Springer ehlers j lammerzahl c (eds) special relativity will it survive the next 101 years (LNP 702 springer 2006)(ISBN 3540345221)(537s)

Lecture Notes in Physics
Editorial Board
R. Beig, Wien, Austria
W. Beiglböck, Heidelberg, Germany
W. Domcke, Garching, Germany
B.-G. Englert, Singapore
U. Frisch, Nice, France
P. Hänggi, Augsburg, Germany
G. Hasinger, Garching, Germany
K. Hepp, Zürich, Switzerland
W. Hillebrandt, Garching, Germany
D. Imboden, Zürich, Switzerland
R. L. Jaffe, Cambridge, MA, USA
R. Lipowsky, Golm, Germany
H. v. Löhneysen, Karlsruhe, Germany
I. Ojima, Kyoto, Japan
D. Sornette, Nice, France, and Zürich, Switzerland
S. Theisen, Golm, Germany
W. Weise, Garching, Germany
J. Wess, München, Germany
J. Zittartz, Köln, Germany


The Lecture Notes in Physics
The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments
in physics research and teaching – quickly and informally, but with a high quality and
the explicit aim to summarize and communicate current knowledge in an accessible way.
Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research to serve the following purposes:
• to be a compact and modern up-to-date source of reference on a well-defined topic;
• to serve as an accessible introduction to the field to postgraduate students and nonspecialist researchers from related areas;
• to be a source of advanced teaching material for specialized seminars, courses and

schools.
Both monographs and multi-author volumes will be considered for publication. Edited
volumes should, however, consist of a very limited number of contributions only. Proceedings will not be considered for LNP.
Volumes published in LNP are disseminated both in print and in electronic formats,
the electronic archive is available at springerlink.com. The series content is indexed,
abstracted and referenced by many abstracting and information services, bibliographic
networks, subscription agencies, library networks, and consortia.
Proposals should be sent to a member of the Editorial Board, or directly to the managing
editor at Springer:
Dr. Christian Caron
Springer Heidelberg
Physics Editorial Department I
Tiergartenstrasse 17
69121 Heidelberg/Germany



Jürgen Ehlers Claus Lämmerzahl (Eds.)

Special Relativity
Will it Survive the Next 101 Years?

ABC


Editors
Jürgen Ehlers
Albert-Einstein-Institut
MPl Gravitationsphysik
Am Mühlenberg 1

14476 Golm, Germany
E-mail: mpoessel@aei-potsdam.
mpg.de

Claus Lämmerzahl
ZARM, Universität Bremen
Am Fallturm
28359 Bremen, Germany
E-mail: laemmerzahl@zarm.
uni-bremen.de

J. Ehlers and C. Lämmerzahl, Special Relativity,
Lect. Notes Phys. 702 (Springer, Berlin Heidelberg 2006), DOI 10.1007/b11758914

Library of Congress Control Number: 2006928275
ISSN 0075-8450
ISBN-10 3-540-34522-1 Springer Berlin Heidelberg New York
ISBN-13 978-3-540-34522-0 Springer Berlin Heidelberg New York
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,
reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication
or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,
1965, in its current version, and permission for use must always be obtained from Springer. Violations are
liable for prosecution under the German Copyright Law.
Springer is a part of Springer Science+Business Media
springer.com
c Springer-Verlag Berlin Heidelberg 2006
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply,
even in the absence of a specific statement, that such names are exempt from the relevant protective laws
and regulations and therefore free for general use.

Typesetting: by the authors and techbooks using a Springer LATEX macro package
Cover design: design & production GmbH, Heidelberg
Printed on acid-free paper

SPIN: 11758914

54/techbooks

543210


Preface

Einstein’s relativity theories changed radically the physicists’ conception of
space and time. The Special Theory, i.e., Minkowski spacetime and Poincar´einvariance, not only removed an inconsistency between the kinematical foundations of mechanics and electrodynamics but provided a framework for all of
physics except gravity. Even General Relativity kept the most essential ingredient of special relativity – a Lorentz-metric – and, therefore, maintained Lorentzinvariance infinitesimally. In the large realm of particle physics where intrinsic, tidal gravitational fields are totally negligible, Poincar´e-invariance combined
with gauge invariance led to relativistic quantum field theories and, specifically,
to the standard model of particle physics.
General Relativity theory and Quantum Field theory generalized classical Poincar´e-invariant field theory in different directions. Both generalizations
turned out to be successful, but their basic assumptions contradict each other.
Attempts to overcome this “most glaring incompatibility of concepts” (F. Dyson)
so far have led to partial successes but not to a unified foundation of physics encompassing gravity and quantum theory. Thus, after about a century of successes
in separate areas, physicists feel the need to probe the limits of validity of the
SR-based theories. Canonical approaches to quantum gravity, non-commutative
geometry, (super-)string theory, and unification scenarios predict tiny violations
of Lorentz-invariance at high energies. Accordingly, the present seminar tries to
cover the basics of Special Relativity, proposed scenarios that lead to violations of
Lorentz-invariance, and experiments designed to find such effects. Furthermore,
some historical and philosophical aspects are treated.
The main topis of this seminar are

