Cauchy problem in spacetimes with closed timelike curves

Friedman, John L.; Morris, Michael S.; Новиков, И. Д.; Echeverria, Fernando; Klinkhammer, Gunnar; Thorne, Kip S.; Yurtsever, Ulvi

doi:10.1103/physrevd.42.1915

Cited by 210 publications

(237 citation statements)

References 1 publication

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“…While this variation does not require a modal step as suspect as the original version, neither (1) nor (2) are obviously true -and it is unclear how they can be established without begging the question. 33 One response to the challenge is simply to abandon Gödel's modal argument and formulate a different argument to the same effect. Consider an alternative argument that adopts a divide and conquer strategy rather than relying on a shaky modal step (suggested to us by John Earman).…”

Section: Implications Of Time Travelmentioning

confidence: 99%

“…CCs are imposed to prevent such inconsistencies. John Friedman et al (1990) encode the demand that CCs are operative in their principle of self-consistency, which "states that the only solutions to the laws of physics that can occur locally in the real Universe are those which are globally self-consistent." 8 This principle guarantees the validity of the local-to-global property, at the cost of introducing non-trivial CCs.…”

Section: Logical Impossibility: the Grandfather Paradoxmentioning

confidence: 99%

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Time Travel and Time Machines

Smeenk

Wüthrich

2011

Oxford Handbooks Online

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This paper is an enquiry into the logical, metaphysical, and physical possibility of time travel understood in the sense of the existence of closed worldlines that can be traced out by physical objects. We argue that none of the purported paradoxes rule out time travel either on grounds of logic or metaphysics. More relevantly, modern spacetime theories such as general relativity seem to permit models that feature closed worldlines. We discuss, in the context of Gödel's infamous argument for the ideality of time based on his eponymous spacetime, what this apparent physical possibility of time travel means. Furthermore, we review the recent literature on so-called time machines, i.e., of devices that produce closed worldlines where none would have existed otherwise. Finally, we investigate what the implications of the quantum behaviour of matter for the possibility of time travel might be and explicate in what sense time travel might be possible according to leading contenders for full quantum theories of gravity such as string theory and loop quantum gravity.

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Section: Implications Of Time Travelmentioning

confidence: 99%

Section: Logical Impossibility: the Grandfather Paradoxmentioning

confidence: 99%

Time Travel and Time Machines

Smeenk

Wüthrich

2011

Oxford Handbooks Online

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“…Here, the noncontractible loops occur at the very largest scale. But there could also be noncontractible loops from nontrivial topology at the very smallest scale, possibly related to the so-called spacetime foam [7][8][9][10][11][12][13][14]. The main question is then whether or not a foam-like structure of spacetime could give rise to some kind of CPT anomaly.…”

Section: Introductionmentioning

confidence: 99%

Spacetime foam,CPTanomaly, and photon propagation

2004

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The CPT anomaly of certain chiral gauge theories has been established previously for flat multiply connected spacetime manifolds M of the type R 3 × S 1 , where the noncontractible loops have a minimal length. In this article, we show that the CPT anomaly also occurs for manifolds where the noncontractible loops can be arbitrarily small. Our basic calculation is performed for a flat noncompact manifold with a single "puncture," namely M = R 2 × (R 2 \ {0}). A hypothetical spacetime foam might have many such punctures (or other structures with similar effects). Assuming the multiply connected structure of the foam to be time independent, we present a simple model for photon propagation, which generalizes the single-puncture result. This model leads to a modified dispersion law of the photon. Observations of high-energy photons (gamma-rays) from explosive extragalactic events can then be used to place an upper bound on the typical length scale of these punctures.

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“…There are several papers in which simplest hyperbolic equations on non-globally hyperbolic manifolds were discussed [10] - [12]. The purpose of this work to study the wave equations on manifolds, which contain closed timelike curves.…”

Section: Introductionmentioning

confidence: 99%

Cauchy problem on non-globally hyperbolic space-times

2008

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Solutions of the Cauchy problem for the wave equation on a non-globally hyperbolic spacetime, which contains closed timelike curves (time machines) are considered. It is proved, that there exists a solution of the Cauchy problem, it is discontinuous and in some sense unique for arbitrary initial conditions, which are given on a hypersurface at time, that precedes the formation of closed timelike curves (CTC). If the hypersurface of initial conditions intersects the region containing CTC, then the solution of the Cauchy problem exists only for such initial conditions, that satisfy a certain requirement of self-consistency.

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Cauchy problem in spacetimes with closed timelike curves

Cited by 210 publications

References 1 publication

Time Travel and Time Machines

Time Travel and Time Machines

Spacetime foam,CPTanomaly, and photon propagation

Cauchy problem on non-globally hyperbolic space-times

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