Generalised Manifolds as Basic Objects of General Relativity

Luc, Joanna

doi:10.1007/s10701-019-00292-w

Cited by 6 publications

(6 citation statements)

References 33 publications

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“…Such a mechanism could potentially make use of the Everett ("many-worlds") interpretation of quantum mechanics [23], and indeed this interpretation has been investigated in the context of time travel [24,25]. Classically, non-Hausdorff manifolds [10,26,27,28,29] were suggested as a possible mathematical model for branching spacetimes. However, in both cases, no concrete mechanism has been suggested so far.…”

Section: Resolving the Paradoxes Using Multiple Historiesmentioning

confidence: 99%

Wormhole Time Machines and Multiple Histories

Shoshany¹,

Jared²

2021

Preprint

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In a previous paper [1], we analyzed a class of time travel paradoxes which cannot be resolved using Novikov's self-consistency conjecture, meaning that the system is fundamentally and irreparably inconsistent. We proved that the paradoxes can nonetheless always be resolved, and the system made consistent, by assuming that traveling back in time creates a new independent history (or timeline), such that any changes to the past affect only the new history and not the original one. Therefore, we argued that if time travel is possible, that would necessarily imply the existence of multiple histories. However, our proof was obtained using a simplistic and unrealistic toy model, which was formulated using contrived laws of physics. The purpose of the present paper is to define and analyze a new model of time travel paradoxes, which is fully compatible with all known physics -provided, of course, that time travel itself is possible. This model consists of a wormhole time machine in 3+1 spacetime dimensions, which can be either permanent (existing eternally) or temporary (activated only for a short time). We define the spacetime topology and geometry of the model, calculate the geodesics of objects passing through the time machine, and prove that this model inevitably leads to paradoxes which cannot be resolved using Novikov's conjecture, but can be resolved using multiple histories. This result provides more substantial support to our claim that time travel necessarily implies multiple histories.

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Section: Resolving the Paradoxes Using Multiple Historiesmentioning

confidence: 99%

Wormhole Time Machines and Multiple Histories

Shoshany¹,

Jared²

2021

Preprint

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“…This requires the addition of just a single extra axiom to the basis of common BST structures. 9 As originally described by Belnap [1], the theory posits the axioms of a common BST structure together with the so-called prior choice principle, which we will denote PCP 92 to indicate its historical origin. Basically, PCP 92 requires that whenever an event e belongs to one history h 1 but not to another history h 2 , these two histories split at a choice point c in the past of e:…”

Section: Branching Via the Prior Choice Principle Of Bst 92mentioning

confidence: 99%

“…However, there have been attempts to relax the Hausdorff property, motivated by particular candidates for space-time. It can also be argued that the Hausdorff property is not needed in General Relativity and can be abandoned at a small price [9]. Finally, there is a method of gluing (Hausdorff) differential manifolds into a larger structure, a so-call generalized manifold, that is not Haudorff.…”

Section: The Diamond Topology In Bst Nfmentioning

confidence: 99%

New Foundations for Branching Space-Times

2020

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The theory of branching space-times, put forward by Belnap (Synthese 92, 1992), considers indeterminism as local in space and time. In the axiomatic foundations of that theory, so-called choice points mark the points at which the (local) possible future can turn out in different ways. Working under the assumption of choice points is suitable for many applications, but has an unwelcome topological consequence that makes it difficult to employ branching space-times to represent a range of possible physical space-times. Therefore it is interesting to develop a branching space-times theory without choice points. This is what we set out to do in this paper, providing new foundations for branching spacetimes in terms of choice sets rather than choice points. After motivating and developing the resulting theory in formal detail, we show that it is possible to translate structures of one style into structures of the other style and vice versa. This result shows that the underlying idea of indeterminism as the branching of spatio-temporal histories is robust with respect to different implementations, making a choice between them a matter of expediency rather than of principle.

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“…Recently, Placek [43] developed a detailed theory of branching spacetime which employs non-Hausdorff (but locally Euclidean) manifolds in order to take multiple histories into account, although he did not discuss time travel paradoxes in this context. Luc [44] (see also [45] with Placek) discussed the issue of non-Hausdorff manifolds and concluded that they can, in fact, be used as fundamental mathematical objects describing spacetime in general relativity. The basic notion of using such manifolds to describe branching universes with multiple timelines seems reasonable, but there are many conceptual and mathematical issues which need to be resolved first.…”

Section: Non-hausdorff Manifoldsmentioning

confidence: 99%

“…Here λ is an affine parameter 44 along the null geodesic. The ANEC is the weakest energy condition we have -but unfortunately, even this condition is violated in some cases.…”

Section: The Averaged Energy Conditionsmentioning

confidence: 99%

Lectures on faster-than-light travel and time travel

Shoshany

2019

SciPost Phys. Lect. Notes

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These lecture notes were prepared for a 25-hour course for advanced undergraduate students participating in Perimeter Institute's Undergraduate Summer Program. The lectures cover some of what is currently known about the possibility of superluminal travel and time travel within the context of established science, that is, general relativity and quantum field theory. Previous knowledge of general relativity at the level of a standard undergraduate-level introductory course is recommended, but all the relevant material is included for completion and reference. No previous knowledge of quantum field theory, or anything else beyond the standard undergraduate curriculum, is required. Advanced topics in relativity, such as causal structures, the Raychaudhuri equation, and the energy conditions are presented in detail. Once the required background is covered, concepts related to faster-than-light travel and time travel are discussed. After introducing tachyons in special relativity as a warm-up, exotic spacetime geometries in general relativity such as warp drives and wormholes are discussed and analyzed, including their limitations. Time travel paradoxes are also discussed in detail, including some of their proposed resolutions. * bshoshany@perimeterinstitute.ca arXiv:1907.04178v3 [gr-qc]

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Generalised Manifolds as Basic Objects of General Relativity

Cited by 6 publications

References 33 publications

Wormhole Time Machines and Multiple Histories

Wormhole Time Machines and Multiple Histories

New Foundations for Branching Space-Times

Lectures on faster-than-light travel and time travel

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