•
•
•
•

The foundations and the mathematics of Special Relativity
Conjectured violations of Lorentz-invariance
Confrontation with high-precision experiments
Philosophical and historical aspects

The 271st WE–Heraeus Seminar on Special Relativity, where these issues
have been discussed, took place in Potsdam from February 13–18, 2005. We


VI

Preface

sincerely thank all speakers for their presentations and especially those who
moreover were willing to write them up for the present volume. Last but not least
we thank the Wilhelm and Else Heraeus Foundation for its generous support,
without which this seminar could not have been realized.
Golm and Bremen
January 2006

J¨
urgen Ehlers
Claus L¨
ammerzahl

Experimental set-up of an early high precision search for an anisotropy of inertia.


Contents

Part I

Historical and Philosophical Aspects

Isotropy of Inertia: A Sensitive Early Experimental Test
R.W.P. Drever . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Early Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Possibilities for Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Some Factors Expected to Affect Sensitivity
in a Simple NMR Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Development of the Experimental Technique . . . . . . . . . . . . . . . . . . . . . . .
6 Initial Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Experiments and Developments for Higher Sensitivity . . . . . . . . . . . . . . .
8 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 Discussion of Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11 Some Personal Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Challenge of Practice: Einstein, Technological Development
and Conceptual Innovation
M. Carrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Knowledge and Power in the Scientific Revolution . . . . . . . . . . . . . . . . . .
2 Contrasting Intuitions on the Cascade Model . . . . . . . . . . . . . . . . . . . . . .
3 Poincar´e, Einstein, Distant Simultaneity,

and the Synchronization of Clocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 The Emerging Rule of Global Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Technology-Based Concepts
and the Rise of Operationalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Technological Problems, Technological Solutions,
and Scientific Progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3
3
4
4
5
5
7
7
9
12
12
13
13

15
15
17
20
24
25
28
30

VIII

Contents

Part II

Foundation and Formalism

Foundations of Special Relativity Theory
J. Ehlers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Inertial Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Poincar´e Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Minkowski Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Axiomatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 The Principle of Special Relativity and Its Limits . . . . . . . . . . . . . . . . . .
7 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Accelerated Frames of Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 SR Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35
35
36
36
39
40
40

41
41
42
43

Algebraic and Geometric Structures in Special Relativity
D. Giulini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Some Remarks on “Symmetry” and “Covariance” . . . . . . . . . . . . . . . . . .
3 The Impact of the Relativity Principle
on the Automorphism Group of Spacetime . . . . . . . . . . . . . . . . . . . . . . . . .
4 Algebraic Structures of Minkowski Space . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Geometric Structures in Minkowski Space . . . . . . . . . . . . . . . . . . . . . . . . .
A Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49
55
71
98
108

Quantum Theory in Accelerated Frames of Reference
B. Mashhoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Hypothesis of Locality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Acceleration Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Nonlocality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Inertial Properties of a Dirac Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 Sagnac Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Spin-Rotation Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 Translational Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

112
112
113
115
116
119
120
121
122
125
129
129

45
45
46

Vacuum Fluctuations, Geometric Modular Action
and Relativistic Quantum Information Theory
R. Verch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
2 From Quantum Mechanics and Special Relativity
to Quantum Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Contents

IX

3

The Reeh–Schlieder–Theorem
and Geometric Modular Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4 Relativistic Quantum Information Theory:
Distillability in Quantum Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Spacetime Metric from Local and Linear Electrodynamics:
A New Axiomatic Scheme
F.W. Hehl and Y.N. Obukhov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Matter – Electrically Charged and Neutral . . . . . . . . . . . . . . . . . . . . . . . .
4 Electric Charge Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Charge Active: Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Charge Passive: Field Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Magnetic Flux Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Premetric Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 The Excitation is Local and Linear in the Field Strength . . . . . . . . . . . .
10 Propagation of Electromagnetic Rays (“Light”) . . . . . . . . . . . . . . . . . . . .
11 No Birefringence in Vacuum and the Light Cone . . . . . . . . . . . . . . . . . . .
12 Dilaton, Metric, Axion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13 Setting the Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Part III

163
163
164
165
166
166
167
168
168
170
173
175
180
181
182
184
184

Violations of Lorentz Invariance?

