Gravitational Measurements, Fundamental Metrology and Constants

546 Pages·1988·27.078 MB·English

by  A. O. Barut (auth.), Venzo De Sabbata, V. N. Melnikov (eds.)

Gravitational Measurements,
Fundamental Metrology and Constants
NATO ASI Series
Advanced Science Institutes Series
ASeries presenting the results of activities sponsored by the NA TO Science Committee,
wh ich aims at the dissemination of advanced scientific and technological knowledge,
with a view to strengthening links between scientific communities.
The Series is published by an international board of publishers in conjunction with
the NATO Scientific Affairs Division
A Life Seien ces Plenum Publishing Corporation
B Physics London and New York
C Mathematical Kluwer Academic Publishers
and Physical Sciences Dordrecht, Boston and London
D Behavioural and Social Sciences
E Applied Sciences
F Computer and Systems Seien ces Springer-Verlag
G Ecological Seien ces Berlin, Heidelberg, New York, London,
H Cell Biology Paris and T okyo
Series C: Mathematical and Physical Sciences -Vol. 230
Gravitational Measurements,
Fundamental Metrology
and Constants
edited by
Venzo Oe Sabbata
Department of Physics,
University of Bologna and Ferrara, Italy
and
V. N. Melnikov
Gosstandart, Moscow, U.S.8.R.
Kluwer Academic Publishers
Dordrecht / Boston / London
Published in cooperation with NATO ScientificAffairs Division
Proceedings of the NATO Advanced Study Institute on
Gravitational Measurements, Fundamental Metrology and Constants
(10th Course of the International School of Cosmology and Gravitation
of the Ettore Majorana Centre for Scientific Culture)
Erice, Italy
2-12 May 1987
Library of Congress Cataloging in Publication Data
NATO Advanced Research Workshop on Gravitational Measurements,
Fundamental Metrology, and Constants <1987 Erice, Sicily)
Gravitatlonal measurements, fundamental metrology, and constants
edlted by Venzo de Sabbata and V.N. Melnikov.
p. cm. -- (NATO ASI series. Series C, Mathematical and
physical sciences ; vol. 230)
"Proceedings of the NATO Advanced Research Workshop on
Gravitational Measurements, Fundamental Metrology, and Constants,
Erice, Italy, 2-12-May 1987"--T.p. verso.
"Publ ished In cooperation with NATO Scientific Affairs Division."
ISBN-13: 978-94-010-7829-0
1. Gravity--Measurement--Congresses. 2. Physical constants-
-Measurement--Congresses. I. Oe Sabbata, Venzo. 11. Melnikov.
V. N. 111. North Atlantic Treaty Organization. Scientific Affairs
Dlvision. IV. Title. V. Series, NATO ASI series. Series C.
Mathematical and physical sciences ; no. 230.
QB330.N38 1987
526' .7--dcI9 88-4393
ISBN-13: 978-94-010-7829-0 e-ISBN: 978-94-009-2955-5
001: 10.1007/978-94-009-2955-5
Published by Kluwer Academic Publishers,
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TABLE OF CONTENTS
Preface vii
A. O. Barut
Can we Calculate the Fundamental Dimensionless
Constants of Physics?
P. G. Bergmann
Observables in General Relativity 15
E. Braun
The Quantum Hall Effect Part I: Basic Experiments 19
The Quantum Hall Effect Part 11: Metrological Applications 39
E. R. Cohen
Fundamental Physical Constants 59
Variability of the Physical Constants 91
Bidyut Kumar Datta and Renuka Datta
The Measurement Problem of the General Matter Field
Theory as Required by the Copenhagen School 107
V. De Sabbata
On the Relations between Fundamental Constants 115
R. N. Faustov
Quantum Electrodynamics and Fundamental Constants 131
C. Talmadge and E. Fischbach
Searching for the Source of the Fifth Force 143
M. Gasperini
Lorentz noninvariance and the Universality of free
fall in Quasi-Riemannian Gravity 181
G. T. Gillies
Status of the Newtonian Gravitational Constant 191
R. W. Hellings
Time Variation of the Gravitational Constant 215
T. H. Ho
The Supernova SN 1987A and the Neutrino Mass 225
R. Cowsik et al.
The Fifth Force Experiment at the TIFR 231
A. A. Logunov et al.
Analysis of Ground States of General Relativity Theory
and Relativistic Theory of Gravitation 241
V. N. Melnikov
Gravitational-Relativistic Metrology 283
S. N. Pandey
Gravitational Waves 299
VI
G. Pizzella
The Gravitational Wave Experiment of the Rome Group.
