, even when the parameters in some terms are outside of the valid range for the formula used, then summing the terms and wondering how you got different prediction (Jaynes' neoclassical ED fell into that trap in his prediction of chirp for spontaneous emissions in the early 1970s, which caused him to drop his theory for over 15 years, until Barut & Dowling http://prola.aps.org/abstract/PRA/v36/i2/p649_1 in 1987 and produced the correct prediction).

Therefore, your plain wave expansion does not show that the QED expression AJP.9 for this experiment (with finite detectors and finite modes as layed out), yield the DT and DR coincidence rate of 0. The reason for the failure to show DT and DR coincidence rate is 0, was the misuse of the formal expression G2() outside of its range of applicability to this problem (you need to predict detector counting rates and their correlation, but your terms stop being any such, cf. [4], 78-88).

That doesn't mean you can't use expression of the G2() form to model the experiment. You can, as shown earlier, assuming the finite volumes for the interaction Hamiltonian H_i in [4], in which case the mode annihilators become different kind of operators from the usual lowering operators of harmonic oscillator, but the normal products expectation value form remains. That is how I deduced that g2>=1 for QED treatment of the problem. You try it or replicate it with Mandel's [9], chap 14 model, and see what you say that QED predicts for coincidence rates.

Note also that the Poissonian distribution of photo-ionizations for the Fock state that my approach yields (as well as the other approaches, such as the recent preprint I cited) is perfectly consistent with treating DT and DR as a single cathode and finding Poissonian distribution of photo-ionizations on this large cathode (a known QO result for the distribution of photo-electron emissions). Alternatively, you could, in principle build a large cathode which extends across the T and R regions and then use regular, non-controversial prediction of QO that the number of photo-electron emissions will be Poissonian. Now you split (conceptually) this large cathode into two, by counting separately the photoelectrons in R half and T half and you will arrive at the g2=1 as a QED prediction. As hinted earlier, the same reasoning invalidates all experimental claims of Bell inequality violations with photons (not that any had ever obtained any violation, anyway) since QED doesn't predict such violation.

The basic problem you're having with this conclusion is that it violates your, apparently hardwired and subconsciousat this point, association between "photon number" and photo-detection count. You may benefit from Mandel's [9] 12.11.5 which shows some pitfalls (different than our case) of such mixup.

 

[vanesch]

The problem is that the Gn() doesn't correspond to coincidence rates for most of the 'plane waves' you stick into the formula. It has relatively narrow range of validity due to numerous approximations used in deducing it as a coincidence counting expression (dipole approximation, interaction cross sections, limited EM intensites, etc, cf [4] 78-88, just note all the invocations of the assumption that (a >> b) holds for various quantities a and b).

I'm sorry but as a *photon number* operator, there are no approximations involved. You seem to be talking about a specific model of how a detector is responding to the EM field, and how one can deduce that it is dependent on the photon number. In other words, how detector response is a function (or not) of g2. Ok, as I said, you are going to find something to complicate the issue such that in the end, it will be hard to argue :-)
But that doesn't change the fact that using photon number operators, no matter how you combine them in linear superpositions, the expression:

|1-photon state> = integral g(k) |1-photon state k> dk
nv1 photon number operator a la Mandel in volume v1
nv2 photon number operator a la Mandel in volume v2

then <1-photon state | :nv1 nv2: | 1-photon state>

is always 0.

Therefore, using the plane wave expansions, especially for these cases of finite detectors and finite modes, you start producing terms which, while mathematically legitimate, have no relation with the coincidence rate for such plane wave. Thus, your calculation has ceased to be a modelling of the coincidence rate for the experiment.

The questions Q-a and b are asking you to use QED/QO via AJP.9 to model the actual experiment and show that it does model this experiment and yields g2=0. I said it doesn't.

So you have to show now that the specific model of the detector, for the plane wave modes that occur in the |1-photon state> above, are not based upon g2.
Because that's in fact your claim. Your claim is not so much that g2 = 1, your claim is that the photon detectors correspond to measurement operators that are not simply a function of the local number operator a la Mandel.
I would be surprised to see your explicit calculation, because that would mean that it depends on something else but E x E(cc) (the intensity of the local electric field).
Remember (from the very beginning of this discussion) that QED being a quantum theory, the superposition principle holds.
Show me your explicit model, of a 1cm^2 detector, and its associated operator.

Therefore, your plain wave expansion does not show that the QED expression AJP.9 for this experiment (with finite detectors and finite modes as layed out), yield the DT and DR coincidence rate of 0. The reason for the failure to show DT and DR coincidence rate is 0, was the misuse of the formal expression G2() outside of its range of applicability to this problem (you need to predict detector counting rates and their correlation, but your terms stop being any such, cf. [4], 78-88).

So, g2 wasn't 1 after all, it was the expectation value of the product of the two operators corresponding to finite detectors, and that happened not to be the number operator. Right. We changed again the goal :-)
g2, as an expectation value of the product of photon number operators is, I think you understood that there is no weaseling out, equal to 0 for a 1-photon state. Now it is up to you to show me that your detector model gives something that doesn't depend on the photon number.

That doesn't mean you can't use expression of the G2() form to model the experiment. You can, as shown earlier, assuming the finite volumes for the interaction Hamiltonian H_i in [4], in which case the mode annihilators become different kind of operators from the usual lowering operators of harmonic oscillator, but the normal products expectation value form remains.

Ok, that's chinese to me, and I don't speak chinese.
I guess you're talking about the interaction hamiltonian of your detector model with the EM field. Now show me explicitly a calculation where you relate your new annihilation operators to the standard plane wave annihilation and creation operators ; after all the standard annihilation and creation operators span algebraically the entire operator space of QED, and show me how you come to that result. I would be *highly* surprised :-)

That is how I deduced that g2>=1 for QED treatment of the problem. You try it or replicate it with Mandel's [9], chap 14 model, and see what you say that QED predicts for coincidence rates.

Hehe, YOU claim, so YOU do.
If it is well done, you can even publish it. I'll try to read it, honestly.

The basic problem you're having with this conclusion is that it violates your, apparently hardwired and subconsciousat this point, association between "photon number" and photo-detection count. You may benefit from Mandel's [9] 12.11.5 which shows some pitfalls (different than our case) of such mixup.

I will read that. Indeed, I associate photodetection and photon number, especially in the simple case of our set up.

My honest impression is that you haven't understood the superposition principle in quantum theory (of which QED is a specific application) ; meaning that you can't somehow accept that if you know the response of a measurement setup to a set of basis states, that this fixes entirely the response of any superposition. That's what I've been trying to point at from the beginning, and it is the reason why I'm convinced that detailled modelling WITHIN QED have nothing to do with the issue.
Given that the two beams out of the beam splitter are a QM superposition of the one beam left, and the one beam right, I ONLY need to know how my detector setup (the entire setup, with the correlations) for the one beam left, and one beam right, and I AUTOMATICALLY know how it reacts for the superposition. This is fundamental quantum theory, which also applies to QED.
This means, in your case, that we will have correlation counts EVEN IF THERE IS ONLY THE LEFT BEAM, or IF THERE IS ONLY THE RIGHT BEAM.
Indeed, if, when there is only the left beam, there is no correlation for sure, then this is an eigenstate of the "correlation measurement operator" with eigenvalue 0;
when there is only a right beam, then this is ALSO an eigenstate of the correlation measurement operator with eigenvalue 0,
This means that any linear combination of both states will ALSO be an eigenstate with eigenvalue 0. So any superposition will also have correlation 0.

