Notes on Special Relativity We Start This Section by Reminding You What
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Accelerator and Beam Physics Research Goals and Opportunities
Accelerator and Beam Physics Research Goals and Opportunities Working group: S. Nagaitsev (Fermilab/U.Chicago) Chair, Z. Huang (SLAC/Stanford), J. Power (ANL), J.-L. Vay (LBNL), P. Piot (NIU/ANL), L. Spentzouris (IIT), and J. Rosenzweig (UCLA) Workshops conveners: Y. Cai (SLAC), S. Cousineau (ORNL/UT), M. Conde (ANL), M. Hogan (SLAC), A. Valishev (Fermilab), M. Minty (BNL), T. Zolkin (Fermilab), X. Huang (ANL), V. Shiltsev (Fermilab), J. Seeman (SLAC), J. Byrd (ANL), and Y. Hao (MSU/FRIB) Advisors: B. Dunham (SLAC), B. Carlsten (LANL), A. Seryi (JLab), and R. Patterson (Cornell) January 2021 Abbreviations and Acronyms 2D two-dimensional 3D three-dimensional 4D four-dimensional 6D six-dimensional AAC Advanced Accelerator Concepts ABP Accelerator and Beam Physics DOE Department of Energy FEL Free-Electron Laser GARD General Accelerator R&D GC Grand Challenge H- a negatively charged Hydrogen ion HEP High-Energy Physics HEPAP High-Energy Physics Advisory Panel HFM High-Field Magnets KV Kapchinsky-Vladimirsky (distribution) ML/AI Machine Learning/Artificial Intelligence NCRF Normal-Conducting Radio-Frequency NNSA National Nuclear Security Administration NSF National Science Foundation OHEP Office of High Energy Physics QED Quantum Electrodynamics rf radio-frequency RMS Root Mean Square SCRF Super-Conducting Radio-Frequency USPAS US Particle Accelerator School WG Working Group 1 Accelerator and Beam Physics 1. EXECUTIVE SUMMARY Accelerators are a key capability for enabling discoveries in many fields such as Elementary Particle Physics, Nuclear Physics, and Materials Sciences. While recognizing the past dramatic successes of accelerator-based particle physics research, the April 2015 report of the Accelerator Research and Development Subpanel of HEPAP [1] recommended the development of a long-term vision and a roadmap for accelerator science and technology to enable future DOE HEP capabilities. -
Physics 9Hb: Special Relativity & Thermal/Statistical Physics
PHYSICS 9HB: SPECIAL RELATIVITY & THERMAL/STATISTICAL PHYSICS Tom Weideman University of California, Davis UCD: Physics 9HB – Special Relativity and Thermal/Statistical Physics This text is disseminated via the Open Education Resource (OER) LibreTexts Project (https://LibreTexts.org) and like the hundreds of other texts available within this powerful platform, it freely available for reading, printing and "consuming." Most, but not all, pages in the library have licenses that may allow individuals to make changes, save, and print this book. Carefully consult the applicable license(s) before pursuing such effects. Instructors can adopt existing LibreTexts texts or Remix them to quickly build course-specific resources to meet the needs of their students. Unlike traditional textbooks, LibreTexts’ web based origins allow powerful integration of advanced features and new technologies to support learning. The LibreTexts mission is to unite students, faculty and scholars in a cooperative effort to develop an easy-to-use online platform for the construction, customization, and dissemination of OER content to reduce the burdens of unreasonable textbook costs to our students and society. The LibreTexts project is a multi-institutional collaborative venture to develop the next generation of open-access texts to improve postsecondary education at all levels of higher learning by developing an Open Access Resource environment. The project currently consists of 13 independently operating and interconnected libraries that are constantly being optimized by students, faculty, and outside experts to supplant conventional paper-based books. These free textbook alternatives are organized within a central environment that is both vertically (from advance to basic level) and horizontally (across different fields) integrated. -
Physics 200 Problem Set 7 Solution Quick Overview: Although Relativity Can Be a Little Bewildering, This Problem Set Uses Just A
Physics 200 Problem Set 7 Solution Quick overview: Although relativity can be a little bewildering, this problem set uses just a few ideas over and over again, namely 1. Coordinates (x; t) in one frame are related to coordinates (x0; t0) in another frame by the Lorentz transformation formulas. 2. Similarly, space and time intervals (¢x; ¢t) in one frame are related to inter- vals (¢x0; ¢t0) in another frame by the same Lorentz transformation formu- las. Note that time dilation and length contraction are just special cases: it is time-dilation if ¢x = 0 and length contraction if ¢t = 0. 3. The spacetime interval (¢s)2 = (c¢t)2 ¡ (¢x)2 between two events is the same in every frame. 4. Energy and momentum are always conserved, and we can make e±cient use of this fact by writing them together in an energy-momentum vector P = (E=c; p) with the property P 2 = m2c2. In particular, if the mass is zero then P 2 = 0. 