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# Traversable Achronal Retrograde Domains In Spacetime

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## Abstract and Figures

There are many spacetime geometries in general relativity which contain closed timelike curves. A layperson might say that retrograde time travel is possible in such spacetimes. To date no one has discovered a spacetime geometry which emulates what a layperson would describe as a time machine. The purpose of this paper is to propose such a space-time geometry. In our geometry, a bubble of curvature travels along a closed trajectory. The inside of the bubble is Rindler spacetime, and the exterior is Minkowski spacetime. Accelerating observers inside of the bubble travel along closed timelike curves. The walls of the bubble are generated with matter which violates the classical energy conditions. We refer to such a bubble as a Traversable Achronal Retrograde Domain In Spacetime.
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1
Classical and Quantum Gravity
domains in spacetime
BenjaminKTippett1 and DavidTsang2
1 University of British Columbia, Okanagan, 3333 University Way,
2 Center for Theory and Computation, Department of Astronomy, University
of Maryland, College Park, MD 20742, United States of America
E-mail: btippett@mail.ubc.ca and dtsang@astro.umd.edu
Received 24 August 2016, revised 8 March 2017
Accepted for publication 8 March 2017
Published 31 March 2017
Abstract
In this paper we present geometry which has been designed to t a laypersons
description of a time machine. It is a box which allows those within it to
travel backwards and forwards through time and space, as interpreted by an
external observer. Timelike observers travel within the interior of a bubble
of geometry which moves along a circular, acausal trajectory through
spacetime. If certain timelike observers inside the bubble maintain a persistent
acceleration, their worldlines will close.
Our analysis includes a description of the causal structure of our spacetime,
as well as a discussion of its physicality. The inclusion of such a bubble in a
spacetime will render the background spacetime non-orientable, generating
additional consistency constraints for formulations of the initial value
problem. The spacetime geometry is geodesically incomplete, contains naked
singularities, and requires exotic matter.
Keywords: closed timelike curves, classical energy conditions,
naked singularities
(Some guresmay appear in colour only in the online journal)
1. Introduction
The possibility that some spacetime geometries permit retrograde time travel has long been a
preoccupation of both general relativists and popular ction [24]. Among physicists, General
Relativitys allowance for closed timelike curves (CTCs) resulting from exotic spacetime
geometry is a subject of heated debate. While CTCs arestrictly speakinga mathematical
possibility; they are philosophically undesirable. In a fashion similar to the debate over the
B K Tippett and D Tsang
Traversable acausal retrograde domains in spacetime
Printed in the UK
095006
CQGRDG
34
Class. Quantum Grav.
CQG
1361-6382
10.1088/1361-6382/aa6549
Paper
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Classical and Quantum Gravity
IOP
2017
1361-6382 /17/095006+12$33.00 © 2017 IOP Publishing Ltd Printed in the UK Class. Quantum Grav. 34 (2017) 095006 (12pp) https://doi.org/10.1088/1361-6382/aa6549 ... General relativity challenges this view. The Einstein equations, describing the relationship between spacetime geometry and mass-energy [1], have counterintuitive solutions containing closed time-like curves (CTCs) [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. An event on such a curve would be both in the future and in the past of itself, preventing an ordinary formulation of dynamics according to an "initial condition" problem. ... Article Full-text available The theory of general relativity predicts the existence of closed time-like curves (CTCs), which theoretically would allow an observer to travel back in time and interact with their past self. This raises the question of whether this could create a grandfather paradox, in which the observer interacts in such a way to prevent their own time travel. Previous research has proposed a framework for deterministic, reversible, dynamics compatible with non-trivial time travel, where observers in distinct regions of spacetime can perform arbitrary local operations with no contradiction arising. However, only scenarios with up to three regions have been fully characterised, revealing only one type of process where the observers can verify to both be in the past and future of each other. Here we extend this characterisation to an arbitrary number of regions and find that there exist several inequivalent processes that can only arise due to non-trivial time travel. This supports the view that complex dynamics is possible in the presence of CTCs, compatible with free choice of local operations and free of inconsistencies. ... General relativity challenges this view. The Einstein equations, describing the relationship between spacetime geometry and mass-energy [1], have counterintuitive solutions containing closed time like curves (CTCs) [2][3][4][5][6][7][8][9]. An event on such a curve would be both in the future and in the past of itself, preventing an ordinary formulation of dynamics according to an "initial condition" problem. ... Preprint The theory of general relativity predicts the existence of closed time-like curves (CTCs), which theoretically would allow an observer to travel back in time and interact with their past self. This raises the question of whether this could create a grandfather paradox, in which the observer interacts in such a way to prevent their own time travel. Previous research has proposed a framework for deterministic, reversible, dynamics in the presence of CTCs, where observers in distinct regions of spacetime can perform arbitrary local operations with no contradiction arising. However, only scenarios with up to three regions have been fully characterised, revealing only one type of process where the observers can verify to both be in the past and future of each other. Here we extend this characterisation to an arbitrary number of regions and find that there exist several inequivalent processes that can only arise in the presence of CTCs. This supports the view that complex dynamics is possible in the presence of CTCs, compatible with free choice of local operations and free of inconsistencies. ... Specifically designed Lorentzian geometries, describing