Cthugha said:
The negative probabilities occur in the quasiprobability distribution in phase space and are therefore not necessarily bound to specific location.
The quasi-probabilities are function of space-time and have very limited regions of negativity in space-time (limited essentially by what can escape undetected within Heisenberg uncertainty). Smearing them with Gaussian distribution, such as in Husimi variant of quasi-probabilities, turns them positive. The only apparent exception are the instances of factors (for specific degree of freedom, such as spin or polarization, formally considred seprately from the spatio-temporal degrees of freedom) of such functions which lack space-time dependency. The "exception" is thus an artificat of formal separation of degrees of freedom and of ignoring the space-time factors. In actual measurements of these internal degrees of freedom, there is always translation to spatio-temporal factors (via coupling between degrees of freedom).
The discussion of a detector triggering or not is pointless.
It's not irrelevant for experiments claiming to demonstrate violations of classicial inequalities which are derived by considering constraints of the event space of single detection events. The obliteration of distintion between sub-ZPF and ZPF level fields by the detectors (due to threshold calibration & background subtractions) is critical for such non-classicality demonstrations, since it makes it appear as if the absence of detection counts on, say, one side of the beam splitter implies nothing on that side could cause interference if detectors were removed and the two beams were brought again into common region.
Except for Bell inequalities the violation of which cannot be simulated by SED, all other non-classicalities of QO can be replicaded in SED via ZPF effects of classical fields.
The way to measure these fields is balanced homodyne detection, where you amplify the field of interest by mixing it with a strong local oscillator to very classical values and afterwards get the signal field in terms of the difference current between the two mixed beams at very classical detectors. You do not need detectors working at the single photon level to measure that.
Data in homodyne detection cannot violate any classical inequality i.e. one could easily simulate results of such measurement via local automata i.e. field in continuum limit. The only way such detection was used for non-classicality claims was by inferring a state of the quantized EM field, which
if measured with "ideal aparatus" of QM MT, which is always beyond present technology, would have violated some classicality condition. The classicality conditions are always derived by looking at constraints of the event space of single detection events.
Also I do not understand why you discuss non-locality at the end when this is about non-classicality. There is non-classicality without non-locality.
Yes, of course there is. But that's not subject of the thread, which is to explain what is surprising about double slit experiment where the system appears in detection localized (as a particle), while passing through separate slits as a wave i.e. it behaves either as a particle which can somehow sense a remote slit it didn't pass through, or as a wave which collapses globally as soon as it trips one detector, preventing any further detections on other/remote detectors (the particle-like exclusivity of wave).
In either picture, particle or wave, it seems that there is some action at a distance or non-locality. At least within QM MT story. Making that work in a real experiment is another matter and in pedagogical settings requires a bit of stage magic as illustrated in an
earlier thread where the particular sleight of hand in demonstrating the above "surprise" was identified.
When and how to neglect the negative frequency operator is already discussed around (2.40). He does not go into rotating wave approximation at this point, but he does so regularly in his book, starting exactly around (2.61).
As pointed out in initial post, the part of the subtractions is done in the chapter on single detector in the earlier chapter. Those results are then used (by being included implicitly via operatior ordering rule he derived earlier) in the n-point case being discussed. While they were perfectly local filtering procedure in single point detector case, they become non-local when carried over to n-detector apparatus. E.g. background subtractions across multiple points can yield appearance of particle-like exclusivity (sub-Poissonian counts) as discussed in that earlier thread.
Yes, at this point he just gets rid of multi-photon absorption.
That is plain wrong. He gets rid of multi-photon absorption (and he also does not consider reemission from the atoms here) and similar processes. He explicitly states that:"Terms involving repetitions of the Hamiltonian for a given atom describe processes other than those we are interested in.". He omits all processes where one atom is involved more than once.
The relevance is that multi-photon absorption on one detector for the n-photon Fock state of the field also results in missed detections on the remaining detectors. For example, in BI violation experiments where G4() is used (in 2-channel variant) with 2-photon state, the events with two detections on one side of the apparatus as well as no detection on one side within coincidence window have to be discarded (resulting in detection loophole).
All these instances are filtering out of the "wrong" number of absorptions or multiple absorptions on "wrong" detectors and they are obviously discarded not because of technological imperfections of the non-ideal apparatus as claimed by QM MT, but because they are not the measurement "we are interested in" as he puts it.
