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Arxiv:1911.08602V1 [Gr-Qc] 19 Nov 2019
Causality violation without time-travel: closed lightlike paths in G¨odel'suniverse Brien C. Nolan Centre for Astrophysics and Relativity, School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland.∗ We revisit the issue of causality violations in G¨odel'suniverse, restricting to geodesic motions. It is well-known that while there are closed timelike curves in this spacetime, there are no closed causal geodesics. We show further that no observer can communicate directly (i.e. using a single causal geodesic) with their own past. However, we show that this type of causality violation can be achieved by a system of relays: we prove that from any event P in G¨odel'suniverse, there is a future-directed lightlike path - a sequence of future-directed null geodesic segments, laid end to end - which has P as its past and future endpoints. By analysing the envelope of the family of future directed null geodesics emanating from a point of the spacetime, we show that this lightlike path must contain a minimum of eight geodesic segments, and show further that this bound is attained. We prove a related general result, that events of a time orientable spacetime are connected by a (closed) timelike curve if and only if they are connected by a (closed) lightlike path. This suggests a means of violating causality in G¨odel'suniverse without the need for unfeasibly large accelerations, using instead a sequence of light signals reflected by a suitably located system of mirrors. I. INTRODUCTION: GODEL'S¨ UNIVERSE In 1949, Kurt G¨odel[1]published a solution of Einstein's equations which provides what appears to be the first example of a spacetime containing closed timelike curves (CTCs). -
You Zombies, Click and a Novel, 1632, Both of Which Are Available Online from Links in the Handout
Instructor's notes to F402 Time Travel in Science Fiction Session 1 – Introduction Welcome to F402, Time Travel in Science Fiction. The objective of this course is to help you to read, understand and enjoy stories in the genre. The course is in two parts; the first is Today's lecture and discussion on the genre while the second is class discussions of two stories of opposite types. click The reading assignment consists of a short story, All You Zombies, click and a novel, 1632, both of which are available online from links in the handout. click For the convenience of those who prefer dead trees, I have listed a number of anthologies1 containing All You Zombies. Reading Assignment for Sessions 2-3 click All You Zombies is one of two tour de force stories by Robert A. Heinlein that left their mark on the genre for decades. Please read All You Zombies prior to the next session click and 1632 click click Part One, chapters 1-14 prior to the third session. Esc Session 1 Keep in mind that science fiction is a branch of literature, so the normal criteria of, e.g., characterization, consistency, continuity, plot structure, style, apply; I welcome comments, especially from those who have expertise in those areas. In addition, while a science fiction author must rely on the willing suspension of disbelief, he should do so sparingly. There is a lapse of continuity in 1632 between chapters 8 and 9; see whether you can spot it. I will suggest specific discussion points to start each discussion, but please bring up any other issues that you believe to be important or interesting. -
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. -
On Closed Timelike Curves, Cosmic Strings and Conformal Invariance Tuesday, 8 October 2019 12:00 (20 Minutes)
The Time Machine Factory [unspeakable, speakable] on Time Travel -TM2019 Contribution ID: 1 Type: talk On Closed Timelike Curves, Cosmic Strings and Conformal Invariance Tuesday, 8 October 2019 12:00 (20 minutes) Abstract In general relativity theory (GRT) one can construct solutions which are related to real physical objects. The most famous one is the black hole solution. One now believes that in the center of many galaxies there is a rotating super-massive black hole, the Kerr black hole. Because there is an axis of rotation, the Kerr solution is a member of the family of the axially symmetric solutions of the Einstein equations. A legitimate ques- tion could be: are there other axially or cylindrically symmetric asymptotically flat solutions of the equations of Einstein with a classical or non-classical matter distribution and with correct asymptotical behavior, just as the Kerr solution? Many attempts are made, such as the Weyl-, Papapetrou- and Van Stockum solution. None of these attempts result is physically acceptable solution. Often, these solutions possess closed timelike curves (CTC’s). The possibility of the formation of CTC’s in GRT seems to be an obstinate problem tosolve in GRT. At first glance, it seems possible to construct in GRT causality violating solutions. CTC’s suggestthe possibility of time-travel with its well-known paradoxes. Although most physicists believe that Hawking’s chronology protection conjecture holds in our world, it can be alluring to investigate the mathematical under- lying arguments of the formation of CTC’s. There are several spacetimes that can produce CTC’s. Famous is the Tipler-cylinder. -
