A Broader View of Relativity: General Implications of Lorentz And Poincare Invariance

by Hsu, Jong-Ping; Hsu, Leonardo

• ISBN13: 9789812566515
• ISBN10: 9812566511
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-09-30
• Publisher: World Scientific Pub Co Inc

Summary

A Broader View of Relativity shows that there is still new life in old physics. The book examines the historical context and theoretical underpinnings of Einstein's theory of special relativity and describes Broad Relativity, a generalized theory of coordinate transformations between inertial reference frames that includes Einstein's special relativity as a special case. It shows how the principle of relativity is compatible with multiple concepts of physical time and these different procedures for clock synchronization can be useful for thinking about different physical problems, including many-body systems and the development of a Lorentz-invariant thermodynamics. Broad relativity also provides new answers to old questions such as the necessity of postulating the constancy of the speed of light and the viability of Reichenbach's general concept of time. The book also draws on the idea of limiting-four-dimensional symmetry to describe coordinate transformations and the physics of particles and fields in non-inertial frames, particularly those with constant linear accelerations. This new edition expands the discussion on the role that human conventions and unit systems have played in the historical development of relativity theories and includes new results on the implications of broad relativity for clarifying the status of constants that are truly fundamental and inherent properties of our universe. Contents: Special Relativity is NOT Incorrect!; Space, Time, and Inertial Frames; The Novel Creation of the Young Einstein; Experimental Tests; Group Properties; Common Relativity and Quantum Mechanics; Extended Relativity; Dynamics of Classical and Quantum Particles; Group and Lie Algebra Properties of Accelerated Transformation of Spacetime; Graphic Representations of the Geometry of Spacetime in Accelerated Frames; Two Rocketships with Constant-Linear Acceleration; On a Gauge Theory of Gravity with Translation Gauge Symmetry in Inertial and Non-Inertial Frames; Appendices: Technical Aspects of Extended Relativity; Coordinate Transformations for Rotating Frames; and other papers. Key Features Includes five new chapters A complete and comprehensive description of Broad Relativity, which generalizes Einstein's original theory of special relativity to new physical time systems and a limited class of non-inertial frames Brings a fresh viewpoint with new physical implications and predictions to old physics Gives an updated discussion on fundamental physical constants and unit systems and their influence on the development of relativity theories Readership: Researchers in the field of relativity theory and advanced undergraduate students as a supplementary text.