1. The earth and sun are 8.3 light-minutes apart. Ignore their relative motion for this problem and assume they live in a single inertial frame, the Earth-Sun frame. Events A and B occur at t = 0 on the earth and at 2 minutes on the sun respectively. Find the time di®erence between the events according to an observer moving at u = 0:8c from Earth to Sun. Repeat if observer is moving in the opposite direction at u = 0:8c. Answer: According to the formula for a Lorentz transformation, ³ u ´ 1 ¢tobserver = γ ¢tEarth-Sun ¡ ¢xEarth-Sun ; γ = p : c2 1 ¡ (u=c)2 Plugging in the numbers gives (notice that the c implicit in \light-minute" cancels the extra factor of c, which is why it's nice to measure distances in terms of the speed of light) 2 min ¡ 0:8(8:3 min) ¢tobserver = p = ¡7:7 min; 1 ¡ 0:82 which means that according to the observer, event B happened before event A! If we reverse the sign of u then 2 min + 0:8(8:3 min) ¢tobserver 2 = p = 14 min: 1 ¡ 0:82 2. -
8. Special Relativity
8. Special Relativity Although Newtonian mechanics gives an excellent description of Nature, it is not uni- versally valid. When we reach extreme conditions — the very small, the very heavy or the very fast — the Newtonian Universe that we’re used to needs replacing. You could say that Newtonian mechanics encapsulates our common sense view of the world. One of the major themes of twentieth century physics is that when you look away from our everyday world, common sense is not much use. One such extreme is when particles travel very fast. The theory that replaces New- tonian mechanics is due to Einstein. It is called special relativity. The effects of special relativity become apparent only when the speeds of particles become comparable to the speed of light in the vacuum. Universally denoted as c, the speed of light is c = 299792458 ms−1 This value of c is exact. In fact, it would be more precise to say that this is the definition of what we mean by a meter: it is the distance travelled by light in 1/299792458 seconds. For the purposes of this course, we’ll be quite happy with the approximation c 3 108 ms−1. ≈ × The first thing to say is that the speed of light is fast. Really fast. The speed of sound is around 300 ms−1; escape velocity from the Earth is around 104 ms−1; the orbital speed of our solar system in the Milky Way galaxy is around 105 ms−1. As we shall soon see, nothing travels faster than c. -
Accelerator Physics and Modeling
BNL-52379 CAP-94-93R ACCELERATOR PHYSICS AND MODELING ZOHREH PARSA, EDITOR PROCEEDINGS OF THE SYMPOSIUM ON ACCELERATOR PHYSICS AND MODELING Brookhaven National Laboratory UPTON, NEW YORK 11973 ASSOCIATED UNIVERSITIES, INC. UNDER CONTRACT NO. DE-AC02-76CH00016 WITH THE UNITED STATES DEPARTMENT OF ENERGY DISCLAIMER This report was prepared as an account of work sponsored by an agency of the Unite1 States Government Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, doea not necessarily constitute or imply its endorsement, recomm.ndation, or favoring by the UnitedStates Government or any agency, contractor or subcontractor thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency, contractor or subcontractor thereof- Printed in the United States of America Available from National Technical Information Service U.S. Department of Commerce 5285 Port Royal Road Springfieid, VA 22161 NTIS price codes: Am&mffi TABLE OF CONTENTS Topic, Author Page no. Forward, Z . Parsa, Brookhaven National Lab. i Physics of High Brightness Beams , 1 M. Reiser, University of Maryland . Radio Frequency Beam Conditioner For Fast-Wave 45 Free-Electron Generators of Coherent Radiation Li-Hua NSLS Dept., Brookhaven National Lab, and A. -
(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. -
Accelerator Physics Third Edition
Preface Accelerator science took off in the 20th century. Accelerator scientists invent many in- novative technologies to produce and manipulate high energy and high quality beams that are instrumental to progresses in natural sciences. Many kinds of accelerators serve the need of research in natural and biomedical sciences, and the demand of applications in industry. In the 21st century, accelerators will become even more important in applications that include industrial processing and imaging, biomedical research, nuclear medicine, medical imaging, cancer therapy, energy research, etc. Accelerator research aims to produce beams in high power, high energy, and high brilliance frontiers. These beams addresses the needs of fundamental science research in particle and nuclear physics, condensed matter and biomedical sciences. High power beams may ignite many applications in industrial processing, energy production, and national security. Accelerator Physics studies the interaction between the charged particles and elec- tromagnetic field. Research topics