A local hidden variables solution of Malus’s Law and a circumvention of Bell’s Theorem. The solution for Bell assumes that antiparticles actually do travel backwards in time and therefore a Bell experiment begins not at the usual source of particle pairs but at the measurement of positrons and ends at the measurement of their paired partner electrons. The solution for Malus’s Law assumes that the distribution of hidden variables in a polarised beam can be deduced by reverse-engineering Malus’s Law intensity calculations. Malus’s Law and Bell’s Experiment can therefore each be explained using local hidden variables. A computer program is given to provide results of a Stern Gerlach detector using local hidden variables in a particle-at-a-time simulation.
A local hidden variables solution of Malus’s Law and a circumvention of Bell’s Theorem. The solution for Bell assumes that antiparticles actually do travel backwards in time and therefore a Bell experiment begins not at the usual source of particle pairs but at the measurement of positrons and ends at the measurement of their paired partner electrons. The solution for Malus’s Law assumes that the distribution of hidden variables in a polarised beam can be deduced by reverse-engineering Malus’s Law intensity calculations. Malus’s Law and Bell’s Experiment can therefore each be explained using local hidden variables. A computer program is given to provide results of a Stern Gerlach detector using local hidden variables in a particle-at-a-time simulation.
This paper shows that, using counterfactual definiteness, there is an enforceable duality between results of Malus Law experiments and the results from Bell experiments. The results are shown here to be equivalent in the two experiments subject to extending the Malus experiment by doubling it to match the structure of the results table of a Bell experiment. The Malus intensities also need to be converted into counterfactual correlations in order to enable results in both experiments to be compared using a common statistic. It is therefore possible to use the duality to explain the more esoteric Bell results via the simpler Malus results. As Malus results involve singleton particles rather than matched pairs of particles then there is no requirement for action at a distance nor entanglement to feature in an explanation of Malus results and therefore, using the duality, neither in Bell results. The ‘magic’ in Bell’s Theorem results is not eliminated as it still exists contained within Malus results, and that ‘magic’ [of somehow exceeding the Bell Inequalities] remains unexplained by this paper, except it is shown that the ‘magic’ does not involve action-at-a-distance nor entanglement.
This paper examines a local deterministic model of an experiment involving correlated photons. The experimental setup involves a source that emits two linearly polarized photons in each act, two two-channel analyzers, and detectors included in the coincidence scheme. The orientation angle of the photon polarization plane is a random variable with a uniform distribution, and it is the same for simultaneously emitted photons. The model presented here is a generalization of the “naive example of hidden variable theory” described in A. Aspect's article ‘Bell's Theorem: The Naive View of an Experimentalist. In our model, the outcome of the photon interaction with the analyzer (hit in one of the two channels) is uniquely determined by the angle between the photon polarization plane and the analyzer axis and is described by a step function. The difference in our model is that the step function contains a large number of segments of different lengths. The location and lengths of the segments are set so that the probability of a photon hitting a specific channel of an ideal analyzer, determined by averaging the outcomes over small neighborhoods of angles, approaches the Malus law when the maximum length of a segment decreases. This ensures that the classical model is self-consistent. When ideal analyzers are used, the absolute value of the correlation coefficient of detector readings mainly does not exceed the values from Aspect's ‘naive example’. However, when analyzers with absorption are used, the calculated correlations for some orientations of the analyzers exceed the quantum mechanical values. Key words: linear polarization of photons, Malus law, entangled photons, correlations, hidden parameters.
Fearnley (2020, Ref. 2) shows that if positrons, the antiparticles of electrons, travel backwards in time then the Bell’s Theorem experiment correlation result (Wikipedia, Ref. 5) can be achieved using classical physics calculations. This would involve a mundane bypassing of the Bell Inequalities instead of a spooky breaking of them. Fearnley (Aug. 2018, Ref. 7 and July 2018, Ref.8) and Farnes (Dec. 2018, Ref. 9) show that particles with negative mass can explain gravitationally both dark energy and dark matter. The current paper brings together these two models in one place and gives an antiparticle with negative mass and also travelling backwards in time. In this paper the idea is raised of a specialised type of space to be the environment of antiparticles, where the space occupied by antiparticles is an opposite-handed (geometric algebra) space to the space occupied by particles. The universe as a whole occupies the same handedness of space as does particles. Time runs backwards in the space of antiparticles compared with the direction of time for the universe and for particles.
Chapter 7 discusses the Bell theorem and its demonstration using Mermin’s machine. The Bell theorem proves that a theory based on local realism (one with hidden variables) must satisfy certain inequalities; quantum mechanics predicts these are violated. Mermin designed a gedanken experiment having a double-particle source and two detectors each having three settings, which can correspond to measurements along three spin orientations. A simple hidden-variable assumption is shown to violate quantum predictions. The CHSH inequality, a form of the general Bell inequality, is proved. This relation has been shown to be violated experimentally in quantum experiments, implying that quantum mechanics indeed has “spooky action at a distance.” Many experiments over the years had loopholes, ways used to explain away the data in order to preserve local reality, but recent experiments have been able to eliminate most of these.
Bell's theorem rests on the following fundamental condition for a local system: P(a,b|alpha, beta, lambda)= P(a|alpha, lambda)P(b|beta, lambda). Here a and b are the outcomes respectively for measurements alpha on one side, and beta on the other, of an experiment involving two entangled particles traveling in opposite directions from a source. The parameter lambda (the set of "hidden variables") represents a more complete description of the joint state of the two particles. Because of lambda, the joint probability of detection is now dependent only on lambda and the local measurement setting of alpha; similarly for the other side and the setting beta. From this equation John Bell derived a simple inequality that is violated by the predictions of quantum mechanics, which is generally taken to imply that quantum mechanics is a nonlocal theory. But, by combining Richard Feynman's formulation of quantum mechanics with a model of particle interaction described by David Deutsch, we develop a system (the "space of all paths," SP) that (1) is immediately seen to replicate the predictions of quantum mechanics, (2) has a single outcome for each quantum event (unlike MWI on which it is partly based), and (3) contains the set lambda of hidden variables consisting of all possible paths from the source to the detectors on each side of the two-particle experiment. However, the set lambda is nonmeasurable, and therefore the above equation is meaningless in SP.