The Problem of Hidden Variables in Quantum Mechanics

1990 ◽  
pp. 235-263 ◽  
Author(s):  
Simon Kochen ◽  
E. P. Specker
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables

Quantum mechanics, «First kind» states and local hidden variables: Three experimentally distinguishable situations

1978 ◽  
Vol 43 (1) ◽  
pp. 65-72 ◽  
Author(s):  
A. Baracca ◽  
A. Cornia ◽  
R. Livi ◽  
S. Ruffo
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables

scholarly journals On the Problem of Hidden Variables in Quantum Mechanics

1966 ◽  
Vol 38 (3) ◽  
pp. 447-452 ◽  
Author(s):  
JOHN S. BELL
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables

scholarly journals Quantum Computer: Quantum Model and Reality

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Turing Machine ◽  
Quantum Computer ◽  
Classical Model ◽  
Hidden Variables ◽  
Quantum Model ◽  
Computational Process ◽  
Intermediate Domain ◽  
And Mathematics ◽  
The Axiom Of Choice

Any computer can create a model of reality. The hypothesis that quantum computer can generate such a model designated as quantum, which coincides with the modeled reality, is discussed. Its reasons are the theorems about the absence of “hidden variables” in quantum mechanics. The quantum modeling requires the axiom of choice. The following conclusions are deduced from the hypothesis. A quantum model unlike a classical model can coincide with reality. Reality can be interpreted as a quantum computer. The physical processes represent computations of the quantum computer. Quantum information is the real fundament of the world. The conception of quantum computer unifies physics and mathematics and thus the material and the ideal world. Quantum computer is a non-Turing machine in principle. Any quantum computing can be interpreted as an infinite classical computational process of a Turing machine. Quantum computer introduces the notion of “actually infinite computational process”. The discussed hypothesis is consistent with all quantum mechanics. The conclusions address a form of neo-Pythagoreanism: Unifying the mathematical and physical, quantum computer is situated in an intermediate domain of their mutual transformations.

scholarly journals Relating causal and probabilistic approaches to contextuality

2019 ◽  
Vol 377 (2157) ◽  
pp. 20190133
Author(s):  
Matt Jones
Keyword(s):  
Quantum Mechanics ◽  
Causal Model ◽  
Probability Distributions ◽  
Hidden Variables ◽  
Measurement Model ◽  
Direct Influence ◽  
Theme Issue ◽  
Full System ◽  
General Systems ◽  
New Interpretation

A primary goal in recent research on contextuality has been to extend this concept to cases of inconsistent connectedness, where observables have different distributions in different contexts. This article proposes a solution within the framework of probabi- listic causal models, which extend hidden-variables theories, and then demonstrates an equivalence to the contextuality-by-default (CbD) framework. CbD distinguishes contextuality from direct influences of context on observables, defining the latter purely in terms of probability distributions. Here, we take a causal view of direct influences, defining direct influence within any causal model as the probability of all latent states of the system in which a change of context changes the outcome of a measurement. Model-based contextuality (M-contextuality) is then defined as the necessity of stronger direct influences to model a full system than when considered individually. For consistently connected systems, M-contextuality agrees with standard contextuality. For general systems, it is proved that M-contextuality is equivalent to the property that any model of a system must contain ‘hidden influences’, meaning direct influences that go in opposite directions for different latent states, or equivalently signalling between observers that carries no information. This criterion can be taken as formalizing the ‘no-conspiracy’ principle that has been proposed in connection with CbD. M-contextuality is then proved to be equivalent to CbD-contextuality, thus providing a new interpretation of CbD-contextuality as the non-existence of a model for a system without hidden direct influences. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

scholarly journals Quantum Contextuality and Indeterminacy

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 867
Author(s):  
Gregg Jaeger
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables ◽  
Equivalence Classes ◽  
Measuring Apparatus ◽  
Classical Physics ◽  
Quantum Contextuality ◽  
Natural Feature ◽  
Classical Models ◽  
Quantum Behavior ◽  
Quantum Observables

The circumstances of measurement have more direct significance in quantum than in classical physics, where they can be neglected for well-performed measurements. In quantum mechanics, the dispositions of the measuring apparatus-plus-environment of the system measured for a property are a non-trivial part of its formalization as the quantum observable. A straightforward formalization of context, via equivalence classes of measurements corresponding to sets of sharp target observables, was recently given for sharp quantum observables. Here, we show that quantum contextuality, the dependence of measurement outcomes on circumstances external to the measured quantum system, can be manifested not only as the strict exclusivity of different measurements of sharp observables or valuations but via quantitative differences in the property statistics across simultaneous measurements of generalized quantum observables, by formalizing quantum context via coexistent generalized observables rather than only its subset of compatible sharp observables. Here, the question of whether such quantum contextuality follows from basic quantum principles is then addressed, and it is shown that the Principle of Indeterminacy is sufficient for at least one form of non-trivial contextuality. Contextuality is thus seen to be a natural feature of quantum mechanics rather than something arising only from the consideration of impossible measurements, abstract philosophical issues, hidden-variables theories, or other alternative, classical models of quantum behavior.

Quantum Probability

2017 ◽  
Author(s):  
Guido Bacciagaluppi
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables ◽  
Quantum Probability ◽  
Classical Probability ◽  
Discrete Probability ◽  
Joint Distributions ◽  
Finite Dimensional ◽  
Main Emphasis ◽  
Probability Spaces ◽  
Incompatible Observables

The topic of probability in quantum mechanics is rather vast. In this chapter it is discussed from the perspective of whether and in what sense quantum mechanics requires a generalization of the usual (Kolmogorovian) concept of probability. The focus is on the case of finite-dimensional quantum mechanics (which is analogous to that of discrete probability spaces), partly for simplicity and partly for ease of generalization. While the main emphasis is on formal aspects of quantum probability (in particular the non-existence of joint distributions for incompatible observables), the discussion relates also to notorious issues in the interpretation of quantum mechanics. Indeed, whether quantum probability can or cannot be ultimately reduced to classical probability connects rather nicely to the question of 'hidden variables' in quantum mechanics.

Sign in / Sign up

Export Citation Format

Share Document