E. Santos gives comments on violation of Bell’s theorem as discussed by A. I. M. Rae, Y. Ben-Aryeh, and A. Postan.(AIP

A. I. M. Rae

A. Postan

E. Santos

Emilio Santos

J. F. Clauser

S. Caser

Physical Review Letters

English

Crossref

Santos replies

Santos Corchero, Emilio

UCrea

VOLUME 68, NUMBER 17 P H YSI CA L R EV I EW LETTERS 27 APRIL 1992Santos Replies: Although I do not understand completelythe Comment by Ben-Ayreh and Postan [1],it seems thattheir essential point is the same as that of Rae [21, name-ly, that for a suitably defined ensemble of photon pairsthe Bell inequality is violated. Before addressing thispoint let me clarify two preliminary and more fundamen-tal ones.The relevance of Bell's theorem derives from the possi-bility that it discriminates empirically between the wholefamily of local hidden-variable (LHV) theories and quan-tum mechanics (QM). Now the first point: If, for agiven experiment, there exists a LHV model which makesthe same predictions as quantum mechanics for all quan-tities actually measurable, then such an experiment can-not discriminate between QM and LHV theories, and thisis true without any need of further discussion about Bellinequalities. Second point: If there are two theories, sayA and B, such that no real (as opposed to gedanken) ex-periment is possible and able to discriminate betweenboth theories, then A and B are compatible from thepoint of view of physics (as opposed to metaphysics). Ihope that the authors, and readers, agree up to here.First point. —In my Letter [3] I exhibited a LHV mod-el for experiments measuring the polarization correlationof optical photon pairs that is in agreement with QM forall measurable quantities (the model did not agree exact-ly because the angular correlation factor a was set equalto 1 for simplicity; a more sophisticated model which alsoreproduces this factor has been presented recently [4]).The agreement with QM includes the quantity p(u~a~,u2) calculated by Rae (unnumbered equation) and byBen-Ayreh and Postan [their Eq. (4)], which was not cal-culated in the Letter, but can be trivially obtained frommy model Eq. (14) with 0/4n substituted for P(k, q, bi).Consequently, these experiments are not suitable tests ofLHV against QM.Second point. —At present, 27 years after Bell's work,there is no real experiment, performed or planned, able todiscriminate between QM and LHV. Therefore, thequestion of whether QM and LHV are compatible remains open (which obviously implies that LHV theorieshave not been refuted, in spite of repeated claims of theopposite in Physical Review Letters and other journalsand books).Having made these two points, I address the specificcriticisms made. For an easier discussion, let us assumeperfect polarizers and detectors, with apertures O«4x.It seems that we may use two diAerent ensembles of pho-ton pairs for the definition of probabilities: (a) the en-semble of all pairs produced by decaying atoms, or (b)the subensemble of these pairs in which each photon haspassed the corresponding aperture. In case (a) the coin-cidence probabilities are a factor of order 0/4x smallerthan the single probability (due to the poor angularcorrelation between the photons) and the Bell inequalitiesare well satisfied. In case (b), single and coincidenceprobabilities are of the same order and QM probabilities2702violate the Bell inequality. Ne conclude that Bell's theo-rem does not forbid LHV models reproducing the QM re-sults, provided it is required that they describe only thetotal ensemble (a), but not the "passed subensemble"(b). The model presented in my Letter does that at theprice of assuming a photon detection probability with thepolarizer removed [P(A, ,O) =0/4n if it is defined for thetotal ensemble (a)], which may be greater than the prob-ability with the polarizer in place [P(l,,a) given by Eq.(12) of my Letter]. That is, for some values of A, mychoice violates the Clauser-Horne "no-enhancement" as-sumption [5]This implies that the model is not compatible with the ex-istence of the passed subensemble, since for such a suben-semble we would have, with perfect detector efficiency,P(k, ,a) =1 and hence P(X,O) & 1.In summary, I agree with the authors of the Commentsthat the Bell inequality, applied to the passed subensem-ble, is violated by QM predictions. But I should add thatthis violation is irrelevant from the point of view of phys-ics, because the "probabilities" involved cannot be mea-sured, as they refer to a hypothetical ensemble not de-fined operationally. It might be believed that the coin-cidence probability for the passed subensemble could bemeasured as the ratio of the coincidence counting ratewith both polarizers in place and the coincidence count-ing rate with one polarizer removed, as is apparently sug-gested by Ben-Ayreh and Postan. I do not agree. This isa ratio of probabilities, not a probability. Then I argue,following the best tradition of Bohr, that QM should notbe interpreted as making predictions for the (purelyimaginary or metaphysical) passed ensemble and, conse-quently, that there is no contradiction between QM andLHV theories for these experiments.Rae defends the existence of such an ensemble by say-ing that "light can reach the detector only by passingthrough a lens or aperture and there is no alternativepath. " This argument is typical and it has been used, im-plicitly or explicitly, by most authors dealing with thematter. But it is inconsistent. In fact, the whole argu-ment of Rae (or Clauser, Shimony, etc. ) appears to be asfollows:(A) Nature is local. Therefore, if something happen-ing in the source produces an effect in the detector, itcannot be by an action at a distance, but, rather, some-thing (a photon) should travel from the source to thedetector. As the velocity of light cannot be surpassed, thetravel should be more or less in a straight line, that is,through the apertures.