Einstein's Relativity and Beyond: New Symmetry Approaches

by Hsu, Jong-Ping

• ISBN13: 9789810238889
• ISBN10: 9810238886
• Format: Hardcover
• Copyright: 2000-03-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

The purposes of this book are (1) to explore and expound relativity physics and four-dimensional symmetry from the logically simplest viewpoint by making one single postulate instead of two; and (2) to indicate the simplest generalization of the Lorentz transformation in order to cope with frames with constant linear acceleration.

Table of Contents

Preface	vii
Overview	x
Logical Connections of Relativity Theories with 4-Dimensional Symmetry	xix
Introduction	1	(8)
Limitations of Special Relativity	1	(1)
Question #1: Can the theory of relativity be formulated solely on the basis of the first principle of relativity (without assuming the constancy of the speed of light)?	2	(2)
Question #2: Can one generalize the 4-dimensional transformation for inertial frames to non-inertial frames with a constant acceleration or rotation? In accelerated frames, the speed of light is no longer a universal; is the Planck constant still a universal constant?	4	(1)
Question #3: Within the 4-dimensional symmetry framework of special relativity, it appears to be impossible, in principle, to generalize the classical Liouville equation for many-particle systems to a Lorentz invariant Liouville equation. Can we overcome this difficulty?	4	(1)
Question #4: In view of the profound divergence difficulties in quantum field theory, is the spacetime 4-dimensional symmetry exact at very large momenta or short distances?	5	(4)
A Brief Review of Space and Time	9	(10)
Space and Objects	9	(2)
Time and Motion	11	(1)
Inertial Frames of References	11	(2)
Space and Time Transformations	13	(1)
Absolute Time, Relative Time, Common Time and Taiji Time	14	(5)
The Nontrivial Pursuit of Earth's Absolute Motion	19	(8)
Newton, Classical Mechanics and Invariant Laws of Motion	19	(3)
Maxwell's Suggestion for Finding Absolute Motion and Michelson's Interferometer	22	(5)
On the Right Track --- Voigt, Lorentz and Larmor	27	(8)
``Absolute Contraction of Length'' and Lorentz's Heuristic Local Time	27	(2)
Exact Transformations Discovered by Larmor and Lorentz	29	(6)
Poincare's Contributions and the Aether (Past and Present)	35	(26)
A Remarkable Insight of Physical Time	35	(2)
Poincare's Innovative Principle of Relativity	37	(2)
Poincare's Theory of relativity Based on 1 Postulate and 1 Definition	39	(7)
The Concept of an ``Aether'' Never Fades Away	46	(2)
Conformal Transformations for Inertial Frames with Absolute Velocity and ``Conformal 4-Dimensional Symmetry'' with the Constant Speed of Light	48	(3)
Poincare's Contributions to Relativity and Symmetry Principles	51	(10)
Young Einstein's Novel Creation Based on 2 Postulates	61	(19)
The Power of a Young Mind	61	(1)
Einstein's Formulation of Special Relativity with 2 Postulates	62	(4)
The Derivation of the Lorentz Transformations	66	(2)
Novel Relative Properties of Space and Time	68	(3)
Physical Implications of Einstein's Special Relativity	71	(1)
Einstein and Poincare	72	(8)
Minkowski's 4-Dimensional Spacetime, Adjustable Clocks and Flexibility in the Concept of Time	80	(7)
The Completion of Special Relativity by Minkowski's Idea of 4-Dimensional Spacetime	80	(2)
The Collision of the Titanic and Haywire Clocks	82	(1)
The Primacy of the 4-Dimensional Symmetry	83	(1)
A Flexible Concept of Time	83	(4)
Taiji Relativity Based Solely on 1 Principle --- the First Principle of Relativity	87	(13)
Refreshingly Innocent Questions	87	(1)
4-Dimensional Taiji Transformations	88	(2)
Taiji Time and Clock Systems	90	(1)
Taiji Velocity Transormations	91	(1)
Comparisons with Special Relativity	92	(3)
Einstein's Time, Common Time, Reichenbach's Time and Unspecified Time	95	(1)
Discussions and Remarks	96	(4)