Overview of the Standard Model Extension: Implications
and Phenomenology of Lorentz Violation
R. Bluhm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Constructing the SME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Spontaneous Lorentz Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Tests in QED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

191
191
194
197
203
212
215
221
222

Anything Beyond Special Relativity?
G. Amelino-Camelia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Some Key Aspects of Beyond-Special-Relativity Research . . . . . . . . . . . .
3 More on the Quantum-Gravity Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 More on the Quantum-Gravity-Inspired DSR Scenario . . . . . . . . . . . . . .

227
227
232
239
244


X

Contents

5 More on the Similarities with Beyond-Standard-Model Research . . . . . . 272
6 Another Century? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Doubly Special Relativity as a Limit of Gravity
K. Imilkowska and J. Kowalski-Glikman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Postulates of Doubly Special Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Constrained BF Action for Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 DSR from 2+1 Dimensional Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

279
279
280
284
290
295
296

Corrections to Flat-Space Particle Dynamics Arising
from Space Granularity
L.F. Urrutia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Basic Elements from Loop Quantum Gravity (LQG) . . . . . . . . . . . . . . .
3 A Kinematical Estimation of the Semiclassical Limit . . . . . . . . . . . . . . . .
4 Phenomenological Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

299
299
304
312
318
340

Part IV

Experimental Search

Test Theories for Lorentz Invariance
C. L¨
ammerzahl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Test Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Model-Independent Descriptions of LI Tests . . . . . . . . . . . . . . . . . . . . . . .
4 The General Frame for Kinematical Test Theories . . . . . . . . . . . . . . . . . .
5 The Test Theory of Robertson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 The General Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 The Mansouri-Sexl Test Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

349
349
351
354

364
367
376
379
381
383

Test of Lorentz Invariance Using a Continuously Rotating
Optical Resonator
S. Herrmann, A. Senger, E. Kovalchuk, H. M¨
uller, A. Peters . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 LLI-Violation Signal According to SME . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 LLI-Violation Signal According to RMS . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

385
385
387
389
394
396
398
400


Contents

A Precision Test of the Isotropy of the Speed of Light
Using Rotating Cryogenic Optical Cavities
S. Schiller, P. Antonini, M. Okhapkin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Characterization of the Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Data Collection and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rotating Resonator-Oscillator Experiments
to Test Lorentz Invariance in Electrodynamics
M. E. Tobar, P.L. Stanwix, M. Susli, P. Wolf, C.R. Locke, E.N. Ivanov . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Common Test Theories
to Characterize Lorentz Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Applying the SME to Resonator Experiments . . . . . . . . . . . . . . . . . . . . . .
4 Comparison of Sensitivity
of Various Resonator Experiments in the SME . . . . . . . . . . . . . . . . . . . . .
5 Applying the RMS to Whispering Gallery Mode
Resonator Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 The University of Western Australia Rotating Experiment . . . . . . . . . . .
7 Data Analysis and Interpretation of Results . . . . . . . . . . . . . . . . . . . . . . .
8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Recent Experimental Tests of Special Relativity
P. Wolf, S. Bize, M.E. Tobar, F. Chapelet, A. Clairon, A.N. Luiten,
G. Santarelli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Theoretical Frameworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Michelson-Morley and Kennedy-Thorndike Tests . . . . . . . . . . . . . . . . . . .
4 Atomic Clock Test of Lorentz Invariance
in the SME Matter Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental Test of Time Dilation
by Laser Spectroscopy on Fast Ion Beams
G. Saathoff, G. Huber, S. Karpuk, C. Novotny, S. Reinhardt,
D. Schwalm, A. Wolf, G. Gwinner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Principle of the Ives Stilwell Experiment . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Ives-Stilwell Experiment at Storage Rings . . . . . . . . . . . . . . . . . . . . . . . . .
4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

XI

401
401
402
407
410
413
414

416
416
417
424
433

437
439
445
448
450

451
451
452
459
468
475
477

479
479
480
481
490
492


XII

Contents

Tests of Lorentz Symmetry in the Spin-Coupling Sector
R.L. Walsworth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 129 Xe/3 He maser