Data Recorded during SN1987A 307
R. D. Reasenberg
Solar-System Tests of General Relativity, the
Transition to Second Order 311
N. Rosen
The Weyl-Dirac Theory and the Variation of the
Gravitational Constant 345
V. N. Rudenko
Selected Problems of Gravitational Wave Experiment 357
V. P. Shelest et al.
Introductory Lectures on the Physics of High Energy
Densities: Theories, Models, Measurements 387
C. C. Speake and T. J. Quinn
Detectors of Laboratory Gravitation Experiments
and a new Method of Measuring G 443
Yoshiro Takano
Introduction to the Theory of Fields in Finsler Spaces 459
J. Weber
Neutrinos, Gravitons, Metrology and Gravitational Radiation 467
Appendix
G. Dragoni
On Quirino Majorana's Papers Regarding Gravitational
Absorption 501
I: Quelques Recherehes sur l'Absorption de la Gravitation
par la Matiere
11: Theoretical and Experimental Researches on Gravitation
Index 541
P R E F ACE
The Tenth Course of the International School of Cosmology and
Gravitation of the "Ettore Majorana" Centre for Scientific
Culture is concerned with "Gravitational Measurements, Fundamental
Metrology and Constants". The choice of this subject was made
because the increasing role that relativistic and quantum metrology
play in practical applications and in the perspective of the
unification of all fundamental interactions.
Practical applications are caused by the increase in precision
of measuring devices, the spread of precise measurements
over large distances and time intervals with the
progress of space technology, the laser interferometer and the
improvement in gravitatlonal wave experiments.
In this respect and in order to have aglobai view of these
problems and a correct perspective of the current state of the
science, arguments as the variability of the fundamental physical
constants, the relations between them, in particular the status
of the Newtonian gravitational constant have been extensively
devploped and discussed.
A great excitation has been generated by the discussion of a new
force in Nature and by the exposition of the various experiments
that are now in progress over the world. Other arguments as
quantum electrodynamics, quantum Hall effect (always in their
relation with fundamental constants) tha status of gravitational
antennas including laser interferometer, the physics at high
densities and also gravity research in the solar system complete
the collection of these interesting papers.
We have added an Appendix where we have liked to reproduce
an old and beautiful paper by Quirino Majorana (the oncle
of Ettore) on the absorption of gravitation by matter.
We have preferred to arrange all contributors alphabetically,
by (first-named) author.
venzo äe sabbata
v.n.melnikov
CAN WB CALCULATE THE FUNDAMENTAL DIMENSIONLESS CONSTANTS OF PHYSICS?
*
A.O. Barut
International Centre
for Theoretical Physics
Trieste
Italy
ABSTRACT. We review some dynamical models to calculate the dimension
less constants a = e2/4TIEotc, ß = Mp/m (or ß' = m Im ),
2 3 e2 ]..l e
y = GFermi me/ct and ö = GNewton m~/(e 14TIcO) which are associated
with the four different manifestations (electromagnetic, strong, weak
and gravitational) of a possible single interaction.
1. WHAT WE CAN CALCULATE IN PHYSICS AND WHAT NOT
There are only four units in physics which determine the sc ales of all
measurable phenomena: length scale t, time scale t, mass scale m and
charge scale q. Since all charge in the world is a multiple of the
electronic charge, q = ne, the last unit may be reduced to a pure
number. (This point will be discussed further 1ater). There are no
generally accepted theories with afundamental length to, fundamental
time to, fundamental mass mO; and the last one is surely not additive.
Thus we must keep these three units and establish some standards for
them. Other basic physical constants maY be used to set the scales
instead of the man-made standards like meter, sec and kg. We must
choose three quantities as uncalculable and try to calculate and
measure everything relative to these quantities, which can then be set
equal to unity.
