The Meaning of Relativity

LIBRARY
	Introduction: John Gribbin	file://Intro.pdf#page=1	Darwin: The Origin of Species	file://darwin.pdf#page=1	Faraday: The Chemical History of a Candle	file://Faraday.pdf#page=1	Lyell: Elements of Geology	file://Lyell.pdf#page=1	Malthus: An Essay on the Principle of Population	file://Malthus.pdf#page=1	Maxwell:  Matter and Motion	file://Maxwell.pdf#page=1	Wallace: The Malay Archipelago	file://Wallace.pdf#page=1Albert Einstein
CONTENTS
SPACE AND TIME IN PRE-RELATIVITY PHYSICS
	Space, concept of  6
	Co-ordinates, Cartesian  7
	Euclidean geometry  7
	Linear orthogonal transformation  10
	Orthogonal transformations  10
	Orthogonality, conditions of  10
	Preferred systems of co-ordinates  10
	Transformation, linear orthogonal  10
	Invariants  12
	Rank of tensor  15
	Tensors  15
	Tensors, operations  15
	Tensors, rank of  15
	Addition and subtraction  of tensors,  16
	Multiplication of tensors  16
	Tensors, addition and subtraction of  16
	Tensors, contraction of  16
	Tensors, multiplication of  16
	Tensors, symmetrical and skew-symmetrical  17
	Homogeneity of space  18
	Isotropy of space  18
	Simultaneity  18
	Co-variance of equation of continuity  22
	Stress tensor  23
	Viscous compressible fluid  23
	Maxwell's equations  24
THE THEORY OF SPECIAL RELATIVITY
	Galilean transformation  27
	Pre-relativity   physics, hypotheses of  27
	Fizeau  28
	Michelson and Morley  28
	Sitter  28
	Transformation, Galilean  28
	Criticisms of theory of relativity  29
	Simultaneity  29
	Time, concept  29
	Lorentz transformation  31
	Four-dimensional   continuum  32
	Light time  32
	Minkowski  32
	Time-space concept  32
	Transformation, Lorentz  32
	Addition theorem of velocities  37
	Clocks, moving  37
	Moving  measuring-rods  and clocks  37
	Velocities, addition theorem of  37
	Transformation, Lorentz  38
	Light-cone  39
	Four-vector  40
	Biot-Savart force  44
	Lorentz electromotive force  44
	Energy and mass  45
	Equations of motion of material particle  48
	Equivalence of mass and energy  48
	Motion of particle, equations of  48
	Energy tensor of electromagnetic field  49
	Conservation principles  52
	Principles of conservation  52
	Energy tensor  of  matter  53
THE GENERAL THEORY OF RELATIVITY
	Mach  58
	Gravitational mass  59
	Inertia and gravitational mass, equality of  59
	Principle of equivalence  59
	Equation  of  continuity, covariance of  60
	Galilean regions  60
	Inertia, criticisms of principle  60
	Rotation  61
	Centrifugal force  62
	Compressible viscous fluid  62
	Gauss, theory of surfaces  62
	Curvilinear co-ordinates  63
	Contravariant vectors  65
	Co-variant vector  65
	Riemann  65
	Vectors, co-variant  66
	Vectors, contra-variant  66
	Fundamental tensor  67
	Tensors  67
	Contravariant  tensors  68
	Co-variant tensors  68
	Differentiation of tensors  69
	Tensors, formation by differentiation  69
	Levi-Civita  70
	Weyl  70
	Riemann tensor  75
	Geodesic lines  78
	Straightest lines  78
GENERAL THEORY OF RELATIVITY (continued)
	Poisson's equation  82
	Equations  of  gravitational field  88
	Gravitation constant  89
	Displacement of spectral lines  92
	Light ray, path of  92
	Spectral lines, displacement of  92
	Path of light ray  93
	Perihelion of Mercury  93
	Solar eclipse expedition  93
	Weyl  93
	Perihelion of Mercury  97
	Kaluza  98
	Mach  98
	Weyl  98
	Finiteness of universe  99
	Mach  99
	Accelerated  masses, inductive action of,  102
	Inductive action of accelerated masses  102
	Thirring  102
	Radius of universe  106
	Mach  107
APPENDIX I: ON THE 'COSMOLOGIC PROBLEM'
	Cosmologic problem  108
	Displacement of spectral lines  108
	Spectral lines, displacement of  108
	Universe, finiteness of  109
	Cosmologic constant  110
	Friedman  110
	Hubble's expansion  110
	Isotropy of space  110
	Radius of universe  115