Minkowski Space-Time and Einstein's Now Conundrum
NeuroQuantology | May 2018 | Volume 16 | Issue 5 | Page 23-30 | doi: 10.14704/nq.2018.16.5.1345 Sorli A., Minkowski Space-time and Einstein’s Now Conundrum Minkowski Space-time and Einstein’s Now Conundrum Amrit Sorli 1*, Steve Kaufman 1, Davide Fiscaletti 2 ABSTRACT The Minkowski formula X4=ict indicates that time t does not express the 4th dimension of space-time, i.e., X4 is not t. Therefore, Minkowski space-time is not a 3D+T manifold, it is 4D. The 4D manifold has 4 spatial dimensions and is timeless, in the sense that it does not contain some physical time in wh ich material changes run. In physics we experience the timelessness of 4D space as “Einstein’s Now.” From this perspective, the time that we measure with clocks is just the sequential numerical order of changes, i.e. motions that run in the timeless space of Now. On the other hand, past and future are nothing more than psychological or conceptual realities that derive from the neuronal activity of the brain. Therefore, “time flow” and “arrow of time” have only a mathematical existence. Key Words: Now, Time, Space, Space-Time, GPS, Closed Timeline Curve, Arrow of Time DOI Number: 10.14704/nq.201 8.16.5.1345 NeuroQuantology 2018; 16(5):23-30 Introduction system S, if complex enough, can be separated into 23 Today, 130 years after the pioneering work of a subsystem S2 whose dynamics is described, and Ernst Mach regarding the interpretation of time as another cyclic subsystem S1 which behaves as a a measure of the changes of things, the related clock and that, as a consequence of the gauge ideas that time cannot be considered as a primary invariance, this separation may be made in many physical reality that flows on its own in the ways. -
The Blue Box White Paper
The Blue Box White Paper Doctor Benjamin K. Tippetta Gallifrey Polytechnic Institute Doctor David Tsangb Gallifrey Institute of Technology (GalTech) (Dated: October 31, 2013) This white paper is an explanation of Ben and Dave’s TARDIS time machine, written for laypeople who are interested in time travel, but have no technical knowledge of Einstein’s Theory of General Relativity. The first part of this paper is an introduction to the pertinent ideas from Einstein’s theory of curved spacetime, followed by a review of other popular time machine spacetimes. We begin with an intro- duction to curvature and lightcones. We then explain the Alcubierre Warp Drive, the Morris-Thorne wormhole, and the Tipler cylinder. We then describe the Traversable Achronal Retrograde Domain in Spacetime (TARDIS), and ex- plain some of its general properties. Our TARDIS is a bubble of spacetime curvature which travels along a closed loop in space and time. A person travelling within the bubble will feel a constant acceleration. A person outside of the TARDIS will see two bubbles: one which is evolving forwards in time, and one which is evolving backwards in time. We then discuss the physical limitations which may prevent us from ever constructing a TARDIS. Finally, we discuss the method through which a TARDIS can be used to travel between arbitrary points in space and time, and the possible dangers involved with exiting a TARDIS from the wrong side. Before we begin, would you like a Jelly Baby? arXiv:1310.7983v1 [physics.pop-ph] 29 Oct 2013 a email: [email protected] b email: [email protected] 2 Figure 1: We ask K9 to steer straight-ahead as he moves over the curved ground of an old quarry in Wales. -
Bayanebartar.Org
Today we're going to talk a little bit more technically about what exactly is time like if we're going to travel through it we probably should know what it is right we're also going to talk about whether or not time travel is going to be possible and the consequences of what would happen if we travel through time and whether we've already time traveled there's a lot to talk about that's why we have four episodes this week which I'm super excited about but today first let's talk about whether time travel is possible so if you're going to travel on something or through something or whatever kind of the first step is knowing what it is if I'm a build a boat to sail on a lake I probably need to understand water so BayaneBartar.org that's what we're talking about and the problem with time travel