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Closed Timelike Curves, Singularities and Causality: a Survey from Gödel to Chronological Protection
Closed Timelike Curves, Singularities and Causality: A Survey from Gödel to Chronological Protection Jean-Pierre Luminet Aix-Marseille Université, CNRS, Laboratoire d’Astrophysique de Marseille , France; Centre de Physique Théorique de Marseille (France) Observatoire de Paris, LUTH (France) [email protected] Abstract: I give a historical survey of the discussions about the existence of closed timelike curves in general relativistic models of the universe, opening the physical possibility of time travel in the past, as first recognized by K. Gödel in his rotating universe model of 1949. I emphasize that journeying into the past is intimately linked to spacetime models devoid of timelike singularities. Since such singularities arise as an inevitable consequence of the equations of general relativity given physically reasonable assumptions, time travel in the past becomes possible only when one or another of these assumptions is violated. It is the case with wormhole-type solutions. S. Hawking and other authors have tried to save the paradoxical consequences of time travel in the past by advocating physical mechanisms of chronological protection; however, such mechanisms remain presently unknown, even when quantum fluctuations near horizons are taken into account. I close the survey by a brief and pedestrian discussion of Causal Dynamical Triangulations, an approach to quantum gravity in which causality plays a seminal role. Keywords: time travel; closed timelike curves; singularities; wormholes; Gödel’s universe; chronological protection; causal dynamical triangulations 1. Introduction In 1949, the mathematician and logician Kurt Gödel, who had previously demonstrated the incompleteness theorems that broke ground in logic, mathematics, and philosophy, became interested in the theory of general relativity of Albert Einstein, of which he became a close colleague at the Institute for Advanced Study at Princeton. -
Quantum Time Machines Are Expectation Values of the Scalar field Squared and Stress- Quantum-Mechanically Stable
Quantum time machine Pedro F. Gonz´alez-D´ıaz Centro de F´ısica “Miguel Catal´an”, Instituto de Matem´aticas y F´ısica Fundamental, Consejo Superior de Investigaciones Cient´ıficas, Serrano 121, 28006 Madrid (SPAIN) (December 6, 1997) The continuation of Misner space into the Euclidean region is seen to imply the topological re- striction that the period of the closed spatial direction becomes time-dependent. This restriction results in a modified Lorentzian Misner space in which the renormalized stress-energy tensor for quantized complex massless scalar fields becomes regular everywhere, even on the chronology hori- zon. A quantum-mechanically stable time machine with just the sub-microscopic size may then be constructed out of the modified Misner space, for which the semiclassical Hawking’s chronology protection conjecture is no longer an obstruction. PACS number(s): 04.20.Gz, 04.62.+v I. INTRODUCTION some attempts intended to violate it [14,15], this con- jecture has survived rather forcefully [16]. However, the After the seminal papers by Morris, Thorne and Yurt- realm where chronology protection holds is semiclassical sever [1], the notion of a time machine has jumped from physics, as it is for all hitherto proposed time machines. the pages of science fiction books to those of scientific Actually, because spacetime foam [17] must entail strong journals, giving rise to a recent influx of papers [2-7] violations of causal locality everywhere, one would expect and books [8,9] on the subject. Several potentially use- the Hawking’s conjecture to be inapplicable in the frame- ful models for time machines have since been proposed, work of quantum gravity proper, and that the divergences including the wormhole of Thorne et al. -
Quantum Fluctuations and Thermodynamic Processes in The
Quantum fluctuations and thermodynamic processes in the presence of closed timelike curves by Tsunefumi Tanaka A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Montana State University © Copyright by Tsunefumi Tanaka (1997) Abstract: A closed timelike curve (CTC) is a closed loop in spacetime whose tangent vector is everywhere timelike. A spacetime which contains CTC’s will allow time travel. One of these spacetimes is Grant space. It can be constructed from Minkowski space by imposing periodic boundary conditions in spatial directions and making the boundaries move toward each other. If Hawking’s chronology protection conjecture is correct, there must be a physical mechanism preventing the formation of CTC’s. Currently the most promising candidate for the chronology protection mechanism is the back reaction of the metric to quantum vacuum fluctuations. In this thesis the quantum fluctuations for a massive scalar field, a self-interacting field, and for a field at nonzero temperature are calculated in Grant space. The stress-energy tensor is found to remain finite everywhere in Grant space for the massive scalar field with sufficiently large field mass. Otherwise it diverges on chronology horizons like the stress-energy tensor for a massless scalar field. If CTC’s exist they will have profound effects on physical processes. Causality can be protected even in the presence of CTC’s if the self-consistency condition is imposed on all processes. Simple classical thermodynamic processes of a box filled with ideal gas in the presence of CTC’s are studied. If a system of boxes is closed, its state does not change as it travels through a region of spacetime with CTC’s. -
