Einstein Chases a Light Beam
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Belated Decision in the Hilbert-Einstein Priority Dispute
(10). As described above, the severely opis- Dinosauria (Univ. of California Press, Berkeley, CA, However, the overall similarity of the pelvis of Archae- 1990). opteryx to those of the enantiornithine birds, espe- thopubic condition of their pelvis is consis- 10. L. Hou, L. D. Martin, Z. Zhou, A. Feduccia, Science cially the presence of the hypopubic cup, as well as tent with the notion that these birds roost- 274, 1164 (1996). the morphology of the London and Berlin Archae- ed in trees. In contrast, based primarily on 11. Q. Ji and S. Ji, Chin. Geol. 10, 30 (1996); see also V. opteryx specimens, offer support for our interpreta- disputed measurements of claw curvature, Morell, Audubon 99, 36 (1997). tion of the pelvic structure of these early birds [L. D. 12. Rather than representing primitive archosaurian Martin, in Origin of the Higher Groups of Tetrapods, Archaeopteryx has been interpreted as structures, it is probable that the hepatic-piston dia- H. P. Schultze and L. Trueb, Eds. (Cornell Univ. adapted primarily for a terrestrial rather phragm systems in crocodilians and theropods are Press, Ithaca, NY, 1991), pp. 485–540. than an arboreal existence (18). However, convergently derived. Pelvic anatomy in early “pro- 18. D. S. Peters and E. Go¨ rgner, in Proceedings of the II todinosaurs” such as Lagosuchus, as well as in all International Symposium of Avian Paleontology, K. as in the enantiornithines, the morphology ornithischian dinosaurs, shows no evidence of the Campbell, Ed. (Los Angeles Museum of Natural His- of Archaeopteryx’s pelvis is best interpreted pubis having served as a site of origin for similar tory Press, Los Angeles, CA, 1992), pp. -
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 ................. -
Dayton C. Miller by Peter Hoekje
The newsletter of The Acoustical Society of America Volume 13, Number 1 Winter 2003 Dayton C. Miller by Peter Hoekje ayton Clarence Miller (1866–1941), a founding member a full body composite of himself, and an injured railroad brake- and second president of the Acoustical Society of man. This latter is claimed to be the first use of x-rays for sur- DAmerica, is remembered for his distinctive gical purposes. Tragically, his laboratory assistant died contributions in the early 20th century in several in 1905, apparently from radiation-related illness. fields. Acousticians appreciate his pioneering With the encouragement of Edward Morley, analysis of sound waveforms and spectra, his Miller revisited the 1887 Michelson-Morley accurate measurements of the speed of sound aether drift experiment with a new interfer- in air, and his study of flutes and their ometer in 1902, and continued working on acoustics. But, he is also known for metic- this problem for nearly 30 years. In making ulous measurementsThe newsletterof aether drift, for of the measurements, the interferometer would first surgical x-ray, and for the huge flute be set in motion once and would rotate collection he donated to the Library of freely for an hour while the experimenter Congress. He balanced an outstanding made observations of the fractional scientific research career with a devotion fringe displacement, several times to the arts and education. throughout each rotation. Miller claimed As a small boy, Dayton started his to have walked 160 miles and made musical and acoustic explorations on his 200,000 observations of fringes in the father’s fife.1 His father bought him his course of his experiments! He consistent- first full-size flute on his thirteenth birth- ly arrived at an observed aether drift speed day, but it was too big for his small fingers. -
Measurement of the Speed of Gravity
Measurement of the Speed of Gravity Yin Zhu Agriculture Department of Hubei Province, Wuhan, China Abstract From the Liénard-Wiechert potential in both the gravitational field and the electromagnetic field, it is shown that the speed of propagation of the gravitational field (waves) can be tested by comparing the measured speed of gravitational force with the measured speed of Coulomb force. PACS: 04.20.Cv; 04.30.Nk; 04.80.Cc Fomalont and Kopeikin [1] in 2002 claimed that to 20% accuracy they confirmed that the speed of gravity is equal to the speed of light in vacuum. Their work was immediately contradicted by Will [2] and other several physicists. [3-7] Fomalont and Kopeikin [1] accepted that their measurement is not sufficiently accurate to detect terms of order , which can experimentally distinguish Kopeikin interpretation from Will interpretation. Fomalont et al [8] reported their measurements in 2009 and claimed that these measurements are more accurate than the 2002 VLBA experiment [1], but did not point out whether the terms of order have been detected. Within the post-Newtonian framework, several metric theories have studied the radiation and propagation of gravitational waves. [9] For example, in the Rosen bi-metric theory, [10] the difference between the speed of gravity and the speed of light could be tested by comparing the arrival times of a gravitational wave and an electromagnetic wave from the same event: a supernova. Hulse and Taylor [11] showed the indirect evidence for gravitational radiation. However, the gravitational waves themselves have not yet been detected directly. [12] In electrodynamics the speed of electromagnetic waves appears in Maxwell equations as c = √휇0휀0, no such constant appears in any theory of gravity. -
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. -
A Plausible Resolution to Hilbert's Failed Attempt to Unify Gravitation & Electromagnetism
Prespacetime Journal| December 2018 | Volume 9 | Issue 10 | pp. xxx-xxx 1000 Christianto, V., Smarandache, F., & Boyd, R. N., A Plausible Resolution to Hilbert’s Failed Attempt to Unify Gravitation & Electromagnetism Exploration A Plausible Resolution to Hilbert’s Failed Attempt to Unify Gravitation & Electromagnetism Victor Christianto1*, Florentin Smarandache2 & Robert N. Boyd3 1Malang Institute of Agriculture (IPM), Malang, Indonesia 2Dept. of Math. Sci., Univ. of New Mexico, Gallup, USA 3Independent Researcher, USA Abstract In this paper, we explore the reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed and outline a plausible resolution of this problem. The latter is based on Gödel’s incompleteness theorem and Newton’s aether stream model. Keywords: Unification, gravitation, electromagnetism, Hilbert, resolution. Introduction Hilbert and Einstein were in race at 1915 to develop a new gravitation theory based on covariance principle [1]. While Einstein seemed to win the race at the time, Hilbert produced two communications which show that he was ahead of Einstein in term of unification of gravitation theory and electromagnetic theory. Hilbert started with Mie’s electromagnetic theory. However, as Mie theory became completely failed, so was the Hilbert’s axiomatic program to unify those two theories [1]. Einstein might be learning from such an early failure of Hilbert to unify those theories, and years later returned to Mie theory [1]. What we would say here is that Hilbert’s axiomatic failure can be explained by virtue of Gödel’s incompleteness theorem: which says essentially that any attempt to build a consistent theory based on axiomatic foundations can be shown to be inconsistent. -
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