UNDERSTANDING PHYSICS
CONTENTS PART I POINT PARTICLES 1 THE SPINLESS POINT PARTICLE POINT PARTICLES VERSUS WORLDLINES CLASSICAL THEORY FIRST QUANTIZATION FLAT SPACETIME CURVED SPACETIME SECOND QUANTIZATION CLASSICAL ?ELD THEORY WITH INVARIANT EVOLUTION PARAMETER THE CANONICAL QUANTIZATION COMPARISON WITH THE CONVENTIONAL RELATIVISTIC QUANTUM ?ELD THEORY 2 POINT PARTICLES AND CLIFFORD ALGEBRA INTRODUCTION TO GEOMETRIC CALCULUS BASED ON CLI?ORD ALGEBRA ALGEBRA OF SPACETIME PHYSICAL QUANTITIES AS POLYVECTORS THE UNCONSTRAINED ACTION FROM THE POLYVECTOR ACTION FREE PARTICLE PARTICLE IN A ?XED BACKGROUND ?ELD QUANTIZATION OF THE POLYVECTOR ACTION ON THE SECOND QUANTIZATION OF THE POLYVECTOR ACTION SOME FURTHER IMPORTANT CONSEQUENCES OF CLI?ORD ALGEBRA RELATIVITY OF SIGNATURE GRASSMANN NUMBERS FROM CLI?ORD NUMBERS THE POLYVECTOR ACTION AND DE WITT–ROVELLI MATERIAL REFERENCE SYSTEM 3 HARMONIC OSCILLATOR IN PSEUDO-EUCLIDEAN SPACE THE 2-DIMENSIONAL PSEUDO-EUCLIDEAN HARMONIC OSCILLATOR HARMONIC OSCILLATOR IN D-DIMENSIONAL PSEUDO-EUCLIDEAN SPACE A SYSTEM OF SCALAR ?ELDS CONCLUSION PART II EXTENDED OBJECTS 4 GENERAL PRINCIPLES OF MEMBRANE KINEMATICS AND DYNAMICS MEMBRANE SPACE M MEMBRANE DYNAMICS MEMBRANE THEORY AS A FREE FALL IN M-SPACE MEMBRANE THEORY AS A MINIMAL SURFACE IN AN EMBEDDING SPACE MEMBRANE THEORY BASED ON THE GEOMETRIC CALCULUS IN M- SPACE MORE ABOUT THE INTERCONNECTIONS AMONG VARIOUS MEMBRANE ACTIONS 5 MORE ABOUT PHYSICS IN M-SPACE GAUGE ?ELDS IN M-SPACE GENERAL CONSIDERATIONS A SPECI?C CASE M-SPACE POINT OF VIEW AGAIN A SYSTEM OF MANY MEMBRANES DYNAMICAL METRIC ?ELD IN M-SPACE METRIC OF VN FROM THE METRIC OF M-SPACE 6 EXTENDED OBJECTS AND CLIFFORD ALGEBRA MATHEMATICAL PRELIMINARIES VECTORS IN CURVED SPACES VECTORS IN AN IN?NITE-DIMENSIONAL SPACE DYNAMICAL VECTOR ?ELD IN M-SPACE DESCRIPTION WITH THE VECTOR ?ELD IN SPACETIME FULL COVARIANCE IN THE SPACE OT PARAMETERS ?A DESCRIPTION IN SPACETIME DESCRIPTION IN M-SPACE DESCRIPTION IN THE ENLARGED M-SPACE CONTENTS 7 QUANTIZATION THE QUANTUM THEORY OF UNCONSTRAINED MEMBRANES THE COMMUTATION RELATIONS AND THE HEISENBERG EQUATIONS OF MOTION THE SCHR¨ODINGER REPRESENTATION THE STATIONARY SCHR¨ODINGER EQUATION FOR A MEMBRANE DIMENSIONAL REDUCTION OF THE SCHR¨ODINGER EQUATION A PARTICULAR SOLUTION TO THE COVARIANT SCHR¨ODINGER EQUATION THE WAVE PACKET THE EXPECTATION VALUES CLI?ORD ALGEBRA AND QUANTIZATION PHASE SPACE WAVE FUNCTION AS A POLYVECTOR EQUATIONS OF MOTION FOR BASIS VECTORS QUANTIZATION OF THE P-BRANE: A GEOMETRIC APPROACH PART III BRANE WORLD 8 SPACETIME AS A MEMBRANE IN A HIGHER-DIMENSIONAL SPACE THE BRANE IN A CURVED EMBEDDING SPACE A SYSTEM OF MANY INTERSECTING BRANES THE BRANE INTERACTING WITH ITSELF A SYSTEM OF MANY BRANES CREATES THE BULK AND ITS METRIC THE ORIGIN OF MATTER IN THE BRANE WORLD MATTER FROM THE INTERSECTION OF OUR BRANE WITH OTHER BRANES MATTER FROM THE INTERSECTION OF OUR BRANE WITH ITSELF COMPARISON WITH THE RANDALL–SUNDRUM MODEL THE METRIC AROUND A BRANE IN A HIGHER-DIMENSIONAL BULK 9 THE EINSTEIN–HILBERT ACTION ON THE BRANE AS THE EFFECTIVE ACTION THE CLASSICAL MODEL THE QUANTUM MODEL 10 ON THE RESOLUTION OF TIME PROBLEM IN QUANTUM GRAVITY 10 1 SPACE AS A MOVING 3-DIMENSIONAL MEMBRANE IN VN 10 2 SPACETIME AS A MOVING 4-DIMENSIONAL MEMBRANE IN VN GENERAL CONSIDERATION A PHYSICALLY INTERESTING SOLUTION INCLUSION OF SOURCES PART IV BEYOND THE HORIZON 11 THE LANDSCAPE OF THEORETICAL PHYSICS: A GLOBAL VIEW 12 NOBODY REALLY UNDERSTANDS QUANTUM MECHANICS 12 1 THE ‘I’ INTUITIVELY UNDERSTANDS QUANTUM MECHANICS 12 2 DECOHERENCE 12 3 ON THE PROBLEM OF BASIS IN THE EVERETT INTERPRETATION 12 4 BRANE WORLD AND BRAIN WORLD 12 5 FINAL DISCUSSION ON QUANTUM MECHANICS, AND CONCLUSION 13 FINAL DISCUSSION 13 1 WHAT IS WRONG WITH TACHYONS? 13 2 IS THE ELECTRON INDEED AN EVENT MOVING IN SPACETIME? 13 3 IS OUR WORLD INDEED A SINGLE HUGE 4-DIMENSIONAL MEMBRANE? 13 4 HOW MANY DIMENSIONS ARE THERE? 13 5 WILL IT EVER BE POSSIBLE TO ?ND SOLUTIONS TO THE CLASSICAL AND QUANTUM BRANE EQUATIONS OF MOTION AND MAKE PREDICTIONS? 13 6 HAVE WE FOUND A UNIFYING PRINCIPLE?