in accelerator science include generation of elec- tromagnetic fields, material science, plasma, ion source, secondary beam production, nonlinear dynamics, collective instabilities, beam cooling, beam instrumentation, de- tection and analysis, beam manipulation, etc. The textbook is intended for graduate students who have completed their graduate core-courses including classical mechanics, electrodynamics, quantum mechanics, and statistical mechanics. I have tried to emphasize the fundamental physics behind each innovative idea with least amount of mathematical complication. The textbook may also be used by advanced undergraduate seniors who have completed courses on classical mechanics and electromagnetism. For beginners in accelerator physics, one begins with Secs. 2.I–2.IV in Chapter 2, and follows by Secs. -
Relativistic Kinematics of Particle Interactions Introduction
le kin rel.tex Relativistic Kinematics of Particle Interactions byW von Schlipp e, March2002 1. Notation; 4-vectors, covariant and contravariant comp onents, metric tensor, invariants. 2. Lorentz transformation; frequently used reference frames: Lab frame, centre-of-mass frame; Minkowski metric, rapidity. 3. Two-b o dy decays. 4. Three-b o dy decays. 5. Particle collisions. 6. Elastic collisions. 7. Inelastic collisions: quasi-elastic collisions, particle creation. 8. Deep inelastic scattering. 9. Phase space integrals. Intro duction These notes are intended to provide a summary of the essentials of relativistic kinematics of particle reactions. A basic familiarity with the sp ecial theory of relativity is assumed. Most derivations are omitted: it is assumed that the interested reader will b e able to verify the results, which usually requires no more than elementary algebra. Only the phase space calculations are done in some detail since we recognise that they are frequently a bit of a struggle. For a deep er study of this sub ject the reader should consult the monograph on particle kinematics byByckling and Ka jantie. Section 1 sets the scene with an intro duction of the notation used here. Although other notations and conventions are used elsewhere, I present only one version which I b elieveto b e the one most frequently encountered in the literature on particle physics, notably in such widely used textb o oks as Relativistic Quantum Mechanics by Bjorken and Drell and in the b o oks listed in the bibliography. This is followed in section 2 by a brief discussion of the Lorentz transformation. -
A Re-Interpretation of the Concept of Mass and of the Relativistic Mass-Energy Relation
A re-interpretation of the concept of mass and of the relativistic mass-energy relation 1 Stefano Re Fiorentin Summary . For over a century the definitions of mass and derivations of its relation with energy continue to be elaborated, demonstrating that the concept of mass is still not satisfactorily understood. The aim of this study is to show that, starting from the properties of Minkowski spacetime and from the principle of least action, energy expresses the property of inertia of a body. This implies that inertial mass can only be the object of a definition – the so called mass-energy relation - aimed at measuring energy in different units, more suitable to describe the huge amount of it enclosed in what we call the “rest-energy” of a body. Likewise, the concept of gravitational mass becomes unnecessary, being replaceable by energy, thus making the weak equivalence principle intrinsically verified. In dealing with mass, a new unit of measurement is foretold for it, which relies on the de Broglie frequency of atoms, the value of which can today be measured with an accuracy of a few parts in 10 9. Keywords Classical Force Fields; Special Relativity; Classical General Relativity; Units and Standards 1. Introduction Albert Einstein in the conclusions of his 1905 paper “Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?” (“Does the inertia of a body depend upon its energy content? ”) [1] says “The mass of a body is a measure of its energy-content ”. Despite of some claims that the reasoning that brought Einstein to the mass-energy relation was somehow approximated or even defective (starting from Max Planck in 1907 [2], to Herbert E. -
Special Relativity: a Centenary Perspective
