Band 49 (2012)
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Summer 2017 Astron 9 Week 5 Final Version
RELATIVITY OF SPACE AND TIME IN POPULAR SCIENCE RICHARD ANANTUA PREDESTINATION (MON JUL 31) REVIEW OF JUL 24, 26 & 28 • Flying atomic clocks, muon decay, light bending around stars and gravitational waves provide experimental confirmation of relativity • In 1919, Einstein’s prediction for the deflection of starlight was confirmed by • The 1971 Hafele-Keating experiment confirmed • The 1977 CERN muon experiment confirmed • In 2016 LIGO confirmed the existence of REVIEW OF JUL 24, 26 & 28 • Flying atomic clocks, muon decay, light bending around stars and gravitational waves provide experimental confirmation of relativity • In 1919, Einstein’s prediction for the deflection of starlight was confirmed by Sir Arthur Eddington • The 1971 Hafele-Keating experiment confirmed motional and gravitational time dilation • The 1977 CERN muon experiment confirmed motional time dilation • In 2016 LIGO confirmed the existence of gravitational waves TIME TRAVEL IN RELATIVITY • Methods of time travel theoretically possible in relativity are • (Apparently) faster than light travel – window into the past? • Closed timelike curved • (Apparent) paradoxes with time travel • Kill your grandfather – past time travel may alter seemingly necessary conditions for the future time traveler to have started the journey • Predestination - apparent cause of past event is in the future SPECIAL RELATIVISTIC VELOCITY ADDITION • In special relativity, no object or information can travel faster than light, a fact reflected in the relativistic law of composition of velocities v &v vAB v = $% %' A !" v$%v%' (& * ) vBC B C • vAB is the (1D) velocity of A with respect to B • vBC is the (1D) velocity of B with respect to C POP QUIZ - FASTER THAN LIGHT TRAVEL • A spaceship traveling at v>c is returning from a moving planet (L0 away right before the journey). -
Closed Timelike Curves Make Quantum and Classical Computing Equivalent
Closed Timelike Curves Make Quantum and Classical Computing Equivalent Scott Aaronson∗ John Watrous† MIT University of Waterloo Abstract While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to nontrivial insights in general relativity, quantum information, and other areas. In this paper we show that if CTCs existed, then quantum computers would be no more powerful than classical computers: both would have the (extremely large) power of the complexity class PSPACE, consisting of all problems solvable by a conventional computer using a polynomial amount of memory. This solves an open problem proposed by one of us in 2005, and gives an essentially complete understanding of computational complexity in the presence of CTCs. Following the work of Deutsch, we treat a CTC as simply a region of spacetime where a “causal consistency” condition is imposed, meaning that Nature has to produce a (probabilistic or quantum) fixed-point of some evolution operator. Our conclusion is then a consequence of the following theorem: given any quantum circuit (not necessarily unitary), a fixed-point of the circuit can be (implicitly) computed in polynomial space. This theorem might have independent applications in quantum information. 1 Introduction The possibility of closed timelike curves (CTCs) within general relativity and quantum gravity theories has been studied for almost a century [11, 15, 13]. A different line of research has sought to understand the implications of CTCs, supposing they existed, for quantum mechanics, computation, and information [9, 8, 5]. In this paper we contribute to the latter topic, by giving the first complete characterization of the computational power of CTCs. -
Light Rays, Singularities, and All That
Light Rays, Singularities, and All That Edward Witten School of Natural Sciences, Institute for Advanced Study Einstein Drive, Princeton, NJ 08540 USA Abstract This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics at the Institute for Advanced Study, and also at the 2020 New Zealand Mathematical Research Institute summer school in Nelson, New Zealand. Contents 1 Introduction 3 2 Causal Paths 4 3 Globally Hyperbolic Spacetimes 11 3.1 Definition . 11 3.2 Some Properties of Globally Hyperbolic Spacetimes . 15 3.3 More On Compactness . 18 3.4 Cauchy Horizons . 21 3.5 Causality Conditions . 23 3.6 Maximal Extensions . 24 4 Geodesics and Focal Points 25 4.1 The Riemannian Case . 25 4.2 Lorentz Signature Analog . 28 4.3 Raychaudhuri’s Equation . 31 4.4 Hawking’s Big Bang Singularity Theorem . 35 5 Null Geodesics and Penrose’s Theorem 37 5.1 Promptness . 37 5.2 Promptness And Focal Points . 40 5.3 More On The Boundary Of The Future . 46 1 5.4 The Null Raychaudhuri Equation . 47 5.5 Trapped Surfaces . 52 5.6 Penrose’s Theorem . 54 6 Black Holes 58 6.1 Cosmic Censorship . 58 6.2 The Black Hole Region . 60 6.3 The Horizon And Its Generators . 63 7 Some Additional Topics 66 7.1 Topological Censorship . 67 7.2 The Averaged Null Energy Condition . -