One such system is based on the electron, perhaps the most basic
elementary particle,presumable absolutely stable. We can take as
uncalculable the mass of the electron me and from special
relativity the velocity of light, and set
c = 1 and (1)
In these units, -~n = ~compton = a -1 = 137.03, class~. cal electron radius
re = (e2/4ncOm) = 1, t e = re/c = 1, Bohr radius aBo r = a-2 = (137.03)2.
The system (1) is based on "classical" quantities, an8 is different than
the familiar units in particle physics: c =~ = 1.
V. De Sabbata anti V. N. Melnikov (eds.),
Gravitational Measurements, Fundamental Metrology and Constants, 1-14.
© 1988 by Kluwer Academic Publishers.
2
Another system of units is based on the assumption that the
gravitational constant G, and c and t are both unca1culab1e and
fundamenta1,and unchanging:
G = 1, c = 1, t. = 1 (2)
In this system the sca1es for length, time and mass
[~r/2 [~r/2 -43
I (~10-35m) ; t = 1 (N= 10 sec);
p
c c
~cr/2 '" -5
m = I (=10 gr)
p
are called the Planck scales and are independent of any properties of
matter 1ike me or e.
The choice of a system, such as (1) or (2), is not rea11y
arbitrary or final. It depends what the theory considers to be more
apriori or basic, an electron or light, or gravitation, or the
quantum of action. Only a successful unified theory based on one such
system can tell us that the chosen system is a good one. And once we
have assumed three such uncalculable quantities, all other quantities
become dimensionless and should be in principle calculable (dimension
less quantities are distinct from dimensionless constants - see next
section).
One should keep in mind that setting c = 1, for example, excludes
the possibility of explaining it further, in terms of the Young modulus
of a relativistic deformable ether, for example; setting t = 1
excludes explaining the sca1e of atomic energy levels; m = 1,
trying to understand the nature of mass, G = 1, the natu~e of gravity,
etc. One might think that with the advance of physics we shall be able
to calculate eventually everything. One might think, for example, that
the mass of the electron is of electromagnetic origin and could be
calculated from the energy of the electromagnetic self-field. But we
see that this is not the case. Even if we give up to calculate any two
of the three constants c, e2/4n€o, or ~ (all three are related) we
still need a scale for mass. This could be a basic mass me, or any
other quantity, a length or a magnetic moment, etc. For example, the
classical calculation of the static Coulomb energy of the electron
requires a cutoff rO:
r
2
1 e
gives (3)
8n
r
e
We see that the choice of the system (1) or (2) is equivalent to the
choice of an elementary length to, elementary time to and elementary
mass mO' all set to unity. But unfortunately they do not imply that
they are smallest possible units of length, time and mass. The
question of a possible ultimate smallest discrete values of length,
time and mass is still open.
3
2. FUNDAMENTAL DlMENSIONLESS CONSTANTS
The fundamental dimension1ess constants are numbers in any system
of units. Hence they must be ca1cu1ab1e using any system. They are
four fundamental dimension1ess constants that can be direct1y
associated with the strength of four basic category of phenomena:
2
1) a. = 4nee otc = (137.0359) -1 = 7.297 x 10- 3 (e1ectromagnetic) (4)
M 3
2) ß = ~ = 1.836 x 10 (strong) (5)
me
3) (weak) (6)
(gravitationa1) (7)
One cou1d also discuss another dimension1ess number which invo1ves
however a model of the universe, based on the relation
(8)
J0
where ~ is the total mass of the universe and the radius cf the
universe. Eq.(8) is of the same nature as the model of the e1ectron,
Eq. (3). The dimension1ess numbers re/R and me/)l are re1ated by 8.
2
r e e /47TI:O (:ff1 i (i]
J,. = 2 = (9)
m c
e
1, m
e
or, r J.{,= 8.
e
m
e
The so-ca11ed Eddington number is sometimes assumed to be of the
order of 82, so that
r
Jve = 8. (10)
There are two other dimension1ess constants associated with two other
strengths of phenomena which we have not 1isted because they have