2019
DOI: 10.1007/s10699-019-09625-4
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On a Possibly Pure Set-Theoretic Contribution to Black Hole Entropy

Abstract: Continuity as appears to us immediately by intuition (in the flow of time and in motion) differs from its current formalization, the arithmetical continuum or equivalently the set of real numbers used in modern mathematical analysis. Motivated by the known mathematical and physical problems arising from this formalization of the continuum, our aim in this paper is twofold. Firstly, by interpreting Chaitin's variant of Gödel's first incompleteness theorem as an inherent uncertainty or fuzziness of the arithmeti… Show more

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Cited by 9 publications
(7 citation statements)
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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%
“…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%
“…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%
“…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%