Terminator and Philosophy
ftoc.indd viii 3/2/09 10:29:19 AM TERMINATOR AND PHILOSOPHY ffirs.indd i 3/2/09 10:23:40 AM The Blackwell Philosophy and Pop Culture Series Series Editor: William Irwin South Park and Philosophy Edited by Robert Arp Metallica and Philosophy Edited by William Irwin Family Guy and Philosophy Edited by J. Jeremy Wisnewski The Daily Show and Philosophy Edited by Jason Holt Lost and Philosophy Edited by Sharon Kaye 24 and Philosophy Edited by Richard Davis, Jennifer Hart Weed, and Ronald Weed Battlestar Galactica and Philosophy Edited by Jason T. Eberl The Offi ce and Philosophy Edited by J. Jeremy Wisnewski Batman and Philosophy Edited by Mark D. White and Robert Arp House and Philosophy Edited by Henry Jacoby Watchmen and Philosophy Edited by Mark D. White X-Men and Philosophy Edited by Rebecca Housel and J. Jeremy Wisnewski ffirs.indd ii 3/2/09 10:23:40 AM TERMINATOR AND PHILOSOPHY I'LL BE BACK, THEREFORE I AM Edited by Richard Brown and Kevin S. Decker John Wiley & Sons, Inc. ffirs.indd iii 3/2/09 10:23:41 AM This book is printed on acid-free paper. Copyright © 2009 by John Wiley & Sons. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or trans- mitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com. -
Mind the Gap a Cognitive Perspective on the flow of Time in Physics
Mind the Gap A cognitive perspective on the flow of time in physics Master's Thesis History and Philosophy of Science Supervisor: Prof. dr. Dennis Dieks Utrecht University August 16th 2009 Annemarie Hagenaars Lange Hilleweg 31b 3073 BH Rotterdam Student number: 3203808 Preface The image on the title page of my thesis is The Persistence of Memory (1931), which is the most famous painting by Salvador Dali. This painting captures many standard issues that relate to time: relativity theory, clocks, memory, and the flow of time. This thesis is about the flow of time. As time moves on and never stops, so will the philosophical and scientific research on its flow be incomplete forever. Never in my life has time flown by as fast as it did this last year of my master's research. So many questions remain unanswered; so much works still needs to be done, while the months were passing like weeks and the weeks were passing like days. One year is too short, to dive into the fascinating river of time. To me it feels like this thesis is a first survey of the possibilities within the field of the philosophy of time. Time's passage has been a source of interest for quite a long time. When I was a child I kept diaries and memo-books to write down what happened each day in the hope I wouldn't forget it. Nowadays it is still a favorite game to exactly remember the date and time of special happenings and pinpoint those on my personal time line in my mind. -
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. -
Cosmic String Lensing and Closed Timelike Curves
PHYSICAL REVIEW D 72, 043532 (2005) Cosmic string lensing and closed timelike curves Benjamin Shlaer* and S.-H. Henry Tye† Laboratory for Elementary Particle Physics, Cornell University, Ithaca, New York 14853, USA (Received 3 March 2005; revised manuscript received 21 July 2005; published 31 August 2005) In an analysis of the gravitational lensing by two relativistic cosmic strings, we argue that the formation of closed timelike curves proposed by Gott is unstable in the presence of particles (e.g. the cosmic microwave background radiation). Because of the attractorlike behavior of the closed timelike curve, we argue that this instability is very generic. A single graviton or photon in the vicinity, no matter how soft, is sufficient to bend the strings and prevent the formation of closed timelike curves. We also show that the gravitational lensing due to a moving cosmic string is enhanced by its motion, not suppressed. DOI: 10.1103/PhysRevD.72.043532 PACS numbers: 98.80.Cq, 04.20.Gz, 04.60.Kz, 11.27.+d I. INTRODUCTION strings in the sense opposite to their motion becomes a CTC. This is sometimes called the Gott spacetime or Gott Although cosmic strings as the seed of structure forma- time machine. tion [1] has been ruled out by observations, their presence Although there is no proof that a time machine cannot at a lower level is still possible. Indeed, cosmic strings are exist in our world [13], their puzzling causal nature leads generically present in brane inflation in superstring theory, many physicists to believe that CTCs cannot be formed. and their properties are close to, but within all observatio- This skepticism has been encoded in Hawking’s chronol- nal bounds [2–7]. -
