Notes on Relativity and Cosmology for PHY312
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Galileo and the Telescope
Galileo and the Telescope A Discussion of Galileo Galilei and the Beginning of Modern Observational Astronomy ___________________________ Billy Teets, Ph.D. Acting Director and Outreach Astronomer, Vanderbilt University Dyer Observatory Tuesday, October 20, 2020 Image Credit: Giuseppe Bertini General Outline • Telescopes/Galileo’s Telescopes • Observations of the Moon • Observations of Jupiter • Observations of Other Planets • The Milky Way • Sunspots Brief History of the Telescope – Hans Lippershey • Dutch Spectacle Maker • Invention credited to Hans Lippershey (c. 1608 - refracting telescope) • Late 1608 – Dutch gov’t: “ a device by means of which all things at a very great distance can be seen as if they were nearby” • Is said he observed two children playing with lenses • Patent not awarded Image Source: Wikipedia Galileo and the Telescope • Created his own – 3x magnification. • Similar to what was peddled in Europe. • Learned magnification depended on the ratio of lens focal lengths. • Had to learn to grind his own lenses. Image Source: Britannica.com Image Source: Wikipedia Refracting Telescopes Bend Light Refracting Telescopes Chromatic Aberration Chromatic aberration limits ability to distinguish details Dealing with Chromatic Aberration - Stop Down Aperture Galileo used cardboard rings to limit aperture – Results were dimmer views but less chromatic aberration Galileo and the Telescope • Created his own (3x, 8-9x, 20x, etc.) • Noted by many for its military advantages August 1609 Galileo and the Telescope • First observed the -
Autobiography of Sir George Biddell Airy by George Biddell Airy 1
Autobiography of Sir George Biddell Airy by George Biddell Airy 1 CHAPTER I. CHAPTER II. CHAPTER III. CHAPTER IV. CHAPTER V. CHAPTER VI. CHAPTER VII. CHAPTER VIII. CHAPTER IX. CHAPTER X. CHAPTER I. CHAPTER II. CHAPTER III. CHAPTER IV. CHAPTER V. CHAPTER VI. CHAPTER VII. CHAPTER VIII. CHAPTER IX. CHAPTER X. Autobiography of Sir George Biddell Airy by George Biddell Airy The Project Gutenberg EBook of Autobiography of Sir George Biddell Airy by George Biddell Airy This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg Autobiography of Sir George Biddell Airy by George Biddell Airy 2 License included with this eBook or online at www.gutenberg.net Title: Autobiography of Sir George Biddell Airy Author: George Biddell Airy Release Date: January 9, 2004 [EBook #10655] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK SIR GEORGE AIRY *** Produced by Joseph Myers and PG Distributed Proofreaders AUTOBIOGRAPHY OF SIR GEORGE BIDDELL AIRY, K.C.B., M.A., LL.D., D.C.L., F.R.S., F.R.A.S., HONORARY FELLOW OF TRINITY COLLEGE, CAMBRIDGE, ASTRONOMER ROYAL FROM 1836 TO 1881. EDITED BY WILFRID AIRY, B.A., M.Inst.C.E. 1896 PREFACE. The life of Airy was essentially that of a hard-working, business man, and differed from that of other hard-working people only in the quality and variety of his work. It was not an exciting life, but it was full of interest, and his work brought him into close relations with many scientific men, and with many men high in the State. -
4. Kruskal Coordinates and Penrose Diagrams
4. Kruskal Coordinates and Penrose Diagrams. 4.1. Removing a coordinate Singularity at the Schwarzschild Radius. The Schwarzschild metric has a singularity at r = rS where g 00 → 0 and g11 → ∞ . However, we have already seen that a free falling observer acknowledges a smooth motion without any peculiarity when he passes the horizon. This suggests that the behaviour at the Schwarzschild radius is only a coordinate singularity which can be removed by using another more appropriate coordinate system. This is in GR always possible provided the transformation is smooth and differentiable, a consequence of the diffeomorphism of the spacetime manifold. Instead of the 4-dimensional Schwarzschild metric we study a 2-dimensional t,r-version. The spherical symmetry of the Schwarzschild BH guaranties that we do not loose generality. −1 ⎛ r ⎞ ⎛ r ⎞ ds 2 = ⎜1− S ⎟ dt 2 − ⎜1− S ⎟ dr 2 (4.1) ⎝ r ⎠ ⎝ r ⎠ To describe outgoing and ingoing