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Index

t space 50 * operation 50 * space 50

act - external - 14 - improper- 117 - internal - 16 - medial - 16 - proper - 20 - proper- 117 action 25,523 - final 13, 14 - final - 360 - initial 13 - initial - 360 - internal 25 - medial - 360 - sharp 14 action principle - Hamilton's - 371 action vector 16 action vectors - space - 402 activation 3 actor 440 actors 24 adjoint 30,50,285,532 - - subspace 118 - adapted - 121 - canonical - 432 - definite- 50 - dynamical - 487 - indefinite- 50 - Minkowski - 322 - physical - 503 - relative - 487 adjoint basis 292 agent 11 Aharanov X, 409 Aharanov-Bohm experiment 413 algebra 529

- Clifford - 279 - coordinate - 88 - double - 451 - framed - 99 - group - 454 - Iordan- 132 - Lie - 534 Ambarzumian 479 ambilinear form 116 ambispinors 350 A Midsummer-Night's Dream 262 amplitude 47,108 ancestor 489 Anderson X, 335 annihilator - initial - 524 anti- 440 antilinear 530 anti symmetric tensor 538 anti symmetrize 536 anti vector 115 Aristotle 153,155,256 Arrow 81 arrow - double 450 Artin 199 assembly - Maxwell-Boltzmann - 209 Austern X automorphism 523 - inner - 529

Bacon 12, 156 Baer 199 Bardeen 482 Barrett X Bartholinus 7 basis - null symmetric 326 Bateson 153 Bell 251 Bergmann 356

570 Index

bicycle 497 black box 53 Bohm X, 153,409 Bohr 9,12,153,171-173,180,364 Boole 3,278 Boole's laws 4 Bose-Einstein 225 Bose-Einstein statistics 220 bottom 543 Bourbaki 125 Brewster angle 7 Bridgman 271 Brouwer 10 BRST 145,149 Bruno 261, 263 Bub XI, 65

C 173 calculus - - rational 262 Camus 255 canonical commutation relation 141 canonical coordinates 374 category 26, 524 category algebra 425 causal - - antecedent 489 - - symmetry -- maximal - 323 - interval 323 - symmetry 323 causal relation 321 - - proper 321 cenad 274 center 529 CGD 491 checkers 479 children 481 chronometric 322 chronon 22,486 Church 425 class 3 - homotopy - 546 classical 8, 65 Clifford 11, 279 closed 190 closure 189 co- 533 co-operation 83 coa1gebra 84 - ordinate- 89 coarrow 83 codomain 521,544 cofinite 297

coherent 361 coherent group 247 coherent manifold 247 coherent state 240,247 Coleman 489 combination principle 176 combinatorics 207 commutativity 8 commutator - general covariant - 339 compatible 19 complement 285,533,534 complement basis 292 complementary 8 complete 18,28 - theory 71 complex 526 complex projective sphere 542 concatenation 4 connection 338, 540 - Galois 191 - metrical - 339 connectionism 271 continue I 8 continuous 546 contravariant 531 control 122 Cooper 482 cooperation - quantum - 138 cooperator 38,83,86, 138 - statistical - 239 coordinate 40, 121 - binary - 94 coordinates - episystemic - 506 - systemic - 506 copath 394 copoint 49,544 coproduct 84 correspondence 490 correspondence principle 173 cosmological constant 344 costar 489 covariance - general - 334 - unimodular 345 covariant 531 co vector 538 cover 427,543 cpalgebra 84 creator 103 crisp 18 curvature 339

- network - 516 curvature scalar 340

David XI Dedekind 509 Deg 265 degree 27 - contravariant - 535 - covariant - 535 density matrix 236 derivative 540 - covariant 338 - general covariant 540 Descartes 153,154,156,255 determine 122 diagonalized 449 diagram - action - 46 - category - 527 - commutative - 527 - Hasse - 543 - lattive - 543 diagram notation 37 dialectic 258 diffuse 18 digit 22 dimension 541 Dirac VII, XI, 10, 12,40 - - equation 354 - bra-ket notation 38 dislocation 512 distinguishable 211 distortion 339 domain 521,544 double arrow 450 double semi group 451 dual 533 Durr XI dynamical transport 384

eigenprojection 91 eigenvalue 542 Eilenberg 425 Einstein 33 election 3 endomorphism 523,524 energy tensor 342 entities - constant 27 - quantum 27 - random 27 epistemology 12 episystem 16 EPR 180

equivalence principle 333 equivalent 213 equivalent entities 208 ergodic 364 etherons 157 event 319 Everett 12 extensionality 423 extensor 265 exterior algebra 537 extraordinary ray 158

Fermi 12 Feynman XI,479 field variable 403 final 43,544 final space 521 finitary 422 Finkelstein XI Fivel 251 fixed 213 flat 339 flip 85 Flynn X form factor 241 frame 20,72,128 frame algebra 99 Fredkin XI, 500 free 529 Frege 278 full 111,268,431,529 full semi roup 187 functor 525

