Black Holes and Complexity via Constructible Universe

Król, Jerzy; Klimasara, Paweł

doi:10.3390/universe6110198

Cited by 8 publications

(19 citation statements)

References 23 publications

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“…Such possibility was so far formally applied by us in analysis of complexity of black holes in ref. 14 and with drawing conclusions about the cosmological constant from the nontrivial model-theoretic vacuum of spacetime in ref. 10…”

Section: Qm and Solovay Generic Randomness -The Infinite-dimensional mentioning

confidence: 99%

“…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%

“…The subtle point here is the fact that ZFC cannot prove its own consistency; still, most of the researchers assume the consistency of ZF and proceed to work in models of ZFC such that the procedure of changing models yields additional information, which can be of special importance also from the point of view of physics e.g. 10,14,15 . One technique of passing between models of ZFC is the set-theoretic forcing, which is both the method of proving theorems and the recipe for ZFC model extension 11 .…”

Section: Introduction -Randomness Formalization and Quantum Probabilitymentioning

confidence: 99%

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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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Section: Qm and Solovay Generic Randomness -The Infinite-dimensional mentioning

confidence: 99%

Section: Is Qm Random?mentioning

confidence: 99%

Section: Introduction -Randomness Formalization and Quantum Probabilitymentioning

confidence: 99%

See 1 more Smart Citation

Random World and Quantum Mechanics

Król¹,

Bielas²,

Asselmeyer-Maluga³

2021

Preprint

Self Cite

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show abstract

“…Such possibility was so far formally applied by us in analysis of complexity of black holes in ref. 14…”

Section: A Way To the Classical 2-valued Realm Goes Through The Homomorphismsmentioning

confidence: 99%

Section: Introduction -Randomness Formalization and Quantum Probabilitymentioning

confidence: 99%

Random World and Quantum Mechanics

Król

Bielas

Asselmeyer-Maluga

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Random World and Quantum Mechanics

2022

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Black Holes and Complexity via Constructible Universe

Cited by 8 publications

References 23 publications

Random World and Quantum Mechanics

Random World and Quantum Mechanics

Random World and Quantum Mechanics

Random World and Quantum Mechanics

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