null geodesics we divide through dλ2 and set ds 2 = 0. −1 ⎛ rS ⎞ 2 ⎛ rS ⎞ 2 ⎜1− ⎟t& − ⎜1− ⎟ r& = 0 (4.2) ⎝ r ⎠ ⎝ r ⎠ or rewritten 2 −2 ⎛ dt ⎞ ⎛ r ⎞ ⎜ ⎟ = ⎜1− S ⎟ (4.3) ⎝ dr ⎠ ⎝ r ⎠ Note that the angle of the light cone in t,r-coordinate.decreases when r approaches rS After integration the outgoing and ingoing null geodesics of Schwarzschild satisfy t = ± r * +const. (4.4) r * is called “tortoise coordinate” and defined by ⎛ r ⎞ ⎜ ⎟ r* = r + rS ln⎜ −1⎟ (4.5) ⎝ rS ⎠ −1 dr * ⎛ r ⎞ so that = ⎜1− S ⎟ . (4.6) dr ⎝ r ⎠ As r ranges from rS to ∞, r* goes from -∞ to +∞. We introduce the null coordinates u,υ which have the direction of null geodesics by υ = t + r * and u = t − r * (4.7) From (4.7) we obtain 1 dt = ()dυ + du (4.8) 2 and from (4.6) 28 ⎛ r ⎞ 1 ⎛ r ⎞ dr = ⎜1− S ⎟dr* = ⎜1− S ⎟()dυ − du (4.9) ⎝ r ⎠ 2 ⎝ r ⎠ Inserting (4.8) and (4.9) in (4.1) we find ⎛ r ⎞ 2 ⎜ S ⎟ ds = ⎜1− ⎟ dudυ (4.10) ⎝ r ⎠ Fig. -
How the Quantum Black Hole Replies to Your Messages
Gerard 't Hooft How the Quantum Black hole Replies to Your Messages Centre for Extreme Matter and Emergent Phenomena, Science Faculty, Utrecht University, POBox 80.089, 3508 TB, Utrecht Qui Nonh, Viet Nam, July 24, 2017 1 / 45 Introduction { Einstein's theory of gravity, based on General Relativity, and { Quantum Mechanics, as it was developed early 20th century, are both known to be valid at high precision. But combining these into one theory still leads to problems today. Existing approaches: { Superstring theory, extended as M theory { Loop quantum gravity { Dynamical triangulation of space-time { Asymptotically safe quantum gravity are promising but not (yet) understood at the desired level. In particular when black holes are considered. 2 / 45 one encounters problems with: { information loss { incorrectly entangled states { firewalls We shall show that fundamental new ingredients in all these theories are called for: { the gravitational back reaction cannot be ignored, { one must expand the momentum distributions of in- and out-particles in spherical harmonics, and { one must apply antipodal identification in order to avoid double counting of pure quantum states. This we will explain. We do not claim that these theories are incorrect, but they are not fool-proof. The topology of space and time is not (yet) handled correctly in these theories. This is why 3 / 45 { the gravitational back reaction cannot be ignored, { one must expand the momentum distributions of in- and out-particles in spherical harmonics, and { one must apply antipodal identification in order to avoid double counting of pure quantum states. This we will explain. We do not claim that these theories are incorrect, but they are not fool-proof. -
Arxiv:Hep-Th/9209055V1 16 Sep 1992 Quantum Aspects of Black Holes
EFI-92-41 hep-th/9209055 Quantum Aspects of Black Holes Jeffrey A. Harvey† Enrico Fermi Institute University of Chicago 5640 Ellis Avenue, Chicago, IL 60637 Andrew Strominger∗ Department of Physics University of California Santa Barbara, CA 93106-9530 Abstract This review is based on lectures given at the 1992 Trieste Spring School on String arXiv:hep-th/9209055v1 16 Sep 1992 Theory and Quantum Gravity and at the 1992 TASI Summer School in Boulder, Colorado. 9/92 † Email address: [email protected] ∗ Email addresses: [email protected], [email protected]. 1. Introduction Nearly two decades ago, Hawking [1] observed that black holes are not black: quantum mechanical pair production in a gravitational field leads to black hole evaporation. With hindsight, this result is not really so surprising. It is simply the gravitational analog of Schwinger pair production in which one member of the pair escapes to infinity, while the other drops into the black hole. Hawking went on, however, to argue for a very surprising conclusion: eventually the black hole disappears completely, taking with it all the information carried in by the infalling matter which originally formed the black hole as well as that carried in by the infalling particles created over the course of the evaporation process. Thus, Hawking argued, it is impossible to predict a unique final quantum state for the system. This argument initiated a vigorous debate in the physics community which continues to this day. It is certainly striking that such a simple thought experiment, relying only on the basic concepts of general relativity and quantum mechanics, should apparently threaten the deterministic foundations of physics. -