See, that's BASIC QUANTUM THEORY. It has nothing to do with the specific model. The only way out is that you now have a model of your detectors that gives us correlated counts when there is only the left beam.

I'm waiting.

cheers,
Patrick.

 

[nightlight]

My honest impression is that you haven't understood the superposition principle in quantum theory (of which QED is a specific application) ;

Well, my impression that you haven't understood the reply (or the earlier related posts) at all. And, sorry, but I won't write your papers for you in here (or waste time on homeworks, which only show how much you missed the argument altogether, but which you keep trying to assign me) having given you more than enough info and references on how to replicate the conclusions on your own if you wish.

The photo-ionization is inherently nonlinear process. That is achieved in [4] by applying series of approximations, which allow the linear formalism to simulate such nonlinearity and obtain the square-law for the detection rates (and the related Gn() as adjusted coincidence rates). But, as explained, the approximations in [4] require numerous restrictions on the fields, which some generic superposition (trying to simulate the finite volumes of DR, DG, R and T beams) will violate for some plane waves, making them invalid as the contributions to the photo-ionization counts. You can check the cited places in [4] and verify whether all your plane waves satisfy all the a>>b type of assumptions made there to justify the approximations, and thus the usage of a particular plane-wave component in the Gn() expressions (while retaining their operational mapping to the photo-detection counting rates; e.g. the high-frequency components arising in Fourier expansions of finite volume fileds and interactions, will violate frequency restrictions in [4], which were used to justify the dipole approximation and the dropping of the E- terms, thus the resulting contribution is not valid counting rate at all, and the sum using such terms can't be assumed as valid either).

Given that the two beams out of the beam splitter are a QM superposition of the one beam left, and the one beam right, I ONLY need to know how my detector setup (the entire setup, with the correlations) for the one beam left, and one beam right, and I AUTOMATICALLY know how it reacts for the superposition. ...

This is where your disregard of the finite detectors leads you into an elementary error. If you have a finite detector, than it is obvious you can easily superpose two components and get 0 counts by the finite detector (e.g. you change the phase of one component, so the detector is in the dark fringe), even though changing phase of a component with an infinite detector would show unchanged counts (since the total EM energy is preserved). Correlations of such counts of multiple finite detectors consequently also depend on the detector sizes. Your assertion that detector sizes make no difference in their counts or coincidence rates is plainly absurd. (It makes the essential difference in this experiment, as already explained via Q-a,b and the finite detector followups.)

Thus, you can't know the counts (much less their correlations) result of the superposition in general, unless you take into account the sizes of the detectors, for which the plane-wave version of G2() in (AJP.9) lacks any formal counterparts , thus it can't possibly account for such differences. It doesn't even show the existence of any difference (thus you don't see any), much less tell you what effect it would have. I already pointed you to Mandel's [8], [9] to help you at least realize that there is a difference and that it can be accounted for by the formalism, and that in our example of finite fields and finite detectors, the detector sizes make the most drastic difference (that should be obvious anyway) which, as Mandel explicitly warns, can lead to errors with the naive photon number reasoning (as it did in your example of supplementing QM with such imagery). You have just cornered yourself into a hopelessly wrong position.

 

[vanesch]

I would like to come back to a very fundamental reason why
the detector correlation in the case of single-photon states
must be zero, and this even INDEPENDENTLY of any consideration
of photon number operators, finite-size detectors, hamiltonians
etc...
It is in fact a refinement of the original argument I put here,
before I was drawn in detailled considerations of the photon
detection process.

It is the following: we have a 1-photon state inpinging on a
beam splitter, which, if we replace it by a full mirror, gives
rise to the incoming state |R> and if we remove it, gives
rise to the state |T> ; with the beam splitter in place, the
ingoing state is 1/sqrt(2) {|R> + |T>}

Up to now, there is no approximation, no coarse graining.
You can replace |T> and |R> with very complicated expressions
describing explicitly the beams. It is just their symbolic expression.

Next, we consider the entire setup, with the two detectors and the
coincidence counter, as ONE SINGLE MEASUREMENT SYSTEM. Out of it can
come 2 results: 0 or 1. 0 means that there was no coincident clicks. 1
means that there was a coincident click detected. It doesn't really
matter exactly how everything is wired up.
As this is an observable measurement, general quantum theory (of which,
as I repeated often, QED is only a specific application) dictates that
there is a hermitean operator that corresponds to this measurement, and
that it is an operator with 2 eigenvalues: 0 and 1.
THIS is the actual content which is modeled by the normal ordering of
the 2 number operators, but for the argument here, there is no need
to make that link.
You can, if you want, analyse in detail, the operator that will give us
the correlation is the above operator, which we will call C.
In Mandelian QO this is :nv1 nv2: but it doesn't matter: if you want to
construct it yourself, based upon interaction hamiltonians, finite size
detectors, finite size beams etc...be my guest. Write down an operator
expression 250 pages long if you want.
At the end of the day, you will have to come up with an operator, that
corresponds to the correlation measurement, and that measurement, for each
individual measurement in a single time frame,
has 2 possible answers: 0 and 1. (no coincidence,or coincidence).

What we want to calculate, is 1/2 (<R|+<T|) C (|R> + |T> )

What do we know about C ?

If we remove the beamsplitter, we have a pure |T> state.
And for |T> we know FOR SURE that we will not see any coincidence.
Indeed, nothing is incident on the R detector.
This means, by general quantum theory (if we know an outcome for sure),
that |T> is an eigenstate of C with eigenvalue 0.

If we put in place a full mirror, we have a pure |R> state.
Again, we know for sure that we will not see any coincidence.
This time, nothing is incident on the T detector.
So |R> is an eigenstate of C, also with eigenvalue 0.

From this it follows that 1/sqrt(2) (|R>+|T>) is also an eigenstate with
eigenvalue 0 of C (a linear combination of eigenvectors with same
eigenvalue).

1/2 (<R|+<T|) C (|R> + |T> ) = 0

This follows purely from general quantum theory, its principal
point being the superposition principle and the definition, in
quantum theory, of what is an operator related to a measurement.

Now, exercise:
If you misunderstood the above explanation, you could think that
this is an absurd result that means that if you have two intensive
beams on 2 detectors, you could never have a coincidence, which is
clearly not true. The answer is that the above reasoning
(put in a mirror, remove the splitter) only works for 1-photon
states. So here is the exercise:
Why does this only work if the incoming states on the beam splitter
are 1-photon states ?

If you understood this, and found the answer, you will have gained
a great insight in quantum theory in general, and in quantum optics
in particular :-)

cheers,
Patrick.

 

[vzn]

hi all, I got zapped by esteemed moderator TM
on a post criticizing vanesch's style here,
so let me backpeddle and just say the following.

I am disappointed in this dialogue which is
breaking down to a deathmatch between
vanesch vs nite. from "observation" vanesch & nite are
clearly both world class physicists at least on a theoretical
level. from his profile page & web page,
vanesch is a phd, and nite I am guessing
is probably "almost phd".

but here we have a supposed break between theory &
prediction & experiment, and the dialogue just seems to keep going in
circles. it seems to me both of you guys
are going in the wrong direction.

it seems to me, when _really_ world class physicists get
into a disagreement, they work on coming up with _new_
experiments that can attempt to discriminate/isolate the problem
or phenomenon, rather
than endlessly disagree on something that was done in a
lab, say, more than 25 years ago.

ie, proactive vs reactive. constructive vs reactionary.

example: einstein, with the EPR paper, bohm, who made
a key switch in it with polarized light, but is rarely credited for
this, and bell, who sharpened the knife further with a mathematical
analysis that escaped bohm, designing an experiment to
force the issue to light.

physicists of the above calibre are rare, I know. as this thread attests.
but, I was hoping to find one in cyberspace SOMEDAY. maybe not
now, but someday.

my other disappointment is that one shouldn't have to use
extremely abstruse theory to make simple predictions about
experiments. a good theory should generally require a reasonably
intelligent person not coming to completely opposite conclusions
in analyzing an experiment. why is it that it seems the better
informed the crowd on qm, sometimes the greater disagreement
over simple setups? as illustrated on this thread.

in this sense I would say both qm & semiclassical
theories often fail.

