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Funky Relativity Concepts the Anti-Textbook* a Work in Progress Funky Relativity Concepts The Anti-Textbook* A Work In Progress. See elmichelsen.physics.ucsd.edu/ for the latest versions of the Funky Series. Please send me comments. Eric L. Michelsen Image Source: http://www.space.com/. Need better graphic?? “A person starts to live when he can live outside himself.” “Weakness of attitude becomes weakness of character.” “We can’t solve problems by using the same kind of thinking we used when we created them.” “Once we accept our limits, we go beyond them.” “If we knew what we were doing, it would not be called ‘research’, would it?” --Albert Einstein * Physical, conceptual, geometric, and pictorial physics that didn’t fit in your textbook. Instead of distributing this document, please link to elmichelsen.physics.ucsd.edu/FunkyRelativityConcepts.pdf . Please cite as: Michelsen, Eric L., Funky Relativity Concepts, elmichelsen.physics.ucsd.edu, 4/26/2021. Physical constants: 2006 values from NIST. For more, see http://physics.nist.gov/cuu/Constants/ . Gravitational constant G = 6.674 28(67) x 10–11 m3 kg–1 s–2 Relative standard uncertainty 1.0 x 10–4 Speed of light in vacuum c = 299 792 458 m s–1 (exact) Boltzmann constant k = 1.380 6504(24) x 10–23 J K–1 Stefan-Boltzmann constant σ = 5.670 400(40) x 10–8 W m–2 K–4 –6 Relative standard uncertainty ±7.0 x 10 23 –1 Avogadro constant NA, L = 6.022 141 79(30) x 10 mol Relative standard uncertainty ±5.0 x 10–8 Molar gas constant R = 8.314 472(15) J mol-1 K-1 calorie 4.184 J (exact) –31 Electron mass me = 9.109 382 15(45) x 10 kg –27 Proton mass mp = 1.672 621 637(83) x 10 kg Proton/electron mass ratio mp/me = 1836.152 672 47(80) Elementary charge e = 1.602 176 487(40) x 10–19 C Electron g-factor ge = –2.002 319 304 3622(15) Proton g-factor gp = 5.585 694 713(46) Neutron g-factor gN = –3.826 085 45(90) –28 Muon mass mμ = 1.883 531 30(11) x 10 kg Inverse fine structure constant α–1 = 137.035 999 679(94) Planck constant h = 6.626 068 96(33) x 10–34 J s Planck constant over 2π ħ = 1.054 571 628(53) x 10–34 J s –10 Bohr radius a0 = 0.529 177 208 59(36) x 10 m –26 –1 Bohr magneton μB = 927.400 915(23) x 10 J T Other values: 1 inch ≡ 0.0254 m (exact) 1 drop ≡ .05 ml (metric system, exact. Other definitions exist.) 1 eV/particle = 96.472 kJ/mole 1 esu ≡ 1 statcoulomb = 3.335 641 10–10 C kiloton ≡ 4.184 x 1012 J = 1 Teracalorie bar ≡ 100,000 N/m2 atm ≡ 101,325 N/m2 = 1.013 25 bar torr ≡ 1/760 atm ≈ 133.322 N/m2 elmichelsen.physics.ucsd.edu/ Funky Relativity Concepts emichels at physics.ucsd.edu Contents 1 Introduction .............................................................................................................................. 8 Why Relativity? ................................................................................................................................... 8 How to Use This Document ................................................................................................................. 8 The Funky Series ................................................................................................................................. 8 What’s Wrong With Existing Relativity Expositions? ..................................................................... 8 My Story .......................................................................................................................................... 8 Thank You ........................................................................................................................................ 9 Scope ................................................................................................................................................... 9 What This Text Covers .................................................................................................................... 9 What This Text Doesn’t Cover ........................................................................................................ 9 What You Already Know ................................................................................................................. 9 Notation ............................................................................................................................................... 9 Ideas for a General Relativity Course .................................................................................................11 Possible Future Topics ........................................................................................................................12 2 Special Relativity.................................................................................................................... 13 Introduction to Special Relativity .......................................................................................................13 Special Relativity Basic Concepts ......................................................................................................13 Relativity Implies New Dynamics, Even for a Single Observer .....................................................13 Why Does Relativity Talk About Astronauts So Much? ................................................................13 Mass Is Invariant .............................................................................................................................14 Coordinates and Reference Frames ....................................................................................................14 Not All Coordinate Systems Are Reference Frames .......................................................................14 Inertial Reference Frames Are Idealized .........................................................................................15 How to Construct a Valid Inertial Reference Frame .......................................................................15 Simple Examples of Special Relativity ...............................................................................................16 Do Things Really Shrink, and Clocks Slow Down, When They Move?.........................................16 How Far is Far? ...............................................................................................................................16 E = mc2 ............................................................................................................................................17 What’s Valid in Relativity? ................................................................................................................17 Of Rockets and Relativity ...................................................................................................................19 Critical Mass ...................................................................................................................................19 The Classical (Non-relativistic) Rocket ..........................................................................................20 Introducing the Relativistic Rocket .................................................................................................21 Imperfect Efficiency ........................................................................................................................22 Relativistic Rocket Equation in the Observer Frame ......................................................................23 Calculations on Rocket Exhaust Strategies .....................................................................................25 Ion Engines, and What Kind of Exhaust Should We Use? .............................................................27 Electromagnetic Exhaust .................................................................................................................29 Common Mistakes ..........................................................................................................................29 Spacetime Diagrams ...........................................................................................................................29 Oblique Coordinates ........................................................................................................................31 Multiple Observers on the Spacetime Diagram ..............................................................................31 Are Time and Space Equivalent? ....................................................................................................38 Time and 2D Space .............................................................................................................................38 Velocity Composition Experiment .....................................................................................................39 One Observer’s Space Is Another’s Time .......................................................................................39 Three Pieces of Velocity Addition ..................................................................................................40 Adding Velocities Quickly With Rapidity ......................................................................................42 Energy For the Masses ........................................................................................................................42 Conclusions .....................................................................................................................................44 Comments on Particle Distributions................................................................................................45 Comment on Geometrized Units .....................................................................................................45
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