Einstein's Discovery of Relativity
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The Special Theory of Relativity
THE SPECIAL THEORY OF RELATIVITY Lecture Notes prepared by J D Cresser Department of Physics Macquarie University July 31, 2003 CONTENTS 1 Contents 1 Introduction: What is Relativity? 2 2 Frames of Reference 5 2.1 A Framework of Rulers and Clocks . 5 2.2 Inertial Frames of Reference and Newton’s First Law of Motion . 7 3 The Galilean Transformation 7 4 Newtonian Force and Momentum 9 4.1 Newton’s Second Law of Motion . 9 4.2 Newton’s Third Law of Motion . 10 5 Newtonian Relativity 10 6 Maxwell’s Equations and the Ether 11 7 Einstein’s Postulates 13 8 Clock Synchronization in an Inertial Frame 14 9 Lorentz Transformation 16 9.1 Length Contraction . 20 9.2 Time Dilation . 22 9.3 Simultaneity . 24 9.4 Transformation of Velocities (Addition of Velocities) . 24 10 Relativistic Dynamics 27 10.1 Relativistic Momentum . 28 10.2 Relativistic Force, Work, Kinetic Energy . 29 10.3 Total Relativistic Energy . 30 10.4 Equivalence of Mass and Energy . 33 10.5 Zero Rest Mass Particles . 34 11 Geometry of Spacetime 35 11.1 Geometrical Properties of 3 Dimensional Space . 35 11.2 Space Time Four Vectors . 38 11.3 Spacetime Diagrams . 40 11.4 Properties of Spacetime Intervals . 41 1 INTRODUCTION: WHAT IS RELATIVITY? 2 1 Introduction: What is Relativity? Until the end of the 19th century it was believed that Newton’s three Laws of Motion and the associated ideas about the properties of space and time provided a basis on which the motion of matter could be completely understood. -
A Mathematical Derivation of the General Relativistic Schwarzschild
A Mathematical Derivation of the General Relativistic Schwarzschild Metric An Honors thesis presented to the faculty of the Departments of Physics and Mathematics East Tennessee State University In partial fulfillment of the requirements for the Honors Scholar and Honors-in-Discipline Programs for a Bachelor of Science in Physics and Mathematics by David Simpson April 2007 Robert Gardner, Ph.D. Mark Giroux, Ph.D. Keywords: differential geometry, general relativity, Schwarzschild metric, black holes ABSTRACT The Mathematical Derivation of the General Relativistic Schwarzschild Metric by David Simpson We briefly discuss some underlying principles of special and general relativity with the focus on a more geometric interpretation. We outline Einstein’s Equations which describes the geometry of spacetime due to the influence of mass, and from there derive the Schwarzschild metric. The metric relies on the curvature of spacetime to provide a means of measuring invariant spacetime intervals around an isolated, static, and spherically symmetric mass M, which could represent a star or a black hole. In the derivation, we suggest a concise mathematical line of reasoning to evaluate the large number of cumbersome equations involved which was not found elsewhere in our survey of the literature. 2 CONTENTS ABSTRACT ................................. 2 1 Introduction to Relativity ...................... 4 1.1 Minkowski Space ....................... 6 1.2 What is a black hole? ..................... 11 1.3 Geodesics and Christoffel Symbols ............. 14 2 Einstein’s Field Equations and Requirements for a Solution .17 2.1 Einstein’s Field Equations .................. 20 3 Derivation of the Schwarzschild Metric .............. 21 3.1 Evaluation of the Christoffel Symbols .......... 25 3.2 Ricci Tensor Components ................. -
Experiments in Topology Pdf Free Download
EXPERIMENTS IN TOPOLOGY PDF, EPUB, EBOOK Stephen Barr | 210 pages | 01 Jan 1990 | Dover Publications Inc. | 9780486259338 | English | New York, United States Experiments in Topology PDF Book In short, the book gives a competent introduction to the material and the flavor of a broad swath of the main subfields of topology though Barr does not use the academic disciplinary names preferring an informal treatment. Given these and other early developments, the time is ripe for a meeting across communities to share ideas and look forward. The experiment played a role in the development of ethical guidelines for the use of human participants in psychology experiments. Outlining the Physics: What are the candidate physical drivers of quenching and do the processes vary as a function of galaxy type? Are there ways that these different theoretical mechanisms can be distinguished observationally? In the first part of the study, participants were asked to read about situations in which a conflict occurred and then were told two alternative ways of responding to the situation. In a one-dimensional absolute-judgment task, a person is presented with a number of stimuli that vary on one dimension such as 10 different tones varying only in pitch and responds to each stimulus with a corresponding response learned before. In November , the E. The study and the subsequent article organized by the Washington Post was part of a social experiment looking at perception, taste and the priorities of people. The students were randomly assigned to one of two groups, and each group was shown one of two different interviews with the same instructor who is a native French-speaking Belgian who spoke English with a fairly noticeable accent. -