Table of Contents

Preface	ix
Preface to the First Edition	xi
(A) The Historical and Physical Context of Relativity Theory	1	(84)
1. Introduction and Overview	3	(9)
1a. Special relativity is NOT incorrect!	3	(1)
1b. Idea #1: Einstein's first postulate of relativity (the principle of relativity) is the only necessary ingredient of a viable theory	4	(3)
1c. Idea #2: The principle of relativity is useful as a limiting principle in the discussion of the physics of accelerated frames	7	(5)
2. Space, Time and Inertial Frames	12	(7)
2a. Space	12	(1)
2b. Time	13	(1)
2c. Inertial frames of reference	14	(1)
2d. Coordinate transformations	15	(1)
2e. Units of space and time	16	(3)
3. The Nontrivial Pursuit of Earth's Absolute Motion	19	(8)
3a. Newton's frame of absolute rest	19	(3)
3b. Measuring Earth's velocity	22	(5)
4. On the Right Track: Voigt, Lorentz, and Larmor	27	(9)
4a. Lorentz's heuristic local time	27	(2)
4b. Development of the Lorentz transformations	29	(7)
5. The Contributions of Poincaré	36	(28)
5a. Poincarés insight into physical time	36	(2)
5b. Poincaré and the principle of relativity	38	(3)
5c. Poincarés theory of relativity	41	(6)
5d. Conformal transformations and a frame of 'absolute rest'	47	(4)
5e. Poincarés impact on relativity and symmetry principles	51	(3)
5f. Retro physics: Past and present views of the ether	54	(10)
6. The Novel Creation of the Young Einstein	64	(21)
6a. Fresh thoughts from a young mind	64	(1)
6b. The theory of special relativity	65	(1)
6c. Derivation of the Lorentz transformation	66	(2)
6d. Relativity of space and time	68	(5)
6e. The completion of special relativity by Minkowski's idea of 4-dimensional spacetime	73	(2)
6f. Einstein and Poincaré	75	(10)
(B) A Broader View of Relativity: The Central Role of the Principle of Relativity	85	(180)
7. Relativity Based Solely on the Principle of Relativity	87	(13)
7a. Motivation	87	(1)
7b. A brief digression: natural units and their physical basis	88	(1)
7c. Taiji relativity: A relativity theory based solely on the principle of relativity	89	(3)
7d. Realization of taiji time	92	(1)
7e. The conceptual difference between taiji relativity and special relativity	93	(2)
7f. The role of a second postulate	95	(5)
8. Common Relativity	100	(14)
8a. A new unit for time	100	(2)
8b. Operationalizing the common-second and the equivalence of inertial frames	102	(2)
8c. Coordinate transformations in common relativity	104	(2)
8d. Physical interpretation of the ligh function b	106	(3)
8e. Implications of common time	109	(5)
9. Experimental Tests I	114	(14)
9a. Time intervals versus optical path length	114	(1)
9b. The Michelson-Morley experiment	114	(4)
9c. The Kennedy-Thorndike experiment	118	(3)
9d. The Fizeau experiment	121	(7)
10. Experimental Tests II	128	(15)
10a. The Ives-Stilwell experiment	128	(1)
10b. Atomic energy levels and Doppler shifts in taiji relativity	128	(2)
10c. Atomic energy levels and Doppler shifts in common relativity	130	(3)
10d. Lifetime dilation of cosmic-ray muons	133	(1)
10e. The cosmic-ray muon experiment and taiji relativity	134	(1)
10f. Decay-length dilation in quantum field theory and taiji relativity	135	(3)
10g. Cosmic-ray muons and common relativity	138	(2)
10h. Quantum field theory and the decay length in common relativity	140	(3)
11. Group Properties of Taiji Relativity and Common Relativity	143	(15)
11a. General group properties	143	(3)
11b. Lorentz group properties	146	(6)
11c. Poincaré group properties	152	(6)
12. Invariant Actions in Relativity Theories and Truly Fundamental Constants	158	(12)
12a. Invariant actions for classical electrodynamics in relativity theories	158	(5)
12b. Universal constants and invariant actions	163	(2)
12c. Dirac's conjecture regarding the fundamental constants	165	(1)
12d. Truly fundamental constants	166	(4)
13. Common Relativity and Many-Body Systems	170	(30)
13a. Advantages of common time	170	(3)
13b. Hamiltonian dynamics in common relativity	173	(5)
13c. Invariant kinetic theory of gases	178	(4)
13d. Invariant Liouville equation	182	(2)
13e. Invariant entropy, temperature and the Maxwell-Boltzmann distribution	184	(2)
13f. Invariant Boltzmann-Vlasov equation	186	(6)
13g. Boltzmann's transport equation with 4-dimensional symmetry	192	(3)
13h. Boltzmann's H theorem with 4-dimensional symmetry	195	(5)
14. Common Relativity and the 3K Cosmic Microwave Background	200	(13)
14a. Implications of an invariant and non-invariant Planck's law for blackbody radiation	200	(1)
14b. Invariant partition function	200	(2)
14c. Covariant thermodynamics	202	(3)
14d. The canonical distribution and blackbody radiation	205	(3)
14e. The question of Earth's "absolute" motion relative to the 3K cosmic microwave background	208	(5)
15. Common Relativity and Quantum Mechanics	213	(12)
15a. Fuzziness at short distances and the invariant genergy	213	(2)
15b. Fuzzy quantum mechanics with an inherent fuzziness in the position of a point particle	215	(5)
15c. Fuzzy point and modified Coulomb potential at short distances	220	(2)
15d. Suppression of the contribution of large momentum states to Physical processes	222	(3)
16. Common Relativity and Fuzzy Quantum Field Theory	225	(15)
16a. Fuzzy quantum field theories	225	(6)
16b. Fuzzy quantum electrodynamics based on common relativity	231	(4)
16c. Experimental tests of the 4-dimensional symmetry of special relativity at very high energies	235	(5)
17. Extended Relativity: A Weaker Postulate for the Speed of Light	240	(25)
17a. Four-dimensional symmetry as a guiding principle	240	(2)
17b. Edwards' transformation with Reichenbach's time	242	(3)
17c. Difficulties of Edwards' transformation	245	(2)
17d. Extended relativity: A 4-dimensional theory with Reichenbach's time (a universal 2-way speed of light)	247	(4)
17e. The two basic postulates of extended relativity	251	(3)