I challenge vanesch/nite to stop trying to whack each other (& me briefly
too :p) over the head with theory & together come up
with a new experiment that would tend to settle the disagreement.

also, nite says that the von neumann projection postulate is
incompatible with the locality of QED, but shouldn't it be possible
to PROVE this mathematically?

"none of us is as smart as all of us"

vzn
http://groups.yahoo.com/group/theory-edge/

 

[vzn]

a question. vanesch just described a simple conceptual
experiment of a 1-photon state going thru a beamsplitter.

as I understand it, an experimental realization of this
would be a laser that emits a very brief pulse, "one photon width"
so to speak.

semiclassical theory (ala nite) will tend to predict that you will get
coincident clicks in the two detectors at each branch of
the beamsplitter. QM in constrast via mainly the projection postulate
predicts zero coincidences (within experimental error.. I know
thats a can of worms wrt semiclassical).

the question: supposed I used a small sample of a radioactive
isotope & emitted gamma rays. the emissions are spaced far
enough apart that we can be fairly sure its a 1-photon state ie
no overlap of emissions due to more atoms in a larger sample.
does this constitute a 1-photon
state in the above experiment?

the idea is, this setup could conceivably be done much more cheaply
than using a laser.

 

[jtbell]

supposed I used a small sample of a radioactive isotope & emitted gamma rays.

What would you use for a beamsplitter?

 

[DrChinese]

...

the question: supposed I used a small sample of a radioactive
isotope & emitted gamma rays. the emissions are spaced far
enough apart that we can be fairly sure its a 1-photon state ie
no overlap of emissions due to more atoms in a larger sample.
does this constitute a 1-photon
state in the above experiment?

the idea is, this setup could conceivably be done much more cheaply
than using a laser.

The idea was to use the entangled pair so that one is the "gate" and demonstrates a purely quantum effect. I guess you could say that the splitting of a single atom is evidence of the quantum nature of particles in general. But I don't think it could be adapted to demonstrate the quantum nature of light in specific.

 

[DrChinese]

Let's talk some more about the Thorn et al experiment itself. The results were approximately as follows (g2 being the second order coincidence rate, relative to intensities, per the Maxwell equations):

g2(1986 Grangier actual)=0.18
g2(2003 Thorn actual)=0.018
g2(classical prediction)>=1
g2(quantum)=0

As you can see, 17 years of technological improvements yielded results significantly closer to the quantum predictions. Considering the dark count rates - which can cause 3-fold coincidences resulting in experimental values slightly on the high side - the results would have to be considered as solidly in the QM camp.

The above actual values DO NOT subtract accidentals. You can't really, because you wouldn't truly know if it is an accidental. Since that is what you are trying to prove in the first place.

There is really no classical explanation for these results. Vanesch has explained it well for those who are interested. Of course, there is no substitute for reading the actual paper itself and following its references. In case you lost the reference he provided originally:

J.J. Thorn, M.S. Neel, V.W. Donato, G.S. Bergreen, R.E. Davies, M. Beck
http://marcus.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf
Am. J. Phys., Vol. 72, No. 9, 1210-1219 (2004).


To break it down further, in terms of how g2 was calculated: g2(2003 Thorn actual) is based on the following values (approximate count rate per second):

3 fold coincidences (G, T and R detected)=3
2 fold coincidences (G and T)=4,000
2 fold coincidences (G and R)=4,000
1 fold coincidences (G only)=100,000
Dark rate count=250

G=Gate (idler)
T=Transmitted (signal)
R=Reflected (signal)

To achieve the classical results, the 3 fold coincidences would need to have been 160 per second, instead of the 3 actually seen.

 

[vanesch]

I am disappointed in this dialogue which is
breaking down to a deathmatch between
vanesch vs nite. from "observation" vanesch & nite are
clearly both world class physicists

Hahahaha :-)))

I don't think I'm a world class physicist, but I think I "know my stuff" in certain areas. I also don't think nite is a world class physicist :-).

but here we have a supposed break between theory &
prediction & experiment,

No, not at all. We're arguing about what standard QED predicts, not whether this is confirmed or not by experiment. Now, I think I know enough about standard QED to understand what ALL "world class physicists" claim it predicts: namely that for one-photon field states, you find anti-correlation in detector clicks.
We're not arguing whether this is how nature behaves, should behave, behaved or whatever. Nightlight just claims that all those people studying QED don't understand their proper theory and miscalculate what it is supposed to predict.
And to do so, he tries to underline the importance of several "secondary" effects, such as finite detector size, beam size, the interaction of EM fields with detectors and so on. I have to say that these issues can become quickly so complicated that nobody (including nightlight) can work out exactly what is going on, and that's a good technique to break down any argument "you are forgetting this complicated effect, so you oversimplify things ; I did it (but I'm not going to show you, expert as you are, you should be able to do it yourself, and then you'll find the same answers as I) and found <fil in anything you like>".
However, nightlight is in a difficult position here, because he's contradicting some BASIC POSTULATES of quantum theory. So I don't need to go into all the detail. It is like proponents of perpetuum mobile systems. They can become hopelessly complicated... but you know from thermodynamics that IF YOU USE THERMODYNAMICS TO SHOW THAT IT MUST WORK, then clearly the claim is wrong, because it is a basic postulate in thermodynamics that perpetuum mobile don't exist.
See the difference: that doesn't mean that one cannot exist in nature (then thermodynamics is wrong) ; but the claim that THERMODYNAMICS PREDICTS that this particular system will be a perpetuum mobile is FALSE FOR SURE.

And that's what nightlight tries to do here: he tries to show that QED PREDICTS coincidence counts for one-photon states, and that if all quantum opticists in the world think it is not, that's because they don't understand their own theory and they over-simplify their calculations.

However, from previous discussions with nightlight, I'm now convinced that nightlight doesn't understand the basic postulates of quantum theory, especially the meaning of the superposition principle.
He confuses it with linear or non-linear dynamics of the interactions. But there is a fundamental difference: non-linear dynamics of the interaction is given by non-linear relationships between the observables or field operators, and the hamiltonian. But the superposition principle is about the LINEARITY OF THE OPERATORS ON THE HILBERT SPACE OF STATES. That has NOTHING to do with linear, or nonlinear, field equations.

Look at the hydrogen atom: the interaction term of the proton and the electron goes in 1/r. Clearly that's a non-linear relationship ! But that doesn't mean that the hamiltonian is not a linear operator on the state space !
The linearity of operators on state space is a fundamental postulate of quantum theory (of which QED is a specific application).
Also, the association of a linear, hermitean operator with every measurement is such a basic postulate.
So if his predictions are in disagreement with these postulates, it is SURE that there's a mistake on his part somewhere.

it seems to me, when _really_ world class physicists get
into a disagreement, they work on coming up with _new_
experiments that can attempt to discriminate/isolate the problem
or phenomenon, rather
than endlessly disagree on something that was done in a
lab, say, more than 25 years ago.