From Relativistic Time Dilation to Psychological Time Perception
From relativistic time dilation to psychological time perception: an approach and model, driven by the theory of relativity, to combine the physical time with the time perceived while experiencing different situations. Andrea Conte1,∗ Abstract An approach, supported by a physical model driven by the theory of relativity, is presented. This approach and model tend to conciliate the relativistic view on time dilation with the current models and conclusions on time perception. The model uses energy ratios instead of geometrical transformations to express time dilation. Brain mechanisms like the arousal mechanism and the attention mechanism are interpreted and combined using the model. Matrices of order two are generated to contain the time dilation between two observers, from the point of view of a third observer. The matrices are used to transform an observer time to another observer time. Correlations with the official time dilation equations are given in the appendix. Keywords: Time dilation, Time perception, Definition of time, Lorentz factor, Relativity, Physical time, Psychological time, Psychology of time, Internal clock, Arousal, Attention, Subjective time, Internal flux, External flux, Energy system ∗Corresponding author Email address: [email protected] (Andrea Conte) 1Declarations of interest: none Preprint submitted to PsyArXiv - version 2, revision 1 June 6, 2021 Contents 1 Introduction 3 1.1 The unit of time . 4 1.2 The Lorentz factor . 6 2 Physical model 7 2.1 Energy system . 7 2.2 Internal flux . 7 2.3 Internal flux ratio . 9 2.4 Non-isolated system interaction . 10 2.5 External flux . 11 2.6 External flux ratio . 12 2.7 Total flux . -
Popular Arguments for Einstein's Special Theory of Relativity1
1 Popular Arguments for Einstein’s Special Theory of Relativity1 Patrick Mackenzie University of Saskatchewan Introduction In this paper I shall argue in Section II that two of the standard arguments that have been put forth in support of Einstein’s Special Theory of Relativity do not support that theory and are quite compatible with what might be called an updated and perhaps even an enlightened Newtonian view of the Universe. This view will be presented in Section I. I shall call it the neo-Newtonian Theory, though I hasten to add there are a number of things in it that Newton would not accept, though perhaps Galileo might have. Now there may be other arguments and/or pieces of empirical evidence which support the Special Theory of Relativity and cast doubt upon the neo-Newtonian view. Nevertheless, the two that I am going to examine are usually considered important. It might also be claimed that the two arguments that I am going to examine have only heuristic value. Perhaps this is so but they are usually put forward as supporting the Special Theory and refuting the neo-Newtonian Theory. Again I must stress that it is not my aim to cast any doubt on the Special Theory of Relativity nor on Einstein. His Special Theory and his General Theory stand at the zenith of human achievement. My only aim is to cast doubt on the assumption that the two arguments I examine support the Special Theory. Section I Let us begin by outlining the neo-Newtonian Theory. According to it the following tenets are true: 1. -
Hypercomplex Algebras and Their Application to the Mathematical
Hypercomplex Algebras and their application to the mathematical formulation of Quantum Theory Torsten Hertig I1, Philip H¨ohmann II2, Ralf Otte I3 I tecData AG Bahnhofsstrasse 114, CH-9240 Uzwil, Schweiz 1 [email protected] 3 [email protected] II info-key GmbH & Co. KG Heinz-Fangman-Straße 2, DE-42287 Wuppertal, Deutschland 2 [email protected] March 31, 2014 Abstract Quantum theory (QT) which is one of the basic theories of physics, namely in terms of ERWIN SCHRODINGER¨ ’s 1926 wave functions in general requires the field C of the complex numbers to be formulated. However, even the complex-valued description soon turned out to be insufficient. Incorporating EINSTEIN’s theory of Special Relativity (SR) (SCHRODINGER¨ , OSKAR KLEIN, WALTER GORDON, 1926, PAUL DIRAC 1928) leads to an equation which requires some coefficients which can neither be real nor complex but rather must be hypercomplex. It is conventional to write down the DIRAC equation using pairwise anti-commuting matrices. However, a unitary ring of square matrices is a hypercomplex algebra by definition, namely an associative one. However, it is the algebraic properties of the elements and their relations to one another, rather than their precise form as matrices which is important. This encourages us to replace the matrix formulation by a more symbolic one of the single elements as linear combinations of some basis elements. In the case of the DIRAC equation, these elements are called biquaternions, also known as quaternions over the complex numbers. As an algebra over R, the biquaternions are eight-dimensional; as subalgebras, this algebra contains the division ring H of the quaternions at one hand and the algebra C ⊗ C of the bicomplex numbers at the other, the latter being commutative in contrast to H. -
