In this note we wish to demonstrate that the concept of efficiency loophole, as far as a local realistic model is concerned, is a self-defeating one since it implies that the static fields (for example, electric or gravitational) of and elementary particle must be in the form of quantized superluminal pulses. The Idea, however, may still be advocated by the proponents of non-local realistic models since it is shown that such superluminal pulses do not contradict the facts of Lorentz transformations. As an alternative to Bell-type experiments we propose an experiment by means of which one can directly verify the validity of otherwise of the concept of efficiency.
In this note we wish to demonstrate that the concept of efficiency loophole, as far as a local realistic model is concerned, is a self-defeating one since it implies that the static fields (for example, electric or gravitational) of and elementary particle must be in the form of quantized superluminal pulses. The Idea, however, may still be advocated by the proponents of non-local realistic models since it is shown that such superluminal pulses do not contradict the facts of Lorentz transformations. As an alternative to Bell-type experiments we propose an experiment by means of which one can directly verify the validity of otherwise of the concept of efficiency.
In this paper I shall demonstrate that an analysis of the concept of "efficiency loophole" leads to the conclusion that any type of charge carried by and elementary particle must be distributed on the surface of a non-spherical object. As a result I shall show that; for example, the eletrostatic field of an electron as seen by an observer, must be in the form of quantized superluminal pulses. Therefore, "efficiency loophole" cannot be used in support of local realistic models. In view of the available experimental results we conclude that a local realistic interpretation of quantum mechanics has now been empirically refuted. However, it can be shown that the inferred superluminal signals do not necessarily contradict the facts of Lorentz transormations and only introduce a weak non-locality into the laws of nature. For this reason we make a preliminary investigation about a possible connection between quantum mechanics and non-spherical charge distributions. We conclude that this idea deserves to be further investigated and its validity or otherwise can be verified experimentally.
It has long been known that the "detection loophole", present when detector efficiencies are below a critical figure, could open the way for alternative "local realist" explanations for the violation of Bell tests. It has in recent years become common to assume the loophole can be ignored, regardless of which version of the Bell test is employed. A simple model is presented that illustrates that this may not be justified. Two of the versions -- the standard test of form -2 <= S <= 2 and the currently-popular "visibility" test -- are at grave risk of bias. Statements implying that experimental evidence "refutes local realism" or shows that the quantum world really is "weird" should be reviewed. The detection loophole is on its own unlikely to account for more than one or two test violations, but when taken in conjunction with other loopholes (briefly discussed) it is seen that the experiments refute only a narrow class of "local hidden variable" models, applicable to idealised situations, not to the real world. The full class of local realist models provides straightforward explanations not only for the publicised Bell-test violations but also for some lesser-known "anomalies".
It has long been known that the "detection loophole", present when detector efficiencies are below a critical figure, could open the way for alternative "local realist" explanations for the violation of Bell tests. It has in recent years become common to assume the loophole can be ignored, regardless of which version of the Bell test is employed. A simple model is presented that illustrates that this may not be justified. Two of the versions -- the standard test of form -2 <= S <= 2 and the currently-popular "visibility" test -- are at grave risk of bias. Statements implying that experimental evidence "refutes local realism" or shows that the quantum world really is "weird" should be reviewed. The detection loophole is on its own unlikely to account for more than one or two test violations, but when taken in conjunction with other loopholes (briefly discussed) it is seen that the experiments refute only a narrow class of "local hidden variable" models, applicable to idealised situations, not to the real world. The full class of local realist models provides straightforward explanations not only for the publicised Bell-test violations but also for some lesser-known "anomalies".
Let us imagine an experimentalist, who has maximally entangled photons and wants to violate Bell’s inequality in his laboratory. Among many obstacles he has to overcome, two of them are the most significant. Firstly, he has to avoid exchanging information about the measurement settings between the particles. Secondly, he has to detect particles with a high enough probability, because if the detection efficiency is too low, one can reproduce quantum correlations using a LHV (Local Hidden Variables) model. These two problems are known in the literature, respectively, as the locality loophole [1] and the detection loophole [2, 3]. Fortunately, it is possible to close the locality loophole using photons in the experiment [4, 5, 6, 7, 8]. However, closing the detection loophole is still an object of study. The authors of [9] showed that for the CHSH inequality, the lower bound for detector efficiency needed to close the loophole is 82.8% for maximally entangled states. This bound was lowered to 66.7% by Eberhard [10]. Furthermore, the detector efficiency has been studied for other Bell inequalities [11, 12, 13, 14, 15, 16]. In our research, we are trying to answer the following question: If we prepare a Bell experiment and we have two detectors, having different efficiencies both smaller than 100%, which detector should each party receive? And also: Which representation of the chosen Bell inequality should we consider? These are very crucial questions, which arise in laboratories. Hence, we hope that our results will be useful for experimentalists. We focus on the I3322 inequality [17], which is a natural candidate for testing, because of its asymmetry [14, 18]. We consider the case of a post-selection strategy, which consists in rejecting all the rounds in the Bell experiment when one of the detectors does not click. We used numerical optimisation methods to find both the best classical strategy for Alice and Bob and the best detector clicking strategy. Thus, we have found minimal efficiencies of the detectors of Alice and Bob needed to violate I3322. We made the same studies also for symmetric representations of I3322 [19]. Our results show that the minimal efficiencies of Alice and Bob’s detectors of the asymmetric representation of I3322 is lower than in case of the symmetric one [20]. It is work in progress, and we are examining other post-selection methods as well as other Bell inequalities. We want to consider also the case when non-maximally entangled states are used in Bell experiments.
We propose the use of entangled pairs of neutral kaons, considered as a promising tool to close the well known loopholes affecting generic Bell's inequality tests, in a specific Hardy-type experiment. Hardy's contradiction without inequalities between local realism and quantum mechanics can be translated into a feasible experiment by requiring ideal detection efficiencies for only one of the observables to be alternatively measured. Neutral kaons are near to fulfill this requirement and therefore to close the efficiency loophole.
Recent experiments have reached detection efficiencies sufficient to close the detection loophole with photons. Both experiments ran multiple successive trials in fixed measurement configurations, rather than randomly re-setting the measurement configurations before each measurement trial. This opens a new potential loophole for a local hidden variable theory. The loophole invalidates one proposed method of statistical analysis of the experimental results, as demonstrated in this note. Therefore a different analysis will be necessary to definitively assert that these experiments are subject only to the locality loophole.