Closed Timelike Curves Via Postselection: Theory and Experimental Test of Consistency
Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Lloyd, Seth, et al. "Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency." American Physical Society, 2011, 106:4, © 2011 The American Physical Society. As Published http://dx.doi.org/10.1103/PhysRevLett.106.040403 Publisher American Physical Society Version Final published version Citable link http://hdl.handle.net/1721.1/63096 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. week ending PRL 106, 040403 (2011) PHYSICAL REVIEW LETTERS 28 JANUARY 2011 Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency Seth Lloyd,1 Lorenzo Maccone,1 Raul Garcia-Patron,1 Vittorio Giovannetti,2 Yutaka Shikano,1,3 Stefano Pirandola,1 Lee A. Rozema,4 Ardavan Darabi,4 Yasaman Soudagar,4 Lynden K. Shalm,4 and Aephraim M. Steinberg4 1xQIT, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA 2NEST-CNR-INFM & Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126, Pisa, Italy 3Department of Physics, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro, Tokyo, 152-8551, Japan 4CQIQC, IOS, Department of Physics, University of Toronto, Canada M5S 1A7 (Received 12 May 2010; revised manuscript received 22 November 2010; published 27 January 2011) Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can interact with its former self in the past. -
Causality Violation and Singularities
TIT/HEP-302/COSMO-59 October, 1995 Causality violation and singularities Kengo Maeda 1 and Akihiro Ishibashi 2 Department of Physics, Tokyo Institute of Technology, Oh-Okayama Meguro-ku, Tokyo 152, Japan ABSTRACT We show that singularities necessarily occur when a boundary of causality violating set exists in a space-time under the physically suitable assumptions except the global causality condition in the Hawking-Penrose singularity theo- rems. Instead of the global causality condition, we impose some restrictions on the causality violating sets to show the occurrence of singularities. 1 Introduction Space-time singularities have been discussed for a long time in general relativity. In 1970, Hawking and Penrose[1] showed that singularities, which mean causal arXiv:gr-qc/9606075v1 27 Jun 1996 geodesic incompleteness, could occur in a space-time under seemingly reasonable conditions in classical gravity. Their singularity theorem has an important impli- cation that our universe has an initial singularity if we do not consider quantum effects. However, this theorem is physically unsatisfactory in the sense that the causality requirement everywhere in a space-time seems too restrictive. We can only experience local events and there is no guarantee that the causality holds in the entire universe. As is well known, Kerr type black holes have causality violating sets if the space-time is maximally extended. Therefore, it will be im- portant to investigate occurrence of singularities in a space-time in which the global causality condition is violated. There are some works on a causality violation concerned with the occurrence of singularity. Tipler[2,3] showed that any attempt to evolve closed timelike curves from an initial regular Cauchy data would cause singularities to form in a 1e-mail:[email protected] 2e-mail:[email protected] 1 space-time. -
The Quantum Mechanics of the Present
The quantum mechanics of the present Lee Smolina and Clelia Verdeb a Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2J 2Y5, Canada and Department of Physics and Astronomy, University of Waterloo and Department of Philosophy, University of Toronto bCorso Concordia, 20129 - Milano April 21, 2021 Abstract We propose a reformulation of quantum mechanics in which the distinction be- tween definite and indefinite becomes the fundamental primitive. Inspired by suggestions of Heisenberg, Schrodinger and Dyson that the past can’t be described in terms of wavefunctions and operators, so that the uncertainty prin- ciple does not apply to past events, we propose that the distinction between past, present and future is derivative of the fundamental distinction between indefinite and definite. arXiv:2104.09945v1 [quant-ph] 20 Apr 2021 We then outline a novel form of presentism based on a phenomonology of events, where an event is defined as an instance of transition between indefinite and definite. Neither the past nor the future fully exist, but for different reasons. We finally suggest reformulating physics in terms of a new class of time coordinates in which the present time of a future event measures a countdown to the present moment in which that event will happen. 