THE CORRELATION OF PHYSICAL FORCES

By EMILY RAMIREZ

CONTENTS PART I THE TAIJI SYMMETRY FRAMEWORK 1 SPACE-TIME SYMMETRY, NATURAL UNITS AND FUNDAMENTAL CONSTANTS 1-1 UNDERPINNINGS 1-2 PHYSICAL BASIS FOR THE SYSTEM OF NATURAL UNITS 1-3 NATURE OF THE FUNDAMENTAL CONSTANTS REFERENCES 2 THE TAIJI RELATIVITY FRAMEWORK 2-1 A NEW SPACE-TIME FRAMEWORK 2-2 TAIJI RELATIVITY 2-3 OPERATIONALIZATION OF TAIJI TIME 2-4 CONCEPTUAL DIFFERENCE BETWEEN TAIJI RELATIVITY AND SPECIAL RELATIVITY 2-5 A SHORT DIGRESSION: THE ROLE OF A SECOND POSTULATE 3 THE PRINCIPLE OF LIMITING CONTINUATION OF PHYSICAL LAWS AND COORDINATE TRANSFORMATIONS FOR FRAMES WITH CONSTANT ACCELERATIONS 3-1 THE PRINCIPLE OF LIMITING CONTINUATION 3-2 CONSTANT LINEAR ACCELERATION: THE WU TRANSFORMATIONS 3-3 OPERATIONAL MEANING OF THE SPACE-TIME COORDINATES AND ‘CONSTANT-LINEAR-ACCELERATION’ 3-4 SINGULAR WALLS AND HORIZONS IN ACCELERATED FRAMES 3-5 THE WU PSEUDO-GROUP 3-6 RELATIONSHIP BETWEEN THE WU AND MØLLER TRANSFORMATIONS 3-7 EXPERIMENTAL TESTS OF THE WU TRANSFORMATIONS 4 COORDINATE TRANSFORMATIONS FOR FRAMES WITH ARBITRARY LINEAR ACCELERATIONS AND THE TAIJI PSEUDO-GROUP 4-1 ARBITRARY LINEAR ACCELERATIONS: THE TAIJI TRANSFORMATIONS 4-2 POINCARÉ METRIC TENSORS FOR ARBITRARY-LINEAR-ACCELERATION FRAMES 4-3 NEW PROPERTIES OF THE TAIJI TRANSFORMATIONS 4-4 PHYSICAL IMPLICATIONS 4-5 EXPERIMENTAL TESTS OF THE TAIJI TRANSFORMATIONS 5 COORDINATE TRANSFORMATIONS FOR ROTATING FRAMES AND EXPERIMENTAL TESTS 5-1 ROTATIONAL TAIJI TRANSFORMATIONS 5-2 METRIC TENSORS FOR THE SPACE-TIME OF ROTATING FRAMES 5-3 THE ROTATIONAL PSEUDO-GROUP 5-4 PHYSICAL IMPLICATIONS 5-5 EXPERIMENTAL TESTS OF THE ROTATIONAL TAIJI TRANSFORMATIONS 6 CONSERVATION LAWS AND SYMMETRIC ENERGY–MOMENTUM TENSORS 6-1 CONSERVATION LAWS IN THE TAIJI SYMMETRY FRAMEWORK 6-2 SYMMETRIC ENERGY–MOMENTUM TENSORS AND VARIATIONS OF METRIC TENSORS IN TAIJI SPACE-TIME 6-3 INTEGRAL FORMS OF CONSERVATION LAWS IN NON-INERTIAL FRAMES 6-4 SYMMETRY IMPLICATIONS OF GLOBAL AND LOCAL SPACE-TIME TRANSLATIONS PART II QUANTUM YANG–MILLS GRAVITY 7 THE YANG–MILLS–UTIYAMA–WEYL FRAMEWORK FOR INTERNAL AND EXTERNAL GAUGE SYMMETRIES 7-1 THE YANG–MILLS–UTIYAMA–WEYL FRAMEWORK 7-2 THE LEVI-CIVITA CONNECTION AND INTERPRETATIONS OF EINSTEIN GRAVITY 7-3 WEYL’S PARALLEL TRANSPORT OF SCALE AND ELECTROMAGNETIC ?ELDS 7-4 CURVATURES ON THE CONNECTIONS 8 YANG–MILLS GRAVITY BASED ON FLAT SPACE-TIME AND EFFECTIVE CURVED SPACE-TIME FOR MOTIONS OF CLASSICAL OBJECTS 8-1 TRANSLATIONAL GAUGE TRANSFORMATIONS IN TAIJI SPACE-TIME 8-2 TRANSLATIONAL GAUGE SYMMETRY AND THE ?ELD-THEORETIC ORIGIN OF EFFECTIVE METRIC TENSORS 8-3 GAUGE INVARIANT