Contexts in Quantum, Classical and Partition Logic

Svozil, Karl

doi:10.1016/b978-0-444-52869-8.50015-3

Cited by 37 publications

(58 citation statements)

References 97 publications

(113 reference statements)

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“…Many toy models serve to illustrate special features of different theories. Let us start first by analyzing L 12 , a non distributive lattice which may be considered as the union of two incompatible experiments [64]. The Hasse diagram of L 12 is represented in Fig.…”

Section: A Finite Non-distributive Examplementioning

confidence: 99%

A discussion on the origin of quantum probabilities

2014

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We study the origin of quantum probabilities as arising from non-boolean propositionaloperational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorvian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case).

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Section: A Finite Non-distributive Examplementioning

confidence: 99%

A discussion on the origin of quantum probabilities

2014

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“…Complementarity expresses the impossibility to measure two observables, such as the spin states of two spin- 24 generalised urn 25 or automaton models 26 demonstrate, complementarity does not necessarily imply value indefiniteness. There still could exist enough two-valued states on the associated propositional structures to allow a faithful embedding into a Boolean algebra associated with classical physical systems.…”

Section: Quantum Value Indefinitenessmentioning

confidence: 99%

Quantum Randomness and Value Indefiniteness

Calude

Svozil

2008

adv sci lett

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“…As new evidence emerged, the lack of classical comprehensibility has gotten even worse: whereas quasi-classical systems-such as generalised urn or finite automaton models [10]-feature complementarity, some quantised systems with more than two measurement outcomes cannot be thought of as possessing any global "truth function." As the Kochen-Specker theorem [11,12] shows, they are value indefinite in the sense that there exist (even finite) sets of observables which, under the hypothesis of non-contextuality, cannot all (for some this might still be possible) have definite values independent of the type of measurement actually being performed.…”

Section: Measurementmentioning

confidence: 99%

Is Feasibility in Physics Limited by Fantasy Alone?

Calude

Svozil

2012

A Computable Universe

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Although various limits on the predicability of physical phenomena as well as on physical knowables are commonly established and accepted, we challenge their ultimate validity. More precisely, we claim that fundamental limits arise only from our limited imagination and fantasy. To illustrate this thesis we give evidence that the well-known Turing incomputability barrier can be trespassed via quantum indeterminacy. From this algorithmic viewpoint, the "fine tuning" of physical phenomena amounts to a "(re)programming" of the universe.Take a few moments for some anecdotal recollections. Nuclear science has made true the ancient alchemic dream of producing gold from other elements such as mercury through nuclear reactions. A century ago, similar claims would have disqualified anybody presenting them as quack. Medical chemistry discovered antibiotics which cure Bubonic plague, tuberculosis, syphilis, bacterial pneumonia, as well as a wide range of bacterial infectious diseases which were considered untreatable only one hundred years ago. For contemporaries it is hard to imagine the kind of isolation, scarcity in international communication, entertainment and transportation most of our ancestors had to cope with. * To appear in H. Zenil (ed. 1This historic anecdotal evidence suggests that what is considered tractable, operational and feasible depends on time. One could even extend speculations to the point where everything that is imaginable is also feasible. In what follows, we shall concentrate on some physical issues which might turn out to become relevant in the no-so-distant future, and which might affect the life of the generations succeeding ours to a considerable degree. In particular, we shall consider the connections between time, space and the limit velocity of light in vacuum; we shall ponder upon measurement; and we shall discuss physical indeterminism and randomness, and its relations to the possibility of trespassing the Turing incomputability barrier. Space-timeOne of the findings of special relativity theory is the impossibility to trespass the speed of light barrier "from below;" i.e., by starting out with subluminal speed. This fundamental limit applies also to communication and information transfer. Amazingly, this holds true even when quantum mechanics and "nonlocal quantum correlations" are taken into account, stimulating a notion of "peaceful coexistence" between quantum mechanics and special relativity theory. Thereby, superluminal particles, as well as the inclusion of field theoretic effects such as an index of refraction smaller than unity, supercavitation in the quantum ether, or general relativistic effects by locally rotating masses, wormholes or local contraction and expansion of space-time, possibly also related to time travel, to name but a few, cannot be excluded a priory.Recent operational definitions of space-time and velocity, in order to physically represent the former, conventionalised the latter: Initially, the constancy of the velocity of light in vacuum in all referen...

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Contexts in Quantum, Classical and Partition Logic

Abstract: Contexts are maximal collections of co-measurable observables "bundled together" to form a "quasi-classical mini-universe." Different notions of contexts are discussed for classical, quantum and generalized urn-automaton systems.

Cited by 37 publications

References 97 publications

A discussion on the origin of quantum probabilities

A discussion on the origin of quantum probabilities

Quantum Randomness and Value Indefiniteness

Is Feasibility in Physics Limited by Fantasy Alone?

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