You cannot do an experiment to verify whether a certain theory predicts a certain outcome or not.

example: einstein, with the EPR paper, bohm, who made
a key switch in it with polarized light, but is rarely credited for
this, and bell, who sharpened the knife further with a mathematical
analysis that escaped bohm, designing an experiment to
force the issue to light.

The problem is that the experiment of Thorn is about the best one can do ; he did it, and others will repeat it.
The reasoning is this:
1)Out of the Thorn experiment comes a quantity which is close to 0.
2)Now, classical theory predicts that it should be bigger than 1.
3)QED, according to all experts, predicts that it should be about 0.
4)Nightlight CLAIMS that they all used badly their own theory, and that
if you do it right, QED predicts also 1 (that's our argument here).
5)Then nightlight claims Thorn is cheating in his experiment, and that he should find 1.

I'm arguing with point 4).
I have been adressing point 5). There are indeed a few minor problems in the paper ; I think they are details - in that if they are truly a problem then Thorn has made a big fool of himself ; the rest is just an argument on "priesthood or not".

cheers,
Patrick.

 

[vanesch]

as I understand it, an experimental realization of this
would be a laser that emits a very brief pulse, "one photon width"
so to speak.

No, that's impossible to do, for fundamental reasons. Every "classical" beam,
such as a laser beam, is a coherent state, which contains a superposition
of vacuum, 1-photon, 2-photon, 3-photon ... states in a special relationship.
So you cannot make "pulses of 1 photon" this way.

The trick is to use a non-linear optical element, that "reshuffles" these states ; for instance, that converts 1-photon states into 2-photon states. That's what such a PDC xtal does. When you do that, out comes a beam, which ALSO contains all n-photon states, but WHICH CONTAINS A BIG SURPLUS in 2-photon states, as compared to a "classical" beam.

And now the trick is to trigger on "one arm of these 2-photon states". If you then limit yourself to time intervals around these triggers, you know that the "other arm" is essentially an almost pure 1-photon state, with which you can then do experiments as you like (as long as your detections are synchronized with the trigger).

What I find funny is that nightlight doesn't attack THIS. It would be much easier for him :-) (hint, hint)


cheers,
patrick.

 

[nightlight]

If you understood this, and found the answer, you will have gained a great insight in quantum theory in general, and in quantum optics in particular :-)

Not that I expected very much, but would that be all the gratitude I get for escorting you out of the "QM measurement" darkness?

Why does this only work if the incoming states on the beam splitter are 1-photon states ?

There are two basic misconception built into this question, one betrayed by "this" another one by "only". The two tie the knot of your tangle.

Your "this" blends together the results of actual observation (the actual counts and their correlation, call them O-results) with the "results" of the abstract observable C (C-results). To free you from the tangle, we'll need finer res conceptual and logical lenses.

The C-results are not same as O-results. There is nothing in the abstract QM postulates that tells you what kind of setup implements C or, for a given setup, what kind of post-processing of O-results yields C-results. The postulates just tell you C exists and it can be implemented. But to implement it, to perform operational mapping between formal C and experiment, you need a more detailed physical model of the setup, where at least part of the 'aparatus' interacting with the 'object' is treated as a physical interaction. In our case one needs QED applied to detectors, such as treatments in [4] or [9].

The first observation of such dynamical analysis is that the "trigger of DT" involves making a decision how to define "trigger" and "no-trigger" O-results (which we can then use to define C-result). The number of photo-electrons ejected will have Poissonian distribution i.e. the (amplified) photo-current corresponding to r photo-electrons with probability p(r,n) = exp(-n) n^r/r!, where n=<r> is the average p-e count (and also a variance). This is the most ideal case, the sharpest p(r,n) you can get (provided you have perfectly reproducable source pulses and precise enough detection windows so that the incident field intensities I(t) are absolutely identical between the tries). Note that EM pulse need not be constant in the window, only the integral of I(t) must be constant for the window to obtain the "ideal" p-e distribution sharpnes p(r,n). If there is any EM amplitude variation between the tries, the p(r,n) will be compounded (smeared or super-) Poissonian which has variance larger than n.

A common sleight of hand in pedagogical QO treatments (initiated by Purcell during the HBT effect controversy, the QO birthing crisis, in 1950s, later elaborated by Mandel and refined into a work of art by Glauber) is to point out one example which provides such nearly perfectly reproducable incident EM fields, the perfectly stable laser light (coherent light), and note that the (single mode) photon number observable [n]=[a+][a] of such source has also the Poissonian distribution of photons. From that, the pedagogues leap to the "conclusion" that O-results r are interchangeable with the [n]-results, the values of the observable [n] (the photon number) i.e. as if measurements of r is an implementation of the observable [n]. From this "conclusion" they then "deduce" that if we can produce Fock state as the incident EM field, thus have a sharp value for observable [n], we will have a sharp value for r. Nothing of the sort follows from the QED model of detection. The association between the [n]'s [n]-values and the measured O-values r is always statistical (the EM intensity 'I' fixes <r>=<r(I)> and its moments) and the sharpest association between the [n]-values and the O-values one can have is Poissonian.

The average r (parameter n), is a function of the incident light intensity I and of the settings on the "detectors" (bias voltage, temperature, amplifier gain, pulse anlyser, window sizes, etc.). Assuming we keep detector & window parameters fixed, <r>=n will be a function of the incident light intensity I only, i.e. n=n(I).

The key observation about this function n(I) from the QED detection model [4] is that, for a given detector settings, the n(I), thus the p(r,n(I)), is determined solely by the EM fields reaching the detector within the detection window. In particular, [4] being a relativistic model, given the incident fields, there are no effects on p(r,n) from any interactions occurring at the spacelike distances from the detector during the detection window.

Following the common convention, we can define O-result "no-trigger" to correspond to r=0 photo-electrons and "trigger" to correspond to r>0 photo-electrons (we're idealising here by assuming perfect amplification of the ejected photo-electrons into the measured currents). We'll define q = p(0) = p(0,n) = exp(-n) and p = p(1) = 1-q.

To obtain the operational interpretation of Glauber's [G1] observable (his single 'detection' rate observable, [G1(x,t)] = [E-][E+], where [E]=[E+]+[E-] is electric field operator [E] decomposition to positive & negative frequency parts [E+] (annihilator) and [E-] (creator)), we need another result of the dynamical analysis (cf. [4] 78-84). The desired behavior of [G1] is that it has <0|[G1]|0>=0, i.e. [G1]-value is 0 when no incident EM field interacts with the detector. Thus we want [G1] to count photo-absorptions of the incident field only. The dynamics for the detection, unfortunately yields only, and at best, the Poissonian r-counts. That means we will have O-triggers with no incident light (corresponding to vacuum rate n0=n(I0), I0 from hv/2 vacuum energy per mode) and absent O-triggers when the incident light is present (since p(0,n)>0).

The Glauber's ideal [G1]=[E-][E+] operationally corresponds to filtering out both types of r-results 'we are not interested in'. While detector designs (including pulse analyser & discriminator/PAD) perform this subtraction atomatically, they cannot compensate for the 'failed triggers'. To account for the failed triggers, detectors have a parameter Quantum Efficiency QE which is obtained (calibrated) as a ratio of vacuum filtered trigger rate and the average photon rate of the incident field. Thus, knowing the measured trigger rate R(I) and R0 (dark rate, the adjustable leftover from the built in vacuum subtractions), one can compute the average 'photon number' rate PN(I)=<[G1]>=<G> of the incident field as PN(I) = (R(I)-R0)/QE (cf. eq (2) [10]).