Singularities, Black Holes, and Cosmic Censorship: a Tribute to Roger Penrose
Foundations of Physics (2021) 51:42 https://doi.org/10.1007/s10701-021-00432-1 INVITED REVIEW Singularities, Black Holes, and Cosmic Censorship: A Tribute to Roger Penrose Klaas Landsman1 Received: 8 January 2021 / Accepted: 25 January 2021 © The Author(s) 2021 Abstract In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose’s work on general rela- tivity. His 1965 singularity theorem (for which he got the prize) does not in fact imply the existence of black holes (even if its assumptions are met). Similarly, his versatile defnition of a singular space–time does not match the generally accepted defnition of a black hole (derived from his concept of null infnity). To overcome this, Penrose launched his cosmic censorship conjecture(s), whose evolution we discuss. In particular, we review both his own (mature) formulation and its later, inequivalent reformulation in the PDE literature. As a compromise, one might say that in “generic” or “physically reasonable” space–times, weak cosmic censorship postulates the appearance and stability of event horizons, whereas strong cosmic censorship asks for the instability and ensuing disappearance of Cauchy horizons. As an encore, an “Appendix” by Erik Curiel reviews the early history of the defni- tion of a black hole. Keywords General relativity · Roger Penrose · Black holes · Ccosmic censorship * Klaas Landsman [email protected] 1 Department of Mathematics, Radboud University, Nijmegen, The Netherlands Vol.:(0123456789)1 3 42 Page 2 of 38 Foundations of Physics (2021) 51:42 Conformal diagram [146, p. 208, Fig. -
History of the Speed of Light ( C )
History of the Speed of Light ( c ) Jennifer Deaton and Tina Patrick Fall 1996 Revised by David Askey Summer RET 2002 Introduction The speed of light is a very important fundamental constant known with great precision today due to the contribution of many scientists. Up until the late 1600's, light was thought to propagate instantaneously through the ether, which was the hypothetical massless medium distributed throughout the universe. Galileo was one of the first to question the infinite velocity of light, and his efforts began what was to become a long list of many more experiments, each improving the Is the Speed of Light Infinite? • Galileo’s Simplicio, states the Aristotelian (and Descartes) – “Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired at great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval.” • Galileo in Two New Sciences, published in Leyden in 1638, proposed that the question might be settled in true scientific fashion by an experiment over a number of miles using lanterns, telescopes, and shutters. 1667 Lantern Experiment • The Accademia del Cimento of Florence took Galileo’s suggestion and made the first attempt to actually measure the velocity of light. – Two people, A and B, with covered lanterns went to the tops of hills about 1 mile apart. – First A uncovers his lantern. As soon as B sees A's light, he uncovers his own lantern. – Measure the time from when A uncovers his lantern until A sees B's light, then divide this time by twice the distance between the hill tops. -
Positional Astronomy Coordinate Systems
Positional Astronomy Observational Astronomy 2019 Part 2 Prof. S.C. Trager Coordinate systems We need to know where the astronomical objects we want to study are located in order to study them! We need a system (well, many systems!) to describe the positions of astronomical objects. The Celestial Sphere First we need the concept of the celestial sphere. It would be nice if we knew the distance to every object we’re interested in — but we don’t. And it’s actually unnecessary in order to observe them! The Celestial Sphere Instead, we assume that all astronomical sources are infinitely far away and live on the surface of a sphere at infinite distance. This is