The Quantum Physics of Chronology Protection
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server The quantum physics of chronology protection Matt Visser Physics Department, Washington University, Saint Louis, Missouri 63130-4899, USA. 2 April 2002; LATEX-ed April 8, 2002 Abstract: This is a brief survey of the current status of Stephen Hawking’s “chronol- ogy protection conjecture”. That is: “Why does nature abhor a time machine?” I’ll discuss a few examples of spacetimes containing “time ma- chines” (closed causal curves), the sorts of peculiarities that arise, and the reactions of the physics community. While pointing out other possibilities, this article concentrates on the possibility of “chronology protection”. As Stephen puts it: It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians. To appear in: The future of theoretical physics and cosmology; Proceedings of the conference held in honour of Stephen Hawking on the occasion of his 60’th birthday. (Cambridge, 7–10 January 2002.) E-mail: [email protected] Homepage: http://www.physics.wustl.edu/~visser Archive: gr-qc/0204022 Permanent address after 1 July 2002: School of Mathematics and Computer Science, Victoria University, PO Box 600, Wellington, New Zealand. [email protected] 1 The quantum physics of chronology protection Simply put, chronology protection is the assertion that nature abhors a time machine. In the words of Stephen Hawking [1]: It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians. -
Parallel Worlds
www.Ael.af Kaku_0385509863_4p_all_r1.qxd 10/27/04 7:07 AM Page i PARALLEL WORLDS www.Ael.af Kaku_0385509863_4p_all_r1.qxd 10/27/04 7:07 AM Page ii www.Ael.af Kaku_0385509863_4p_all_r1.qxd 10/27/04 7:07 AM Page iii Also by Michio Kaku Beyond Einstein Hyperspace Visions Einstein’s Cosmos www.Ael.af Kaku_0385509863_4p_all_r1.qxd 10/27/04 7:07 AM Page iv MICHIO KAKU DOUBLEDAY New York London Toronto Sydney Auckland www.Ael.af Kaku_0385509863_4p_all_r1.qxd 10/27/04 7:07 AM Page v PARALLEL WORLDS A JOURNEY THROUGH CREATION, HIGHER DIMENSIONS, AND THE FUTURE OF THE COSMOS www.Ael.af Kaku_0385509863_4p_all_r1.qxd 10/27/04 7:07 AM Page vi published by doubleday a division of Random House, Inc. doubleday and the portrayal of an anchor with a dolphin are regis- tered trademarks of Random House, Inc. Book design by Nicola Ferguson Illustrations by Hadel Studio Library of Congress Cataloging-in-Publication Data Kaku, Michio. Parallel worlds : a journey through creation, higher dimensions, and the future of the cosmos/Michio Kaku.—1st ed. p. cm. Includes bibliographical references 1. Cosmology. 2. Big bang theory. 3. Superstring theories. 4. Supergravity. I. Title. QB981.K134 2004 523.1—dc22 2004056039 eISBN 0-385-51416-6 Copyright © 2005 Michio Kaku All Rights Reserved v1.0 www.Ael.af Kaku_0385509863_4p_all_r1.qxd 10/27/04 7:07 AM Page vii This book is dedicated to my loving wife, Shizue. www.Ael.af Kaku_0385509863_4p_all_r1.qxd 10/27/04 7:07 AM Page viii www.Ael.af Kaku_0385509863_4p_all_r1.qxd 10/27/04 7:07 AM Page ix CONTENTS acknowledgments xi -
The Quantum Physics of Chronology Protection
The quantum physics of chronology protection Matt Visser Physics Department, Washington University, Saint Louis, Missouri 63130-4899, USA. 2 April 2002; Additional references 17 April 2002; LATEX-ed February 3, 2008 Abstract: This is a brief survey of the current status of Stephen Hawking’s “chronol- ogy protection conjecture”. That is: “Why does nature abhor a time machine?” I’ll discuss a few examples of spacetimes containing “time ma- chines” (closed causal curves), the sorts of peculiarities that arise, and the reactions of the physics community. While pointing out other possibilities, this article concentrates on the possibility of “chronology protection”. As Stephen puts it: It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians. To appear in: The future of theoretical physics and cosmology; Proceedings of the conference held in honour of Stephen Hawking on the occasion of his 60’th birthday. (Cambridge, 7–10 January 2002.) arXiv:gr-qc/0204022v2 17 Apr 2002 E-mail: [email protected] Homepage: http://www.physics.wustl.edu/˜visser Archive: gr-qc/0204022 Permanent address after 1 July 2002: School of Mathematics and Computer Science, Victoria University, PO Box 600, Wellington, New Zealand. [email protected] 1 The quantum physics of chronology protection Simply put, chronology protection is the assertion that nature abhors a time machine. In the words of Stephen Hawking [1]: It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians. -
Take a Ride on a Time Machine*