This relation among averages does not get around the Poissonian spread p(r,n) for the r-counts, thus of the dark triggers p(r>0,n0) and the missed triggers p(r=0,n>n0). Namely, even if the EM field has a perfectly sharp incident photon number within the detection window (as we have approximately in PDC on TR photon), the r-counts still have at best the Poissonian distribution, thus the variance of at least n. This implies a tradeoff between the TE (trigger efficiency, TE=R(I)/PN(I), which is different than QE=(R(I)-R0)/PN(I)) and the 'false' triggers for the r-counts, no matter what n we select or how we adjust n0 of our detector (n0=<r> for no incident field). Defining the average of r-count for incident field 'alone' as nf=<r>-n0, for given sharp [n] incident field we can maintain the fixed nf. We can still adjust detector sensitivity by tuning n0, thus adjust n=nf+n0, which adjusts the loss rate as LR=p(r=0,n)=exp(-(nf+n0)) and the false trigger rate FT=p(r>0,n0)=1-exp(-n0). If we reduce losses LR->0, then we need n0->inf, which causes FT->1, thus making nearly all triggers false. If we reduce false triggers via n0->0, then we are maximizing the loss rate to exp(-nf).

In particular, for single (on avg) mode absorption per window, nf=1, and reducing the false triggers to 0, will yield the loss rate (per window) at least LR=exp(-nf)=1/e=36.79%, which is well above the max loss rate for an absolutely loophole free Bell's test of (1-0.83)=17%. But, to avoid only the natural semiclassical models, the tests require a less demanding than 83% (limit for any conceivable local model) efficiency. They require at least 2/Pi=63.66% trigger efficiency i.e. the max loss allowed to eliminate natural classical models is LR=1-2/Pi=36.34%, which is almost there, yet it is 0.45% below the unavoidable (when false triggers are minimized) p-e Poissonian loss of 36.79%. Thus any optical Bell test will fail, falling short of eliminating the natural classical models by mere .45%, precisely because of the dynamically deduced statistical association between the r-counts (the O-triggers) and the photon numbers of the incident field (which [G1] counts via photon absorption counts).

As a mnemonic device, one can think of [G1] as corresponding to r-counts on 1-by-1 basis instead as a relation among averages (and moments) of the two distributions. For coherent or chatoic states this causes no problem, since averages and moments agree. But for the Fock state |1> (or similarly any Glauber "non-classical" states), [G1] has sharp [G1]-values 1, while the r-counts remain Poissonan with average 1 (which requires the lost counts to be at least 1/e=36.79%). As cited earlier [11], one can introduces a different kind of (nonlinear) annihiliation operator E_ which does maintain consistency between the distributions of r-counts and these 'new-photo-counts', and consequently the result in [11] for the Fock state is also the Poissonian 'new-photo-count' distribution. The regular annihilator shows other strange properties, as well, if one takes it literally as 'photon absorption' operators [12], such as increasing the number of field quanta for super-Poissonian states (and even more so than the creation operator [a+] for some states!).

The operational meaning of Glauber's 2 point "correlation" G2(x1,x2)=<[G2]> where [G2]=[E1-][E2-][E2+][E1+] and its "non-locality" (convention) has been discussed at length already. Here I will only add that the same Poissonian r-counts limitations and the caveats apply when heuristically identifying, on 1-by-1 basis, the r-counts coincidences as the observable [G2]-values. The association is still statistical (in the sense of being able to map only the averages & the moments between the two). Additional important caveat here is that [G2] implementation requires non-local operations to subtract the rates of accidentals and unpaired singles (or losses from p(r=0,n>n0)), which now occur at different locations, thus any "non-locality" one deduces from it is just a matter definitions, not anything genuinly non-local (since one can graft the same non-local subtraction conventions to the semiclassical models and make them Glauber "non-local", too).

Before constructing operational rules for your C observable on the |Psi.1>, we'll look at the actual observation results. The O-results of the superposed state will be (T,R) pairs: (0,0), (0,1), (1,0), (1,1). If the average r on DT for the single state |T> is <r>=n, then the <r> for the superposed state |Psi> = (|T>+|R>)/s will be n/2 for individual DT and DR "trigger" probabilities (per window or per try).

Assuming DT and DR are at spacelike distance during the detection windows (defined via DG events) and that the PDC pump is stable enough so that within the sampling windows we get repeatably the 'same' EM fields, (i.e. at least the same Integral{I(t)*dt}) on DT and on DR in each window (so we can get the sharpest possible distribution of the p-e r-counts predicted by the QED model), and that the light intensity is low enough so that we can ignore dead time on the detectors, the probabilities of the four kinds of O-triggers are simple products p00=q^2, p01=p10=pq and p11=p^2. In short, whatever interactions are going on at the spacelike location DR, it has no effect on the evolution of the fields and their interactions at the DT location, thus no effect on the probabilities of the r-counts on DT. This is, of course, the same result that the finite detectors and finite R & T fields model predicts, as described [post=538215]earlier[/post].

Now, finally, your observable C. Nothing in the QM axioms specifes or limits how the C must be computed from the r-counts, and certainly does not require that computed C-values are the same as O-values (the observed r-counts) on 1-by-1 basis. QM only says such C exists and it can be mapped to the experimental data. The fact that C "predicts" indeed the avg r-counts <r> for setups with "mirror" or with "transparent" have no implication for the setup with PBS. Similarly, the fact that via (AJP.9) one could write down your C in a concise form, implies nothing regarding the operational mapping of C to our setup, and implies nothing about the O-values for the setup (since AJP.9 plane wave operators don't describe DT and DR setup with the |Psi.1> incident fields). On the other hand, the Glauber's model [4], augmented with the finite detectors & EM volumes does predict proper O-values p00...p11, and does provide a simple operational mapping for your C.

Note first that the r-counts for the actual finite DT and DR are not exclusive, whether |Psi> is a single photon or multi-photon or partial photon state (no sharp [n]). Thus your requirement of exclusivity "only for single photon state" is an additional ad hoc requirement, an extra control variable for the C-observable mapping algorithm, instructing it to handle the case of EM fields with <[n]>=N=1 differently than case N != 1 (N need not be an integer). Nothing in the r-counts, though, is different in any drastic way (other than the difference in n=<r> used in p(r,n)).

Note that your C is not sensitive to PBS split ratio i.e. since |T> and |R> are basis in the 0 eigenspace of C, any Psi(a,b) = a|T> + b|R>, will yield C=0, which simplifies the C mapping algorithm since it doesn't have to care about the values of a and b, but at most it needs to take a note that a beam splitter is there so it can enforce C=0. As luck would have it, though, from the r-count probabilities p00...p11, when either a->0 or b->0, the proportion of (1,1) cases automatically converges to 0 (or background accidentals, globally discarded for C, same as for [G2]), which were the cases of the "mirror" or "transparent" setups, thus no special C-algorithm adjustments are needed for all 3 of your setups.

For N=1, one could thus simply compute C-values by treating the (1,1) O-values as (0,0) O-values, discarding them (it discards double O-triggers the same way that the triple and quadruple O-triggers are discarded in Bell tests, i.e. by definition, cf.[post=531880]Ou, Mandel[/post] [5]). Note that the fact that |a|^2+|b|^2=1 for C, has no operational mapping implications on the variability of the number of 'C-values obtained' (and the total of C-values which gave no-result, such as (0,0)), since the any 'results obtained' are normalized to the "results obtained" total (for all eigenvalues), hence we get C=0 for 100% of the obtained results for any a,b, just as the observable C "predicts". For N!=1, the algorithm will report result of (1,1) as C=1. The (0,0) cases, as in [G2] observable, are always reported as no-result (disposal of the unpaired DG trigger singles built into the Glauber's QO subtraction conventions).