the celestial sphere. If we define a coordinate system on this sphere, we know where to point! Furthermore, stars (and galaxies) move with respect to each other. The motion normal to the line of sight — i.e., on the celestial sphere — is called proper motion (which we’ll return to shortly) Astronomical coordinate systems A bit of terminology: great circle: a circle on the surface of a sphere intercepting a plane that intersects the origin of the sphere i.e., any circle on the surface of a sphere that divides that sphere into two equal hemispheres Horizon coordinates A natural coordinate system for an Earth- bound observer is the “horizon” or “Alt-Az” coordinate system The great circle of the horizon projected on the celestial sphere is the equator of this system. Horizon coordinates Altitude (or elevation) is the angle from the horizon up to our object — the zenith, the point directly above the observer, is at +90º Horizon coordinates We need another coordinate: define a great circle perpendicular to the equator (horizon) passing through the zenith and, for convenience, due north This line of constant longitude is called a meridian Horizon coordinates The azimuth is the angle measured along the horizon from north towards east to the great circle that intercepts our object (star) and the zenith. -
Spacetime Continuity and Quantum Information Loss
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Nazarbayev University Repository universe Article Spacetime Continuity and Quantum Information Loss Michael R. R. Good School of Science and Technology, Nazarbayev University, Astana 010000, Kazakhstan; [email protected] Received: 30 September 2018; Accepted: 8 November 2018; Published: 9 November 2018 Abstract: Continuity across the shock wave of two regions in the metric during the formation of a black hole can be relaxed in order to achieve information preservation. A Planck scale sized spacetime discontinuity leads to unitarity (a constant asymptotic entanglement entropy) by restricting the origin of coordinates (moving mirror) to be timelike. Moreover, thermal equilibration occurs and total evaporation energy emitted is finite. Keywords: black hole evaporation; information loss; remnants 1. Introduction In this note, the role of continuity and information loss (via the tortoise coordinate, r∗), in understanding the crux of the phenomena of particle creation from black holes [1], is explored. In particular, the relationship to the simplified model of the moving mirror [2–4] is investigated because it has identical Bogolubov coefficients [5]. Uncompromising continuity is relaxed in favor of unitarity by a single additional parameter generalization of the r∗ coordinate. An understanding of the correspondence between the black hole and the moving mirror in this new context is initiated [6–8]. We prioritize information preservation, and find finite evaporation energy, thermal equilibrium, and analytical beta coefficients. Moreover, we determine and assess a left-over remnant (e.g., [9,10]). Broadly motivating, delving into the ramifications of external effects on quantum fields have led to interesting results on a wide variety of phenomena all the way from, e.g., relativistic superfluidity [11,12] to the creation of quantum vortexes in analog spacetimes [13,14]. -
The Luminiferous Ether Consequences of the Ether
Experimental basis for The luminiferous ether special relativity • Mechanical waves, water, sound, strings, etc. require a medium • Experiments related to the ether • The speed of propagation of mechanical hypothesis waves depends on the motion of the • Experiments on the speed of light from medium moving sources • It was logical to accept that there must be a • Experiments on time-dilation effects medium for the propagation of light, so that • Experiments to measure the kinetic energy em waves are oscillations in the ether of relativistic electrons • Newton, Huygens, Maxwell, Rayleigh all believed that the ether existed 1 2 The aberration of starlight Consequences of the ether (James Bradley 1727) • If there was a medium for light wave • Change in the apparent position of a star due to changes in the velocity of propagation, then