(Harvard-Smithsonian Center for Astrophysics) . . . . . . . . . . . . . . . . . . . .
3 Hydrogen Maser
(Harvard-Smithsonian Center for Astrophysics) . . . . . . . . . . . . . . . . . . . .
4 Spin-Torsion Pendula
(University of Washington and Tsing-Hua University) . . . . . . . . . . . . . . .
5 K/3 He Co-Magnetometer
(Princeton University) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Do Evanescent Modes Violate Relativistic Causality?
G. Nimtz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Photonic Barriers, Examples of Evanescent Modes . . . . . . . . . . . . . . . . . .
4 Evanescent Modes Are not Observable . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Velocities, Delay Times, and Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Partial Reflection: An Experimental Method
to Demonstrate Superluminal Signal Velocity
of Evanescent Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Evanescent Modes a Near Field Phenomenon . . . . . . . . . . . . . . . . . . . . . .
8 Superluminal Signals Do not Violate Primitive Causality . . . . . . . . . . . .
9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

493
493
494
497
499
502
504

506
506
508
510
515
516

522
524
527
529
530


List of Contributors

Giovanni Amelino–Camelia
Dipartimento di Fisica
Universit´
a di Roma “La Sapienza” and
Sez. Roma1 INFN
P.le Moro 2
00185 Roma
Italy

Piergiogio Antonini
Institut f¨
ur Experimentalphysik
Heinrich–Heine–Universit¨
at D¨

usseldorf
40225 D¨
usseldorf
Germany
piergiorgio.antonini@
uni-duesseldorf.de
S´
ebastien Bize
BNM-SYRTE
Observatoire de Paris
61 avenue de l’Observatoire
75014 Paris
France

Robert Bluhm
Colby College
Waterville ME 04901
USA

Martin Carrier
University of Bielefeld
Faculty of the History of Science

Philosophy and Theology
Department of Philosophy
P.O.B. 100131
33501 Bielefeld
Germany

Fr´

ederic Chapelet
BNM-SYRTE
Observatoire de Paris
61 avenue de l’Observatoire
75014 Paris
France

Andr´
e Clairon
BNM-SYRTE
Observatoire de Paris
61 avenue de l’Observatoire
75014 Paris
France

Ronald W.P. Drever
California Institute of Technology, 200-36
Pasadena, CA 91125
USA

J¨
urgen Ehlers
Max–Planck–Institut f¨
ur Gravitationsphysik
Albert–Einstein–Institut
Am M¨
uhlenberg
14476 Golm
Germany

XIV

List of Contributors

Domenico Giulini
Physikalisches Institut
Universit¨
at Freiburg
Hermann–Herder–Str. 3
79104 Freiburg
Germany

Gerald Gwinner
Department of Physics & Astronomy
University of Manitoba
Winnipeg, MB R3T 2N2
Canada

Friedrich W. Hehl
Institute for Theoretical Physics
University of Cologne
50923 K¨
oln
Germany

Sven Herrmann
Institut f¨
ur Physik

Humboldt Universit¨
at zu Berlin
10117 Berlin
Germany

Gerhard Huber
Institut f¨
ur Physik
Universit¨
at Mainz
55099 Mainz
Germany

Katarzyna Imilkowska
Institute of Theoretical Physics
University of Wroclaw
Pl. Maxa Borna 9
50-204 Wroclaw
Poland

Eugene N. Ivanov
University of Western Australia
School of Physics M013
35 Stirling Hwy.
Crawley 6009 WA
Australia


Sergej Karpuk
Institut f¨

ur Physik
Universit¨
at Mainz
55099 Mainz
Germany

Evgeny Kovalchuk
Institut f¨
ur Physik
Humboldt Universit¨
at zu Berlin
10117 Berlin
Germany

Jerzy Kowalski–Glikman
Institute of Theoretical Physics
University of Wroclaw
Pl. Maxa Borna 9
50-204 Wroclaw
Poland

Claus L¨
ammerzahl
ZARM
Universit¨
at Bremen
Am Fallturm
28359 Bremen
Germany

Clayton R. Locke
University of Western Australia
School of Physics M013
35 Stirling Hwy.
Crawley 6009 WA
Australia

Andr´
e N. Luiten
University of Western Australia
School of Physics
Nedlands 6907 WA
Australia

Bahram Mashhoon
Department of Physics and Astronomy
University of Missouri–Columbia
Columbia, Missouri 65211
USA



