Life without special relativity Chocolate Tree Books Copyright © 2007, Eric Baird. First printings: September 2007 (pb), July 2008 (hb) All rights reserved. No reproduction, copy or transmission of any part of this publication may be made in any format or medium, including but not limited to photographic, electronic or holographic, without prior written permission. The right of Eric Baird to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Published by Chocolate Tree Books, UK www.chocolatetreebooks.com A CIP catalogue record for this book is available from the British Library Baird, Eric Relativity in curved spacetime: Life without special relativity / Eric Baird. First edition. 394 pp. (i-xvi, 1-378) size: 234 mm × 156 mm Includes bibliographic references and index, and >200 figures and illustrations Subjects: Relativity (Physics): Space and Time: Special Relativity (Physics) Dewey Classification: 530.11 hardback: ISBN10: 0955706823 ISBN13: 978 0 9557068 2 0 paperback: ISBN10: 0955706807 ISBN13: 978 0 9557068 0 6 5-69-10-162 I do not see any reason to assume that … the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity … I do not believe that it is justifiable to ask: what would physics look like without gravitation? Albert Einstein, 1950 v RELATIVITY IN CURVED SPACETIME OVERVIEW 00 [ BOOK INTRODUCTION ] The usual things that one finds at the start of a book, abbreviations, and a table of contents 01 BACKGROUND PHYSICS The speed of light, local and global … Gravity, light and time, space and spacetime curvature … Inertial and gravitational mass, energy has gravity, E=mc² … Different principles of relativity, Mach's principle … Wave-particle duality and the Newtonian crisis 02 EFFECTS DUE TO RELATIVE MOTION Doppler effects on signal frequencies and wavelengths … Analogous effects on the apparent lengths of rulers … Aberration: associated distortion of angles … Moving and accelerated bodies drag light, light-dragging as a fundamental aspect of the General Principle 03 LIMITS TO OBSERVATION Quantum Mechanics and observability, observerspace, "Copenhagen" and "Hidden Variable" interpretations … Dark Stars and Black Holes, the "classical" and "quantum" versions of Hawking Radiation, the Black Hole Information Paradox and some associated black hole paradoxes and problems 04 UPDATING STANDARD THEORY Problems with the current implementation of general relativity, should GR ever have incorporated Einstein's Special Theory? … Zooming in on a single solution, Special Relativity's relationships seem to be incompatible with fully curvature-based models 05 THE FLAT SPACETIME PARADIGM The build-up to Einstein's special theory – Lorentz, Einstein and Minkowski, Einstein's "special" theory in brief … Some shortcomings of the Special Theory, cumulative redshift issues … Experimental evidence for Special Relativity, the way it has been presented, and some unsettling procedural discrepancies 06 FUTURE PHYSICS A few interesting universes, the Hartle-Hawking Bubble … Wormholes, antiwormholes and pseudo-wormholes … Warp drive theory 07 THE HUMAN FACTOR Logic and language, limitations of sequential logic, "thinkable" vs. "unthinkable", quality control and filtering, belief systems, quantum mechanics applied to the behaviour of societies (including physicists) … Seeing what we want to see, what do experiments really tell us?, exploration is a dangerous business … Two possible histories, signs associated with systemic failure, coming to terms with the potential loss of special relativity 08 [ BOOK LEADOUT ] Calculations too tedious to include in the main body of the book (but demanded by physicists) … Lists of some relevant reference papers and books (about 400 entries), a few significant people, and the final, inevitable, keyword index vi Introduction and Contents TABLE OF CONTENTS OVERVIEW.................................................................................VI TABLE OF CONTENTS...............................................................VII WELCOME...............................................................................XIII ABOUT THE AUTHOR...............................................................XIV NOTES TO THE FIRST EDITION...............................................XIV ACKNOWLEDGEMENTS AND CREDITS.....................................XV ABBREVIATIONS................................................................................................................XVI PART I BACKGROUND PHYSICS 1 1 THE SPEED OF LIGHT...............................................................3 1.1 : LIGHT IS PRETTY FAST...................................................................................................5 1.2 : LIGHTSPEED VARIES......................................................................................................6 1.3 : LIGHTSPEED IS NOT JUST THE SPEED OF LIGHT..............................................................7 1.4 : LIGHTSPEED AFFECTS