On a Possibly Pure Set-Theoretic Contribution to Black Hole Entropy

Etesi, Gabor

doi:10.1007/s10699-019-09625-4

Cited by 9 publications

(7 citation statements)

References 18 publications

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“…We have no criterion that could tell us which of the four additions -( 61), ( 63), (65), or (66) -defines the level of description we employ in everyday life. Which of these two probabilities, and which of the several ways of adding them, is our usual way of processing experimental data?…”

Section: Copernican Hierarchiesmentioning

confidence: 99%

Contra Bellum: Bell's Theorem as a Confusion of Languages

Czachor

2023

Acta Phys. Pol. A

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Bell's theorem is a conflict of mathematical predictions formulated within an infinite hierarchy of mathematical models. Inequalities formulated at level k ∈ Z are violated by probabilities at level k + 1. We are inclined to think that k = 0 corresponds to the classical world, while k = 1 -to the quantum one. However, as the k = 0 inequalities are violated by k = 1 probabilities, the same relation holds between k = 1 inequalities violated by k = 2 probabilities, k = −1 inequalities violated by k = 0 probabilities, and so forth. By accepting the logic of the Bell theorem, can we prove by induction that nothing exists? topics: Bell's theorem, black holes, non-Newtonian calculus, quantum cryptography

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Section: Copernican Hierarchiesmentioning

confidence: 99%

Contra Bellum: Bell's Theorem as a Confusion of Languages

Czachor

2023

Acta Phys. Pol. A

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“…This indicates a rather deep theoretical connection on the level of topology between spacetime structure, QM and randomness. From a practical point of view, since gravity is very weak comparing to other forces we need extreme densities of energies or cosmological scales of our Universe to 'see' gravitational effects responsible for randomness of QM (see [62,35,87]). Even in the case of confirmation of the Solovay genericity in such extreme phenomena, their practical applicability would require much additional and conceptual work.…”

Section: Is Qm Random?mentioning

confidence: 99%

Random World and Quantum Mechanics

2022

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Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin-Löf. We extend this result and demonstrate that QM is algorithmic ω-random and generic, precisely as described by the 'miniaturisation' of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo-Fraenkel Solovay random on infinite-dimensional Hilbert spaces. Moreover, it is more likely that there exists a standard transitive ZFC model M , where QM is expressed in reality, than in the universe V of sets. Then every generic quantum measurement adds to M the infinite sequence, i.e. random real r ∈ 2 ω , and the model undergoes random forcing extensions M [r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit, therefore showing the structural resemblance of both in this limit. We discuss several questions regarding measurability and possible practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC; however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself, the issues considered here remain hidden to a great extent.

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“…From a practical point of view, since gravity is very weak comparing to other forces we need extreme densities of energies or cosmological scales of our Universe to 'see' gravitational effects responsible for randomness of QM (see ref. 14,62,63 ). Even in the case of confirmation of the Solovay genericity in such extreme phenomena, their practical applicability would require much additional and conceptual work.…”

Section: Is Qm Random?mentioning

confidence: 99%

Random World and Quantum Mechanics

Król¹,

Bielas²,

Asselmeyer-Maluga³

2021

Preprint

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Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin-Löf. We extend this result and demonstrate that QM is algorithmic ω-random and generic precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo-Fraenkel Solovay random on infinite dimensional Hilbert spaces. Moreover it is more likely that there exists a standard transitive model of ZFC M where QM is expressed in reality than in the universe V of sets. Then every generic quantum measurement adds the infinite sequence, i.e. random real r ∈ 2ω, to M and the model undergoes random forcing extensions, M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit. This shows the structural resemblance of both in the limit. We discuss several questions regarding measurability and eventual practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC, however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself the issues considered here become mostly hidden.

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On a Possibly Pure Set-Theoretic Contribution to Black Hole Entropy

Cited by 9 publications

References 18 publications

Contra Bellum: Bell's Theorem as a Confusion of Languages

Contra Bellum: Bell's Theorem as a Confusion of Languages

Random World and Quantum Mechanics

Random World and Quantum Mechanics

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