Hence, the non-local post-selection is how you pick which Gn() you are measuring. It is particular Gn() (which encodes the info about the field state hence about its past interactions) that one wants to measure, not just anything that happens on the n detectors. But
to extract the target Gn() requires non-local filtering as his derivation shows -- you have to drop the terms that don't contribute to the Gn() you're "interested in."
While that's all perfectly fine when all one is interested in is extracting the given Gn() from detection events, the
non-local filtering procedure invalidates the subsystem independence and locality assumptions of QM MT i.e. it preculudes one from making prediction based on such non-locally filtered Gn() that require factorization of probabilities as used in derivation of Bell inequalities.
The probabilities on such non-locally filtered counts need not factorize hence the prediction of violation of classical tautologies cannot be derived within QED MT. It's a unique peculiarity of the old QM MT that allows such prediction -- the imaginary "ideal apparatus" of QM MT on which S1xS2 can be measured via two local, independent measurements: S1 on subsystem #1 and S2 on subsystem #2. In QED MT, the concidences expressed in Gn() are obviously not independent, as the required non-local filtering to derive them shows.
He, however, does not care whether all detections are caused by a signal field or whether there are noise contributions. Noise will just give you different correlation functions.
There is no "noise" or "signal" in the exact dynamical treatment of the system of EM field and n atoms which he carries out up to some point. There is simply what happens in the interaction of n detectors with quantized EM field.
The "noise" and "signal" concepts come into picture when one wishes to extract specific Gn() out of all the events on n detectors. That's where the non-local filtering is mandated as his derivation of Gn() shows. Such filtering has nothing to do with the technological imperfections as QM MT suggests. His detectors are already the idealized point-like detectors as perfect as they can be (single atoms).
There have been numerous papers and books about detector theory. Check, for example, the QO book by Vogel and Welsch.
Could you please point out where he explicitly claims that he gets rid of noise here? Otherwise your claim is simply without any substance.
As explained above, there is no "noise" in his dynamical treatment. But he seeks expression containing specific Gn(), i.e. he wishes to perform the measurement he "is interested in" such as the eq. (2.64) he arrives at. Everything else (other terms or events at the detectors) is discarded as not belonging to the target measurement of given Gn().
Similarly, in BI violations where G4() is measured, everything else (such as accidental & background counts, missed detections) is discarded since it doesn't contribute to G4() extraction sought there.
The labels "signal" and "noise" is my characterization of the procedure in which you seek to identify certain subset of events you are "interested in" ("signal" i.e. his Gn() in 2.64), while dropping events you are "not interested in" i.e. the "noise" as he does from eq. (2.60) (plus vacuum contributions in single detector chapter, which are implicit in the n-detector chapter).
You seem to be distracted by the arbitrary terms (such as noise/signal), while missing the point -- the fundamental non-local filtering required to extract a given Gn() out of all events on the n ideal point detectors derived via pure dynamical treatment. The point is that
Gn() doesn't come for free out of n indepent local detection events on n detectors making up some imaginary "ideal aparatus" (his detectors are already ideal) but
has to be filtered out non-locally.
But once you have such non-local filtering procedure, required to extract Gn() on n-detector apparatus, the
factorization of probabilities assumed by Bell (in his treatment of G4() example)
doesn't apply or hold according to Glauber's QED MT.
Hence, there is
no prediction of QED MT of BI violation since the G4() extracted via non-local filtering (2.60) -> (2.61) (plus the implicit vacuum effects subtractions via operator ordering rules) violates the independence assumption of "ideal apparatus" of QM MT i.e. the measurement of S1xS2 observable on composite system is witin QED MT not even in principle the same as the independent local measurements of S1 on subsystem #1 and and S2 on subsystem #2 as assumed by Bell by using QM MT and its conjectured "ideal apparatus."
While it is true, that only n-detection events are considered for the nth order correlation function, this is trivial. n-1 and n+1 detection events are covered by the correlation functions of order n-1 and n+1, respectively (however, n+1 photon detection events also represent n+1 n-photon detection events, obviously). The hierarchy of those gives the description of the total light field. Their normalized version is the one that gives clues about non-classicality.
That paragraph is somewhat non sequitur for the discussion at hand. In any case, you seem to be conflating above the "n detector" correlations, which his Gn() represent (after the non-local filtering) and n-photon field states which one may measure with the above n-detector apparatus. In the BI violations you are "interested in" measuring G4() on 2-photon state.
Could you please tell me where I could find a picture of perfect “wind/forest interference patterns”?? That repeats itself every time...