The Arbitrary Speed of Light in Taiji Relativity and the Michelson-Morley Experiment	100	(12)
Does the Michelson-Morley Experiment Imply a Constant and Isotropic Speed of Light?	100	(3)
The Michelson-Morely Experiment Supports the First Postulate of Relativity	103	(3)
Do Any Experiments Really Show the Universal Constancy of the Speed of Light c?	106	(3)
Physical Quantities Measured by Using Taiji Time	109	(3)
Lorentz and Poincare Invariance Without Involving a Constant Corresponding to the Speed of Light	112	(13)
Group Properties of Taiji Transormations	112	(3)
The Lorentz Group Without Involving the Constant Speed of Light	115	(5)
The Poincare Group with Ten Generators and Without Involving the Constant Speed of Light	120	(5)
Truly Universal Constants and Physical Laws Based on Taiji Relativity	125	(13)
Truly Universal Constants and Invariant Actions	125	(3)
Atomic Structures and Doppler Shifts	128	(3)
Dirac's Conjecture of Truly Fundamental Constants vs. Taiji Relativity's Results, and the Origin of the ``Universal Value'' c = 29979245800cm/sec	131	(3)
The Maxwell Equations Without the Constant Speed of Light c	134	(4)
Quantum Electrodynamics Based on Taiji Relativity and Dilatation of Lifetimes and Decay-Lenghts	138	(10)
Quantum Electrodynamics Based on Taiji Relativity	138	(4)
Experimental Measurements of Dilatation for Decay-Lenghts and Decay-Lifetimes	142	(6)
Common Relativity: A Common Time for All Observers	148	(19)
Why Common Time?	148	(1)
Two Basic Postulates of Common Relativity	149	(1)
The Space-Lightime Transformations and Physical Clocks	150	(3)
Relativity of the Speed of Light Measured by Using Common Time	153	(1)
The Symmetry Between Any Two Frames F and F'	154	(1)
The Two-Way Speed of Light	155	(2)
The Inverse Transformations and the Lorentz Group	157	(1)
4-Dimensional Maxwell Equations and Lorentz Force with Scalar Physical Time	158	(4)
Quantum Electrdynamics Based on Common Relativity	162	(2)
New Properties in Common Relativity	164	(3)
Common Time and Many-Particle Systems in a 4-Dimensional Symmetry Framework	167	(28)
Problems of Relative Simultaneity for Many-Particle Systems	167	(3)
Invariant Hamiltonian Dynamics and Phase Space	170	(4)
The Invariant Kinetic Theory of Gases	174	(4)
The Invariant Liouville Equation	178	(2)
Invariant Entropy, Temperature and Maxwell-Boltzmann Distribution	180	(2)
The Invariant Boltzmann-Vlasov Equation	182	(6)
Boltzmann's Transport Equation with 4-Dimensional Symmetry	188	(3)
Boltzmann's H Theorem with 4-Dimensional Symmetry	191	(4)
Common Relativity and Quantum Mechanics	195	(12)
Fuzziness at Short Distances and the Invariant `Genergy'	195	(2)
Fuzzy Quantum Mechanics with an Inherent Fuzziness in the Position of a Point Particle	197	(5)
A Fuzzy Point and Modified Coulomb Potential at Short Distances	202	(2)
Inherent Probability for Suppression of Large Momentum States	204	(3)
Common Relativity and Fuzzy Quantum Field Theory	207	(14)
Fuzzy Quantum Field Theories	207	(5)
Fuzzy Quantum Electrodynamics Based on Common Relativity	212	(4)
Experimental Tests of Possible Approximate 4-Dimensional Symmetry of Special Relativity at Very High Energies and Short Distances	216	(5)
Common Relativity and the 3 K Cosmic Background Radiation	221	(11)
Implications of Non-Invariant Planck's Law of Blackbody Radiation	221	(1)
The Invariant Partition Function	221	(2)
Covariant Thermodynamics	223	(3)
Canonical Distribution and Blackbody Radition	226	(2)
Question on Earth's ``Absolute'' Motion in the 3 K Radiation	228	(4)
Extended Relativity: A Weaker Postulate for the Speed of Light	232	(16)
4-Dimensional Symmetry as a Guiding Principle	232	(2)
Edwards' Transformations with Reichenbach's Time	234	(2)
Difficulties of Edwards' Transformations	236	(2)
Extended Relativity --- A 4-Dimensional Theory with Reichenbach's Time	238	(4)
Two Basic Postulates of Extended Relativity	242	(2)
Invariant Action for a Free Particle in Extended Relativity	244	(4)
