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Wheeler J.A. — Topics of modern physics. Vol. I. Geometrodynamics
Wheeler J.A. — Topics of modern physics. Vol. I. Geometrodynamics

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Название: Topics of modern physics. Vol. I. Geometrodynamics

Автор: Wheeler J.A.

Аннотация:

This is a collection of papers dealing with geometrodynamics. Geometrodynamics is the study of the geometry of curved empty space and the evolution of this geometry with time according to the equations of Einstein's standard 1916 general relativity.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1962

Количество страниц: 334

Добавлена в каталог: 29.08.2013

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Предметный указатель
"Maxwell square root", of Ricci tensor      90
"Maxwell square root", of stress-energy tensor      228 245—249
"Maxwell square" of electromagnetic field      239 240 242
$\mu$-meson      6 79 103—105
3-geometry, as argument of state functional for geometrodynamics      75 81
3-geometry, as carrier of information about time      36—39 43 44
3-geometry, conceived as a coordinate-free concept      35
3-geometry, plus extrinsic curvature as initial value data, case of time symmetric gravitational wave      54
3-sphere, type of topology      92
3-surface, as relevant to initial value conditions      see "Initial value conditions"
3-surface, as testing ground to determine whether 4-geometry satisfies Einstein's field equations      51
3-surface, initial, as launching platform for orthogonal geodesies which eventually cross      53
3-surfaces, family of geodesically parallel      53
4-geometry, found from Einstein's field equations      35—40
4-manifold, bounded in space, as model of universe      59
40 Eri B, gravitational red shift caused by      46
Abrikosov, A.A.      79 n
Accelerated source, fields produced by, electromagnetic and gravitational      111—114
Accelerators, as source of neutrinos      107
Achieser, A.      103 n 140
Acoustical images, multiple, and analogous effect in curved space      115 130
Action option, relevant to distinction between Fermi — Dirac and Einstein — Bose statistics      101 102
Action principle, for general relativity plus electromagnetism      134
Action, change of, as geon leaks energy      146
Action, classical, role of in method of sum over histories      84
Adams, J.B.      62 n
Adams, Miss      46 n
Adiabatic equation of state, in expansion of universe      60
Adiabatic in variance, principle of, applied to change of modes of oscillation of electromagnetic field in slowly changing metric      208—211
Air line distances, table of as illustrative of general relativity      12
Airy function, in analysis of simple spherical geon      159
Akasa      236 n
Aleksandrov, P.S.      255 n
Alexandroff, P.      xiv
Algebraic curve, used in construction of minimal surface      52
Allen, J.S.      107 n 111
Alpha particle decay, as related to leakage out of geon      26 27
Alpha particle reactions, irrelevant for big A problem      125
Already unified field theory      xii 9 16 20 21 228—231 237—253
Already unified field theory, as example of taking square root      90
Already unified field theory, assessed      24
Already unified field theory, case of region where complexion is not defined      22 23
Already unified field theory, defined      230
Alvarez, L.      108
Anderson, J.      184 n
Anticommuting c-numbers, avoidability of      97—102
Antineutrino      3 5 6
Aperture, of lens for electromagnetic radiation      57
Araki, H.      55 n
Arena concept of space time      8 68 225
Arnowitt, R.      xv
Asymptotic approach to Schwarzschildean character      56
Asymptotic flatness, of universe, regarded by Einstein less simple than closure      58 59
Asymptotic flatness, without singularity      63
Atoms, identity of, after following different routes      13
Attrition, of geon      144 163—168
Attritivity, of geon      145
Auslander, L.      244
Automobile fender, comparison of 4-manifold with      35 36 41
Axially symmetric, as subclass of time symmetric gravitational waves      55
Babcock, D.      xvi
Bach, R.      305 n
Bacher, R.F.      89 n
Background fields, as relevant to motion of geon      29 30
Background fields, in theory of motion      134
Bade, W.L.      96 n
Bargmann, V.      17 n 96 97 228 248 306 307
Baryon      1
Basis, countable, as property of a manifold      256
Benard, H.      189
Bentley      235
Bergmann, P.      xiv xv 66 96 184 230 307
Bernstein, S., theorem on regular solutions of minimal surface problem      52
Bers, L.F. Lipman      52 n
Bertotti, B.      115 n
Beta coupling      see "Fermi coupling"
Beta decay      xiii 1
Bethe, H.A.      89 n
Betti number      270—272
Betti number, and Coulomb fields      292
Betti number, second, non-vanishing of, as condition for possibility of charge      278
Betti, E.      231
Bianchi identity, relation of, to Maxwell's equations      251
Bidelman, W.C.      46 n
Big A problem      6 120—127
Birkhoff, G.      47
Blackbody container, analogy of thermal geon to      191
Blades, of space-time geometry, failure to mesh      249
Blades, of two-bladed structure of electromagnetic field      243
Bleakney, W.      188 n
Bocchieri, P.      90 n
Body, concept of, in general relativity      133
Bohm, D.      91 n
Bohr, Niels      76 n 109 137 221
Bondi, H.      55 63 118
Bonnor, W.B.      17 n 228
Boundaries of p-chains      267