List of Contributors
Holger M¨
uller
Physics Department
Stanford University
Stanford, CA 94305
USA

G¨
unter Nimtz
II. Physikalisches Institut
Universit¨
at zu K¨
oln
Z¨
ulpicher Str. 77
50937 K¨
oln
Germany

Christian Novotny
Institut f¨
ur Physik
Universit¨
at Mainz
55099 Mainz
Germany

Yuri N. Obukhov
Department of Theoretical Physics
Moscow State University
117234 Moscow
Russia

Maxim Okhapkin
Institut f¨
ur Experimentalphysik
Heinrich–Heine–Universit¨

at D¨
usseldorf
40225 D¨
usseldorf
Germany

Achim Peters
Institut f¨
ur Physik
Humboldt Universit¨
at zu Berlin
10117 Berlin
Germany

Sascha Reinhardt
Max-Planck-Institut f¨
ur Kernphysik
69029 Heidelberg
Germany


XV

Guideo Saathoff
Max-Planck-Institut f¨
ur Kernphysik
69029 Heidelberg
Germany

Giorgio Santarelli

BNM-SYRTE
Observatoire de Paris
61 avenue de l’Observatoire
75014 Paris
France

Stephan Schiller
Institut f¨
ur Experimentalphysik
Heinrich–Heine–Universit¨
at D¨
usseldorf
40225 D¨
usseldorf
Germany

Dirk Schwalm
Max-Planck-Institut f¨
ur Kernphysik
69029 Heidelberg
Germany

Alexander Senger
Institut f¨
ur Physik
Humboldt Universit¨
at zu Berlin
10117 Berlin
Germany

Paul L. Stanwix
University of Western Australia
School of Physics M013
35 Stirling Hwy.
Crawley 6009 WA
Australia

Mohamad Susli
University of Western Australia
School of Physics M013
35 Stirling Hwy.
Crawley 6009 WA
Australia



XVI

List of Contributors

Michael E. Tobar
University of Western Australia
School of Physics M013
35 Stirling Hwy.
Crawley 6009 WA
Australia

Luis F. Urrutia
Instituto de Ciencias Nucleares
Universidad Nacional Aut´

onoma de
M´exico
Circuito Exterior, C.U.
04510 M´exico, D.F.
M´exico

Rainer Verch
Institut f¨r Theoretische Physik
Universit¨
at Leipzig
Postfach 10 09 20
04009 Leipzig
Germany


Ronald L. Walsworth
Harvard–Smithsonian Center for
Astrophysics
Cambridge, MA 02138
USA

Andreas Wolf
Max-Planck-Institut f¨
ur Kernphysik
69029 Heidelberg
Germany

Peter Wolf
BNM-SYRTE
Observatoire de Paris

61 avenue de l’Observatoire
75014 Paris
France



Isotropy of Inertia: A Sensitive Early
Experimental Test
R.W.P. Drever
California Institute of Technology, 200-36, Pasadena, CA 91125, USA


Abstract. An experimental test for anisotropy of inertia performed by a nuclear freeprecession experiment is described. The precession was observed in the Earth’s magnetic field, in a countryside location in the open air. The experiment was exceptionally
sensitive, and slightly unusual in other ways. Some of the background and other aspects
are briefly discussed.

1 Introduction
When I was asked to give an account of an early experiment1 on “Isotropy of
Inertia” which I conceived and carried out many years ago I was reluctant at
first. Then I realized that there might be some usefulness, and possibly interest,
in this since the experiment was unusual in several ways, and was very different
from typical experiments done now. And it might be interesting to explain how
some of the ideas arose, and how some of the problems were overcome, in a more
personal way than usual.
This experiment was conceived and carried out around 1960, at a time when I
was working on experimental nuclear physics in the Natural Philosophy (physics)
Department of the University of Glasgow, in Scotland. I had obtained a Ph.D.
a few years earlier for work relating to low energy beta spectroscopy and other
research on radioactive nuclei carried out using special gas proportional counter
techniques developed for the purpose. I was, however, also interested in possibilities of experimental work relating to cosmology, and in the book on cosmology

by H. Bondi [1] had come across the suggestion that a test of Mach’s Principle ideas on inertia might be possible by looking for some anisotropy in inertial
mass. If the inertial mass of a body on the Earth arose from coupling to all
other matter in the universe, then the Earth’s position to one side of the centre
of our galaxy might lead to some anisotropy in the inertial mass of bodies on the
Earth. A fairly specific hypothesis of this kind was that of Kaempffer [2], which
1