The C-algorithm is non-local, by its convention of course, but that doesn't contradict any QM postulates which only say that observable C exists and it can be computed (but not how). Even without your ad hoc exclusivity requirement for N=1, even the finite-detector/EM augmented [G2] algorithm is already non-local as well due to the requirement for the non-local subtractions.


[10] Edo Waks et al. "High Efficiency Photon Number Detection for Quantum Information Processing" quant-ph/0308054

[11] M. C. de Oliveira, S. S. Mizrahi, V. V. Dodonov "A consistent quantum model for continuous photodetection processes" quant-ph/0307089

[12] S.S. Mizrahi, V.V. Dodonov "Creating quanta with 'annihilation' operator" quant-ph/0207035

 

[nightlight]

However, from previous discussions with nightlight, I'm now convinced that nightlight doesn't understand the basic postulates of quantum theory, especially the meaning of the superposition principle.
He confuses it with linear or non-linear dynamics of the interactions. But there is a fundamental difference: non-linear dynamics of the interaction is given by non-linear relationships between the observables or field operators, and the hamiltonian. But the superposition principle is about the LINEARITY OF THE OPERATORS ON THE HILBERT SPACE OF STATES. That has NOTHING to do with linear, or nonlinear, field equations.

The linearity (and thus the fields superposition) are violated for the fields evolution in Barut's self-field approach (these are non-linear integro-differential equations of Hartree type). One can approximate these via piecewise-linear evolution of the QED formalism.

Note that Barut has demonstrated this linearization explicitly for finite number of QM particles. He first writes the action S of, say, interacting Dirac fields F1(x) and F2(x) via EM field A(x). He eliminates A (expressing it as integrals over currents), thus gets action S(F1,F2,F1',F2') with current-current only interaction of F1 and F2.

Regular variation of S via dF1 and dF2 yields nonlinear Hartree equations (similar to those that already Schrodinger tried in 1926, except that Schr. used K-G fields F1 & F2). Barut now does an interesting ansatz. He defines a function:

G(x1,x2)=F1(x1)*F2(x2) ... (1)

Then he shows that the action S(F1,F2..) can be rewritten as a function of G(x1,x2) and G' with no leftover F1 and F2. Then he varies S(G,G') action via dG, and the stationarity of S yields equations for G(x1,x2), also non-linear. But unlike the non-linear equations for fermion fields F1(x) and F2(x), the equations for G(x1,x2) become linear if he drops the self-interaction terms. They are also precisely the equations of standard 2-fermion QM in configuration space (x1,x2), thus he obtains the real reason for using the Hilbert space products for multi-particle QM.

The price paid for the linearization is that the evolution of G(x1,x2) contains non-physical solutions. Namely the variation in dG is weaker than the independent variations in dF1 and dF2. Consequently, the evolution of G(x1,x2) is less constrained by its dS=0, thus the G(x1,x2) can take paths that the evolution of F1(x) and F2(x), under their dS=0 for independent dF1 and dF2, cannot.

In particular, the evolution of G(x1,x2) can produce states such Ge(x1,x2)=F1a(x1)F2a(x2) + F1b(x1)F2b(x2), corresponding to the entangled two particle states of QM. The mapping (1) cannot reconstruct any more the exact solution F1(x) and F2(x) uniquely from this Ge, thus the indeterminism and entanglement arise as the artifacts of the linearization approximation, without adding any physical content which was not already present in the equations for F1(x) and F2(x) ("quantum computing" enthusiasts will likely not welcome this fact since the power of qc is result of precisely the exponential explosion of paths to evolve the qc "solutions" all in parallel; unfortunately almost all of these "solutions" are non-solutions for the exact evolution).

The von Neumann's projection postulate is thus needed here as an ad hoc fixup of the indeterministic evolution of F1(x) and F2(x) produced by the approximation. It selects probabilistically one particular physical solution (those that factorize Ge) of actual fields F1(x), F2(x) which the linear evolution of Ge() cannot. The exact evolution equations for F1(x) and F2(x), don't need such ad hoc fixups since they always produce only the valid solutions (whenever one can solve them).

Thus, the exact evolution of F1(x), F2(x) is just like taking a single path in the MWI exponential tree of universes, except that this one makes sense and there is no need for outside intervention to pick the branches -- the evolution of F1(x), F2(x) is deterministic, the branches are artifact of the Ge() approximation. Since in Barut's self-fields, there is no prediction of any non-locality via Bell tests violations, and since no test ever violated them, there is no reason within self-fields to worry about encountering any contradiction in what in MWI one could see as amounting to picking just one path.


The same results hold for any finite number of particles, each particle adding 3 new dimensions to the configuration space and more indeterminism. The infinite N cases (with the anti/-symmetrization reduction of H(N), which Barut uses in the case of 'identical' particles for F1(x) and F2(x), as well) are exactly the fermion and boson Fock spaces of the QED. For all values of N, though, the QM description in 3N dimensional configurations space (the product H^N, with anti/symmetrization reductions) remains precisely the linearized approximation (with the indeterminism, entanglement and projection price paid) of the exact evolution equations, and absolutely nothing more. You can check the couple of his references (links to ICTP preprints) on this topic I posted few messages back.

 

[nightlight]

As you can see, 17 years of technological improvements yielded results significantly closer to the quantum predictions.

Just wait till someone figures out an even more advanced technology: how to cut the triple unit wire altogether, so it will give exactly the perfect 0 for g2. Why not get rid of the pesky accidentals, and make it look just like rolling the marble, to DT or to DR.

After all, that's how they got their g2 -- by using the 6ns delay, they had cut off the START from DT completely, blocking the triple unit from counting almost any triple coincidences other than the accidentals. Without it the experiment won't "work" and that's why the 6ns is repeated 11 times in the paper -- the 6ns is the single most mentioned numeric fact about the experiment in the paper. And it is wrong, as acknowledged by the chief experimenter (and as anyone can verify as well from the data sheet). Isn't that little bit funny.

Go see if they issue errata on their site at least, and say perhaps what was the secret "true" delay they used ... and what were any of the 'confidential' counts used to compute Table I. You couldn't pry any of it with the pliers out them the last time I tried. Let us know if you have any luck.

 

[vzn]

ok guys I think I can see a way to reconcile this or at least
restate it in a way acceptable to both parties.

lets attempt to state this schism in terms of a "kuhnian paradigm shift".

let me postulate a new version of QM in a thought experiment.
call it "QM v 2". now vanesch, suppose I told you that
measuring simultaneous eigenstates is not forbidden in this
NEW theory. where QM predicts mutually exclusive eigenstates,
this new QM v 2 predicts that they are not mutually exclusive.