Einstein and Gravitational Waves
Einstein and gravitational waves By Alfonso León Guillén Gómez Independent scientific researcher Bogotá Colombia March 2021 [email protected] In memory of Blanquita Guillén Gómez September 7, 1929 - March 21, 2021 Abstract The author presents the history of gravitational waves according to Einstein, linking it to his biography and his time in order to understand it in his connection with the history of the Semites, the personality of Einstein in the handling of his conflict-generating circumstances in his relationships competition with his colleagues and in the formulation of the so-called general theory of relativity. We will fall back on the vicissitudes that Einstein experienced in the transition from his scientific work to normal science as a pillar of theoretical physics. We will deal with how Einstein introduced the relativistic ether, conferring an "odor of materiality" to his geometric explanation of gravity, where undoubtedly it does not fit, but that he had to give in to the pressure that was justified by his most renowned colleagues, led by Lorentz. Einstein had to do it to stay in the queue that would lead him to the Nobel. It was thus, as developing the relativistic ether thread, in June 1916, he introduced the gravitational waves of which, in an act of personal liberation and scientific honesty, when he could, in 1938, he demonstrated how they could not exist, within the scenario of his relativity, to immediately also put an end to the relativistic ether. Introduction Between December 1969 and February 1970, the author formulated -
Chasing the Light Einsteinʼs Most Famous Thought Experiment 1
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by PhilSci Archive November 14, 17, 2010; May 7, 2011 Chasing the Light Einsteinʼs Most Famous Thought Experiment John D. Norton Department of History and Philosophy of Science Center for Philosophy of Science University of Pittsburgh http://www.pitt.edu/~jdnorton Prepared for Thought Experiments in Philosophy, Science and the Arts, eds., James Robert Brown, Mélanie Frappier and Letitia Meynell, Routledge. At the age of sixteen, Einstein imagined chasing after a beam of light. He later recalled that the thought experiment had played a memorable role in his development of special relativity. Famous as it is, it has proven difficult to understand just how the thought experiment delivers its results. It fails to generate problems for an ether-based electrodynamics. I propose that Einstein’s canonical statement of the thought experiment from his 1946 “Autobiographical Notes,” makes most sense not as an argument against ether-based electrodynamics, but as an argument against “emission” theories of light. 1. Introduction How could we be anything but charmed by the delightful story Einstein tells in his “Autobiographical Notes” of a striking thought he had at the age of sixteen? While recounting the efforts that led to the special theory of relativity, he recalled (Einstein, 1949, pp. 52-53/ pp. 49-50): 1 ...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. -
Coordinates and Proper Time
Coordinates and Proper Time Edmund Bertschinger, [email protected] January 31, 2003 Now it came to me: . the independence of the gravitational acceleration from the na- ture of the falling substance, may be expressed as follows: In a gravitational ¯eld (of small spatial extension) things behave as they do in a space free of gravitation. This happened in 1908. Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning. | A. Einstein (quoted in Albert Einstein: Philosopher-Scientist, ed. P.A. Schilpp, 1949). 1. Introduction These notes supplement Chapter 1 of EBH (Exploring Black Holes by Taylor and Wheeler). They elaborate on the discussion of bookkeeper coordinates and how coordinates are related to actual physical distances and times. Also, a brief discussion of the classic Twin Paradox of special relativity is presented in order to illustrate the principal of maximal (or extremal) aging. Before going to details, let us review some jargon whose precise meaning will be important in what follows. You should be familiar with these words and their meaning. Spacetime is the four- dimensional playing ¯eld for motion. An event is a point in spacetime that is uniquely speci¯ed by giving its four coordinates (e.g. t; x; y; z). Sometimes we will ignore two of the spatial dimensions, reducing spacetime to two dimensions that can be graphed on a sheet of paper, resulting in a Minkowski diagram. -
JOHN EARMAN* and CLARK GL YMUURT the GRAVITATIONAL RED SHIFT AS a TEST of GENERAL RELATIVITY: HISTORY and ANALYSIS
