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# Funky Relativity Concepts - University of California, Relativity Concepts ... Formulas ......

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• Funky Relativity Concepts The Anti-Textbook*

A Work In Progress. See physics.ucsd.edu/~emichels 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 cant 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 didnt fit in your textbook. Instead of distributing this document, please link to physics.ucsd.edu/~emichels/FunkyPending.pdf. Please cite as: Michelsen, Eric L., Funky Relativity Concepts, physics.ucsd.edu/~emichels, 2/4/2015.

http://physics.ucsd.edu/~emichelshttp://www.space.com/http://physics.ucsd.edu/~emichels/FunkyPending.pdf

• Physical constants: 2006 values from NIST. For more, see http://physics.nist.gov/cuu/Constants/ .

Gravitational constant G = 6.674 28(67) x 1011 m3 kg1 s2 Relative standard uncertainty 1.0 x 104

Speed of light in vacuum c = 299 792 458 m s1 (exact)

Boltzmann constant k = 1.380 6504(24) x 1023 J K1

Stefan-Boltzmann constant = 5.670 400(40) x 108 W m2 K4 Relative standard uncertainty 7.0 x 106

Avogadro constant NA, L = 6.022 141 79(30) x 1023 mol1 Relative standard uncertainty 5.0 x 108

Molar gas constant R = 8.314 472(15) J mol-1 K-1

calorie 4.184 J (exact)

Electron mass me = 9.109 382 15(45) x 1031 kg

Proton mass mp = 1.672 621 637(83) x 1027 kg

Proton/electron mass ratio mp/me = 1836.152 672 47(80)

Elementary charge e = 1.602 176 487(40) x 1019 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)

Muon mass m = 1.883 531 30(11) x 1028 kg

Inverse fine structure constant 1 = 137.035 999 679(94)

Planck constant h = 6.626 068 96(33) x 1034 J s

Planck constant over 2 = 1.054 571 628(53) x 1034 J s

Bohr radius a0 = 0.529 177 208 59(36) x 1010 m

Bohr magneton B = 927.400 915(23) x 1026 J T1

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 1010 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

http://physics.nist.gov/cuu/Constants/

• physics.ucsd.edu/~emichels Funky Relativity Concepts emichels at physics.ucsd.edu

2/4/2015 10:50 Copyright 2002 - 2011 Eric L. Michelsen. All rights reserved. 3 of 72

Contents 1 Introduction ........................................................................................................................6

How to Use This Document............................................................................................................ 6 The Funky Series ........................................................................................................................... 6

Whats Wrong With Existing Relativity Expositions? .................................................................. 6 My Story .................................................................................................................................... 6 Thank You.................................................................................................................................. 7

Scope............................................................................................................................................. 7 What This Text Covers ............................................................................................................... 7 What This Text Doesnt Cover .................................................................................................... 7 What You Already Know............................................................................................................ 7

Notation......................................................................................................................................... 7 Ideas for a Relativity Course........................................................................................................... 9

2 Special Relativity ..............................................................................................................10 Introduction to Special Relativity.................................................................................................. 10 Special Relativity Basic Concepts................................................................................................. 10

Why Relativity Talks About Astronauts So Much...................................................................... 10 E = mc2..................................................................................................................................... 10 Mass Is Invariant....................................................................................................................... 11 Do Things Really Shrink, and Clocks Slow Down, When They Move? ...................................... 11 How Far is Far? ........................................................................................................................ 11 Not All Coordinate Systems Are Reference Frames ................................................................... 12 Inertial Reference Frames Are Idealized .................................................................................... 13

Whats Valid in Relativity? .......................................................................................................... 13 Of Rockets and Relativity............................................................................................................. 15

Critical Mass............................................................................................................................. 15 The Classical (Non-relativistic) Rocket ..................................................................................... 16 The Relativistic Rocket ............................................................................................................. 17 Observations on the Relativistic Rocket, and Common Mistakes................................................ 19 Ion Engines, and What Kind of Exhaust Should We Use? .......................................................... 23

How to Construct a Valid Inertial Reference Frame ...................................................................... 24 Spacetime Diagrams..................................................................................................................... 25

Oblique Coordinates ................................................................................................................. 26 Multiple Observers on the Spacetime Diagram ......................................................................... 26 Are Time and Space Equivalent?............................................................................................... 32

Lorentz Transformations .............................................................................................................. 32 Tensors ........................................................................................................................................ 33

3 Special Relativity Shorts ...................................................................................................35 Rest-Mass Is Typically Considered Potential Energy..................................................................... 35 Nuclear Energy: Isnt That Special?.............................................................................................. 35 The Twin Effect in Brief............................................................................................................... 35 Metric Systems: Connecting the Dots ........................................................................................... 36

Consequences of Metric Convention for Some Common Operators............................................ 39 4 General Relativity Basic Concepts ...................................................................................40

One of These Twins Is Not Like the Other .................................................................................... 40 A Better (Non-) Paradox ........................................................................................................... 42

Special Relativity Implies Curved Space....................................................................................... 43 Straight and Curved Simultaneously.......................................................................................... 44 Merry-Go-Rounds to General Relativity.................................................................................... 44

Tempus Fugit: Example of the gtt Component of the Metric .......................................................... 44 5 Building Up General Relativity ........................................................................................47

Topology, Geometry, and the Universe......................................................................................... 47 Torus, and No Bull: Geometries of a Donut ......................................................................

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