Galois 9,188, 189,509 Galois connection 191 Galois lattice 197 gauge 336,541 - - curvature 337 - - vector field 336,541 - -group 541 - curvature 337,541 - derivative 336,541 gauge condition 145 gauge generator 148 gauge transformation 146 - - of the first kind 150 - - of the second kind 150 - - of the third kind 150

Index 571

general covariant derivative 338 general order 290 general-relativization 334 general-relativizing 334 generate 552

572 Index

generator 202 generators 246 geodesic 322 geometry - projective - 542 Gersch 479 ghost 148 - Faddeev-Popov - 149 Gibbs X Glauber 240 GOdel 10, 262 grade-commute 227 gradient 540 graph 526 grating 64 group 527 - abelian - 528 - additive - 528 - alternating - 528 - causal 323 - double - 451 - fundamental - 547 - homotopy - 547 - involutory - 464 - local- 336 - relativity - 19 - symmetric - 528 group algbera 448 guides 146

Hamiltonian 202,375 head 521 height 433 Heisenberg X, XI, 9,10,36,40,153 Heisenberg indeterminacy principle 165 Hessian 374 Hibbs 479 Hilbert space 552 Hodge star 267 hole 289 Holm X homogeneous 537 homomorphism 523 homotopy 546 hyperalgebra 485 hyperdiamond 476 hyperoperator 484 hyperspace 481

Iceland spar 6 identification 312 identity 81, 522, 527, 544 - final - 523 - initial - 523

image 544 inclusion 53 index notation 37 index-free notation 37 indistinguishable objects 212 inertial transport 338,384 Infeld 356 information dump 264 infraspace 481 initial 43, 544 initial space 19,521 initial transpose 450 interaction 211 interference 74 - quantum 68 interval 322 inverse 523, 527 inversor 460 involution - main - 532 - transpose - 532 isometry 119 isomorphism 524 isotropic 368 Ivanenko 479

Jacobi identity 534 Jacobson XI, 479 James 271 Jauch XI John Von Neumann 424 Jordan normal form 125 jump 79,80

Kalam 260,263,479 Kant 11 Keller XI Kelvin 155 ket 16 Kklauder 240 Koopman 108 Kripke 263 Krishnamurti 153 Kruskal 240

lambda conversion 425 Lande 276 lattice 543 - final 191 - initial 191 Leibniz 153,155 - law 539 limit 545 Uull 260

local 418,488 - - frame 249 - - system 249 locality 333,334 logic 3 - intuitionistic - 10 - modal 69 logistics 262 Logos 255,277 loop 546 Lorentz transformation - infinitesimal - 331 Lorenz condition 147 lozenge 339

Maclane 425 Maimon 260 Malus VIII, 6, 7 Malusian 6 Mandula 489 manifold - spin - 357 Mantke X mapping 544 - partial - 544 - pointed - 546 - topological - 546 - total- 544 mass 341 - gravitational -- active 340 - - passive 340 - inertial 340 mathesis 154 matrix - binary - 95 - Booolean - 95 measure 321 measurement problem 363 mental 5 metric - - density 322 - transition 30 minimal coupling 343 minimal polynomial 124 Minkowski spacetime 321 Minkowskian 321,334 Minkowskian adjoint 335 mode 14 module 529 monad 155 monoid - double- 451 monoid algebra 448

monoid module 448 morph 524 morphism 523, 524 Moses XI multiplication - final - 530 - initial - 530

Index 573

multiplicity 55,67,79,91,191

Nambu 482 Ne'eman 356 negation 534 negative vector 114 neighborhood 542, 545 net 484 network 475,483 Nevanlinna space 40 Newton VIII Newtonian limit 343 nil vector 114 nilpotent - Jordan - 124 nil quadratic 314 non-objective 26 non-objective physics 165 normal 119, 121 normal form - Backus - 519 normal order 290,537 normal subgroup 528 null 268 null photon 145 null vector 114

object 22 - of a transformation 523 Omnilingua 263 ontic 11 ontism 26 pperation 17,38,40 - - semi group 11 0 - classical -) 80 - double - 451 - quantum - 110 operator 81,109,530 - simple - 32 - annihilation - 103 - creation - 102, 103 - Dirac - 354 - double - 451 - Majorana - 354 - nilpotent - 124 - projection - 119 - shift - 103

574 Index

operator algebra 110 operon 454 opposite 266,285,533 opposite basis 292 OR 520 or-ion convention 40 orbit 213 order 27,438 - normal - 537 ordinary ray 158 Orion convention 40 orthogonal 119

partial order 543 partner spaces 289 path 546 - - tensor 390 - quantum - 390 Patterson 153 Peano 278 Peirce 153,271 Penrose XI perturbation 547 Petersen XI, 184 photon 6 physical 5 physical entity 19 Pisello XI Plato 153 pleiad 274 point 188, 544 - spacetime - 319 Poisson bracket 374 polar - - subspace 118 polarizer 6 paR 273,520 positi ve vector 114 possible worlds 264 Post 10 power 221 power set 521 pragmatism 271 praxic 11 praxism 26 predicate 257 principal - point 200 - vector 200 principle - - of maximal astonishment 27 product 522,544 - diagonalizer - 451 - equalizer - 449