(in fact throw out my idea of measuring the binomial distribution
in coincidences--that means they are random, let's no longer imagine
that for the moment).

lets say that since QM v 1 denies they exist, we build our experiments
to throw them out if we detect them. either in the electronics or
data selection etc. now let's say QM v 2 argues that this procedure
is biasing the sample! QM v 2 uses QM v 1 as a starting point
and argues that QM v 1 is PERFECTLY VALID
for the specific samples it refers to (which is very broad, if it is given
that coincidences are rare)..

however QM v 2 would assert QM v 1 is inherently referring only
to a BIASED SAMPLE by throwing out detected simultaneous eigenstates
(informally "coincidences"). ie as einstein argued, INCOMPLETE. and maybe
just maybe, the experimenters attempting to test QM v 1 vs QM v 2
are INADVERTENTLY doing things that bias the test in favor of QM v 1,
naturally being guided by QM v 1 theory.

now just putting aside all these experiments that have been done
so far, can we agree on the above? it seems to me this is the crux
of the disagreement between vanesch/nite.

further, nite argues
that the experiments so far are not really testing QM v 1 vs QM v 2,
but in fact are just testing QM v 1-- by "accidentally"
throwing out coincidences based on experimental & experimenter bias.

lets push it a little further. suppose QM v 1 is not merely "undefined"
in talking about simultaneously measured eigenstates, but goes further
and asserts they
are RANDOM. suppose QM v 2 actually can predict, in contrast,
a NONRANDOM co-occurence.
then we have not merely a hole but a break/inconsistency
between these two theories, agreed?
one that can be tested in practice, right?

given all this, I think we can try to devise better experiments.

ps re doing a test using gamma emissions. my main question is this:
gamma rays are "photons" ie EM radiation.
has anyone ever figured out how to
make a beamsplitter using gamma rays? is that in the literature anywhere?
seems like it shouldn't be hard...? if you guys will bear with me just
a little on this, I have something up my sleeve that should be of great
interest to everyone on the thread..

 

[vanesch]

The linearity (and thus the fields superposition) are violated for the

fields evolution in Barut's self-field approach (these are non-linear

integro-differential equations of Hartree type). One can approximate

these via piecewise-linear evolution of the QED formalism.

It was indeed this discussion that made me decide you didn't make the

distinction between the linearity of the dynamics and the linearity of

the operators over the quantum state space.

Note that Barut has demonstrated this linearization explicitly for finite

number of QM particles. He first writes the action S of, say, interacting

Dirac fields F1(x) and F2(x) via EM field A(x). He eliminates A

(expressing it as integrals over currents), thus gets action

S(F1,F2,F1',F2') with current-current only interaction of F1 and F2.

Regular variation of S via dF1 and dF2 yields nonlinear Hartree equations

(similar to those that already Schrodinger tried in 1926, except that

Schr. used K-G fields F1 & F2). Barut now does an interesting ansatz. He

defines a function:

G(x1,x2)=F1(x1)*F2(x2) ... (1)

Then he shows that the action S(F1,F2..) can be rewritten as a function

of G(x1,x2) and G' with no leftover F1 and F2. Then he varies S(G,G')

action via dG, and the stationarity of S yields equations for G(x1,x2),

also non-linear. But unlike the non-linear equations for fermion fields

F1(x) and F2(x), the equations for G(x1,x2) become linear if he drops the

self-interaction terms. They are also precisely the equations of standard

2-fermion QM in configuration space (x1,x2), thus he obtains the real

reason for using the Hilbert space products for multi-particle QM



The price paid for the linearization is that the evolution of G(x1,x2)

contains non-physical solutions. Namely the variation in dG is weaker

than the independent variations in dF1 and dF2. Consequently, the

evolution of G(x1,x2) is less constrained by its dS=0, thus the G(x1,x2)

can take paths that the evolution of F1(x) and F2(x), under their dS=0

for independent dF1 and dF2, cannot.

In particular, the evolution of G(x1,x2) can produce states such

Ge(x1,x2)=F1a(x1)F2a(x2) + F1b(x1)F2b(x2), corresponding to the entangled

two particle states of QM. The mapping (1) cannot reconstruct any more

the exact solution F1(x) and F2(x) uniquely from this Ge, thus the

indeterminism and entanglement arise as the artifacts of the

linearization approximation, without adding any physical content which

was not already present in the equations for F1(x) and F2(x) ("quantum

computing" enthusiasts will likely not welcome this fact since the power

of qc is result of precisely the exponential explosion of paths to evolve

the qc "solutions" all in parallel; unfortunately almost all of these

"solutions" are non-solutions for the exact evolution).

All this is not amazing in fact. It only means that the true solution of

the classical coupled field problem gives different solutions than the

quantum theory of finite particle number. That's not surprising at all,

for the basic postulates are completely different: a quantum theory of a

finite number of particles has a totally different setup than a classical

field theory with non-linear interactions. If by coincidence, in certain

circumstances, both ressemble, doesn't mean much.
It also means that you cannot conclude anything about a quantum theory of

a finite number of particles by studying a classical field theory with

non-linear terms. They are simply two totally different theories.

The von Neumann's projection postulate is thus needed here as an ad hoc

fixup of the indeterministic evolution of F1(x) and F2(x) produced by the

approximation. It selects probabilistically one particular physical

solution (those that factorize Ge) of actual fields F1(x), F2(x) which

the linear evolution of Ge() cannot. The exact evolution equations for

F1(x) and F2(x), don't need such ad hoc fixups since they always produce

only the valid solutions (whenever one can solve them).

No, a quantum theory of a finite number of particles is just something

different. It cannot be described by a linear classical field theory,

nor by a non-linear classical field theory, except for the 1-particle

case, where it is equivalent to a linear classical field theory.
A quantum theory of a finite number of particles CAN however, be

described by a linear "field theory" in CONFIGURATION SPACE. That's

simply the wave function. So for 3 particles, we have an equivalent

linear field theory in 9 dimensions. That's Schroedinger's equation.

However, von Neumann's postulate is an integral part of quantum theory.

So if you have another theory that predicts other things, it is simply

that: another theory. You cannot conclude anything from that other

theory to talk about quantum theory.

The same results hold for any finite number of particles, each particle

adding 3 new dimensions to the configuration space and more

indeterminism. The infinite N cases (with the anti/-symmetrization

reduction of H(N), which Barut uses in the case of 'identical' particles

for F1(x) and F2(x), as well) are exactly the fermion and boson Fock

spaces of the QED. For all values of N, though, the QM description in 3N

dimensional configurations space (the product H^N, with

anti/symmetrization reductions) remains precisely the linearized

approximation (with the indeterminism, entanglement and projection price

paid) of the exact evolution equations, and absolutely nothing more. You

can check the couple of his references (links to ICTP preprints) on this

topic I posted few messages back.

It is in fact not amazing that the linear field theory in 3 dimensions is

equivalent to the "non-interacting" quantum theory... up to a point you

point out yourself: the existence, in quantum theory, of superpositions

of states, which disappears, obviously (I take your word for it), in the

non-linear field theory.
In quantum theory, their existence is EXPLICITLY POSTULATED, so this

already proves the difference between the two theories.

But all this is about "finite-number of particle" quantum theory, which

we also know, can only be non-relativistic.
Quantum field theory is the quantum theory of FIELDS. So this time, the

configuration space is the space of all possible field configurations,

and each configuration is a BASIS VECTOR in the Hilbert space of states.

This is a HUGE space, and it is in this HUGE SPACE that the superposition

principle holds, not in the configuration space of fields.
For ANY non-linear field equation, (such as Barut's, which simply sticks

to the classical equations at the basis of QED) you can set up such a

corresponding Hilbert space. If you leave the field equations linear,

this corresponds to the free field situation, and this corresponds to a

certain configuration space, and to it corresponds a quantum field

hilbert space called Fock space. If you now assume that the

*configuration space* for the non-linear field equations is the same (not

the solutions, of course), this Fock space will remain valid for the

interacting quantum field theory.
There is however, not necessary a 1-1 relation between the solutions of

the classical non-linear field equations, and the evolution equations in

the quantum theory, even if starting from the quantum state that

corresponds to a classical state to which the classical theory can be

applied.
Indeed, as an example: in the hydrogen atom, there is not necessary an

identity between the classically calculated Bohr orbits and the solutions

to the quantum hydrogen atom. But of course, there will be links, and

the Feynman path integral formulation makes this rather clear, as is well

explained in most QFT texts. Note that the quantum theory has always

MANY MORE solutions than the corresponding classical field theory,

because of the superposition principle.