JOHN EARMAN* and CLARK GL YMUURT THE GRAVITATIONAL RED SHIFT AS A TEST OF GENERAL RELATIVITY: HISTORY AND ANALYSIS CHARLES St. John, who was in 1921 the most widely respected student of the Fraunhofer lines in the solar spectra, began his contribution to a symposium in Nncure on Einstein’s theories of relativity with the following statement: The agreement of the observed advance of Mercury’s perihelion and of the eclipse results of the British expeditions of 1919 with the deductions from the Einstein law of gravitation gives an increased importance to the observations on the displacements of the absorption lines in the solar spectrum relative to terrestrial sources, as the evidence on this deduction from the Einstein theory is at present contradictory. Particular interest, moreover, attaches to such observations, inasmuch as the mathematical physicists are not in agreement as to the validity of this deduction, and solar observations must eventually furnish the criterion.’ St. John’s statement touches on some of the reasons why the history of the red shift provides such a fascinating case study for those interested in the scientific reception of Einstein’s general theory of relativity. In contrast to the other two ‘classical tests’, the weight of the early observations was not in favor of Einstein’s red shift formula, and the reaction of the scientific community to the threat of disconfirmation reveals much more about the contemporary scientific views of Einstein’s theory. The last sentence of St. John’s statement points to another factor that both complicates and heightens the interest of the situation: in contrast to Einstein’s deductions of the advance of Mercury’s perihelion and of the bending of light, considerable doubt existed as to whether or not the general theory did entail a red shift for the solar spectrum. -
The Theory of Relativity and Applications: a Simple Introduction
The Downtown Review Volume 5 Issue 1 Article 3 December 2018 The Theory of Relativity and Applications: A Simple Introduction Ellen Rea Cleveland State University Follow this and additional works at: https://engagedscholarship.csuohio.edu/tdr Part of the Engineering Commons, and the Physical Sciences and Mathematics Commons How does access to this work benefit ou?y Let us know! Recommended Citation Rea, Ellen. "The Theory of Relativity and Applications: A Simple Introduction." The Downtown Review. Vol. 5. Iss. 1 (2018) . Available at: https://engagedscholarship.csuohio.edu/tdr/vol5/iss1/3 This Article is brought to you for free and open access by the Student Scholarship at EngagedScholarship@CSU. It has been accepted for inclusion in The Downtown Review by an authorized editor of EngagedScholarship@CSU. For more information, please contact [email protected]. Rea: The Theory of Relativity and Applications What if I told you that time can speed up and slow down? What if I told you that everything you think you know about gravity is a lie? When Albert Einstein presented his theory of relativity to the world in the early 20th century, he was proposing just that. And what’s more? He’s been proven correct. Einstein’s theory has two parts: special relativity, which deals with inertial reference frames and general relativity, which deals with the curvature of space- time. A surface level study of the theory and its consequences followed by a look at some of its applications will provide an introduction to one of the most influential scientific discoveries of the last century. -
(Special) Relativity
(Special) Relativity With very strong emphasis on electrodynamics and accelerators Better: How can we deal with moving charged particles ? Werner Herr, CERN Reading Material [1 ]R.P. Feynman, Feynman lectures on Physics, Vol. 1 + 2, (Basic Books, 2011). [2 ]A. Einstein, Zur Elektrodynamik bewegter K¨orper, Ann. Phys. 17, (1905). [3 ]L. Landau, E. Lifschitz, The Classical Theory of Fields, Vol2. (Butterworth-Heinemann, 1975) [4 ]J. Freund, Special Relativity, (World Scientific, 2008). [5 ]J.D. Jackson, Classical Electrodynamics (Wiley, 1998 ..) [6 ]J. Hafele and R. Keating, Science 177, (1972) 166. Why Special Relativity ? We have to deal with moving charges in accelerators Electromagnetism and fundamental laws of classical mechanics show inconsistencies Ad hoc introduction of Lorentz force Applied to moving bodies Maxwell’s equations lead to asymmetries [2] not shown in observations of electromagnetic phenomena Classical EM-theory not consistent with Quantum theory Important for beam dynamics and machine design: Longitudinal dynamics (e.g. transition, ...) Collective effects (e.g. space charge, beam-beam, ...) Dynamics and luminosity in colliders Particle lifetime and decay (e.g. µ, π, Z0, Higgs, ...) Synchrotron radiation and light sources ... We need a formalism to get all that ! OUTLINE Principle of Relativity (Newton, Galilei) - Motivation, Ideas and Terminology - Formalism, Examples Principle of Special Relativity (Einstein) - Postulates, Formalism and Consequences - Four-vectors and applications (Electromagnetism and accelerators) § ¤ some slides are for your private study and pleasure and I shall go fast there ¦ ¥ Enjoy yourself .. Setting the scene (terminology) .. To describe an observation and physics laws we use: - Space coordinates: ~x = (x, y, z) (not necessarily Cartesian) - Time: t What is a ”Frame”: - Where we observe physical phenomena and properties as function of their position ~x and time t.