17f. Invariant action for a free particle in extended relativity	254	(2)
17g. Comparison of extended relativity and special relativity	256	(2)
17h. An unpassable limit and a non-constant speed of light	258	(1)
17i. Lorentz group and the space-lightime transformations	259	(2)
17j. Decay rate and "lifetime dilation" of unstable particles	261	(4)
(C) The Role of the Principle of Relativity in the Physics of Accelerated Frames	265	(158)
18. The Principle of Limiting Lorentz and Poincaré Invariance	267	(17)
18a. An answer to the young Einstein's question and its implications	267	(4)
18b. Generalizing Lorentz transformations from inertial frames to accelerated frames	271	(3)
18c. Physical time and 'spacetime clocks' in linearly accelerated frames	274	(1)
18d. Møller's gravitational approach to accelerated transformations	275	(4)
18e. Accelerated transformations with the limiting Lorentz and Poincaré invariance	279	(5)
19. Extended Lorentz Transformations for Frames with Constant-Linear-Accelerations	284	(13)
19a. Generalized Møller-Wu-Lee transformation	284	(4)
19b. Minimal generalization of the Lorentz transformation: The Wu transformations	288	(2)
19c. A comparison of the generalized MWL and Wu transformations	290	(2)
19d. Four-momentum and constant-linear-acceleration of an accelerated particle	292	(2)
19e. Experiments on Wu-Doppler effects of waves emitted from accelerated atoms	294	(3)
20. Physical Properties of Spacetime in Accelerated Frames	297	(22)
20a. A general transformation for a CLA frame with an arbitrary β(w)	297	(3)
20b. The singular wall and horizons in the Wu transformation	300	(5)
20c. Generalized Møller-Wu-Lee transformation for an accelerated frame	305	(5)
20d. Decay-length dilations due to particle acceleration	310	(4)
20e. Discussions	314	(5)
21. Extended Lorentz Transformations for Accelerated Frames and a Resolution to the "Two-Spaceship Paradox"	319	(11)
21a. The two-spaceship paradox	319	(2)
21b. Generalized Møller and Wu transformations	321	(3)
21c. Motion and length contraction involving accelerations	324	(2)
21d. Discussion	326	(4)
22. Dynamics of Classical and Quantum Particles in Constant-Linear-Acceleration Frames	330	(26)
22a. Classical electrodynamics in constant-linear-acceleration frames	330	(4)
22b. Quantum particles and Dirac's equation in a CLA frame	334	(2)
22c. Stability of atomic levels against constant accelerations	336	(4)
22d. Electromagnetic fields produced by a charge with a constantlinear-acceleration	340	(9)
22e. Covariant radiative reaction force in special relativity and common relativity	349	(7)
23. Quantizations of Scalar, Spinor, and Electromagnetic Fields In Constant-Linear-Acceleration Frames	356	(22)
23a. Scalar field in constant-linear-acceleration frames	356	(3)
23b. Quantization of scalar fields in CLA frames	359	(7)
23c. Quantization of spinor fields in CLA frames	366	(7)
23d. Quantization of the electromagnetic field in CLA frames	373	(5)
24. Group and Lie Algebra Properties of Accelerated Spacetime Transformations	378	(11)
24a. The Wu transformation with acceleration in an arbitrary direction	378	(2)
24b. Generators of the Wu transformation in cotangent spacetime	380	(4)
24c. The Wu algebra in a modified momentum space and the classification of particles	384	(5)
25. Coordinate Transformations for Frames with a General-Linear Acceleration	389	(13)
25a. Spacetime transformations based on limiting Lorentz and Poincaré invariance	389	(7)
25b. Physical implications and discussion	396	(6)
26. A Taiji Rotational Transformation with Limiting 4-Dimensional Symmetry	402	(14)
26a. A smooth connection between rotational and inertial frames	402	(1)
26b. A taiji rotational transformation with limiting 4-dimensional symmetry	403	(3)
26c. Physical properties of the taiji rotational transformation	406	(2)
26d. The metric tensors for the spacetime of rotating frames	408	(2)
26e. The invariant action for electromagnetic fields and charged particles in rotating frames and truly fundamental constants	410	(2)
26f. The 4-momentum and the 'lifetime dilation' of a particle at rest in a rotating frame	412	(4)
27. Epilogue	416	(7)
(D) Appendices	423	(86)
A. Systems of Units and the Development of Relativity Theories	425	(16)
Aa. Units, convenience and physical necessity	425	(1)
Ab. Time, length and mass	426	(4)
Ac. Other SI base units	430	(4)
Ad. Other units	434	(1)
Ae. Status of the fundamental constants	434	(2)
Af. Discussion and conclusion	436	(5)
B. Can one Derive the Lorentz Transformation from Precision Experiments?	441	(24)
Ba. Introduction	442	(1)
Bb. Three classical tests of special relativity	443	(3)
Bc. Deriving the Lorentz transformation?	446	(9)
Bd. A more general form	455	(7)
Be. Discussions and conclusions	462	(3)
C. Quantum Electrodynamics in Both Linearly Accelerated and Inertial Frames	465	(18)
Ca. Quantum electrodynamics based on taiji relativity	465	(5)
Cb. Experimental measurements of dilations of decay-lengths and decay-lifetimes in inertial frames	470	(1)
Cc. Quantum electrodynamics of bosons in accelerated and inertial frames	470	(6)
Cd. Feynman rules for QED with fermions in both CLA and inertial frames	476	(2)
Ce. Some QED results in both CLA and inertial frames	478	(5)
D. Yang-Mills Gravity with Translation Gauge Symmetry in Inertial and Non-inertial Frames	483	(26)
Da. Translation gauge transformations and an 'effective metric tensor' in flat spacetime	483	(6)
Db. Yang-Mills theory with translation gauge symmetry	489	(1)
Dc. Gravitational action with quadratic gauge-curvature	490	(2)
Dd. Linearized equations of the tensor field and the Hamilton-Jacobi equation for particles	492	(2)
De. The gauge field equation in inertial and non-inertial frames	494	(4)
Df. Perihelion shifts and bending of light	498	(6)
Dg. The Yang-Mills gravitational force	504	(5)
Author Index	509	(4)
Subject Index	513