Experiment performed (in 1960/61) while at: Department of Natural Philosophy,
University of Glasgow, Glasgow, G12 9QD, Scotland

R.W.P. Drever: Isotropy of Inertia: A Sensitive Early Experimental Test, Lect. Notes Phys. 702,
3–14 (2006)
c Springer-Verlag Berlin Heidelberg 2006
DOI 10.1007/3-540-34523-X 1


4

R.W.P. Drever

I found quite appealing. Cocconi and Salpeter [3] took the general idea further
by estimating possible shifts of atomic energy levels, and set an upper limit to
mass anisotropy from this.

2 Early Ideas
At around this time I realized that similar effects could show up in suitable
nuclei, and these could set more sensitive limits since the nuclear building energies involved are so much larger than the binding of electrons in atoms. Cocconi and Salpeter realized this also, and suggested [4] use of the M¨
ossbauer
Effect to measure this. It had occurred to me that more sensitive and direct
measurements could be made by measuring transitions between levels involving predominantly different distributions of nucleon momentum, using nuclear

magnetic resonance techniques (NMR). In fact I found it possible to set new
upper limits to anisotropic effects from the width of published NMR resonances
already measured with spin 3/2 nuclei for other purposes.
This finding seemed to me to be worth publishing, and I wrote a brief note
on it and submitted it to a major letters journal. My manuscript was returned
to me with a comment from the Editor saying that the idea was a good one, but
it was already being investigated in experiments by a group at Yale led by V.W.
Hughes.
I was at first very saddened by this rejection, and also by learning that the
same idea was already being experimentally investigated by a group which was
probably very experienced and almost certainly had much better equipment and
resources than were available to me for such an experiment.

3 Possibilities for Experiments
I was keen, however, to attempt some experiment of this type myself, and the
knowledge that a group in a major institution must have decided it was worth
doing was a strong additional stimulus for me. I started to consider all the
experimental possibilities I could think of, and assess the factors likely to limit
sensitivity in each.
The simplest kind of experiment seemed to be an NMR measurement of
transitions between the levels of a nucleus with spin 3/2 in a uniform magnetic
field, as a function of the direction of the magnetic field relative to the direction
to the centre of our galaxy. In the absence of any anisotropy there would be four
equally-spaced magnetic sublevels, with spins +3/2, +1/2, −1/2, and −3/2;
giving a single NMR frequency. Cocconi and Salpeter suggested that in the
presence of a mass anisotropy it was possible that the levels could be slightly
shifted, the +3/2 and −3/2 levels in one direction, and the +1/2 and −1/2
levels in the opposite direction. This would split the NMR line into a triplet,
with a splitting which would be a function of the direction of the magnetic field
relative to the direction of the galactic centre. If the magnet providing the field

Isotropy of Inertia

5

was attached to the Earth it would rotate as the Earth rotates, giving splitting
which would be modulated with a periodicity related to 24 hours (sidereal time).

4 Some Factors Expected to Affect Sensitivity
in a Simple NMR Measurement
Estimating sensitivity of an NMR experiment of this type involves the following
considerations:
(a) The width of the observed resonance could set a limit to sensitivity for small
splitting. Factors affecting line width include the relaxation time, which for a
suitable liquid solution may be several seconds, and variations in the magnetic
field over the volume of the sample.
(b) In this particular experiment, the strength of the magnetic field is not as
directly significant as in other NMR measurements, since the frequency splitting is independent of the field, and has to be compared with the frequency
corresponding to a fixed nuclear binding energy.
Consideration of factor (b) might suggest that using a weak magnetic field
might be an advantage in this case, as it is usually easier to reduce the spatial
variation of the magnetic field if the absolute value of the field itself is small.
In the present application it seemed appropriate to consider use of the magnetic
field of the Earth itself. Free precession techniques had been developed for measuring the Earth’s magnetic field, and it seemed these might be adapted for this
experiment. In a location far from ferromagnetic materials the field can be very
uniform. This seemed to give an opportunity for a sensitive and relatively simple
experiment to be performed at very low cost. This was the technique developed
and used in this research.
It may be mentioned that the idea of using the Earth’s magnetic field here was

stimulated in part by the fact that in the Honours Natural Philosophy student
laboratories in the University there was an Earth’s-field free precession system,
to help educate (and challenge) some of the students. The problem of finding a
location having a sufficiently uniform magnetic field near steel-framed buildings
made this experiment difficult for students, but free precession proton signals of
short duration could be observed with a sample suspended from a rope between
upper floors of two different buildings.2

5 Development of the Experimental Technique
The original technique for measuring the Earth’s magnetic field used a 250 cm3
sample of water surrounded by a coil, with its axis perpendicular to the direction
of the Earth’s field. A current is passed through the coil for a few seconds to
2

It is thought that this interesting experiment was originally introduced to the student
laboratory by Dr. Jack M. Reid.


