Table Of ContentA Tale of
Two Twins
The Langevin Experiment of
a Traveler to a Star
b2530 International Strategic Relations and China’s National Security: World at the Crossroads
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A Tale of
Two Twins
The Langevin Experiment of
a Traveler to a Star
Lucien Gilles Benguigui
Technion — Israel Institute of Technology, Israel
World Scientific
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A TALE OF TWO TWINS
The Langevin Experiment of a Traveler to a Star
Copyright © 2021 by World Scientific Publishing Co. Pte. Ltd.
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Preface
Is it really possible that after more than 100 years, something new
may be published about this unbelievable result of the Theory of
Relativityofatravelerwho,afterreachingastar,comesbackyounger
than people on earth?
Today,itisalmostimpossibletopublishanarticleonthissubject
in a respectable physics journal: the subject is exhausted. About ten
years ago, I began to be interested in the subject and discovered two
facts.Thefirstis thatthisstory (implyinginnumerablepublications)
did not receive a complete survey. The story is well known by
physicists and people interested in Relativity, but I did not find an
article recalling all of what happened from 1911 when the French
physicist Paul Langevin published his article. I confess that, due
to the huge expanse of the literature, I might have missed such an
article, but the probability is small. The second fact is the almost
infinite number of publications presenting a solution, explaining how
the Theory of Relativity reaches this result for the younger traveler.
I wrote an article to fillthe absenceof a survey andof astandard
solution accepted by all. Of course, I did not try a physics journal
but I published in arXiv. However, the impact was very small and
few authors mentioned my article.
After a time of frustration, I decided to write a book and looked
forapublisher.IwanttothankWorld ScientificPublishingforaccep-
ting my manuscript. For a long time, the subject was at the center
of discussions and polemics, and I hope that my book will not awake
new antagonisms. There is a little risk since in some parts of the
v
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vi Preface
book, I do not agree with well accepted opinions. I ask the reader to
be careful in his reading before raising objections.
Finally,Iwanttoacknowledgeseveralimportantdiscussionswith
mycolleagueOriAmos.Allmyfamily(mywifeSuzanne,mychildren
andmygrandchildren)hadbeensupportiveandencouragedmetogo
onwhenIwashesitating.Iexpressmythanksforallandinparticular
my granddaughter Hadar for her help in using Word.
Haifa, May 2020 Lucien Gilles Benguigui
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Contents
Preface v
1. Introduction 1
Part I: Langevin 7
2. The Story in Short 9
2.1 The Langevin Article. . . . . . . . . . . . . . . . . . . 9
2.2 Einstein in Paris: The Meeting with Bergson . . . 11
2.3 The First Reactions . . . . . . . . . . . . . . . . . . . 12
2.4 The Deluge of Solutions After 1950 . . . . . . . . . 13
2.5 The Solution of Møller (1952) . . . . . . . . . . . . . 14
2.6 The Dingle and Sachs Controversies . . . . . . . . . 14
2.7 The Deniers . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.8 The Article . . . . . . . . . . . . . . . . . . . . . . . . . 17
3. The Article of Langevin 19
Part II: Physics 45
4. The Clock or The Twin Paradox 47
4.1 Inertial Frames . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 The Lorentz Transformation . . . . . . . . . . . . . . 49
4.2.1 Application of the Lorentz
transformation . . . . . . . . . . . . . . . . . . . 50
4.2.2 Simultaneity and length contraction . . . . . 51
vii
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viii Contents
4.3 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4 The Formulation. . . . . . . . . . . . . . . . . . . . . . 55
4.5 When a Frame Stops Its Motion . . . . . . . . . . . 57
4.6 A Graphical Solution . . . . . . . . . . . . . . . . . . . 63
4.7 The Two Aspects of the Concept of Mass . . . . . 64
4.8 The Gravitation–Acceleration Equivalence . . . . . 65
4.9 The Time in a Non-inertial Frame . . . . . . . . . . 66
4.10 The Langevin Problem. . . . . . . . . . . . . . . . . . 70
5. The First Solutions 73
5.1 The First Einstein Argument . . . . . . . . . . . . . 73
5.2 The Lorentz Solution . . . . . . . . . . . . . . . . . . . 75
5.3 The Langevin Solution . . . . . . . . . . . . . . . . . . 77
5.4 The Einstein Solution . . . . . . . . . . . . . . . . . . 79
5.5 The Born Solution . . . . . . . . . . . . . . . . . . . . 83
6. The Einstein-Møller Solution 87
6.1 Determination of the Travel Times . . . . . . . . . . 87
6.1.1 The point of view of the observer on the
earth . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.1.2 The point of view of the traveler . . . . . . . 93
6.2 Analysis of the Travel Times . . . . . . . . . . . . . . 93
6.3 The Hafele–Keating Experiment . . . . . . . . . . . 100
6.4 The Precursor and the Followers . . . . . . . . . . . 101
7. The Disappearance of the Acceleration
and the Symmetry Breaking 103
7.1 How to Clear the Acceleration? . . . . . . . . . . . . 104
7.2 The Symmetry Breaking . . . . . . . . . . . . . . . . 106
7.3 The Exchange of Signals . . . . . . . . . . . . . . . . 108
7.4 The Three-Frame Model . . . . . . . . . . . . . . . . 110
7.4.1 Solution of the three-frame model . . . . . . 111
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Contents ix
Part III: Discussions 117
8. Physicists Out of the Mainstream 119
8.1 The Dingle Controversy . . . . . . . . . . . . . . . . . 121
8.2 The Sachs Controversy . . . . . . . . . . . . . . . . . 126
8.3 Dingle Versus Sachs . . . . . . . . . . . . . . . . . . . 128
9. Questions With and Without Answers 131
9.1 The Time Dilation and the Time Reciprocity . . . 132
9.2 Forgetting Reciprocity . . . . . . . . . . . . . . . . . . 136
9.3 The Acceleration . . . . . . . . . . . . . . . . . . . . . 140
9.4 The Multiplicity of Solutions. . . . . . . . . . . . . . 142
9.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . 144
10. Bergson and the Relativity 145
10.1 The Philosopher Bergson . . . . . . . . . . . . . . . . 145
10.2 The Content of “Duration and Simultaneity” . . . 147
10.3 Debates and Critics. . . . . . . . . . . . . . . . . . . . 149
10.4 The Journey of the Projectile (the Clock
Paradox) . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
11. The Langevin Effect 155
Bibliography 159
Index 163