(B) As a photon is localized at birth (at an atom) andlocalized at death (when detected), it should maintain lo-calization through its whole life. Then either it passesfully or not at all through the apertures.(C) We define the subensemble of pairs passingthrough the apertures and, applying Bell's theorem, weVOLUME 6S, NUMBER 17 P H YSICA L R EV I EW LETTERS 27 APRIL 1992conclude that nature is nonlocal.What I do not understand is why if Rae is able to ac-cept (C), he does not reject (A) and (B). Up until now Ifind no reason to reject (A) and so I am compelled to re-ject (B). But then I argue that this rejection fits fairlywell with the quantum formalism. In fact, as I stressed inmy Letter, QM needs to define probabilities only betweenthe (initial) preparation and the (final) measurement.For instance, in the two-slit experiment, QM allows us tocalculate the amplitude, say p~, for a photon of thesource going to the upper slit or to the lower slit, p2.Also, QM allows us to calculate the amplitude for a pho-ton going from the upper slit to the point x on the screen,say Itr~(x), and similarly for the lower slit, y2(x). How-ever, although in QM all probabilities are squares of am-plitudes, not all amplitudes squared should be takenas probabilities. In the two-slit experiment, l&~IIrl(x)+Pziiri(x)l is a (measurable) probability, but neitherldll n« lp&iir|(x)l, etc. , is measurable (I mean in thesame, interference, experiment). If one insists in takingthem as probabilities, then one is led to the necessity ofchanging the laws of probability, or even logic, in dealingwith quantum mechanics. Such a dramatic changeshould be avoided, according to Occam's razor, not beingstrictly necessary. (This does not exclude the usefulnessof quantum logic and quantum probability in purely for-mal approaches. ) Consequently, we should not assumethat "the subensemble of photons passing through theupper (or lower) slit" does exist. We should assume thatall photons pass, in some sense, through both slits (orbetter, we might avoid speaking about photons at all).Also in the (atomic cascade) experiments that we arediscussing, we should assume that all photons pass par-tially, in some sense, through the apertures, and this fol-lows naturally from the quantum formalism. In fact,quantum electrodynamics (as well as the classical theory)shows that an emission in the source produces an elec-tromagnetic field which propagates —according to Max-well's equations even in the quantum case—through theapertures and, possibly, polarizers to the detectors.There, as the field is quantized, it does not act determin-istically, but statistically, and all we can calculate is theprobability of a count. For a popular explanation it mayseem good (in my opinion it is very bad) to say that thisis because the electromagnetic quantized field consists ofa set of particles (photons), but this does not followstrictly from QM. Indeed, photons are not particles, but(nonlocalized) quanta of the electromagnetic field.I conclude by using this opportunity to put my Letterin due context by comparing it with the well-known arti-cle of Clauser and Horne [4].The first half of my Letter was devoted to showing thatatomic cascade experiments are not suitable tests of LHUtheories against QM due to the poor angular correlationof the photons involved. I acknowledge that this fact hadof the photons involved. I acknowledge that this fact hadbeen already very clearly stated in the paper by Clauserand Horne. My difference from these authors on thispoint may be qualified as a matter of opinion, but I thinkit is important. While they attempted to solve the prob-lem by deriving new tests with the introduction of "plau-sible auxiliary assumptions, " in my opinion plausibilitycannot be used as a valid criterion of scientific truth.Consequently I have attempted to make clear that LHVtheories might only be refuted if there were a real experi-ment where no LHV model is possible that makes thesame predictions as QM for measurable quantities.In the second part of my Letter, I exhibited a LHVmodel for atomic cascade experiments which agrees withQM even for perfect apparatus. (After publication of theLetter I realized that the model was inspired by a previ-ous one used by Caser [6] for a different purpose, whichthis author had discussed with me several years ago. ) Incontrast, Clauser and Horne were only able to find amodel resting upon the low efficiency of the availablephoton detectors (their model was untenable with effi-ciencies above 3$/o). In my view this is substantial im-provement because the Bell inequalities are not suScientconditions for the existence of LHV models, and beforemy Letter it was unknown whether they actually existedin agreement with QM even for ideal polarizers anddetectors Indeed. , the lack of such a model has misledmost people to believe that LHV theories have alreadybeen empirically refuted, modulo the low efficiency loop-hole. This wrong belief, not attributable to the paper ofClauser and Horne, has stooped the search for truly reli-able experiments, and so it has delayed the solution of anextremely important open problem„by almost a quarterof a century.Emilio SantosDepartamento de Fisica ModernaUniversidad de CantabriaSantander, SpainReceived 17 September 1991;revised manuscript received 18 February 1992PACS numbers: 03.6S.BX, 42.50.%'mfl] Y. Ben-Aryeh and A. Postan, preceding Comment, Phys.Rev. Lett. 6$, 2701 (1992}.[2] A. I. M. Rae, preceding Comment, Phys. Rev. Lett. 6$,2700 (1992).[3] Emilio Santos, Phys. Rev. Lett. 66, 1388 (1991).[4] E. Santos, in Proceedings of the Conference on Bell' sTheorem and the Foundations of Modern Physics, Cese-na, Italy, October 1991 (to be published}.[5] J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526(1974).[6] S. Caser, Phys. Lett. A 121, 331 (1987).2703

Santos Replies

https://repositorio.unican.es/xmlui/bitstream/10902/1825/1/Reply%20to%20Comment%20on%20Does%20quantum%20mechanics.pdf

Santos Replies

Abstract

Similar works

Full text

Available Versions

Crossref

UCrea