6

R.W.P. Drever

polarize the magnetic moment arising from the protons in the water, and when
the current is suddenly interrupted, the proton field precesses about the Earth’s
field, generating a signal in the coil which is detected by switching to a suitable
amplifier system [5, 6].
The nucleus with spin 3/2 chosen for the present experiment was Li7 . A
solution of lithium nitrate in water was found to have a suitable relaxation time
of around 4 seconds. The Li7 precession signal had a frequency of 803 Hz in
the local Earth’s field, which with protons gave a frequency near 2068 Hz. The

lower frequency and relative weakness of the Li signal compared with that from
protons made it necessary use a larger sample, of around 2 litres, and a stronger
magnetizing field, with current from a bank of 6 lead-acid car batteries. This
in turn required a more extensive uniform magnetic field than available near
the University laboratories. The equipment was therefore moved to a country
location in the village of Bishopton, 12 miles West of Glasgow, in the back
garden of the house in which I was living at the time. In this area the direction
of Earth’s magnetic field dips steeply towards the North, in such a way that it
passed within 10◦ of the centre of the Galaxy once each sidereal day, a convenient
situation for this experiment.
A simplified schematic diagram of the overall arrangement as eventually developed is shown in Fig. 1.
The lithium nitrate solution is contained in a polythene bottle, surrounded
by the coil used for magnetizing and sensing, shown at the extreme left side of

Fig. 1. Simplified diagram of experimental arrangement. Passing a current through
the coils produces a net polarization of Li7 nuclei perpendicular to the direction of the
Earth’s magnetic field, in a lithium nitrate solution. Rapid switch-off of the current
leads to precession of the resulting nuclear magnetization, giving a signal which is
examined for beats corresponding to small differential shifts in the nuclear magnetic
levels


Isotropy of Inertia

7

the figure. The signal was weak, and to minimize interference by electromagnetic
fields from the frame time bases of television receivers occasionally operating in
the neighborhood, a second similar coil connected in opposition to the sample coil
was arranged to cancel signals induced by external magnetic fields. In operation,

a magnetizing current is passed through the coils for several seconds to build up
a polarization of the nuclear spins perpendicular to the Earth’s field. The current
is then suddenly turned off, in a time short compared with the precession period,
causing the nuclear magnetization to precess about the Earth’ field. After a delay
of about 0.6 seconds to allow induced voltage transients to decay, the coils are
connected to a sensitive tuned amplifier and oscilloscope system to record the
free precession signal.
For a single precession frequency, and a uniform magnetic field, the observed
signal would be expected to exhibit an exponential decay with a time constant
corresponding to the transverse relaxation time of the spin system. If, however
the resonance were split into a close triplet it would be expected that the signal
would exhibit beats, corresponding to interference between oscillations at the
three resonance frequencies which would be detected in a steady-state experiment. A detailed analysis by Das and Saha [7] of the analogous situation of
free precession in the presence of a weak electric quadruple interaction indicates
that there would be a strong modulation of the signal amplitude at the splitting
frequency. If this were due to an anisotropy of inertial mass arising from an interaction with our galaxy it would be expected that the modulation would vary
throughout the sidereal day as the direction to the center of our galaxy changes.

6 Initial Observations
The non-uniformity of the Earth’s magnetic field in the vicinity of the steelframed buildings in the Glasgow laboratories had made it very hard to observe
free-precession signals from lithium there. However, moving the equipment to
the countryside location almost immediately made the lithium precession signals
much more detectable. A photographic record of a typical free-precession lithium
signal obtained with the arrangement outlined above is shown in Fig. 2. No
indication of beating effects of the type expected from anisotropic phenomena
were observed at any time, and there were no immediately obvious changes in the
records with time of day. Even these initial observations could set better limits
to the phenomena being looked for than previous work, and were themselves
quite encouraging.
Work then began on a series of further experiments, technical developments,

and experimental precautions aimed at improving the sensitivity of the work.