ACTION AND QUADRATIC GAUGE CURVATURE 8-4 THE GRAVITATIONAL ?ELD EQUATION AND FERMION EQUATIONS IN GENERAL FRAMES OF REFERENCE 8-5 DERIVATIONS OF THE T4 EIKONAL AND EINSTEIN–GROSSMANN EQUATIONS IN THE GEOMETRIC-OPTICS LIMIT 8-6 EFFECTIVE ACTION FOR CLASSICAL OBJECTS AND GAUGE INVARIANCE 8-7 CLASSICAL OBJECTS AS A COHERENT COLLECTION OF CONSTITUENT PARTICLES 8-8 REMARKS ON YANG–MILLS GRAVITY AND TELEPARALLEL GRAVITY 9 EXPERIMENTAL TESTS OF CLASSICAL YANG–MILLS GRAVITY 9-1 MOTION IN A CENTRAL GRAVITATIONAL ?ELD 9-2 THE PERIHELION SHIFT OF MERCURY 9-3 DE?ECTION OF LIGHT IN A GRAVITATIONAL ?ELD 9-4 GRAVITATIONAL QUADRUPOLE RADIATION 10 THE S-MATRIX IN YANG–MILLS GRAVITY 10-1 THE GAUGE-INVARIANT ACTION AND GAUGE CONDITIONS 10-2 FEYNMAN–DEWITT–MANDELSTAM (FDM) GHOST ?ELDS IN YANG–MILLS GRAVITY 10-3 UNITARITY AND GAUGE INVARIANCE OF THE S-MATRIX AND FDM GHOST PARTICLES 10-4 DISCUSSION 11 QUANTIZATION OF YANG–MILLS GRAVITY AND FEYNMAN–DYSON RULES 11-1 A GAUGE INVARIANT ACTION FOR GRAVITONS AND FERMIONS AND THEIR ?ELD EQUATIONS 11-2 THE FEYNMAN–DYSON RULES FOR QUANTUM YANG–MILLS GRAVITY 12 GRAVITATIONAL SELF-ENERGY OF THE GRAVITON 12-1 GRAVITON SELF-ENERGY IN THE DEWITT GAUGE 12-2 GRAVITON SELF-ENERGY IN A GENERAL GAUGE 12-3 DISCUSSION 13 SPACE-TIME GAUGE IDENTITIES AND FINITE-LOOP RENORMALIZATION 13-1 SPACE-TIME (T4) GAUGE IDENTITIES 13-2 SPACE-TIME GAUGE IDENTITIES AND A GENERAL GRAVITON PROPAGATOR 13-3 GAUGE IDENTITIES IN QUANTUM ELECTRODYNAMICS WITH A NON-LINEAR GAUGE CONDITION 13-4 THE IN?NITE CONTINUOUS GROUP OF GENERAL COORDINATE TRANSFORMATIONS IN ?AT SPACE-TIME 13-5 REMARKS ON ULTRAVIOLET DIVERGENCES AND ?NITE-LOOP RENORMALIZATION FOR GRAVITY 14 A UNI?ED GRAVITY–ELECTROWEAK MODEL 14-1 THE GAUGE COVARIANT DERIVATIVE AND GAUGE CURVATURES OF A UNI?ED GRAVITY–ELECTROWEAK MODEL 14-2 THE LAGRANGIAN IN THE GRAVIELECWEAK MODEL 14-3 THE EQUATIONS OF MOTION FOR QUANTUM AND CLASSICAL PARTICLES 14-4 VIOLATIONS OF U1 AND SU2 GAUGE SYMMETRIES BY GRAVITY 15 A UNI?ED GRAVITY–STRONG FORCE MODEL 15-1 UNI?ED GAUGE COVARIANT DERIVATIVES AND GAUGE CURVATURES GAUGE SYMMETRY BY GRAVITY 15-3 EFFECTIVE CURVED SPACE-TIME FOR MOTIONS OF QUARKS AND GLUONS IN THE CLASSICAL LIMIT 15-4 DISCUSSION 16 OUTLOOK 16-1 TAIJI SPACE-TIME — A BASIC FRAMEWORK FOR ALL PHYSICS 16-2 THE COSMIC LEE–YANG FORCE AND A LINEAR POTENTIAL FOR THE ACCELERATED EXPANSION OF THE UNIVERSE 16-3 POSSIBLE ORIGINS OF MASS IN A UNI?ED MODEL: CONSTANT VACUUM ?ELD OR HIGGS ?ELD? 16-4 FINITE QUANTUM GRAVITY AND A POSSIBLE DEPARTURE FROM EXACT LORENTZ INVARIANCE AT HIGH ENERGIES 16-5 TOWARD A TOTAL UNI?CATION OF ALL INTERACTIONS 16-6 CONCLUSION