On Thought Experiments: Mach and Einstein (Part I)
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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 ................. -
Michelson–Morley Experiment
Michelson–Morley experiment Figure 1. Michelson and Morley's interferometric setup, mounted on a stone slab that floats in an annular trough of mercury The Michelson–Morley experiment was an attempt to detect the existence of the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between April and July 1887 by Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University in Cleveland, Ohio, and published in November of the same year.[1] It compared the speed of light in perpendicular directions in an attempt to detect the relative motion of matter through the stationary luminiferous aether ("aether wind"). The result was negative, in that Michelson and Morley found no significant difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles. This result is generally considered to be the first strong evidence against the then-prevalent aether theory, and initiated a line of research that eventually led to special relativity, which rules out a stationary aether.[A 1] Of this experiment, Einstein wrote, "If the Michelson–Morley experiment had not brought us into serious embarrassment, no one would have regarded the relativity theory as a (halfway) redemption."[A 2]:219 Michelson–Morley type experiments have been repeated many times with steadily increasing sensitivity. These include experiments from 1902 to 1905, and a series of experiments in the 1920s. More recent optical -
Implementation of the Fizeau Aether Drag Experiment for An
Implementation of the Fizeau Aether Drag Experiment for an Undergraduate Physics Laboratory by Bahrudin Trbalic Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 c Massachusetts Institute of Technology 2020. All rights reserved. ○ Author................................................................ Department of Physics May 8, 2020 Certified by. Sean P. Robinson Lecturer of Physics Thesis Supervisor Certified by. Joseph A. Formaggio Professor of Physics Thesis Supervisor Accepted by . Nergis Mavalvala Associate Department Head, Department of Physics 2 Implementation of the Fizeau Aether Drag Experiment for an Undergraduate Physics Laboratory by Bahrudin Trbalic Submitted to the Department of Physics on May 8, 2020, in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics Abstract This work presents the description and implementation of the historically significant Fizeau aether drag experiment in an undergraduate physics laboratory setting. The implementation is optimized to be inexpensive and reproducible in laboratories that aim to educate students in experimental physics. A detailed list of materials, experi- mental setup, and procedures is given. Additionally, a laboratory manual, preparatory materials, and solutions are included. Thesis Supervisor: Sean P. Robinson Title: Lecturer of Physics Thesis Supervisor: Joseph A. Formaggio Title: Professor of Physics 3 4 Acknowledgments I gratefully acknowledge the instrumental help of Prof. Joseph Formaggio and Dr. Sean P. Robinson for the guidance in this thesis work and in my academic life. The Experimental Physics Lab (J-Lab) has been the pinnacle of my MIT experience and I’m thankful for the time spent there. -
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. -
Einstein's Mistakes
Einstein’s Mistakes Einstein was the greatest genius of the Twentieth Century, but his discoveries were blighted with mistakes. The Human Failing of Genius. 1 PART 1 An evaluation of the man Here, Einstein grows up, his thinking evolves, and many quotations from him are listed. Albert Einstein (1879-1955) Einstein at 14 Einstein at 26 Einstein at 42 3 Albert Einstein (1879-1955) Einstein at age 61 (1940) 4 Albert Einstein (1879-1955) Born in Ulm, Swabian region of Southern Germany. From a Jewish merchant family. Had a sister Maja. Family rejected Jewish customs. Did not inherit any mathematical talent. Inherited stubbornness, Inherited a roguish sense of humor, An inclination to mysticism, And a habit of grüblen or protracted, agonizing “brooding” over whatever was on its mind. Leading to the thought experiment. 5 Portrait in 1947 – age 68, and his habit of agonizing brooding over whatever was on its mind. He was in Princeton, NJ, USA. 6 Einstein the mystic •“Everyone who is seriously involved in pursuit of science becomes convinced that a spirit is manifest in the laws of the universe, one that is vastly superior to that of man..” •“When I assess a theory, I ask myself, if I was God, would I have arranged the universe that way?” •His roguish sense of humor was always there. •When asked what will be his reactions to observational evidence against the bending of light predicted by his general theory of relativity, he said: •”Then I would feel sorry for the Good Lord. The theory is correct anyway.” 7 Einstein: Mathematics •More quotations from Einstein: •“How it is possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” •Questions asked by many people and Einstein: •“Is God a mathematician?” •His conclusion: •“ The Lord is cunning, but not malicious.” 8 Einstein the Stubborn Mystic “What interests me is whether God had any choice in the creation of the world” Some broadcasters expunged the comment from the soundtrack because they thought it was blasphemous. -