7 Experiments and Developments for Higher Sensitivity
(a) A number of initial tests were made with the coil and sample in various locations, to avoid local non-uniformities of magnetic field. It was found very


8

R.W.P. Drever

Fig. 2. Typical decay of a free precession signal recorded photographically showing
absence of obvious beats over the 15 second time scale indicated

early that allowing the coil to lie directly on the ground gave shorter relaxation times than placing it on a wooden support above the ground. A
photograph of an early version of the coil assembly on a wooden metal-free
stool in one of the garden locations is shown in Fig. 3, with a close-up view
shown in Fig. 4. Tests were also made with the coil assembly supported in
the branches of the crab-apple tree seen towards the left side of Fig. 3. No
significant difference was observed between the results obtained on the stool
and a few metres higher in the tree. Most of the subsequent experiments
were made using the wooden stool. The later work was done with the coil
assembly nearer the center of a lawn, about 20 m away from the brick wall
seen in the background.
(b) The relaxation time in a liquid is a function of temperature, so for observations over 24 hour periods it was important to monitor and control the
temperature of the lithium nitrate solution. A later version of the apparatus shown in Fig. 5 incorporates a thermocouple monitor within a polythene
sleeve with the end which is inside the bottle sealed. There is also a simple
stirring device consisting of a curved copper wire within a similar flexible
sealed polythene sleeve. Rotating the wire manually could flex the sleeve,
giving effective stirring. In later observations it was arranged that the stirrer
could be operated by a small electric motor placed about 20 m from the coil,

and coupled to the stirrer by a very light, long belt made from soft medical
rubber tubing, 2 mm in diameter. During observations the coil assembly was
covered by light plastic sheeting to prevent condensation of dew in the early
hours of the morning.


Isotropy of Inertia

9

Fig. 3. Photograph of coil and sample bottle on a wooden iron-free stool during early
tests in a countryside garden location

(c) To maximize the decay time constant and help keep it constant, nitrogen was
bubbled through the lithium nitrate solution to remove dissolved oxygen and
the sample bottle was hermetically sealed.
(d) To improve the signal to noise ratio for the lithium precession signal, a slightly
more elaborate switching arrangement than that shown in Fig. 1 was eventually used. This involved relays operating in sequence to disconnect and
short-circuit the low-noise amplifier system in several places to adequately
attenuate the large pulses induced during switch-off of the magnetizing current in the signal coil. A photograph taken during development and testing
of the electronic system in one of the teaching laboratories in the University,
during a student vacation, is shown in Fig. 6.

8 Experimental Procedure
In operation, a free-precession signal was examined at intervals of 20 or 30
minutes throughout the sidereal day, and photographically recorded using a


10

R.W.P. Drever

Fig. 4. Close-up of the coil and polythene sample bottle

Fig. 5. A later version of the coil and sample system, with a thermocouple temperature
monitor. There is a sealed stirrer, operated manually at the time of the photograph and
later belt-driven by a small motor from a distance of 20 m. The top of an interferencecanceling coil located directly behind the sample coil is just visible


Isotropy of Inertia

11

Fig. 6. A photograph taken during development and testing of the electronics and
switching system in one of the Honours Natural Philosophy laboratories. A modified low
noise nuclear physics amplifier and preamplifier used are on the left and an oscilloscope
with a long persistence phosphor on the right. The sample coil was suspended outside
the building for these tests

camera with continuously moving film from an oscilloscope with its timebase
turned off. The temperature of the lithium nitrate solution was monitored and
maintained constant at 37 ± 1◦ C by manually adjusting a small current passed
through the magnetising coil between the observations.
No sign of a beating pattern or any significant change in the envelope of the
precession signal was observed. An upper limit to any effect near the instrumental noise level was determined by projecting the recorded signals onto expected
envelope shapes for various assumed energy level shifts. Comparison with a theoretical envelope for the case of a splitting of the resonances by 0.04 Hz, for
which the first minimum in the beat pattern occurs near 10 seconds after the
start of the precession showed that a slowly varying splitting of this magnitude,
which would arise from individual energy level shifts of 0.02 Hz, would have been
readily detectable.

This finding alone might not have been enough to completely rule out a much
larger effect which moved the outer components of the triplet right outside the
pass-band of the amplifier and coil system for most of the sidereal day, allowing
them only to pass through the sensitive frequency region at times which happened to coincide with intervals between observations. To check on this unlikely
situation a separate experiment was carried out in which the amplitude of the