CTCs at the price of violating the usual energy conditions. Examples of such geometries are those analysed by Ori and Soen [5,32,33,35,37], and by Tippett and Tsang [42]. Third class. ... Chapter Full-text available This work is essentially a review of a new spacetime model with closed causal curves, recently presented in another paper. The spacetime at issue is topologically trivial, free of curvature singularities, and even time and space orientable. Besides summarizing previous results on causal geodesics, tidal accelerations, and violations of the energy conditions, here redshift/blueshift effects and the Hawking–Ellis classification of the stress–energy tensor are examined. ... The premise that the working mechanisms of mindfulness (as one example of meditation practice) are multi-dimensional [4,35,36,37,38] is accruing, in addition to multi-levelled neural pathway approaches for complex mind states, such as unified non-dual compassion [22], and very subtle mind states during "emptiness insight practices" [33,39]. Non-linear statistics, such as Lyapunov stability theory and stochastic analysis [40], and nonlinear interdependence to _____________________________________________________________________________________ 1 TARDIS: Traversable Acausal Retrograde Domain in Space-Time [47] describing a "vehicle" or "bubble" that traverses the space-time manifold, based on the theory that rather than viewing the Universe as 3D + a 4 th dimension of Time, these dimensions must be imagined as instantaneous and concurrent (popularly depicted as a 'time machine' in science-fiction classics such as "Doctor Who"). reflect dynamical systems complexity [41], are being embraced to investigate the poly-dimensionality and nonlinearity of meditation EEG-substrates. ... ... Specifically designed Lorentzian geometries, describing CTCs at the price of violating the usual energy conditions. Examples of such geometries are those analysed by Ori and Soen [5, 32, 33, 35, 37], and by Tippett and Tsang [42]. Third class. ... ... Specifically designed Lorentzian geometries, describing CTCs at the price of violating the usual energy conditions. Examples of such geometries are those analysed by Ori and Soen [5,32,33,35,37], and by Tippett and Tsang [42]. Third class. ... Preprint Full-text available This work is essentially a review of a new spacetime model with closed causal curves, recently presented in another paper (Class. Quantum Grav. \textbf{35}(16) (2018), 165003). The spacetime at issue is topologically trivial, free of curvature singularities, and even time and space orientable. Besides summarizing previous results on causal geodesics, tidal accelerations and violations of the energy conditions, here redshift/blueshift effects and the Hawking-Ellis classification of the stress-energy tensor are examined. ... A second reason is that several mathematical models which allow travel to an earlier time or the transmission of information to the past have been detailed in the technical literature (e.g. Morris et al. 1988;Friedman et al. 1990;Gott 1991;Visser 1996;Mallett 2003;Ralph & Downes 2012;Yuan et al. 2015;Tippett & Tsang 2017) along with popular physics books (e.g. Thorne 1994;Gott 2001;Mallett & Henderson 2008;Kaku 2009;Clegg 2011;Al-Khalili 2016). ... Article Abstract It is not uncommon in time travel stories to find that the mechanism by which the time travel is achieved is not invented. A time traveller could journey to his/her own past and give the designs of the time travel machine to his/her earlier self as s/he was given the designs as a younger person. These designs never get thought up by anyone. Such a situation would conflict with the usual conception of the acquisition of knowledge. This situation is called the Temporal Epistemic Anomaly and would arise if knowledge is gained at a time prior to the information in question being transmitted but is not discovered or invented at any time. This article examines the implications of information propagating around a causal chain that is closed in time (which is required to create the Anomaly) and whether this information need have a specific origin point. ... The spacetime Q 4 p is acausal in the broad sense of lacking a causal structure, but also in the particular, technical, sense that for any pair of points on it, there exists no causal curve connecting them (which, in particular, also implies that it is achronal). The question of the intrinsic (a)causality of spacetime has been studied sometime ago [31], and is a topic of obligated discussion when dealing with the possibility of 'travels in time' [34,54]. Acausal (portions of) spacetimes appears often in relation with wormholes in General Relativity [38]. ... Article Full-text available We construct a family of quantum scalar fields over a$p-$adic spacetime which satisfy$p-$adic analogues of the G\aa rding--Wightman axioms. Most of the axioms can be formulated the same way in both, the Archimedean and non-Archimedean frameworks; however, the axioms depending on the ordering of the background field must be reformulated, reflecting the acausality of$p-$adic spacetime. The$p-$adic scalar fields satisfy certain$p-$adic Klein-Gordon pseudo-differential equations. The second quantization of the solutions of these Klein-Gordon equations corresponds exactly to the scalar fields introduced here. ... The spacetime Q 4 p is acausal in the broad sense of lacking a causal structure, but also in the particular, technical, sense that for any pair of points on it, there exists no causal curve connecting them (which, in particular, also implies that it is achronal). The question of the intrinsic (a)causality of spacetime has been studied sometime ago [31], and is a topic of obligated discussion when dealing with the possibility of 'travels in time' [34,54]. Acausal (portions of) spacetimes appears often in relation with wormholes in General Relativity [38]. ... Preprint Full-text available We construct a family of quantum scalar fields over a p−adic space-time which satisfy p−adic analogues of the Gårding-Wightman axioms. Most of the axioms can be formulated the same way in both, the Archimedean and non-Archimedean frameworks; however, the axioms depending on the ordering of the background field must be reformulated, reflecting the acausality of p−adic spacetime. The p−adic scalar fields satisfy certain p−adic Klein-Gordon pseudo-differential equations. The second quantization of the solutions of these Klein-Gordon equations corresponds exactly to the scalar fields introduced here. 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