Formalization of the “Twin Paradox” for Non-uniformly Accelerated Motions

Boccaletti, Dino; Catoni, F.; Catoni, Vincenzo

doi:10.1007/s00006-007-0051-x

Cited by 4 publications

(5 citation statements)

References 6 publications

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“…However, if one grants the latter viewpoint (to the reference frame of the space-traveler), the homebody should be younger 20 There are many papers (e.g. Ben-Ya'acov 2016;Franson 2016;Fung, Clark, Lewis, Wu 2016;de Wolf 2016;Garcia-Escartin, Chamorro-Posada 2015;Gasperini 2014;Lindkvist, Sabín, Fuentes, Dragan, Svensson, Delsing, Johansson 2014;Moreau, Devaux, Lantz 2014;Sokołowski, Golda 2014;2014a;Grøn 2013;Carvalho 2012;Friebe 2012;Ord 2012;Sfarti 2012;Sokołowski 2012;Boblest, Müller, Wunner 2011;Grøn, Braeck 2011;Lichtenegger, Iorio 2011;Székely 2010;Grandou, Rubin 2009;Müller, King, Adis 2008;Roukema, Bajtlik 2008;Abramowicz, Bajtlik, Kluźniak 2007;Boccaletti, Catoni, Catoni 2007;2007a;Grøn 2006;Kohler 2006;McCall 2006;Madarász, Németi, Székely 2006;Ghosal, Nepal, Das 2005;Pesic 2003;Soni 2002;Uzan, Luminet, Lehoucq, Peter 2002;Barrow, Levin 2001;Dolby, Gull 2001;Weeks 2001;Cranor, Heider, Price 2000;Schön 1998;…”

Section: Why Entanglement Was Neglectedmentioning

confidence: 99%

This Year's Nobel Prize (2022) in Physics for Entanglement and Quantum Information: the New Revolution in Quantum Mechanics and Science

Penchev

2023

SSRN Journal

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Section: Why Entanglement Was Neglectedmentioning

confidence: 99%

This Year's Nobel Prize (2022) in Physics for Entanglement and Quantum Information: the New Revolution in Quantum Mechanics and Science

Penchev

2023

SSRN Journal

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“…So, if the Copenhagen interpretation of quantum mechanics, restricting it only to propositions about observable effects and to the theory able to predict precisely enough those observable effects, general relativity is really the theory of quantum gravity since it foresees the results of any measurements very well. The hypothesis that entanglement underlies gravitation on the quantum scale is out of the Copenhagen interpretation 39 since it does not imply any measurable macro-effects different from those according to general relativity. ` Finally, one can consider the transition from the description according to quantum mechanics by two entangled separable complex Hilbert spaces and that by pseudo-Riemannian space (equivalent to two Minkowski spaces variably overlapping each other at any point of pseudo-Riemannian space thus equivalent to variable entanglement at it), as a generalization of the concept of reference frame, being inherent for the latter (discussed in detail in another paper: Penchev 2021 June 8).…”

Section: Quantum Mechanics With the Standard Model Versus Gen-eral Re...mentioning

confidence: 99%

“…However, the case of a finite relative speed, but exceeding the speed of light in a vacuum, corresponds to partly discrete or partly external reference frames, i.e., to entanglement in all of its phenomena. If the case meant by classical quantum mechanics can be 39 Paty's research (1995) summarizes the "nature of Einstein's objections to the Copenhagen interpretation of quantum mechanics" and that of Redei (2010): "Einstein's dissatisfaction with non-relativistic quantum mechanics and relativistic quantum field theory," liken to inertial discrete reference frames: thus, the counterpart of the standard inertial reference frames of special relativity, the case of partly discrete reference frames would correspond to the quantum counterpart of the generalized reference frames moving to each other with any variable acceleration. Respectively, the quantity of acceleration is the counterpart of the newly introduced quantity of an arbitrary and variable entanglement as in the case of decoherence (as well as in the reverse case of appearing of a single coherent whole or in any combination of alternating phases of decoherence and of "coherence').…”

Section: Quantum Mechanics With the Standard Model Versus Gen-eral Re...mentioning

confidence: 99%

The 2022 Nobel Prize in Physics for Entanglement and Quantum Information: The New Revolution in Quantum Mechanics and Science

Пенчев¹

2023

Preprint

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The paper discusses the 2022 Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum information science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by the 2022 Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview.

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“…In recent times a two-dimensional system of number, called hyperbolic, has been widely studied and the comparison with complex numbers has allowed an exhaustive formalization of space time geometry and trigonometry [2], [3,4]. Otherwise for hyperbolic numbers too a theory of functions of a hyperbolic variable has been formalized [5,Chap.…”

Section: Introductionmentioning

confidence: 99%

Cauchy-Like Integral Formula for Functions of a Hyperbolic Variable

Catoni

Zampetti

2011

Adv. Appl. Clifford Algebras

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It has been recently shown that, working in a plane with the geometry associated with hyperbolic numbers, a complete "Euclidean" formalization of geometry and trigonometry of Minkowski space-time has been obtained.In this paper we show a first result that indicates that also for the studies of functions of a hyperbolic variable, the more appropriate way is to work in a plane with pseudo-Euclidean metric.In particular it is shown that a theorem equivalent to the Cauchy integral formula for the functions of a complex variable holds for the functions of a hyperbolic variable studied in the pseudo-Euclidean plane.

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Formalization of the “Twin Paradox” for Non-uniformly Accelerated Motions

Abstract: The use of hyperbolic numbers for studying space-time geometry and trigonometry is extended for demonstrating the Frenet's formulas in space-time.By means of this introduction the twin paradox for non-uniformly accelerated motions is formalized in a straightforward way.

Cited by 4 publications

References 6 publications

This Year's Nobel Prize (2022) in Physics for Entanglement and Quantum Information: the New Revolution in Quantum Mechanics and Science

This Year's Nobel Prize (2022) in Physics for Entanglement and Quantum Information: the New Revolution in Quantum Mechanics and Science

The 2022 Nobel Prize in Physics for Entanglement and Quantum Information: The New Revolution in Quantum Mechanics and Science

Cauchy-Like Integral Formula for Functions of a Hyperbolic Variable

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