1 Take a Ride on a Time Machine* John Earman, Christopher Smeenk, and Christian Wüthrich 1. Introduction Early in his career Arthur Fine made contributions to the philosophy of space and time. But he was so thoroughly seduced by the verdammt quantum that he never returned to this field. Although our project on the twin topics of time travel and time machines cannot take any specific directions from Arthur’s pronouncements on these topics–for there are none–we have been guided by his views on the relation between science and the philosophy of science. In the “Afterword” to The Shaky Game (1986, 1996) Arthur comments on how his Natural Ontological Attitude (NOA) impacts the agenda of philosophy. To pursue NOA means to situate humanistic concerns about the sciences within the context of ongoing scientific concerns, to reach out with our questions and interests to scientist’s questions and interests–and to pursue inquiry as a common endeavor ... For me it has frequently meant learning new science in order to pursue standard topics on the philosophical agenda. (1996, 174-175) The central message here can be divorced from the controversial aspects of NOA: in a nutshell, Arthur is telling us to see philosophy of science as continuous with science. In his PSA Presidential Address, “Interpreting Science” (1988), Arthur spells out what this means in concrete terms: it means that philosophers of science should seek to “engage with active science in a more or less equal basis” (p. 9), that they should see themselves as “engaged cooperatively with scientists” (p. 10). -
A Four-Dimensional Generalization of Misner Space in Curved Spacetime
Journal of Physics Communications PAPER • OPEN ACCESS Related content - Closed Timelike Curves in Type II Non- A four-dimensional generalization of Misner space Vacuum Spacetime Faizuddin Ahmed in curved spacetime - A Type D Non-Vacuum Spacetime with Causality Violating Curves, and Its Physical Interpretation To cite this article: Faizuddin Ahmed 2018 J. Phys. Commun. 2 035036 Faizuddin Ahmed - Shear-free, irrotational, geodesic, anisotropic fluid cosmologies Des J McManus and Alan A Coley View the article online for updates and enhancements. This content was downloaded from IP address 131.169.5.251 on 06/11/2019 at 20:53 J. Phys. Commun. 2 (2018) 035036 https://doi.org/10.1088/2399-6528/aab37d PAPER A four-dimensional generalization of Misner space in curved OPEN ACCESS spacetime RECEIVED 14 November 2017 Faizuddin Ahmed REVISED Ajmal College of Arts and Science, Dhubri-783324, Assam, India 8 February 2018 ACCEPTED FOR PUBLICATION E-mail: [email protected] 2 March 2018 Keywords: exact solution, causality violation, EMT Type I fluid PUBLISHED 21 March 2018 Original content from this Abstract work may be used under We present a topologically trivial nonvacuum solution of the Einstein’s field equations in curved the terms of the Creative Commons Attribution 3.0 spacetime with stress-energy tensor Type I fluid, satisfying the energy conditions. The metric admits licence. closed timelike curves which appear after a certain instant of time, and the spacetime is a four- Any further distribution of this work must maintain dimensional generalization of flat Misner space in curved spacetime. attribution to the author(s) and the title of the work, journal citation and DOI. -
Closed Timelike Curves, Singularities and Causality: a Survey from Gödel to Chronological Protection
universe Review Closed Timelike Curves, Singularities and Causality: A Survey from Gödel to Chronological Protection Jean-Pierre Luminet Review Observatoire de Paris (LUTH), Centre de Physique Théorique (CPT), Laboratoire d’Astrophysique de Closed Timelike Curves,Marseille (LAM), Singularities Aix-Marseille Universit andé, CNRS, Causality: LAM, 38 rue F. A Joliot-Curie, Survey 13013 Marseille, France; from Gödel to [email protected] Protection Abstract: I give a historical survey of the discussions about the existence of closed timelike curves in Jean-Pierre Luminet general relativistic models of the universe, opening the physical possibility of time travel in the past, as first recognized by K. Gödel in his rotating universe model of 1949. I emphasize that journeying Observatoire de Paris (LUTH), Centre de Physique Théorique (CPT), Laboratoire d’Astrophysique de Marseille (LAM),into Aix-Marseille the past Université, is intimately CNRS, LAM, linked 38 rue to F. Joliot-Curie, spacetime 13013 models Marseille, devoid France; of timelike singularities. Since such [email protected] arise as an inevitable consequence of the equations of general relativity given physically Abstract:reasonable I give a historical assumptions, survey of time the discussions travel in theabout past the becomesexistence of possible closed timelike only curves when one or another of these in generalassumptions relativistic ismodels violated. of the Ituniverse, is the caseopening with the wormhole-typephysical possibility solutions.of time travel S. in Hawking the and other authors past, haveas first triedrecognized to “save” by K. Gödel the paradoxical in his rotating consequences universe model of 1949. time I travelemphasize in thethat pastjour- by advocating physical neyingmechanisms into the past is ofintimately chronological linked to spacet protection;ime models however, devoid of such timelike mechanisms singularities. -
Closed Timelike Curves
