Contextuality, Complementarity, Signaling, and Bell Tests

This article reconsiders the double-slit experiment from the nonrealist or, in terms of this article, “reality-without-realism” (RWR) perspective, grounded in the combination of three forms of quantum discontinuity: (1) “Heisenberg discontinuity”, defined by the impossibility of a representation or even conception of how quantum phenomena come about, even though quantum theory (such as quantum mechanics or quantum field theory) predicts the data in question strictly in accord with what is observed in quantum experiments); (2) “Bohr discontinuity”, defined, under the assumption of Heisenberg discontinuity, by the view that quantum phenomena and the data observed therein are described by classical and not quantum theory, even though classical physics cannot predict them; and (3) “Dirac discontinuity” (not considered by Dirac himself, but suggested by his equation), according to which the concept of a quantum object, such as a photon or electron, is an idealization only applicable at the time of observation and not to something that exists independently in nature. Dirac discontinuity is of particular importance for the article’s foundational argument and its analysis of the double-slit experiment.

Section: Reality Without Realism: Quantum Discontinuity and Quantum E...mentioning

confidence: 99%

“Yet Once More”: The Double-Slit Experiment and Quantum Discontinuity

Plotnitsky

2022

“…Notice that this implies that two incompatible experiments give place to different probability distributions and random variables. This strong dependence on the context of measurement can be called Bohr contextuality and is closely related to the notion of incompatibility of observables [ 57 ].…”

Section: The Main Features Of Quantum Probabilitymentioning

confidence: 99%

“…However, something really amazing happens in quantum physics. The theory predicts that the marginal probabilities associated with a given experiment do not depend on the context in which it is considered (but see the discussion of experiments presented in [ 57 ]). This peculiar feature is called a no-signal condition and can also be given a very precise mathematical formulation.…”

Section: The Main Features Of Quantum Probabilitymentioning

confidence: 99%

“… There is a joint probability distribution (that obeys Kolmogorov’s axioms) for experiments that can be jointly performed. However, the physics changes radically from context to context (consider the wave-particle behavior in a Mach–Zehnder interferometer): the strong dependence on the context is an expression of what can be called Bohr contextuality [ 57 ]. There is no joint (Kolmogorovian) probability distribution for all possible contexts.…”

Section: The Main Features Of Quantum Probabilitymentioning

confidence: 99%

See 1 more Smart Citation

Non-Kolmogorovian Probabilities and Quantum Technologies

Holik

2022

In this work, we focus on the philosophical aspects and technical challenges that underlie the axiomatization of the non-Kolmogorovian probability framework, in connection with the problem of quantum contextuality. This fundamental feature of quantum theory has received a lot of attention recently, given that it might be connected to the speed-up of quantum computers—a phenomenon that is not fully understood. Although this problem has been extensively studied in the physics community, there are still many philosophical questions that should be properly formulated. We analyzed different problems from a conceptual standpoint using the non-Kolmogorovian probability approach as a technical tool.

“…As was emphasized in the review [ 58 ], signaling patters can be found in practically all statistical datasets collected in the Bell experiments. This is natural.…”

Section: Introductionmentioning

confidence: 99%

On Applicability of Quantum Formalism to Model Decision Making: Can Cognitive Signaling Be Compatible with Quantum Theory?

Khrennikov

2022

Self Cite

This note is devoted to the problem of signaling (marginal inconsistency) in the Bell-type experiments with physical and cognitive systems. It seems that in quantum physics, this problem is still not taken seriously. Only recently have experimenters started to check the signaling hypothesis for their data. For cognitive systems, signaling was statistically significant in all experiments (typically for decision making) performed up to today. Here, one cannot simply ignore this problem. Since signaling contradicts the quantum theory of measurement for compatible observables, its statistical significance in experiments with humans can be considered as an objection for quantum-like modeling—applications of quantum theory to cognition, decision making, psychology, economics and finance, social and political science. In this paper, we point to two possible sources of signaling generation that are consistent with quantum measurement theory. Thus, the signaling objection for quantum-like modeling is not catastrophic. One of these sources is the direct physical signaling about selection of experimental settings, questions or tasks in quantum-like studies. Another possible source is a state modification dependent on experimental settings. The latter was a rather common source of signaling in quantum physics. Since the physical size of the brain is very small comparing with the light velocity, it seems to be impossible to prevent the direct physical signaling (with electromagnetic waves) between the brain’s areas processing two questions a and b. However, if, for these questions, not the electromagnetic waves, but electrochemical communication plays the crucial role, the experimenter may hope to make signaling weaker by answering the questions faster. The problem of question-dependent mental state modification seems to be solvable via smarter experimental design. This paper can be useful both for physicists interested in quantum foundations and for researchers working in quantum-like studies, e.g., applying the quantum theory to model decision making or psychological effects. This paper is solely about quantum theory. Thus, we do not consider general contextual probabilistic models.