Unification Accomplished and Forgotten! the Story of H.T. Flint
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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. -
Philosophy and the Physicists Preview
L. Susan Stebbing Philosophy and the Physicists Preview il glifo ebooks ISBN: 9788897527466 First Edition: December 2018 (A) Copyright © il glifo, December 2018 www.ilglifo.it 1 Contents FOREWORD FROM THE EDITOR Note to the 2018 electronic edition PHILOSOPHY AND THE PHYSICISTS Original Title Page PREFACE NOTE PART I - THE ALARMING ASTRONOMERS Chapter I - The Common Reader and the Popularizing Scientist Chapter II - THE ESCAPE OF SIR JAMES JEANS PART II - THE PHYSICIST AND THE WORLD Chapter III - ‘FURNITURE OF THE EARTH’ Chapter IV - ‘THE SYMBOLIC WORLD OF PHYSICS’ Chapter V - THE DESCENT TO THE INSCRUTABLE Chapter VI - CONSEQUENCES OF SCRUTINIZING THE INSCRUTABLE PART III - CAUSALITY AND HUMAN FREEDOM Chapter VII - THE NINETEENTH-CENTURY NIGHTMARE Chapter VIII - THE REJECTION OF PHYSICAL DETERMINISM Chapter IX - REACTIONS AND CONSEQUENCES Chapter X - HUMAN FREEDOM AND RESPONSIBILITY PART IV - THE CHANGED OUTLOOK Chapter XI - ENTROPY AND BECOMING Chapter XII - INTERPRETATIONS BIBLIOGRAPHY INDEX BACK COVER Susan Stebbing 2 Foreword from the Editor In 1937 Susan Stebbing published Philosophy and the Physicists , an intense and difficult essay, in reaction to reading the works written for the general public by two physicists then at the center of attention in England and the world, James Jeans (1877-1946) and Arthur Eddington (1882- 1944). The latter, as is known, in 1919 had announced to the Royal Society the astronomical observations that were then considered experimental confirmations of the general relativity of Einstein, and who by that episode had managed to trigger the transformation of general relativity into a component of the mass and non-mass imaginary of the twentieth century. -
The Son of Lamoraal Ulbo De Sitter, a Judge, and Catharine Theodore Wilhelmine Bertling
558 BIOGRAPHIES v.i WiLLEM DE SITTER viT 1872-1934 De Sitter was bom on 6 May 1872 in Sneek (province of Friesland), the son of Lamoraal Ulbo de Sitter, a judge, and Catharine Theodore Wilhelmine Bertling. His father became presiding judge of the court in Arnhem, and that is where De Sitter attended gymna sium. At the University of Groniiigen he first studied mathematics and physics and then switched to astronomy under Jacobus Kapteyn. De Sitter spent two years observing and studying under David Gill at the Cape Obsen'atory, the obseivatory with which Kapteyn was co operating on the Cape Photographic Durchmusterung. De Sitter participated in the program to make precise measurements of the positions of the Galilean moons of Jupiter, using a heliometer. In 1901 he received his doctorate under Kapteyn on a dissertation on Jupiter's satellites: Discussion of Heliometer Observations of Jupiter's Satel lites. De Sitter remained at Groningen as an assistant to Kapteyn in the astronomical laboratory, until 1909, when he was appointed to the chair of astronomy at the University of Leiden. In 1919 he be came director of the Leiden Observatory. He remained in these posts until his death in 1934. De Sitter's work was highly mathematical. With his work on Jupi ter's satellites, De Sitter pursued the new methods of celestial me chanics of Poincare and Tisserand. His earlier heliometer meas urements were later supplemented by photographic measurements made at the Cape, Johannesburg, Pulkowa, Greenwich, and Leiden. De Sitter's final results on this subject were published as 'New Math ematical Theory of Jupiter's Satellites' in 1925. -
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. -
The 29 of May Or Sir Arthur and The
International Journal of Management and Applied Science, ISSN: 2394-7926 Volume-4, Issue-4, Apr.-2018 http://iraj.in THE 29TH OF MAY OR SIR ARTHUR AND THE BENDING LIGHT (TEACHING SCIENCE AND LITERATURE JOINTLY) MICHAEL KATZ Faculty of Education, Haifa University, Mount Carmel, Haifa, Israel E-mail: [email protected] Abstract - In this paper I present an instance illustrating a program of joint teaching of science and literature. The instance sketched here rests on recognition that at the age when children read books like Kästner's "The 35th of May" they can already taste notions of Relativity Theory through the story of Eddington's expedition to Principe Island. Eddington's story is briefly recounted here with references to Kästner's book. The relationships thus exhibited between science and fiction, fantasy and reality, theory and actuality, humor and earnestness, should help evoke school age children's interest in science and literature at early stages in their studies' endeavor. Keywords - Bending Light, Fantasy, Gravitation, Relativity, Science and Literature. I. INTRODUCTION South Seas" – a story of adventure and humor by Erich Kästner, the well known German author of The idea that teaching science and humanities in more than a few dearly loved novels, mostly for primary and secondary schools needn't necessarily be children and adolescents. The book was first seen as disjoint objectives is prevalent in the thought published in German in 1931 and in English shortly and practice of more than a few scholars and teachers after. in recent years. Carole Cox [1], for example, unfolds forty strategies of literature based teaching of various Twelve years earlier, in 1919, another journey topics in arts and sciences. -