1 Contents 1 Introduction 2 2 Constructions of space and time 3 3 A phenomonology of present events 4 3.1 Thedefiniteandtheindefinite. .... 5 3.2 Thepast ....................................... 6 3.3 Thefuture ...................................... 6 3.4 Causalitywithoutdeterminism . ..... 7 4 Thequantummechanicsofdefiniteandindefinite 7 5 Theframeofreferenceforanobserverinapresentmoment 10 6 Closing remarks 11 1 Introduction The idea we will discuss here has arisin from time to time since the invention of quan- tum mechanics. -
Arxiv:0710.4474V1 [Gr-Qc] 24 Oct 2007 I.“Apdie Pctmsadspruia Travel Superluminal and Spacetimes Drive” “Warp III
Exotic solutions in General Relativity: Traversable wormholes and “warp drive” spacetimes Francisco S. N. Lobo∗ Centro de Astronomia e Astrof´ısica da Universidade de Lisboa, Campo Grande, Ed. C8 1749-016 Lisboa, Portugal and Institute of Gravitation & Cosmology, University of Portsmouth, Portsmouth PO1 2EG, UK (Dated: February 2, 2008) The General Theory of Relativity has been an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes, gravitational radiation to the cosmological models, predicting a primordial beginning, namely the big-bang. All these solutions have been obtained by first considering a plausible distri- bution of matter, i.e., a plausible stress-energy tensor, and through the Einstein field equation, the spacetime metric of the geometry is determined. However, one may solve the Einstein field equa- tion in the reverse direction, namely, one first considers an interesting and exotic spacetime metric, then finds the matter source responsible for the respective geometry. In this manner, it was found that some of these solutions possess a peculiar property, namely “exotic matter,” involving a stress- energy tensor that violates the null energy condition. These geometries also allow closed timelike curves, with the respective causality violations. Another interesting feature of these spacetimes is that they allow “effective” superluminal travel, although, locally, the speed of light is not surpassed. These solutions are primarily useful as “gedanken-experiments” and as a theoretician’s probe of the foundations of general relativity, and include traversable wormholes and superluminal “warp drive” spacetimes. Thus, one may be tempted to denote these geometries as “exotic” solutions of the Einstein field equation, as they violate the energy conditions and generate closed timelike curves. -
KRITERION | Journal of Philosophy
KRITERION JOURNAL OF PHILOSOPHY Volume 30, Issue 2 2016 Special issue: New Developments in Philosophy of Time Guest edited by Florian Fischer Florian Fischer: Philosophy of time: A slightly opinionated intro- duction ............................................................3 Jesse M. Mulder: Defining Original Presentism . 29 Florian Fischer: Carnap's Logic of Science and Reference to the Present Moment ..............................................61 Cord Friebe: Time Order, Time Direction, and the Presentist's View on Spacetime ................................................91 Sonja Deppe: The Mind-Dependence of the Relational Structure of Time (or: What Henri Bergson Would Say to B-theorists) . 107 Pamela Zinn: Lucretius On Time and Its Perception . .125 EDITORIAL KRITERION { Journal of Philosophy is a forum for contributions in any field of analytic philosophy. We welcome submissions of previously unpublished papers, not under consideration for publication anywhere else. Submissions are reviewed in double-blind peer review mode. Con- tributions should meet the following conditions: (1) The content must be philosophical. (2) The language must be intelligible to a broader readership. (3) The contribution must contain a traceable argumentation. The length should be between 4000 and 8000 words. Only contributions in English (preferred) and German are accepted. IMPRESSUM Editors-in-Chief: Christian J. Feldbacher-Escamilla, Alexander Gebharter Editorial Board: Albert J. J. Anglberger, Laurenz Hudetz, Christine Schurz, Christian Wallmann Address: Franziskanergasse 1, 5020 Salzburg, Austria. E-Mail: [email protected] Web: http://www.kriterion-journal-of-philosophy.org Indexing: KRITERION { Journal of Philosophy is indexed and abstracted by The Philosopher's Index and EBSCOhost Humanities Source. Infor- mation about the journal's ranking is available at SJR. The journal was also approved of satisfying the ERIH (European Reference Index for the Humanities) criteria: ERIH PLUS.