Boundary value data      see "Initial value data or two-surface data"
Boundary, 2-surface, used in evaluation of flux integral and charge      50
Boyle, R.      235
Brahman      236 n
Breit, G.      103 n 176 219
Bridge, Einstein — Rosen, contrasted with wormhole      47 48
Brill, D.K.      4 n 55 57 62 91 96 104 110
Brodsky, A.      91 n 109
Bubble, undersea, analogous to universe in its dynamics      61—63
c-number formalism, contrasted with operator formalism      84—87
c-numbers, anticommuting, avoidability of      97—102
Cajori, F.      235 n
Callaway, J.      24 n 131 234
Carbon-nitrogen cycle, irrelevant for big A problem      125
Carbon-nitrogen cycle, neutrinos produced in      107
Cartan, E.      xiv xv 92 237 255 260 238 295
Carter, R.E.      1 n 107
Case, K.M.      89 n 181
Casimir, H.B.G.      92
Casuality, and short wormhole connection between two distant points      48
Casuality, and signals sent through throat of wormhole      65
Catalysis, of conversion of nucleons into radiation, by high pressure      127
Cauchy problem, prediction of geometrodynamical future from present      62
Cauchy — Kowaleski theory      283 n 288
Cavitation, in bubble contraction, connection with question of singularities      62
Cayley — Klein parameters      92
Chains, as related to oriented cubes      266
Chains, closed, compared with closed forms      279
Chains, p-chains, examples of      268
Chains, vector space defined by      271
Chandrasekhar, S.      115 n 121 122 124
Chandratreya, G.L.      236 n
Characteristic field for pair production, sets limit to smallness of thermal geons      193
Characteristic length associated with gravitational field fluctuations      67 71 72 76 120 137
Charge reversal, and parity inversion      130
Charge, "dressed" and "undressed"      233
Charge, as an aspect of a multiply connected space      8 49—50 183—184 226 232 254—306
Charge, classical, of wormhole model, distinguished from physical charges      50 68 76 77 81 82
Charge, electric and magnetic, excluded in source-free formulation of Einstein — Maxwell theory      135
Charge, problem of single complexion for      304—305
Chase, D.M.      24 n 133 302
Chern, S.      xiv
Chevalley, C.      260 n
Choquard, P.      83
Classical physics, as contained in geometrodynamics      21
Classical physics, considered as comprising relativity and electro magnetism      14
Classical physics, legalistic description of state in, by electromagnetic fields and metric alone      31
Classical physics, summarized in structure law of space time      22
Clemence, G.M.      46 n 133
Clifford, W.K.      8 129 231 235
Clock, geodesic      10—12
Clock, rate of ticking of inside geon      26
Clocks, in general relativity      9
Closed space, Einstein's arguments for      58 59
Closed space, properly and not properly closed      63 64 66
Closed universe, associated with time symmetric gravitational wave of critical strength      57
Closure of space, by sufficient density of mass-energy      117
Cobordism and freedom of choice of topology      44
Cole, R.H.      61 n
Collective disturbances, and the nature of elementary particles      79 81
Collective motions, of geons      170
Collision of two photons as mechanism of escape from geon      165—169
Commutators, topological analysis of      83 84 87
Complexion, as describing lack of uniqueness in square root      90
Complexion, considered as a new aspect of geometry      23
Complexion, found from integration of its gradient      20
Complexion, gradient integral conditions on, in a multiply connected space      253—254
Complexion, not defined for null field      23
Complexion, of electromagnetic field, defined      18 19 229 230 241
Complexion, of electromagnetic field, illustrated      19
Complexion, of electromagnetic field, question of determination from curvature      19 20
Complexion, question of more geometric rephrasing of      130
Composition law for propagators      85—87
Composition of vector and tensor fields out of spinor field      89
Compton wave length      2 72
Computer, applied to thermal geon      215
Computer, as tool to analyse two-body problem      49
Computer, electronic, and analysis of geon      161
Condon, E.U.      xv 143
Configuration, in method of sum over histories      84—86
Configurations of electromagnetic field different, giving same metric (table)      23
Confucius      225
Connor, P.      307
Conservation law deduced from Stokes theorem      274
Constants, large dimensionless      119—120
Constants, primitive unexplained of physics      68 82
Constraint, equations of      see "Initial value equations" "Equations
Continuity, as conceived in topology      255
Contraction effect, on energy of electromagnetic field      208
Contraction, of universe      59—61
Conversion factor, charge to length      14
Conversion factor, electromagnetic field to inverse length      14
Conversion factor, mass to length      13
Conversion factor, time to length      13
Coordinate patches      259—260
Coordinate-free representation of mechanics and geometrodynamics      187
Coordinates as distinguished from intrinsic geometry      35
Coordinates, freedom of choice of      43 44
Corben, H.C.      90 n
Correspondence principle, inapplicable to neutrinos      88 91
Cosmic radiation, contribution of, to density of mass-energy in universe      116—117
Cosmic ray neutrinos      107
Cosmological term, absence of from field, equations of general relativity      131
