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In deterministic theories, one can start from a set of ontological states to formulate the dynamical laws, but these may not be directly observable. Observable are only equivalence classes of states, and these will span a basis of…

High Energy Physics - Theory · Physics 2007-05-23 Gerard 't Hooft

Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…

Neurons and Cognition · Quantitative Biology 2026-04-13 Sean Tull , Masanao Ozawa

We first prove that ontological models of the quantum state which are capable of reproducing the Born probability rule and fall in the class of $\psi$-epistemic models are inconsistent with the Sch{\"o}dinger time evolution. We then model…

Quantum Physics · Physics 2014-01-30 Arun Kumar Pati , Partha Ghose , A. K. Rajagopal

Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…

Quantum Physics · Physics 2013-12-04 M. S. Leifer , R. W. Spekkens

The title refers to the Free Will Theorem by Conway and Kochen whose flashy formulation is: if experimenters possess free will, then so do particles. In more modest terms, the theorem says that individual pairs of spacelike separated…

Quantum Physics · Physics 2021-04-14 Ehtibar N. Dzhafarov , Janne V. Kujala

We propose a toy-model theory, that mimics various characteristic features of quantum mechanics. Unlike the toy-models previously studied in the literature, our toy-model allows for an observer to have a full knowledge of a system's real…

Quantum Physics · Physics 2011-07-26 Berry Groisman

The completeness of quantum mechanics in predictive power is a central question in its foundational study. While most investigations focus on two-dimensional systems, high-dimensional systems are more general and widely applicable. Building…

Quantum Physics · Physics 2025-01-07 Jianqi Sheng , Dongkai Zhang , Lixiang Chen

Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many…

Quantum Physics · Physics 2016-10-03 John-Mark A. Allen

Contrary to common belief, it is not difficult to construct deterministic models where stochastic behavior is correctly described by quantum mechanical amplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What is…

Quantum Physics · Physics 2007-05-23 Gerard 't Hooft

We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by…

Quantum Physics · Physics 2007-05-23 Lee Smolin

According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory which removes this indeterminism, as suspected…

Quantum Physics · Physics 2011-08-10 Roger Colbeck , Renato Renner

This is a paper in the field of ontological deterministic theories behind Quantum Field Theories, like for example the cellular automaton theories proposed by 't Hooft. In these theories one has ontological states in which the state of…

Quantum Physics · Physics 2025-11-25 Marcel van Kessel

We give a counter example to show that determinism as such is in contradiction to quantum mechanics. More precisely, we consider a simple quantum system and its environment, including the measurement device, and make the assumption that the…

Quantum Physics · Physics 2009-09-21 Ramon Lapiedra

The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Mark J Hadley

One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…

Quantum Physics · Physics 2024-11-15 Johannes Fankhauser

It is useful to have a criterion for when the predictions of an operational theory should be considered classically explainable. Here we take the criterion to be that the theory admits of a generalized-noncontextual ontological model.…

Quantum Physics · Physics 2024-03-14 David Schmid , John H. Selby , Matthew F. Pusey , Robert W. Spekkens

The conspiracy of ontic states responding to measurements contextually to comply with noncontextual quantum mechanical probabilities is analyzed for general ontological models. A general physical picture of ontological space structure and…

Quantum Physics · Physics 2021-02-24 Yiruo Lin

This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…

Quantum Physics · Physics 2007-12-12 Tung Ten Yong

Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a…

Artificial Intelligence · Computer Science 2026-04-16 Song-Ju Kim

One of the basic observations of the classical world is that physical entities are real and can be distinguished from each other. However, within quantum theory, the idea of physical realism is not well established. A framework to analyse…

Quantum Physics · Physics 2023-04-25 Shubhayan Sarkar