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The Extended Bloch Representation of Quantum Mechanics and the Hidden-Measurement Solution to the Measurement Problem Vrije Universiteit Brussel

Diederik Aerts, Massimiliano Sassoli De Bianchi
A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it allows to derive the Born rule as an average over hidden-variables, describing not the state of the quantum entity, but its interaction with the ...

Do Spins Have Directions? Vrije Universiteit Brussel

Diederik Aerts, Massimiliano Sassoli De Bianchi

The standard Bloch sphere representation has been recently generalized to describe not only systems of arbitrary dimension, but also their measurements, in what has been called the extended Bloch representation of quantum mechanics. This model, which offers a solution to the longstanding measurement problem, is based on the hidden-measurement interpretation of quantum mechanics, according to which the Born rule results from our lack of ...

The GTR-model: A universal framework for quantum-like measurements. Vrije Universiteit Brussel

Diederik Aerts, Massimiliano Sassoli De Bianchi
We present a very general geometrico-dynamical description of physical or more abstract entities, called the 'general tension-reduction' (GTR) model, where not only states, but also measurement-interactions can be represented, and the associated outcome probabilities calculated. Underlying the model is the hypothesis that indeterminism manifests as a consequence of unavoidable fluctuations in the experimental context, in accordance with the ...

Using abstract elastic membranes to learn about quantum measurements Vrije Universiteit Brussel

Massimiliano Sassoli De Bianchi

The objectives of the Center Leo Apostel for Interdisciplinary Studies were summarized by his creator as: interdisciplinarity, construction of world views and broad dissemination of scientific knowledge. In compliance with the third of these objectives, we provide a rigorous but accessible popular science version of a research article published by Aerts and Sassoli de Bianchi (Ann Phys 351:975–1025, 2014), where an extended version of the ...

Taking quantum physics and consciousness seriously: what does it mean and what are the consequences? Vrije Universiteit Brussel

Massimiliano Sassoli De Bianchi
We present some of the foundational ideas of so-called hidden-measurement interpretation of quantum mechanics, whose proposed solution to the measurement problem does not require any deus ex machina intervention from an abstract ego, but asks in exchange to accept that our physical reality would be mostly non-spatial, and therefore much larger than what we could expect from our ordinary experience of it. We also emphasize that, similarly to ...

Quantum measurements as weighted symmetry breaking processes: the hidden measurement perspective Vrije Universiteit Brussel

Diederik Aerts, Massimiliano Sassoli De Bianchi
The purpose of the present note is twofold. Firstly, we highlight the similarities between the ontologies of Kastner's possibilist transactional interpretation (PTI) of quantum mechanics - an extension of Cramer's transactional interpretation - and the authors' hidden-measurement interpretation (HMI). Secondly, we observe that although a weighted symmetry breaking (WSB) process was proposed in the PTI, to explain the actualization of incipient ...

Many-Measurements or Many-Worlds? A Dialogue Vrije Universiteit Brussel

Diederik Aerts, Massimiliano Sassoli De Bianchi
Many advocates of the Everettian interpretation consider that theirs is the only approach to take quantum mechanics really seriously, and that this approach allows to deduce a fantastic scenario for our reality, one that consists of an infinite number of parallel worlds that branch out continuously. In this article, written in dialogue form, we suggest that quantum mechanics can be taken even more seriously, if the 'many-worlds' view is replaced ...

The extended Bloch Representation of Entanglement and Measurement in Quantum Mechanics Vrije Universiteit Brussel

Diederik Aerts, Massimiliano Sassoli De Bianchi, Sandro Sozzo

The quantum formalism can be completed by assuming that density operators also represent genuine states. An ‘extended Bloch representation’ (EBR) then results, in which not only the states but also the measurement-interactions can be described. Consequently, the Born rule can be obtained as an expression that quantifies the lack of knowledge about the measurement-interaction that is each time actualized, during a measurement. Entanglement can ...

Beyond-Quantum Modeling of Question Order Effects and Response Replicability in Psychological Measurements Vrije Universiteit Brussel

Diederik Aerts, Massimiliano Sassoli De Bianchi
A general tension-reduction (GTR) model was recently considered to derive quantum probabilities as (universal) averages over all possible forms of non-uniform fluctuations, and explain their considerable success in describing experimental situations also outside of the domain of physics, for instance in the ambit of quantum models of cognition and decision. Yet, this result also highlighted the possibility of observing violations of the ...

The Extended Bloch Representation of Quantum Mechanics. Explaining Superposition, Interference and Entanglement Vrije Universiteit Brussel

Diederik Aerts, Massimiliano Sassoli De Bianchi
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states, explaining the interference effects, and the entanglement correlations, in terms of the different orientations that a state-vector can take within the generalized Bloch sphere. We also introduce a tensorial ...