Cosmological term, in general relativity, status of      59
Cosmology, spherically symmetrical universe in      59 — 61
Cotime      10—12 71 227
Coulomb field as a harmonic field      289—293
Coulomb law, valid over many powers of ten      66
Coupling constant for gravitational forces, absence of      21
Coupling constants      68 78 82
Courant, R.      52 n
Covariance, employed in deriving field equations from initial value equations      41
Covariant derivative, of curvature      20
Covariant derivative, relevant for spinor field      96
Covering group, for rotation group      93
Cowan, C.L., Jr.      1 n 6 106 127 128 179
Crest of water wave, eventual singularity at      67 68 72
Critical field, for pair production, as relevant to minimum size of classical geon      138
Critical mass, of gravitationally attracting nucleons at end point of thermonuclear reaction      120—127
Crushing points, two, in building up cold dense star      124
Crystal lattice, zero point vibration in      69
Cube, oriented unit, as employed in integration      265
Curl, generalized      see "Exterior derivative"
Curvature, conditions on, to be represent able as due to an electromagnetic field      18
Curvature, Einstein tensor description of      15 17 18
Curvature, extrinsic to a 3-dimensional hypersurface      34 (diagram)
Curvature, intrinsic to a 3-dimensional hypersurface      33 34
Curvature, invariant for 3-dimensional hypersurface      33
Curvature, invariants      47
Curvature, invariants, as coordinates      187
Curvature, invariants, as tool to characterize intrinsic geometry in a coordinate-free way      35 36
Curvature, of space time      10—12
Curvature, of space time, as indicator of electromagnetic field      16
Curvature, of space time, in a geon      27
Curvature, Ricci, covariant derivative of      20
Curvature, Ricci, tensor description of      15 18
Curvature, scalar invariant of      15 18 see
Curvature, tensor, effect on elementary particles      120
Curved empty space, rich physics of      29
Curved space or curved space-time      8
Cycles, bounding and non-bounding      269—270
Cycles, examples of      268
Cycles, vector space defined by      271
Cycloid, curve connecting radius of universe and time      60
d'Alembert's operator      15
d'Alembertian, generalized, in Einstein's theory      132
Darboux, G.      52 n
Darrow, K.K.      232 n
Davis, R., jr.      108 n
de Broglie, L.      89 n 181
de Groot, S.R.      307
de Rham's first theorem, regarding forms with periods (charge)      278
de Rham's theorem and the initial value problem      288
de Rham, G.      xv 255 260
de Witt, B.      xv 44
Debever, R.      187 n
Degrees of freedom, internal, in some models for mass      25
Degrees of freedom, number of, for source-free gravitation field      43 44
Degrees of freedom, number of, for time symmetric source-free gravitational wave      54
Degrees of freedom, per space unit      32—39
Dempster, H.      74 n 83
Density of mass energy in universe      46
derivatives      xv
Derived quantities emerging from pure geometry      83
Deser, S.      xv 79
Diagonalization of a symmetric tensor, not always possible      248
Dicke, R.H.      10 n 119
Dietz, R.S.      114
Differentiable manifold      257—259
Differential equations, fourth order, derived by union of Maxwell and Einstein equations      21 23
Differential equations, of general relativity, non-linearity of, essential for derivation of equations of motion      25
Differential forms      see "Forms"
Differential geometry, intrinsic      260
Differential geometry, shortcomings as device to bring out geometrical character of complexion      23
Differentiate functions and fields      259—260
Differentiation, exterior      262
Dimensionless constants, question of change with time      119—120
Dimensionless ratios in physics      10
Dirac's equation for neutrino      108
Dirac's equation for neutrino, and sea of negative energy states      69 70
Dirac's equation for neutrino, equation for neutrino in curved space      95
Dirac's equation for neutrino, equation in curved space      178
Dirac's equation for neutrino, matrices as mechanism to take root      184
Dirac, P.A.M.      xv 10 119
Dispersion relation, applied to neutrino interaction in geon      179—180
Dispersion relation, applied to scattering of light and neutrinos      103—104
Dispersion relation, for scattering of light by light      103
Disposable constants per space point, number of      32—39
Divergence conditions, in electromagnetism      32 33
Divergence of quantum electrodynamics, and phenomena at small distances      78 79
Divergence relations, for electromagnetic field      see "Initial value conditions"
Divergence via duality and exterior derivative      281
Divergent logarithm in neutrino scattering, in stopping power and in plasma physics      104
Droplets from breakup of wave crest      67 68
Dual and duality, defined for electromagnetic field      19
Dual electromagnetic field tensor      40
Dual forms      31
Dual language of electromagnetic fields and metric, convenience of      24
Dual, defined      227
Duality rotation, compared and contrasted with Lorentz transformation      240
Duality rotation, defined      239
Duality rotation, effect of, on a null field      248—249
Duality rotation, of electromagnetic field and spinor field, compared      91
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