Paperpresented at the 13th Int. Conf. on General Relativity and Gravitation 295 Cordoba, Argentina, 1992: Part 1, Plenary Lectures Closed timelike curves Kip S. Thorne California lnstitute of Technology, Pasadena, California. 9]]25, and Institute for Theoretical Physics, UCSB, Santa Barbara, California. 93106 Abstract. This lecture reviews recent research on closed timelike curves (CTCS), including these questions: Do the laws of physics prevent CTCs from ever forming in classical spacetime? If so, by what physical mechanism are C'I‘Cs prevented? Can the laws of physics be adapted in any reasonable way to a. spacetime that contains C'I‘Cs, or do they necessarily give nonsense? What insights into quantum gravity can one gain by asking questions such as these? 1. Introduction Much of the forefront of theoretical physics deals with situations so extreme that there is no hope to probe them experimentally. Such, largely, was the case nearly a, century ago for Einstein’s formulation of general relativity, and such is the case today for the attempt to quantize gravity. ln these situations, thought experiments can be helpful. Of all thought experiments, perhaps the most helpful are those that push the laws of physics in the most extreme ways. A class of such thought experiments, which I and others have found useful in the last few years, asks [l] What constraints do the laws of physics place on the activities of an arbitrarily advanced civilization? ln asking this question, we have in mind all the laws of physics that govern our universe, taken together including those, such as quantum gravity, that are not yet well understood, and others, such as classical general relativity, that are, and with each set of laws holding sway only in its own domain of validity. -
Evolution of Time Concept in Physics and in Philosophy
Physics International Original Research Paper Evolution of Time Concept in Physics and in Philosophy 1Sivaram, C., 2Kenath Arun and 2Kiren, O.V. 1Indian Institute of Astrophysics, Bangalore-560 034, India 2Department of Physics, Christ Junior College, Bangalore-560 029, India Article history Abstract: What is ‘time’? This is a question that has perplexed many a Received: 07-02-2015 physicist and philosophers alike. The perception of the passage of time Revised: 25-03-2015 appears ingrained in all biological systems where growth, evolution and Accepted: 25-03-2015 decay of objects, etc. are measurable indicators of the passage of time. Here we look at various physical models of time, from Newtonian to Corresponding Author: Kenath Arun relativistic. We also explore the idea of perception of time including the Department of Physics, Christ Junior possibility of travel into the past and future. Time in the quantum world College, Bangalore-560 029, India (as measured by differences in energy transitions of various levels) and Email: [email protected] classical world (as energy transformations) are also discussed. Keywords: Newtonian Time, Relativistic Time, Steady State Universe, Multiverse, Tachyon, Closed Time-like Curves, Arrow of Time Introduction up development of accurate pendulum clocks improving on earlier devises like sundials, water clocks and The perception of the passage of time, either periodic hourglass sand clocks etc.). or continuous, appears ingrained in all living (biological) The sexadecimal measure, introduced by the systems. The diurnal cycle and the annual passage of Babylonians applied both to measurements of angles seasons create visible changes in ambient parameters and time, the hour being sixty minutes and a minute influencing the behaviour of organized systems which being sixty seconds. -
Closed Timelike Curves and Causality Violation
Closed timelike curves and causality violation Francisco S. N. Lobo∗ Centro de Astronomia e Astrof´ısica da Universidade de Lisboa, Campo Grande, Ed. C8 1749-016 Lisboa, Portugal (Dated: August 9, 2010) The conceptual definition and understanding of time, both quantitatively and qualitatively is of the utmost difficulty and importance. As time is incorporated into the proper structure of the fabric of spacetime, it is interesting to note that General Relativity is contaminated with non-trivial geometries which generate closed timelike curves. A closed timelike curve (CTC) allows time travel, in the sense that an observer that travels on a trajectory in spacetime along this curve, may return to an event before his departure. This fact apparently violates causality, therefore time travel and it’s associated paradoxes have to be treated with great caution. The paradoxes fall into two broad groups, namely the consistency paradoxes and the causal loops. A great variety of solutions to the Einstein field equations containing CTCs exist and it seems that two particularly notorious features stand out. Solutions with a tipping over of the light cones due to a rotation about a cylindrically symmetric axis and solutions that violate the energy conditions. All these aspects are analyzed in this review paper. Contents I. Introduction 1 II. Stationary and axisymmetric solutions generating CTCs 2 A. Van Stockum spacetime 3 1. The Interior solution 4 2. The Exterior solution 4 3. Chronology violation region 5 B. The G¨odel Universe 5 C. Gott Cosmic String time machine 6 1. Gravitational field of a Cosmic String 6 2.