is we don't really have a lot of definition of what time is because to be honest a minute a second an hour days it's all relative depending on what planet you're on and depending on your experience we invented the idea of time time is our perception of things right it's how we divide ourselves in our lives in our you know days but all of that is completely relative so what is time on a bigger question needs to be answered before we can travel through it and many people have been trying to answer this for a long long time and there are so many aspects to think about when considering time or explaining time but where I always start is the super simple easy to understand second law of thermodynamics I'm sure I don't have to tell you guys the first law -
CTC 1 Running Head: Curva Temporal Cerrada Curva Temporal Cerrada, Viajes En El Tiempo. Miguel Ángel Flores Saldívar 20091151
CTC 1 Running head: Curva Temporal Cerrada Curva Temporal Cerrada, viajes en el tiempo. Miguel Ángel Flores Saldívar 200911518 Habilidades para la Comunicación Escrita CTC 2 Abstract En el siguiente ensayo abordaré un tema que gran parte de la humanidad se ha preguntado, ¿Es posible físicamente, viajar en el tiempo? En este documento mostraré la opinión de diferentes físicos reconocidos y especialistas en las CTC (Closed Timelike Curve) o como mejor se conoce, en el mundo no científico, viajes en el tiempo. Mostrando que viajar en el tiempo sí es posible y cuantas formas hay para viajar en el tiempo. CTC 3 Introducción Todos los seres humanos desde nuestra infancia hemos visto películas de ciencia ficción que mostraban que era posible viajar en el tiempo y que se podría crear una máquina del tiempo en la cual podríamos viajar a través del tiempo ya sea en el pasado como en el futuro o simplemente cuando hacemos cosas que nos arrepentimos o suceden hechos que nos afectan demasiado y decimos “Como quisiera viajar al pasado para evitar aquel suceso.” El ser humano siempre se ha preguntado si es posible viajar en el tiempo. Es difícil definir el tiempo, ya que este no se puede ver, no se puede oler, no se puede tocar pero afecta a nuestra vida y a nuestro universo. Este se ve implicado en todo nuestro universo, pero gracias a los avances en la Física y en la tecnología ahora nos podemos contestar esta pregunta. Pero que haríamos si podríamos viajar por el pasado y el futuro. No sólo se puede viajar hacia adelante y hacia atrás a través del tiempo si no que también hacia los lados. -
Blackholeswormholesandtimemachines.Pdf
B LACK H OLES WORMHOLES &TIME M ACHINES CONTENTS PREFACE ix ACKNOWLEDGMENTS xiii INTRODUCTION xv SPACE 1 THE 4TH DIMENSION 3 To do with shapes • What is space? • 2Dworld and 2D’ers • Curved space • Is there really a fourth dimension? 2 MATTERS OF SOME GRAVITY 22 Apples and moons • Einstein’s gravity • Free fall • Rubber space • Twinkle, twinkle • Cooking the elements • Champagne supernovae in the sky 3 THE UNIVERSE 41 The night sky • How big is the Universe? • The expanding Universe • Hubble, bubble . • Space is stretching • Did the Big Bang really happen? • The edge of space • A closed universe • An open universe • What shape is the Universe then? • Invisible matter • 1998: a big year in cosmology • Is the Universe infinite? • Why is it dark at night? • Before the Big Bang? • Summary 4 BLACK HOLES 78 More to light than meets the eye! • Invisible stars • Beyond the horizon • A hole that can never be filled • Spinning black holes • Falling into a black hole • To see a black hole • Not so black after all • White holes vii BLACK HOLES, WORMHOLES & TIME MACHINES TIME 5 TIMES ARE CHANGING 111 What is time? • Who invented time? • The first moment • Does time flow? • Something called entropy • Arrows of time • Stephen Hawking gets it wrong • A possible solution 6 EINSTEIN’S TIME 139 What is so special about special relativity? • The two faces of light • Thought experiments and brain teasers • Slowing down time • Shrinking distances • Light—the world speed record • When time runs backwards • Little green men • Fast forward to the future • Spacetime—the -
A Study of Temporal Metaphysics Through Hard Science Fiction and Its Restrictions on the Past and Future Lindsey E