INERTIA......................................................................................8 1.5 : LIGHTSPEED CONTROLS TIMEFLOW...............................................................................8 1.6 : LIGHTSPEED IS LOCALLY CONSTANT.............................................................................8 1.7 : LIGHTSPEED IS NOW DEFINED AS CONSTANT.................................................................9 1.8 : THE GRAVITY WELL......................................................................................................9 1.9 : LIGHT TRAVELS IN STRAIGHT LINES. EXCEPT WHEN IT DOESN'T.................................11 1.10 : LIGHT USED TO DEFINE A STRAIGHT LINE..................................................................12 2 GRAVITY, ENERGY AND MASS...............................................13 2.1 : WHAT IS MASS?...........................................................................................................15 2.2 : DOES LIGHT HAVE MASS?............................................................................................16 2.3 : GENIE IN A BOTTLE: THOUGHT-EXPERIMENTS WITH BOTTLED LIGHT.........................17 2.4 : DIFFICULTY OF DETECTING THE EFFECT......................................................................19 2.5 : MASS-TO-ENERGY CONVERSION.................................................................................20 2.6 : HISTORY OF E=MC².....................................................................................................21 2.7 : ENERGY HAS MASS, PERIOD........................................................................................22 3 CURVED SPACE AND TIME.....................................................23 3.1 : GRAVITY IS … WHAT, EXACTLY?...............................................................................25 3.2 : GRAVITY BENDS LIGHT...............................................................................................25 3.3 : GRAVITY WARPS GEOMETRY.......................................................................................26 3.4 : GRAVITY AS A VARIATION IN INERTIA.........................................................................28 3.5 : ENERGY-CHANGE IN LIGHT DUE TO GRAVITY..............................................................28 3.6 : GRAVITATIONAL REDSHIFTS AND BLUESHIFTS............................................................29 3.7 : GRAVITATIONAL TIME DILATION................................................................................30 3.8 : NOT JUST CURVED SPACE, BUT CURVED SPACETIME...................................................32 4 RELATIVITY............................................................................33 4.1 : RELATIVITY OF SPACE.................................................................................................35 4.2 : RELATIVITY OF TIME...................................................................................................35 4.3 : RELATIVITY OF VELOCITY...........................................................................................36 4.4 : ISAAC NEWTON'S "PRINCIPIA"....................................................................................37 4.5 : MACH AND RELATIVITY..............................................................................................38 4.6 : PRACTICAL ADVANTAGES OF "RELATIVISTIC" ARGUMENTS........................................39 4.7 : APPLYING OCCAM'S RAZOR........................................................................................39 4.8 : DIFFERENT "PRINCIPLES OF RELATIVITY"...................................................................40 4.9 : CAUSES OF CONFUSION...............................................................................................41 4.10 : RELATIVITY OF ACCELERATION................................................................................42 4.11 : RELATIVE ACCELERATION VS. ABSOLUTE ACCELERATION........................................43 4.12 : RELATIVITY OF ROTATION........................................................................................45 vii RELATIVITY IN CURVED SPACETIME 4.13 : "CENTRIFUGAL" AND "CORIOLIS" FIELDS.................................................................45 4.14 : ROTATIONAL DRAGGING...........................................................................................47 4.15 : EXPERIMENTAL VERIFICATION..................................................................................49 4.16 : EQUIVALENCE PRINCIPLES........................................................................................50 5 THE NEWTONIAN CATASTROPHE..........................................51 5.1 : NEWTON'S UNIFICATION SCHEME:...............................................................................53 5.2 : THE LIGHTSPEED MISTAKE ….....................................................................................54 5.3 : THE "SPACE-DENSITY" MISTAKE.................................................................................54 5.4 : THE LIGHT-ENERGY MISTAKE......................................................................................55 5.5 : LOSS OF WAVE-PARTICLE DUALITY.............................................................................55 5.6 : NEWTON VS. HUYGHENS.............................................................................................56 5.7 : THE LIGHTSPEED TRAP................................................................................................57 5.8 : CONSEQUENCES FOR PHYSICS.....................................................................................59 PART II EFFECTS DUE TO RELATIVE MOTION 61 6 DOPPLER SHIFTS....................................................................63 6.1 : "STATIONARY OBSERVER" DOPPLER EFFECT..............................................................65 6.2 : "STATIONARY SOURCE" DOPPLER EFFECT..................................................................66 6.3 : COMPARISONS.............................................................................................................66 6.4 : TRANSVERSE DOPPLER EFFECTS (AUDIO)....................................................................67 6.5 : OPTICAL DOPPLER EFFECTS........................................................................................69 6.6 : LONGITUDINAL DOPPLER EFFECT UNDER SPECIAL RELATIVITY.................................69 6.7 : TRANSVERSE DOPPLER EFFECT UNDER SPECIAL RELATIVITY.....................................70 7 APPARENT LENGTH-CHANGES IN MOVING OBJECTS...........71 7.1 : APPARENT CHANGES IN LENGTH.................................................................................73 7.2 : APPROACHING OBJECTS APPEAR ELONGATED.............................................................73 7.3 : RECEDING OBJECTS APPEAR CONTRACTED..................................................................73 7.4 : DEGREE OF CONTRACTION OR ELONGATION...............................................................74 7.5 : SPECIAL RELATIVITY AND LENGTH-CHANGES.............................................................75 7.6 : RULERS AND GRAVITATION.........................................................................................76 8 ABERRATION OF ANGLES.......................................................77 8.1 : ABERRATION OF ANGLES............................................................................................79 8.2 : RELATIVISTIC ABERRATION AT 90 DEGREES...............................................................80 8.3 : THE RELATIVISTIC ELLIPSE.........................................................................................81 8.4 : PUTTING IT ALL TOGETHER.........................................................................................83 8.5 : RELATIVISTIC ELLIPSE: NEWTONIAN THEORY.............................................................83 8.6 : RELATIVISTIC ELLIPSE: SPECIAL RELATIVITY.............................................................84 9 MOVING BODIES DRAG LIGHT................................................85 9.1 : GENERALITY OF DRAGGING EFFECTS..........................................................................87 9.2 : NAMING CONVENTIONS: GRAVITOMAGNETISM, FRAME-DRAGGING...........................87 9.3 : ARGUMENT #1: LINEAR GM AS A GRAVITATIONAL TIMELAG EFFECT.........................87 9.4 : ARGUMENT #2: "EFFECTIVE GRAVITATIONAL POTENTIAL" DEPENDS ON RELATIVE VELOCITY.................................................................88 9.5 : ARGUMENT #3: GRAVITATIONAL SMUDGING..............................................................89 9.6 : ARGUMENT #4: THE SLINGSHOT EFFECT.....................................................................89 9.7 : ARGUMENT #5: ROTATIONAL GM AND GRAVITATIONAL TIMELAG............................90 9.8 : ARGUMENT #6: QM AND "PROBABILISTIC" SMUDGING..............................................91 9.9 : ARGUMENT #7: EXPERIMENT: THE FIZEAU EFFECT....................................................91 9.10 : INCONSISTENCIES IN OUR APPROACH TO VELOCITY..................................................92 9.11 : CANCELLATION AND UNIFICATION?..........................................................................94 9.12 : IMPLEMENTATION – THE TILTED GRAVITY-WELL......................................................95 9.13 : ZENO REVISITED: THE "IMPOSSIBILITY" OF MOTION..................................................96 9.14 : WORLDLINES AND CURVATURE................................................................................97 9.15 : UH-OH …..................................................................................................................98 9.16 : THE SCORE CHART....................................................................................................99 9.17 : "RELATIVISTIC" IMPLEMENTATIONS OF LIGHTSPEED CONSTANCY..........................100 viii