(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. -
Principle of Relativity in Physics and in Epistemology Guang-Jiong
Principle of Relativity in Physics and in Epistemology Guang-jiong Ni Department of Physics, Fudan University, Shanghai 200433,China Department of Physics , Portland State University, Portland,OR97207,USA (Email: [email protected]) Abstract: The conceptual evolution of principle of relativity in the theory of special relativity is discussed in detail . It is intimately related to a series of difficulties in quantum mechanics, relativistic quantum mechanics and quantum field theory as well as to new predictions about antigravity and tachyonic neutrinos etc. I. Introduction: Two Postulates of Einstein As is well known, the theory of special relativity(SR) was established by Einstein in 1905 on two postulates (see,e.g.,[1]): Postulate 1: All inertial frames are equivalent with respect to all the laws of physics. Postulate 2: The speed of light in empty space always has the same value c. The postulate 1 , usually called as the “principle of relativity” , was accepted by all physicists in 1905 without suspicion whereas the postulate 2 aroused a great surprise among many physicists at that time. The surprise was inevitable and even necessary since SR is a totally new theory out broken from the classical physics. Both postulates are relativistic in essence and intimately related. This is because a law of physics is expressed by certain equation. When we compare its form from one inertial frame to another, a coordinate transformation is needed to check if its form remains invariant. And this Lorentz transformation must be established by the postulate 2 before postulate 1 can have quantitative meaning. Hence, as a metaphor, to propose postulate 1 was just like “ to paint a dragon on the wall” and Einstein brought it to life “by putting in the pupils of its eyes”(before the dragon could fly out of the wall) via the postulate 2[2]. -
Reconsidering Time Dilation of Special Theory of Relativity
International Journal of Advanced Research in Physical Science (IJARPS) Volume 5, Issue 8, 2018, PP 7-11 ISSN No. (Online) 2349-7882 www.arcjournals.org Reconsidering Time Dilation of Special Theory of Relativity Salman Mahmud Student of BIAM Model School and College, Bogra, Bangladesh *Corresponding Author: Salman Mahmud, Student of BIAM Model School and College, Bogra, Bangladesh Abstract : In classical Newtonian physics, the concept of time is absolute. With his theory of relativity, Einstein proved that time is not absolute, through time dilation. According to the special theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other. As a result a clock that is moving relative to an observer will be measured to tick slower than a clock that is at rest in the observer's own frame of reference. Through some thought experiments, Einstein proved the time dilation. Here in this article I will use my thought experiments to demonstrate that time dilation is incorrect and it was a great mistake of Einstein. 1. INTRODUCTION A central tenet of special relativity is the idea that the experience of time is a local phenomenon. Each object at a point in space can have it’s own version of time which may run faster or slower than at other objects elsewhere. Relative changes in the experience of time are said to happen when one object moves toward or away from other object. This is called time dilation. But this is wrong. Einstein’s relativity was based on two postulates: 1. -
Albert Einstein's Key Breakthrough — Relativity
{ EINSTEIN’S CENTURY } Albert Einstein’s key breakthrough — relativity — came when he looked at a few ordinary things from a different perspective. /// BY RICHARD PANEK Relativity turns 1001 How’d he do it? This question has shadowed Albert Einstein for a century. Sometimes it’s rhetorical — an expression of amazement that one mind could so thoroughly and fundamentally reimagine the universe. And sometimes the question is literal — an inquiry into how Einstein arrived at his special and general theories of relativity. Einstein often echoed the first, awestruck form of the question when he referred to the mind’s workings in general. “What, precisely, is ‘thinking’?” he asked in his “Autobiographical Notes,” an essay from 1946. In somebody else’s autobiographical notes, even another scientist’s, this question might have been unusual. For Einstein, though, this type of question was typical. In numerous lectures and essays after he became famous as the father of relativity, Einstein began often with a meditation on how anyone could arrive at any subject, let alone an insight into the workings of the universe. An answer to the literal question has often been equally obscure. Since Einstein emerged as a public figure, a mythology has enshrouded him: the lone- ly genius sitting in the patent office in Bern, Switzerland, thinking his little thought experiments until one day, suddenly, he has a “Eureka!” moment. “Eureka!” moments young Einstein had, but they didn’t come from nowhere. He understood what scientific questions he was trying to answer, where they fit within philosophical traditions, and who else was asking them. -
Equivalence Principle (WEP) of General Relativity Using a New Quantum Gravity Theory Proposed by the Authors Called Electro-Magnetic Quantum Gravity Or EMQG (Ref