Special Relativity: A Centenary Perspective Clifford M. Will McDonnell Center for the Space Sciences and Department of Physics Washington University, St. Louis MO 63130 USA Contents 1 Introduction 1 2 Fundamentals of special relativity 2 2.1 Einstein’s postulates and insights . ....... 2 2.2 Timeoutofjoint ................................. 3 2.3 SpacetimeandLorentzinvariance . ..... 5 2.4 Special relativistic dynamics . ...... 7 3 Classic tests of special relativity 7 3.1 The Michelson-Morley experiment . ..... 7 3.2 Invariance of c ................................... 9 3.3 Timedilation ................................... 9 3.4 Lorentz invariance and quantum mechanics . ....... 10 3.5 Consistency tests of special relativity . ......... 10 4 Special relativity and curved spacetime 12 4.1 Einstein’s equivalence principle . ....... 13 4.2 Metrictheoriesofgravity. .... 14 4.3 Effective violations of local Lorentz invariance . ........... 14 5 Is gravity Lorentz invariant? 17 arXiv:gr-qc/0504085v1 19 Apr 2005 6 Tests of local Lorentz invariance at the centenary 18 6.1 Frameworks for Lorentz symmetry violations . ........ 18 6.2 Modern searches for Lorentz symmetry violation . ......... 20 7 Concluding remarks 21 References........................................ 21 1 Introduction A hundred years ago, Einstein laid the foundation for a revolution in our conception of time and space, matter and energy. In his remarkable 1905 paper “On the Electrodynamics of Moving Bodies” [1], and the follow-up note “Does the Inertia of a Body Depend upon its Energy-Content?” [2], he established what we now call special relativity as one of the two pillars on which virtually all of physics of the 20th century would be built (the other pillar being quantum mechanics). The first new theory to be built on this framework was general relativity [3], and the successful measurement of the predicted deflection of light in 1919 made both Einstein the person and relativity the theory internationally famous. -
Special Relativity (Pdf)
Special relativity Thomas DeGrand February 18, 2012 Relativity 2 Contents 1 A top-down view of relativity 5 1.1 Whatthesenotesareallabout . .. 6 1.2 Thegeometryofspace-time . .. 7 2 Relativity for clocks and rulers 11 2.1 Non-relativisticrelativity. ....... 12 2.2 The Michaelson-Morley experiment . ..... 15 2.3 Introductiontorelativity. ..... 18 2.4 Space-timediagrams .............................. 27 2.5 Revisitingsomeexamples . .. 29 2.6 Velocityaddition ................................ 31 2.7 Dopplershift ................................... 33 3 Relativistic kinematics 37 3.1 Energy and momentum in special relativity . ...... 38 3.2 Summarizing results, and some useful formulas . ......... 41 3.3 Simpleexamples ................................. 42 3.4 Simple homework-style examples . .... 44 4 The end of special relativity 51 3 Relativity 4 4.1 Summary of the important concepts and results . ....... 52 4.2 What’sleft .................................... 52 Chapter 1 A top-down view of relativity 5 Relativity 6 “The non-mathematician is seized by a mysterious shuddering when he hears of ‘four- dimensional’ things, by a feeling not unlike that awakened by thoughts of the occult. And yet there is no more commonplace statement, that the world in which we live is a four- dimensional space-time continuum.”–A. Einstein 1.1 What these notes are all about I am a theorist who studies elementary particle physics. The phenomena I study take place on an energy scale where the effects of special relativity are so important that they dominate everything else. This means that, right from the beginning, everything I do has to be made consistent with the rules of special relativity, or what I compute will simply be wrong. This forces me to think in a particular way about special relativity. -
Neutrino Proper Time?
Neutrino Proper Time? Richard Shurtleff ∗ March 8, 2000 Abstract An electron neutrino can have the quantum phase of an electron, i.e. share its internal clock, if the neutrino takes a path in space-time that is not in the direction of its energy-momentum. Each flavor neutrino would then have a different internal clock; a muon neutrino would have a muon clock and a tau neutrino would have a tau clock. Perhaps surprisingly, there is some evidence suggesting neutrinos have such clocks. If muon neutrinos travel on space-like paths then some atmospheric muon neutrinos would take such paths backwards into outer space and not be observed. These are lost at the source and have nothing to do with oscillations or flavor-changing in flight. The expected depletion of source muon neutrinos is shown here to be 9%, which accounts for half of the missing muon neutrino source flux reported by Super- Kamiokande. Since there is no depletion in the electron neutrino flux source reported at SK and SN1987A electron neutrinos seem to have traveled at the speed of light, the electron neutrino travels on a light-like path. Accelerator-based experiments could be arranged to confirm the reverse motion of muon neutrinos. arXiv:hep-ph/0003071v1 8 Mar 2000 PACS numbers: 03.65.Bz, 14.60.Lm, 96.40.Tv ∗affiliation and mailing address: Department of Mathematics and Applied Sciences, Wentworth Institute of Technology, 550 Huntington Avenue, Boston, MA, USA, ZIP 02115, telephone number: (617) 989-4338, fax number: (617) 989-4591 , e-mail address: shurtleff[email protected] 1 1 INTRODUCTION 2 1 Introduction The quantum phase of a free electron on a given path Γ is the product of its mass and the proper time along Γ, divided by the constanth.