Oglethorpe Journal of Undergraduate Research Volume 2 | Issue 2 Article 2 August 2013 Shadows in Time: A Study of Temporal Metaphysics through Hard Science Fiction and its Restrictions on the Past and Future Lindsey E. Mitchell Oglethorpe University, [email protected] Follow this and additional works at: https://digitalcommons.kennesaw.edu/ojur Part of the Cosmology, Relativity, and Gravity Commons, Fiction Commons, and the Other Physics Commons Recommended Citation Mitchell, Lindsey E. (2013) "Shadows in Time: A Study of Temporal Metaphysics through Hard Science Fiction and its Restrictions on the Past and Future," Oglethorpe Journal of Undergraduate Research: Vol. 2 : Iss. 2 , Article 2. Available at: https://digitalcommons.kennesaw.edu/ojur/vol2/iss2/2 This Article is brought to you for free and open access by DigitalCommons@Kennesaw State University. It has been accepted for inclusion in Oglethorpe Journal of Undergraduate Research by an authorized editor of DigitalCommons@Kennesaw State University. For more information, please contact [email protected]. Shadows in Time: A Study of Temporal Metaphysics through Hard Science Fiction and its Restrictions on the Past and Future Cover Page Footnote In Collaboration With Dr. Michael Rulison, Dr. Nicholas Maher, and Dr. Linda Taylor Dedicated To My father, who introduced me to the wonders of science fiction all those years ago and fed my hunger for it with his library of the classics My mother, who has read to me both as a child and an adult, teaching me to write stories that are a joy to read And to my other cherished family and friends, who patiently let me rail about the stupidity of paradoxes and who always inspire me to do better than what I believe myself capable of This article is available in Oglethorpe Journal of Undergraduate Research: https://digitalcommons.kennesaw.edu/ojur/vol2/iss2/2 Mitchell: Shadows in Time Reconciling Science Fiction and Temporal Metaphysics I Two different kinds of science fiction have evolved over time. -
Romero Introduction to Black Hole Astrophysics
Black hole astrophysics Gustavo E. Romero Grupo de Astrofísica Relativista y Radioastronomía Instituto Argentino de Radioastronomía, CONICET-CIC Facultad de Ciencias Astronómicas y Geofísicas, UNLP [email protected], [email protected] What is a star? e What is a star? Eddington proposed (1926): 1.Thermonuclear reactions are the source of energy in the stars 2.The outward pressure of raditation should be taken into account in the equation for equilibrium. What is a star? What is a star? What is a star? What is a star? What is a star? What is a star? The end of stars The end of stars A pair-instability supernova occurs when pair production, the production of free electrons and positrons in the collision between atomic nuclei and energetic gamma rays, reduces thermal pressure inside a supermassive star's core. This pressure drop leads to a partial collapse, then greatly accelerated burning in a runaway thermonuclear explosion which blows the star completely apart without leaving a black hole remnant behind. Pair-instability supernovae can only happen in stars with a mass range from around 130 to 250 solar masses and low to moderate metallicity (low abundance of elements other than hydrogen and helium, a situation common in Population III stars). Oppenheimer & Snyder (1939): non-stopping collapse. Collapse to what? The answer is in General Relativity. Black holes Albert Einstein John A. Wheeler Letter from Karl Schwarzschild to Einstein, 22 December 1915 Schwarzschild is one of the few astronomers who are interested in Einstein's General Theory of Relativity. In December 1915, he is based at the Russian front line. -
JEZIK, KNJIŽEVNOST, VREME: KNJIŽEVNA ISTRAŽIVANJA Biblioteka NAUČNI SKUPOVI
Vesna Lopičić / Biljana Mišić Ilić JEZIK, KNJIŽEVNOST, VREME: KNJIŽEVNA ISTRAŽIVANJA Biblioteka NAUČNI SKUPOVI Urednice: Prof. dr Vesna Lopičić Prof. dr Biljana Mišić Ilić Glavni i odgovorni urednik: Doc. dr Gordana Đigić Akademski odbor: Prof. dr Miloš Kovačević Prof. dr Vesna Lopičić Prof. dr Biljana Mišić Ilić Prof. dr Đorđe Vidanović Prof. dr Sofija Miloradović Prof. dr. Tatjana Paunović Prof. dr Mihailo Antović Prof. dr. Milica Živković Prof. dr. Savka Blagojević Prof. dr Slávka Tomaščíková Prof. dr Walter Epp Prof. dr. Janoš Kenjereš Prof. dr. Kristobal Kanovas Prof. dr. Marija Knežević Sekretari konferencije: Sanja Ignjatović Nikola Tatar Recenzenti: Prof. dr. Zorica Đergović-Joksimović Prof. dr. Tatjana Bijelić Prof. dr. Zoran Paunović Univerzitet u Nišu Filozofski fakultet JEZIK, KNJIŽEVNOST, VREME KNJIŽEVNA ISTRAŽIVANJA Zbornik radova Urednice: Vesna Lopičić Biljana Mišić Ilić Niš, 2017. Recenzenti pojedinačnih radova: Radmila Bodrič Snežana Gudurić Vladimir Jovanović Aleksandar Kavgić Miloš Kovačević Vesna Lopičić Maja Marković Biljana Mišić Ilić Ljilja Nedeljkov Predrag Novakov Vladan Pavlović Anđelka Pejović Dušan Stamenković Selena Stanković Strahinja Stepanov Violeta Stojičić Amina Šiljak-Jesenković Đorđe Vidanović Maja Vukić SADRŽAJ JEZIK, KNJIŽEVNOST, VREME: KNJIŽEVNA ISTRAŽIVANJA UVOD NARATIVNO KONSTRUISANJE TEMPORALNOSTI .............................................. 11 I TEORETSKA RAZMATRANJA Snežana Milosavljević Milić ВРЕМЕНСКО ИСКУСТВО ПРИЧЕ – КА РЕВИЗИЈИ АТЕМПОРАЛНИХ АСПЕКАТА ТЕКСТА ...................................................................................................