However, all this is disgression, through I've been already through this

with you. At the end of the day, it is clear that classical (non-linear)

field theory, and its associated quantum field theory, ARE DIFFERENT

THEORIES.
The quantum field theory is a theory which has, by postulate, a LINEAR

behaviour in an INFINITELY MUCH BIGGER space than the non-linear

classical theory. It allows (that's the superposition principle) much

more states as physically distinct states, than the classical theory.

The non-linearity of the interacting classical field theory is taking

into account fully by the relationships between the LINEAR operators over

the Hilbert space.
In the case h->0, all the solutions of the non-linear field equations

correspond to solutions of the quantum field theory. However, the

quantum field theory has many MORE solutions, because of the

superposition principle.
Because of the hugely complicated problem (much more complicated than the

non-linear classical field equations) an approach is by Feynman diagrams.

But there are other techniques, such as lattice QFT.

QED is such a theory, and it is WITHIN that theory that I've been giving

my answers, which stand unchallenged (and given their simplicity it will

be hard to challenge them :-)
The linearity over state space (the superposition principle) together

with the correspondence between any measurement and a hermitean operator,

as set out by von Neumann, are an integral part of QED. So I'm allowed

to use these postulates to say things about predictions of QED.

We can have ANOTHER discussion over Barut's approach. But it is not THIS

discussion. This discussion is about you denying that standard QED

predicts anti-correlations in detector hits between two detectors, when

the incoming state is a 1-photon state.
I think I have demonstrated that this cannot be right.

cheers,
Patrick.

 

[vanesch]

I said:

If you understood this, and found the answer, you will have gained a

great insight in quantum theory in general, and in quantum optics in

particular :-)

Why does this only work if the incoming states on the beam splitter are

1-photon states ?

Your "this" blends together the results of actual observation (the actual

counts and their correlation, call them O-results) with the "results" of

the abstract observable C (C-results). To free you from the tangle, we'll

need finer res conceptual and logical lenses.

The C-results are not same as O-results.

That would then simply mean that one made a mistake.
To every "actual" observation corresponds, by postulate, AN OPERATOR, and

that operator, taking into account ALL EXPERIMENTAL DETAILS, is:
- hermitean
- has as eigenvalues all possible experimental outcomes
- etc...

It can be very difficult to construct exactly that operator, so obviously

often one makes approximations, idealisations etc... That's nothing new

in physics. It takes some intuition (or a lot of work) to know what is

essential, and what not. But that's just a calculational difficulty. In

principle, to ALL observations (actual, real) corresponds a hermitean

operator.

There is nothing in the abstract QM postulates that tells you what kind

of setup implements C or, for a given setup, what kind of post-processing

of O-results yields C-results. The postulates just tell you C exists and

it can be implemented.

Well, that's all I needed !
That, plus two facts:
- that the outcome of a single "correlation test" (one time slice) gives

0 or 1.
- that, when you have only one beam (by putting in a full mirror, or

removing the splitter), that your correlation test gives with certainty

0.

Now, finally, your observable C. Nothing in the QM axioms specifes or

limits how the C must be computed from the r-counts, and certainly does

not require that computed C-values are the same as O-values (the observed

r-counts) on 1-by-1 basis.

QM only says such C exists and it can be mapped to the experimental data.

The fact that C "predicts" indeed the avg r-counts <r> for setups with

"mirror" or with "transparent" have no implication for the setup with

PBS.

It does ! In the case of a PBS, the outgoing state, when the ingoing

state is a 1-photon state, is a superposition of the 1-photon state

"left" and the 1-photon state "right". (you seem to have accepted that).

That's sufficient, because the "left" state and the "right" state are

both eigenstates with eigenvalue 0.

Thus your requirement of exclusivity "only for single photon state" is an

additional ad hoc requirement, an extra control variable for the

C-observable mapping algorithm, instructing it to handle the case of EM

fields with <[n]>=N=1 differently than case N != 1 (N need not be an

integer).

Absolutely not. That was the exercise ! I didn't have to SPECIFY it,

the exercise was to find WHY this was so. Apparently you didn't find the

answer (which is not surprising, as you have a big confusion on the

issue). If you would have found it, you would have shown you understood

quantum optics much better than I thought you did :-)

So here's the answer:

It is only for incoming 1-photon states that a PBS has as an outgoing

states a superposition of 1-photon states, which are those states one can

obtain by replacing the PBS by a mirror, or by removing it.

However, if you send a 2-photon state on a PBS, out comes a superposition

which can be written as follows:

a |T,T> + b |T,R> + c |R,R>

here, |T,T> is the photon state with a "2 transmitted photons", ...

If we replace the PBS by a mirror, we only have |R,R> and if we remove

it, we have |T,T>, and it is only for those states that we know that we

have an eigenstate with eigenvalue 0.


So the ingoing state with the PBS is NOT a superposition of the case

(full mirror) and (nothing). As such, the state coming out of the PBS

doesn't stay within the 0-eigenspace. Indeed, the |T,R> state is

another, orthogonal Fock state, and will be not in the 0-eigenvalue space

(if the detectors are perfect, it will be an eigenvector with eigenvalue

1, but that's not necessary in the argument).

You can apply similar reasonings for n-photon states.
It is only the special case of the 1-photon state that, after splitting,

is a superposition of the "exclusive" cases (left and right).

cheers,
Patrick.

PS: that said, I have learned more quantum optics with you than with anybody else, just by you defying me, I go and read a lot of stuff :-) It is in fact a pity you don't master the essentials, and know a lot of publications about lots of "details". Your work about Barut and de Santos would win from "knowing the ennemy better" ;-)

 

[DrChinese]

however QM v 2 would assert QM v 1 is inherently referring only
to a BIASED SAMPLE by throwing out detected simultaneous eigenstates
(informally "coincidences"). ie as einstein argued, INCOMPLETE. and maybe
just maybe, the experimenters attempting to test QM v 1 vs QM v 2
are INADVERTENTLY doing things that bias the test in favor of QM v 1,
naturally being guided by QM v 1 theory.

now just putting aside all these experiments that have been done
so far, can we agree on the above? it seems to me this is the crux
of the disagreement between vanesch/nite.

1. There are no results being discarded, other than a time window is created. I.e. there is no subtraction of accidentals. The time window begins BEFORE the gate fires and is easily wide enough to pick up triple coincidences. That this is true is seen by the fact that the T and R detectors separately (and equally) fire 4000 times per second within this same window. Given this rate for double coincidences, there should be 160 triple coincidences if the classical theory held. The actual was 3. Clearly, there is anti-correlation of the T and R detections and the reason has nothing to do with the window size.

2. The disagreement goes a lot deeper than this experiment. Nightlight denies the results of most any experiment based on entangled photon pairs, i.e. Bell tests such as Aspect. He is a diehard local realist as far as I can determine, and such tests violate their sensibilities. (Nightlight, if you are not a local realist then please correct me.) Vanesch knows that IF there was a QM1 and QM2 whose difference could be detected by this kind of test, then it would be. That is because he abides by the results of scientifically conducted experiments regardless of their outcome. I wouldn't expect much movement on the part of either of them.