A Model with Varying Fluctuations in the Measurement Context

Aerts, Diederik; Aerts, Sven; Coecke, Bob; D’Hooghe, Bart; Durt, Thomas; Valckenborgh, Frank

doi:10.1007/978-94-011-5886-2_2

Cited by 29 publications

(38 citation statements)

References 4 publications

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“…This is however not the case, as No-Go theorems for hidden variables only apply to models with hidden variables referring to the state of the system, and not to models where the hidden variables refer instead to the measurement process (see the discussion in [22] and the references cited therein).…”

Section: Discussionmentioning

confidence: 99%

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Using simple elastic bands to explain quantum mechanics: a conceptual review of two of Aerts’ machine-models

Bianchi¹

2013

Open Physics

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Abstract:From the beginning of his research, the Belgian physicist Diederik Aerts has shown great creativity in inventing a number of concrete machine-models that have played an important role in the development of general mathematical and conceptual formalisms for the description of the physical reality. These models can also be used to demystify much of the strangeness in the behavior of quantum entities, by allowing to have a peek at what's going on behind the "quantum scenes," during a measurement. In this author's view, the importance of these machine-models, and of the approaches they have originated, have been so far seriously underappreciated by the physics community, despite their success in clarifying many challenges of quantum physics. To fill this gap, and encourage a greater number of researchers to take cognizance of the important work of so-called Geneva-Brussels school, we describe and analyze in this paper two of Aerts' historical machine-models, whose operations are based on simple breakable elastic bands. The first one, called the spin quantum-machine, is able to replicate the quantum probabilities associated with the spin measurement of a spin-1/2 entity.

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Section: Discussionmentioning

confidence: 99%

“…A discussion of these more general situations would however go beyond the scope of the present paper, and we refer the interested readers to [6][7][8][9]22], and the references therein.…”

Section: Discussionmentioning

confidence: 99%

Using simple elastic bands to explain quantum mechanics: a conceptual review of two of Aerts’ machine-models

Bianchi¹

2013

Open Physics

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“…The model puts forward an explanation of the quantum probabilities as due to the presence of fluctuations on the interaction between the measuring apparatus and the physical entity under consideration. We have called this aspect of the formalism the 'hidden measurement approach' [21,22,23,24,25,26,27,28,29]. The name refers to the fact that the presence of these fluctuations can be interpreted as the presence of hidden variables in the measuring apparatus (hidden measurements) instead of the presence of hidden variables in the state of the physical entity, which is what traditional hidden variable theories suppose.…”

Section: Applying the Formalism To Situations Outside The Microworldmentioning

confidence: 99%

Being and Change: Foundations of a Realistic Operational Formalism

Aerts¹

2002

Probing the Structure of Quantum Mechanics

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The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity of a more abstract nature, for example a concept, or a cultural artifact, or the mind of a person, etc..., which means that we aim at very general description. The effect that a context has on the state of the entity plays a fundamental role, which means that our approach is intrinsically contextual. The approach is inspired by the mathematical formalisms that have been developed in axiomatic quantum mechanics, where a specific type of quantum contextuality is modelled. However, because in general states also influence contextwhich is not the case in quantum mechanics -we need a more general setting than the one used there. Our focus on context as a fundamental concept makes it possible to unify 'dynamical change' and 'change under influence of measurement', which makes our approach also more general and more powerful than the traditional quantum axiomatic approaches. For this reason an experiment (or measurement) is introduced as a specific kind of context. Mathematically we introduce a state context property system as the structure to describe an entity by means of its states, contexts and properties. We also strive from the start to a categorical setting and derive the morphisms between * Published as: D. Aerts, "Being and change: foundations of a realistic operational formalism", in Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Computation and Axiomatics, eds. D. Aerts, M. Czachor and T. Durt, World Scientific, Singapore (2002). 1 state context property systems from a merological covariance principle. We introduce the category SCOP with as elements the state context property systems and as morphisms the ones that we derived from this merological covariance principle. We introduce property completeness and state completeness and study the operational foundation of the formalism.

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“…In the hidden measurement approach to quantum mechanics the quantum probability is interpreted as due to a lack of knowledge about the precise measurement interaction which leads to indeterministic outcomes (see, e.g., [16,17,19,20,27,28,29,22,30,31]). In this approach, an experiment is identified with a family of deterministic sub-measurements with a lack of knowledge about which submeasurement actually takes place during a measurement.…”

Section: Intermediate Models Between Quantum and Classicalmentioning

confidence: 99%

“…This lack of knowledge about the measurement interaction is described by the parameter , that as a consequence controls this uncertainty. The introduction of makes it possible to describe a continuous transition from the (quantum) sphere model towards a (classical) deterministic spin state particle [16,17]. The parameter ρ makes it possible to describe a continuous transition from a (quantum) coupling to a completely decoupled situation, which means that both parameters allow a continuous transition from a quantum register to a classical register of N bits.…”

Section: Introductionmentioning

confidence: 99%

Quantum Computation: Towards the Construction of a ‘Between Quantum and Classical’ Computer

Aerts

D’Hooghe

2002

Probing the Structure of Quantum Mechanics

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Using the 'between quantum and classical' models that have been constructed explicitly within the hidden measurement approach of quantum mechanics we investigate the possibility to construct a 'between quantum and classical' computer. In this view, the pure quantum computer and the classical Turing machine can be seen as two special cases of our general computer. We have shown in earlier research that the intermediate 'between quantum and classical' systems cannot be described within standard quantum theory. We argue that the general categoral approach of state property systems might provide a unified framework for the study of these 'between quantum and classical' models, and hence also for the study of classical and quantum computers as special cases.

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A Model with Varying Fluctuations in the Measurement Context

Cited by 29 publications

References 4 publications

Using simple elastic bands to explain quantum mechanics: a conceptual review of two of Aerts’ machine-models

Using simple elastic bands to explain quantum mechanics: a conceptual review of two of Aerts’ machine-models

Being and Change: Foundations of a Realistic Operational Formalism

Quantum Computation: Towards the Construction of a ‘Between Quantum and Classical’ Computer

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