the speed of light must be the earth in its orbit measured relative to that medium • Fresnel attempted to explain this • Thus the ether could provide an absolute from a theory of the velocity of light reference frame for all measurements in a moving medium • According to Fresnel, the ether was • The ether must have some strange properties dragged along with the earth and this – it must be solid-like to support high-frequency gave rise to the aberration effect transverse waves • However, Einstein gave the correct – yet it had to be of very low density so that it did not explanation in terms of relativistic velocity addition. A light ray will have disturb the motion of planets and other astronomical a different -
EXPLORING SPECIAL RELATIVITY (Revised 24/9/06)
EXPLORING SPECIAL RELATIVITY (revised 24/9/06) Objectives The aim of this experiment is to observe how things would appear if you could travel at speeds near that of light, c = 3×108 m/s. From your observations you can deduce, or verify, aspects of relativistic physics. Both qualitative and quantitative understanding is sought. Important Information The “Real Time Relativity” (RTR) simulator you will use in this lab was created at ANU by Lachlan McCalman, Antony Searle, and Craig Savage. It is under development and has many limitations. In particular you may not be able to make precise measurements. When you are asked for a quantitative result just do the best you can: 10% accuracy is fine. If you have trouble using RTR, ask a demonstrator for help. Take a note of things that make it difficult to use, and include them on the post-lab evaluation. Thanks for your patience! Evaluation This is a new lab, and we are evaluating its effectiveness. To help us, please answer the questions on the evaluation handouts: complete one before the lab, and one after the lab. This will help us to assess the effectiveness of the lab, and to improve it. To receive a bonus mark, hand them in by 5pm on the Friday of the week of your lab. Skills In this experiment you will practice: making observations, critical evaluation, designing experiments. Basic Principles Computer simulations are used in science to conduct investigations that might otherwise be difficult or impossible. The objects in the simulation are big, because the speed of light is fast. -
Effect of the Gravitational Aberration on the Earth Gravity Field
ARTIFICIAL SATELLITES, Vol. 56, No 1 – 2021 DOI: 10.2478/arsa-2021-0001 EFFECT OF THE GRAVITATIONAL ABERRATION ON THE EARTH GRAVITY FIELD Janusz B. ZIELIŃSKI1, Vladimir V. PASHKEVICH2 1 Space Research Centre, Polish Academy of Sciences, Warsaw, Poland 2 Central Astronomical Observatory at Pulkovo, Russian Academy of Sciences, St. Petersburg, Russia e-mails: [email protected], [email protected] ABSTRACT. Discussing the problem of the external gravitational potential of the rotating Earth, we have to consider the fundamental postulate of the finite speed of the propagation of gravitation. This can be done using the expressions for the gravitational aberration compared to the Liénard–Wiechert solution of the retarded potentials. The term gravitational counter- aberration or co-aberration is introduced to describe the pattern of the propagation of the gravitational signal emitted by the rotating Earth. It is proved that in the first approximation, the classic theory of the aberration of light can be applied to calculate this effect. Some effects of the gravitational aberration on the external gravity field of the rotating Earth may influence the orbit determination of the Earth artificial satellites. Keywords: propagation of gravitation, speed of gravity, aberration of gravity, retarded potential, Earth gravitational potential 1. INTRODUCTION In the excellent book Relativistic Celestial Mechanics of the Solar System (Kopeikin et al., 2011), we find the notion aberration of gravity, understood as the effect of the Liénard– Wiechert retarded potential of the moving mass on the propagation of gravity. It is a very interesting concept, which could be discussed more closely in the context of the classic definitions of the aberration of light and the relativistic gravitational potential.