Testing Born’s Rule in Quantum Mechanics with a Triple Slit Experiment

2009

Found Phys

Recently a new attempt to go beyond quantum mechanics (QM) was presented in the form of so called prequantum classical statistical field theory (PCSFT). Its main experimental prediction is violation of Born's rule which provides only an approximative description of real probabilities. We expect that it will be possible to design numerous experiments demonstrating violation of Born's rule. Moreover, recently the first experimental evidence of violation was found in the triple slit interference experiment, see Sinha, et al. (Foundations of Probability and Physics-5. . Although this experimental test was motivated by another prequantum model, it can be definitely considered as at least preliminary confirmation of the main prediction of PCSFT. In our approach quantum particles are just symbolic representations of "prequantum random fields," e.g., "electron-field" or "neutron-field"; photon is associated with classical random electromagnetic field. Such prequantum fields fluctuate on time and space scales which are essentially finer than scales of QM, cf. 't Hooft's attempt to go beyond QM (see 't Hooft arXiv:hep-th/0105105, 2001; arXiv:quant-ph/0212095, 2002; arXiv:quant-ph/0701097, 2007). In this paper we elaborate a detection model in the PCSFT-framework. In this model classical random fields (corresponding to "quantum particles") interact with detectors inducing probabilities which match with Born's rule only approximately. Thus QM arises from PCSFT as an approximative theory. New tests of violation of Born's rule are proposed.

Section: Introductionmentioning

confidence: 72%

Section: Discussion On the Triple Slit Experimentsmentioning

confidence: 97%

Section: Deviation From Predictions Of Quantum Mechanicsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Detection Model Based on Representation of Quantum Particles by Classical Random Fields: Born’s Rule and Beyond

2009

Found Phys

“…We remark that our activity is similar to studies questioning applicability of the formalism of quantum physics; for example, recent experimental studies of Weihs et al [24] questioning the possibility to use the standard quantum formalism (as was proposed by R. Sorkin) to describe the data from the three slit experiment. Another experiment of such a type was discussed in [25].…”

Section: Discussionmentioning

confidence: 92%

On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements

Basieva

2015

Found Phys

In this paper we study the problem of a possibility to use quantum observables to describe a possible combination of the order effect with sequential reproducibility for quantum measurements. By the order effect we mean a dependence of probability distributions (of measurement results) on the order of measurements. We consider two types of the sequential reproducibility: adjacent reproducibility ( A − A) (the standard perfect repeatability) and separated reproducibility(A − B − A). The first one is reproducibility with probability 1 of a result of measurement of some observable A measured twice, one A measurement after the other. The second one, A − B − A, is reproducibility with probability 1 of a result of A measurement when another quantum observable B is measured between two A's. Heuristically, it is clear that the second type of reproducibility is complementary to the order effect. We show that, surprisingly, this may not be the case. The order effect can coexist with a separated reproducibility as well as adjacent reproducibility for both observables A and B. However, the additional constraint in the form of separated reproducibility of the B − A − B type makes this coexistence impossible. The problem under consideration was motivated by attempts to apply the quantum formalism outside of physics, especially, in cognitive psychology and psychophysics. However, it is also important for foundations of quantum physics as a part of the problem about the structure of sequential quantum measurements.

Quantum Probability for Modeling Cognition, Decision Making, and Artificial Intelligence

Springer Proceedings in Mathematics &Amp; Statistics

2022

The aim of this review is to highlight the possibility to apply the mathematical formalism and methodology of quantum theory to model behaviour of complex biosystems, from genomes and proteins to animals, humans, ecological and social systems. Such models are known as quantum-like and they should be distinguished from genuine quantum physical modeling of biological phenomena. One of the distinguishing features of quantum-like models is their applicability to macroscopic biosystems, or to be more precise, to information processing in them. Quantum-like modeling has the base in quantum information theory and it can be considered as one of the fruits of the quantum information revolution. Since any isolated biosystem is dead, modeling of biological as well as mental processes should be based on theory of open systems in its most general form -theory of open quantum systems. In this review we advertise its applications to biology and cognition, especially theory of quantum instruments and quantum master equation. We mention the possible interpretations of the basic entities of quantum-like models with special interest to QBism is as may be the most useful interpretation.