WHAT ARE THE HIDDEN QUANTUM PROCESSES IN EINSTEIN’S WEAK PRINCIPLE OF EQUIVALENCE? Tom Ostoma and Mike Trushyk 48 O’HARA PLACE, Brampton, Ontario, L6Y 3R8 [email protected] Monday April 12, 2000 ACKNOWLEDGMENTS We wish to thank R. Mongrain (P.Eng) for our lengthy conversations on the nature of space, time, light, matter, and CA theory. ABSTRACT We provide a quantum derivation of Einstein’s Weak Equivalence Principle (WEP) of general relativity using a new quantum gravity theory proposed by the authors called Electro-Magnetic Quantum Gravity or EMQG (ref. 1). EMQG is manifestly compatible with Cellular Automata (CA) theory (ref. 2 and 4), and is also based on a new theory of inertia (ref. 5) proposed by R. Haisch, A. Rueda, and H. Puthoff (which we modified and called Quantum Inertia, QI). QI states that classical Newtonian Inertia is a property of matter due to the strictly local electrical force interactions contributed by each of the (electrically charged) elementary particles of the mass with the surrounding (electrically charged) virtual particles (virtual masseons) of the quantum vacuum. The sum of all the tiny electrical forces (photon exchanges with the vacuum particles) originating in each charged elementary particle of the accelerated mass is the source of the total inertial force of a mass which opposes accelerated motion in Newton’s law ‘F = MA’. The well known paradoxes that arise from considerations of accelerated motion (Mach’s principle) are resolved, and Newton’s laws of motion are now understood at the deeper quantum level. We found that gravity also involves the same ‘inertial’ electromagnetic force component that exists in inertial mass. -
Revised Theory of Gravity Doesn't Predict a Big Bang 12 July 2010, by Lisa Zyga
Revised theory of gravity doesn't predict a Big Bang 12 July 2010, By Lisa Zyga decades he became more interested in finding a theory to unify gravity and quantum mechanics - a task that is still being studied today. In 1924, Eddington proposed a new “gravitational action” as an alternative to the Einstein-Hilbert action, which could serve as an alternative starting point to general relativity. In astrophysics, a gravitational action is the mechanism that describes how gravity can emerge from space-time being curved by matter and energy. However, Eddington’s theory of gravity only worked for empty space and didn’t Illustration: Time Line of the Universe Credit: include any source of energy such as matter, NASA/WMAP making it an incomplete theory. Since Eddington’s proposal, scientists have attempted various ways of including matter into the (PhysOrg.com) -- The Big Bang theory has formed theory, although they have run into problems. In the basis of our understanding of the universe's this study, Banados and Ferreira have tried a new origins since it was first proposed in 1927 by way to extend the theory to include matter by using Georges Lemaitre. And for good reason: the theory a gravitational action called the Born-Infeld action. is supported by scientists' latest observations and experiments, and is based on Einstein's widely In their analysis, the scientists found that a key accepted theory of general relativity. But scientists characteristic of Eddington’s revised theory of are always on the lookout for any evidence that gravity is that it reproduces Einstein gravity might suggest an alternative to the Big Bang. -
Eddington, Lemaître and the Hypothesis of Cosmic Expansion in 1927
Eddington, Lemaître and the hypothesis of cosmic expansion in 1927 Cormac O’Raifeartaigh School of Science and Computing, Waterford Institute of Technology, Cork Road, Waterford, Ireland Author for correspondence: [email protected] 1 1. Introduction Arthur Stanley Eddington was one of the leading astronomers and theorists of his generation (Smart et al. 1945; McCrea 1982; Chandrasekhar, S. 1983). An early and important proponent of the general theory of relativity, his 1918 ‘Report on the Relativity Theory of Gravitation’ for the Physical Society (Eddington 1918) provided an early authoritative exposition of the subject for English-speaking physicists (Vibert Douglas 1956 p42; Chandrasekhar 1983 p24). He played a leading role in the eclipse observations of 1919 that offered early astronomical evidence in support of the theory (Vibert Douglas 1956 pp 39-41; Chandrasekhar 1983 pp 24- 29; Kennefick, this volume) while his book ‘Space, Time and Gravitation’ (Eddington 1920) was one of the first popular treatises on general relativity for an English-speaking audience. In addition, Eddington’s textbook ‘The Mathematical Theory of Relativity’ (Eddington 1923) became a classic reference for English-speaking physicists with an interest in relativity (McCrea 1982; Chandrasekhar 1983 p32). Indeed, the book provided one of the first textbook accounts of relativistic models of the cosmos, complete with a discussion of possible links to one of the greatest astronomical puzzles of the age, the redshifts of the spiral nebulae (Eddington 1923 pp 155-170). It seems therefore quite surprising that, when Eddington’s former student Georges Lemaître suggested in a seminal article of 1927 (Lemaître 1927) that a universe of expanding radius could be derived from general relativity, and that the phenomenon could provide a natural explanation for the redshifts of the spiral nebulae, Eddington (and others) paid no attention.