	Age of universe  127
	Age of universe  128
	Age of universe  130
APPENDIX II: RELATIVISTIC THEORY OF THE NON-SYMMETRIC FIELD
	Field, equations  of  gravitational  131
INDEX
	Accelerated  masses, inductive action of, 102
	Addition and subtraction  of tensors, 16
	Addition theorem of velocities 37
	Age of universe 127
	Age of universe 128
	Age of universe 130
	Biot-Savart force 44
	Centrifugal force 62
	Clocks, moving 37
	Compressible viscous fluid 62
	Conservation principles 52
	Continuum, four-dimensional 32
	Contravariant vectors 65
	Contravariant  tensors 68
	Co-ordinates, Cartesian 7
	Cosmologic problem 108
	Cosmologic constant 110
	Co-variance of equation of continuity 22
	Co-variant vector 65
	Co-variant tensors 68
	Criticisms of theory of relativity 29
	Curvilinear co-ordinates 63
	Differentiation of tensors 69
	Displacement of spectral lines 92
	Displacement of spectral lines 108
	Energy and mass 45
	Energy tensor of electromagnetic field 49
	Energy tensor  of  matter 53
	Equation  of  continuity, covariance of 60
	Equations of motion of material particle 48
	Equivalence of mass and energy 48
	Euclidean geometry 7
	Field, equations  of  gravitational 88
	Field, equations  of  gravitational 154
	Finiteness of universe 99
	Fizeau 28
	Four-dimensional   continuum 32
	Four-vector 40
	Friedman 110
	Fundamental tensor 67
	Galilean regions 60
	Galilean transformation 27
	Gauss, theory of surfaces 62
	Geodesic lines 78
	Gravitation constant 89
	Gravitational mass 59
	Homogeneity of space 18
	Hubble's expansion 110
	Inductive action of accelerated masses 102
	Inertia and gravitational mass, equality of 59
	Inertia, criticisms of principle 60
	Invariants 12
	Isotropy of space 18
	Isotropy of space 110
	Kaluza 98
	Levi-Civita 70
	Light-cone 39
	Light ray, path of 92
	Light time 32
	Linear orthogonal transformation 10
	Lorentz electromotive force 44
	Lorentz transformation 31
	Mach 58
	Mach 98
	Mach 99
	Mach 107
	Mass and energy 45
	Mass, equality of gravitational and inertia 59
	Maxwell's equations 24
	Mercury, perihelion of 93
	Mercury, perihelion of 97
	Michelson and Morley 28
	Minkowski 32
	Motion of particle, equations of 48
	Moving  measuring-rods  and clocks 37
	Multiplication of tensors 16
	Newtonian gravitation constant 89
	Orthogonal transformations 10
	Orthogonality, conditions of 10
	Path of light ray 93
	Perihelion of Mercury 93
	Perihelion of Mercury 97
	Poisson's equation 82
	Preferred systems of co-ordinates 10
	Pre-relativity   physics, hypotheses of 27
	Principle of equivalence 59
	Principles of conservation 52
	Radius of universe 106
	Radius of universe 115
	Rank of tensor 15
	Riemann 65
	Riemann tensor 75
	Rotation 61
	Simultaneity 18
	Simultaneity 29
	Sitter 28
	Skew-symmetrical tensor 17
	Solar eclipse expedition 93
	Space, concept of 6
	Space, homogeneity of 18
	Space, isotropy of 18
	Space, isotropy of 110
	Spectral lines, displacement of 92
	Spectral lines, displacement of 108
	Straightest lines 78
	Stress tensor 23
	Symmetrical tensor 17
	Tensors 15
	Tensors 67
	Tensors, addition and subtraction of 16
	Tensors, contraction of 16
	Tensors, formation by differentiation 69
	Tensors, fundamental 67
	Tensors, multiplication of 16
	Tensors, operations 15
	Tensors, rank of 15
	Tensors, symmetrical and skew-symmetrical 17
	Theory of relativity, criticisms 29
	Thirring 102
	Time, concept 29
	Time-space concept 32
	Transformation, Galilean 28
	Transformation, linear orthogonal 10
	Transformation, Lorentz 32
	Transformation, Lorentz 38
	Universe, finiteness of 99
	Universe, finiteness of 109
	Universe, radius of 106
	Universe, radius of 115
	Vectors, co-variant 66
	Vectors, contra-variant 66
	Velocities, addition theorem of 37
	Viscous compressible fluid 23
	Weyl 70
	Weyl 93
	Weyl 98
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