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 -
Michou Interferometer
July 21st 2016 Michou interferometer Costel Munteanu Montreal, QC, Canada [email protected] Abstract: The speed of light c defined as a constant of nature is in fact the “twoway speed of light” calculated from the measured time of travel of light from a light source to a reflector and back to a detector situated next to the source. In a “twoway” experiment (like FizeauFoucault apparatus) the constant c is the harmonic mean of “forward” and “backward” speeds [13]. A simple MichelsonMorley interferometer with equal length arms detects a difference between the time of travel of light along its two perpendicular arms in certain frames of reference in motion or in gravitational field and this is interpreted as Lorentz–FitzGerald contraction of length in the direction of motion or along the gradient of gravitational field [5]. While no experiment seemed to allow the precise “oneway” measurement of speed of light, LorentzFitzGerald length contraction interpretation is preferred. In this article I present an interferometer that determines the difference between “forward” and “backward” speed of light in certain frames of reference the anisotropy of speed of light along one direction showing a flow of electromagnetic medium through the frame of reference of the device contradicting the LorentzFitzGerald length contraction hypothesis and bring proof for the first time of (local) preferred frame effects. The device determines the direction of the flow and allows to calculate the velocity of that flow using the measured (or calculated) value of canonical “twoway” speed of light c in that particular frame of reference and the anisotropy measured by the device presented herein. -
Philosophy of Science -----Paulk
PHILOSOPHY OF SCIENCE -----PAULK. FEYERABEND----- However, it has also a quite decisive role in building the new science and in defending new theories against their well-entrenched predecessors. For example, this philosophy plays a most important part in the arguments about the Copernican system, in the development of optics, and in the Philosophy ofScience: A Subject with construction of a new and non-Aristotelian dynamics. Almost every work of Galileo is a mixture of philosophical, mathematical, and physical prin~ a Great Past ciples which collaborate intimately without giving the impression of in coherence. This is the heroic time of the scientific philosophy. The new philosophy is not content just to mirror a science that develops independ ently of it; nor is it so distant as to deal just with alternative philosophies. It plays an essential role in building up the new science that was to replace 1. While it should be possible, in a free society, to introduce, to ex the earlier doctrines.1 pound, to make propaganda for any subject, however absurd and however 3. Now it is interesting to see how this active and critical philosophy is immoral, to publish books and articles, to give lectures on any topic, it gradually replaced by a more conservative creed, how the new creed gener must also be possible to examine what is being expounded by reference, ates technical problems of its own which are in no way related to specific not to the internal standards of the subject (which may be but the method scientific problems (Hurne), and how there arises a special subject that according to which a particular madness is being pursued), but to stan codifies science without acting back on it (Kant). -
PLUNGE #305 - William K
20--MANCHESTER HERALD, Friday, Oct. 1.^, 1989 READ YOUR AD: ClassiFed odvertlsoments a r t I qi^ cars I CARS [g^CARS I CARS W E D ELIVER taken by telephone os o conyenlence. The FOR SALE FOR SALE FOR SALE Manchester Herald Is responsible For only one FOR SALE For Horr>© Del: 'sry. Call Incorrect Insertion and then only tor the size oF 6 4 7 - 9 9 4 6 the original Insertion. E . rorswhichdonot lessen the yolue oF the advertisement will not be 1984 HONDA Civic Wagon CHEVROLET 1980 Ma O L D S M O B IL E 1981 R e CHEVROLET 1985 Celeb Monday to Friday. 9 to 6 - 646-0767 or 649-4554, libu - 4 door, good gency - Loaded, must rity wagon. Excellent corrected by on additional Insertion._____________ J o c k . ________ condition. $1,250. 643- sell. 643-1364.___________ condition. V-6 auto 1986 JEEP Wogoneer Li 5484. 1984 CELEBRITY-4door, matic, power steerlng- /brakes, air, cruise. CARS mited - Excellent con CHEVROLET 1974 Co Fully equipped, excel CARS CARS dition, 43,000 miles, moro - New point, new lent condition. $3,500. $4,500 or best otter. IQI i FOR SALE 647-8894. FOR SALE automatic, olr condl- vinvl top, 6 cylinder 1987 MUSTANG LX - 4 I^^H foR sale FOR SALE tlonlng, om/tm automatic, $1,750. Ne cylinder, hatchback, 5 cassette, leather Inte- gotiable. 649-8944, speed, $6,500. 646-2392. rlor. $10,900, 643-2938. leave message. TRUCKS/VANS 1984 FORD Escort Wagon C O R V E T T E 1971 S tlno STEAL It.