Extended Relativity with the Lorentz Group and Lifetime Dilatation	248	(8)
A Comparison of Extended Relativity and Special Relativity	248	(2)
An Unpassable Limit and Non-Constant Speed of Light	250	(1)
The Lorentz Group and the Space-Lightime Transformations	251	(2)
The Decay Rate and ``Lifetime Dilatation''	253	(3)
Physical Implications of Extended Relativity	256	(17)
4-Dimensional Symmetry with a Universal 2-Way Speed of Light	256	(3)
Some Experimental Implications of Extended Relativity	259	(1)
Doppler Shifts of Frequency and Atomic Energy Levels	260	(3)
Classical Electrodynamics Based on Extended Relativity	263	(3)
Quantum Electrodynamics Based on Extended Relativity	266	(4)
A Clock System for Lightime, Lifetime Dilatation and the Maximum Speed of Physical Objects	270	(3)
Determination of the Parameters of General Linear Transformations by Precision Experiments	273	(9)
A General Parameterization of Linear Transformations	273	(2)
Determinations of Parameters by Three Experiments	275	(3)
Flexibility of the Relation for t and t' in 4-Dimensional Symmetry Framework	278	(4)
Generalized Lorentz Transformations for Non-Inertial Frames Based on the Limiting 4-Dimensional Symmetry	282	(22)
An Answer to Young Einstein's Question and Its Implications	282	(4)
Physical Time and Clocks in Linearly Accelerated Frames	286	(4)
Moller's Gravitational Approach to Accelerated Transformations	290	(3)
A Kinematical Approach to Accelerated Transformations Based on the Limiting 4-Dimensional Symmetry	293	(3)
Generalized Moller-Wu-Lee Transformations Based on the Limiting 4-Dimensional Symmetry	296	(4)
Minimal Generalization of the Lorentz Transformations --- the Wu Transformations	300	(4)
Dynamics of Classical and Quantum Particles in Non-Inertial Frames with the Limiting 4-Dimensional Symmetry	304	(23)
Classical Electrodynamics in Constant-Linear-Acceleration Frames	304	(3)
Quantum Particles and Dirac's Equation in CLA Frame	307	(2)
Stability of Atomic Levels Against Constant Accelerations	309	(3)
Electromagnetic Fields Produced by a Charge with Constant Linear Acceleration	312	(8)
Covariant Randiative Reaction Force in Special Relativity and Common Relativity, and Conservation Laws for Radiations	320	(7)
Experimental Tests of Generalized Lorentz Transformations for Constant-Linear-Acceleration Frames	327	(9)
Tests of Physical Time in Non-Inertial Frames	327	(3)
Experiments of Accelerated Decay-Length Dilatation and the Limiting 4-Dimensional Symmetry	330	(3)
Experiments on Wu-Doppler Effects of Waves Emitted from Accelerated Atoms	333	(3)
Quantizations of Scalar, Spinor and Electromagnetic Fields in Constant-Linear-Acceleration Frames	336	(19)
Scalar Fields in Constant-Linear-Accelerations Frames	336	(3)
Quantization of Scalar Fields in CLA Frames	339	(6)
Quantization of Spinor Fields in CLA Frames	345	(6)
Quantization of the Electromagnetic Field in CLA Frames	351	(4)
Taiji Rotational Transformations with the Limiting 4-Dimensional Symmetry	355	(13)
A Smooth Connection of Rotational and Inertial Frames	355	(1)
Taiji Rotational Transformations with the Limiting 4-Dimensional Symmetry	356	(3)
Physical Properties of Taiji Rotational Transformations	359	(2)
The Metric Tensors for Rotating Frames	361	(2)
The Invariant Action for Electromagnetic Fields and Charged Particles in Roting Frames and Truly Universal Constants	363	(1)
The 4-Momentum and `Lifetime Dilatation' of a Particle at Rest in a Rotating Frame	364	(4)
Epilogue	368	(4)
Appendix A Noether's Theorem in Both Linearly Accelerated and Inertial Frames	372	(12)
Appendix B Quantum Electrodynamics in Both Linearly Accelerated and Inertial Frames	384	(12)
Appendix C De Sitter and Poincare Gauge-Invariant Fermion Lagrangians and Gravity	396	(7)
Appendix D The Relativity of Lifetime Dilatation and an Experimental Test of ``Twin Particles'' Involving Linear Accelerations	403	(10)
Name Index	413	(2)
Subject Index	415