- group - 527 - Lie - 534, 539 - parallel - 450 - semidirect - 523 - serial - 80,450 - tensor - 535 projection 531 projectively equal 542 projector 74,90,119,121, 550 propagation 82 propagator 83 proper - - distance 322 - - time 322 proposition 256 pure set 427

q group 480 quantifier 257 - existential - 257 - numerical - 257 - universal - 257 quantization 134 quantum 3,9 - - law of large numbers 232 - -principle 161 - - set theory 15 quantum - - Liouville equation 387 quantum group 460 quantum interference 68 quantum theory - metric - 52 - old - 171 - projective - 52 quantum-relativity analogy 36,73 quotient object 209

Racah 61 random phases 364 range 544 ray 31,109,541 re-relativization 132 real time 21 recipient 11 reciprocal basis 292 reconnection 450 recursive definition 519 Regge 477 relation 544 relativity 8, 10 - classical - 73 - quantum - 73 rephase 133

rephasing 25 represent 47 representation - projective - 532 - vector - 532 resolvable 123 resolvent 124 respects 213 reversal - total - 61 Ricci tensor 340 Riemann 11 ring - unital - 528 Ritz XI Rodriguez X Rota XI

Saller XI, 125 Schiller XI Schopenhauer 255 Schrieffer 482 SchrMinger 12, 176,240 Schwartz XI Schwarz inequality 143 Scott XI Scotus 255 selection rule 16 Selesnick XI semantic ensemble semantics 262 semifinite 298 semigroup 47,522 - * 115 - t- 50,115

* 50 - Baer- 524 - reversible - 50

58

semi group quantum theory semilinear 529 sensorium 157 sequence 208, 209 serial action 4 series 209,212,216 sero-point energy 143 sesquilinear 116 sesquispinors 323 set 99,209 - - algebra 283 - - calculus 283 - open - 545 set theory 208 - random - 426 sharp 18,54, 191

186

Index

sib 99,209 signature 116 - full- 116 simply connected 546 singular dynamics 374 Sirag XI Skyrme 287 Smith X, XI, 476 Smolin XI Snell's law 158 solder 357 solitons 240 Sorkin XI source 400 space -t- 40,41 - complement - 538 - connected- 547 - - multiply - 547 - covering- 546 - Dirac- 40 - dual- 538 - Krein- 40 - opposite- 538 - principal- 124 - projective - 542 - tensor- 535 - topological--- pointed- 546 spacetime - microstructure 481 span 189,541 spectral theorem 92 spectral value 124 spectrum 124 sphere 546 spin - - distortion 357 - - tensor 357 - anomalous- 436 standard order 292,293 Stapp XI star 489 state 13,22 statistical actor - final- 238 - initial- 237 statistical cooperator 97, 139 statistical operator 236 - initial 97 statistics 208 statistor 249 stop 0 7 strain acceleration 345

575

576 Index

stress tensor 342 structural relations 525 structure 525 subobject 209 succession 484 successor - - operator 245 successor relation 484 succotash 30 Sudarshan XI, 108,240 super 482 supercrystal 478 superposition 198 - coherent 31 - coherent- 32 - incoherent 31 - incoherent- 32 - proper - 190 - quantum 31 - quantum- 32 superquantum theory 395 superselection 77,129 supers pace 480 supersymmetry 395,480 support 544 Susskind XI symmetric 220 symmetry 225 symplectic form 373 symplectic geometry 373 synechism 271,275 syntax 262 system 16 - active - 22 - closed - 67 - closed- 49 - open - 67 - passive - 22 system cut 16

tail 521 Tang X tangent vector 539 tensor - - bundle 540 - anti symmetric - 536 - Einstein - 345 - homogeneous - 536 Thomism 255 time 21 - - space 329 time reversal 494 - total - 62 - Racah VIII

- Racah - 61 - total VIII - Wigner VIII - Wigner - 62 Toffoli 500 Toller XI topology 321,477 - Hausdorff - 545 - spacetime - 323 torsion tensor 340 torsional derivative 339 transition 16,45 - - improbability 252 - allowed 16 - assured 30 - assured - 49 - forbidden 16 - spontaneous 29 transition amplitude 135 transition metric 113 transition semigroup 196 transitive 521 transport 338 transpose 84, 532 trivial transformation 20 Turing 10 tychism 271 type 224,535,549 - tensor - 535

Unger 153 unimodular 344 union - disjoint - 520 unit 99,522 unitary 119 unitizer 422 ur 480

vacuum 23 vacuum expectation value van der Waerden 356 variance 233 vector 529,530,539 - conjugate- 116 - final 44 - initial - 44 vector space 529 vertex 489 Vikings 7 von Glasersfeld XI

389

Von Neumann X, 10, 240 Von-Neumann-Bemays set theory 425

wandering singularity 168 Weizsacker XI Wess 489 Weyl 146 white box 53 Whitehead 153, 185 Wigner 12,179,180 Wilson X

work function 167

XAND 280 XOR 279, 520

zero 522 Zumino 489

Index 577