Relativistic Mechanics, Time and Inertia

269 Pages·1984·5.057 MB·English

by  Emil Tocaci (auth.), C. W. Kilmister (eds.)

Relativistic Mechanics, Time and Inertia
Fundamental Theories of Physics
A New International Book Series on The Fundamental Theories of
Physics: Their Clarification, Development and Application
Editor: ALWYN VAN DER MER WE
University 0/ Denver, U.S.A.
Editorial Advisory Board:
AS 1M BARUT, University o/Colorado, U.S.A.
HERMANN BONDI, Natural Environment Research Council, U.K.
BRIAN D. JOSEPHSON, Universityo/Cambridge, U.K.
CLIVE KILMISTER, University o/London, U.K.
GUNTER LUDWIG, Philipps-Universitiit, Marburg, F.R.G.
NATHAN ROSEN, Israel Institute o/Technology, Israel
MENDEL SACHS, State University o/New York at Buffalo, U.S.A.
ABDUS SALAM, International Centre/or Theoretical Physics, Trieste, Italy
HANS-JURGEN TREDER, ZentralinstitutjUr Astrophysik der Akademie der
Wissenschaften, G.D.R.
Relativistic Mechanics,
Time and Inertia
by
Emil Tocaci
Institute of Civil Engineering, Bucharest, Romania
Institute of Oil and Gas, Ploesti, Romania
Edited and with a Foreword by C. W. Kilmister
D. Reidel Publishing Company
A MEMBER OF THE KLUWER ACADEMIC PUBLISHERS GROUP
Dordrecht / Boston / Lancaster
Library of Congress Cataloging in Publication Data
Tocaci, Emil.
Relativistic mechanics, time, and inertia.
(Fundamental theories of physics)
Translation with revisions of: Mecanica relativist~, timpul ~i inertia.
Includes index.
1. Relativistic mechanics. 2. Time. 3. Inertia (Mechanics)
I. Kilmister, C. W. (Clive William) II. Title. III. Series.
QA808.5.T6713 1984 530.1'1 84-9763
ISBN-13: 978-94-009-6408-2 e-ISBN-I3: 978-94-009-6406-8
DOl: 10.1007/978-94-009-6406-8
Published by D. Reidel Publishing Company
P.O. Box 17,3300 AA Dordrecht, Holland.
Sold and distributed in the U.S.A. and Canada
by Kluwer Academic Publishers,
190 Old Derby Street, Hingham, MA 02043, U.S.A.
In all other countries, sold and distributed
by Kluwer Academic Publishers Group,
P.O. Box 322, 3300 AH Dordrecht, Holland.
Translated from the Romanian by Vasile Vasilescu.
This book is an extensively revised version of Mecanica Reiativista, Timpul si Inertia,
published in 1980 by Editura Stiintifica si Enciclopedica, Bucharest.
All Rights Reserved
© 1985 by D. Reidel Publishing Company, Dordrecht, Holland
Softcover reprint of the hardcover 1st edition 1985
No part of the material protected by this copyright notice may be reproduced or utilized
in any form or by any means, electronic or mechanical, including photocopying,
recording or by any information storage and retrieval system,
without written permission from the copyright owner.
TABLE OF CONTENTS
FOREWORD ix
A. ASPECTS OF RELATIVISTIC MECHANICS
A.I. General remarks
A.II. Remarks on the theory of relativity 2
A.II.1. Special relativity 3
A.II.1.1. Synchronization of clocks 3
A.II.1.2. The Lorentz-Einstein relations 5
A.II.1.3. The invariant of Lorentz-Einstein
transformations 16
A.II.1.4. Classification of space-time
intervals 17
A.II.1.5. Minkowski space 20
A.II.1.6. Transformation of velocity
components 23
A.II.1.7. The velocity and acceleration
4-vectors 29
A.II.1.B. The momentum 4-vector 39
A.II.1.9. The 4-force 43
A.II.1.10. The fundamental law of dynamics
and the energy of a particle in relat-
ivistic dynamics 46
A.II.1.11. The momentum-energy vector and
the properties of its components 49
vi Table of Contents
A.II.1.12. The conservative case. Potential
energy 51
A.II.1.13. The mass defect 53
A.II.1.14. The relativistic study of
collisions 56
A.II.1.1S. Some physical interpretations
and other remarks on relativistic
mechanics 60
A.II.2. Some aspects of general relativity 66
A.III. The main aims of this work 69
B. TIME 71
B.I. The concept of time 71
B.I.1. The evolution of the concept of time 71
B.I.2. Time as measure and consequence of
motion 76
B.1. 2.1. Motion 77
B.I.2.2. The clock 84
B.I.2.3. Examples of mechanical motion 94
B.I.2.4. Time as an abstraction of general
motion 96
B.I.3. The properties of time 107
B.I.3.1. The irreversibility of time 108
B.I.3.2. The velocities and accelerations
in various equivalence classes 116
B.I.3.3. The transport of information 119
B.I.3.4. Information transport as a timing
motion 126
B.I.3.S. The character of the unique con-
stant velocity of light in all inertial
frames 137
B.I.3.6. Relativity of time and the problem
of several information carriers 144
Table of Contents vii
B.II. Examples 155
B.II.1. The irreversibility and continuity
of time 155
B.II.1.1. The probabilistic irreversibility 155
B.II.1.2. The continuity of the time
variable 159
B.II.2. The forced open curves in Minkowski
space 164
C. INERTIA 166
C.I. Use of time in defining some elements of
space 166
C.I.1. The definition of the straight line 166
C.I.1.1. Inertial spaces 166
C.I.1.2. The straight line 168
C.I.1.3. Non-inertial spaces 171
C.I.1.4. The rigid line 172
C.I.2. Reference frames 173
C.I.2.1. Inertial frames 174
C.I.2.2. Non-inertial frames 183
C.II. The inertia 187
C.II.1. Aspects related to motion of particles
in inertial and non-inertial spaces 187
C.II.1.1. General aspects of the study of
motion in non-inertial spaces 188
C.II.1.2. Mescerski-Levi-Civita equation
in the relativistic case 192
C.II.1.3. The effect of percussion force
in the relativistic case 198
C.II.2. Manifestation of inertia 202
C.II.2.1. The inertial spaces 202
C.II.2.2. Non-inertial spaces 203
C.II.3. Some aspects of the motion of a
particle in a non-inertial situation 208
viii Table of Contents
C.II.3.1. Accelerated translation 209
C.II.3.2. A particular gravitational field 218
C.II.3.3. The case of relative motion of
the frame 220
C.III. Some aspects of classical mechanics 245
C.III.1. Grounding mechanics on a single axiom 246
C.III.1 .1. The single axiom of mechanics 246
C.III.1.2. Definition of force and deriv-
ation of the fundamental laws of
mechanics 247
C.III.2. The inertial or non-inertial charac
ter of frames 249
C.III.2.1. Inertial frames 250
C.III.2.2. Non-inertial frames 251
INDEX 252
FOREWORD
To accept the special theory of relativity has, it is
universally agreed, consequences for our philosophical
views about space and time. Indeed some have found
these consequences so distasteful that they have refused
to accept special relativity, despite its many satis
factory empirical results, and so they have been forced
to try to account for these results in alternative
ways. But it is surprising that there is much less
agreement about exactly what the philosophical conse
quences are, especially when looked at in detail.
Partly this arises because the results of the theory
are derived in an elegant mathematical notation which
can conceal as much as it reveals, and which, accord
ingly, offers no incentive to engage in the thankless
task of dissection.
The present book is an essay in careful analysis of
special relativity and the concepts of space and time
that it employs. Those who are familiar with the theory
will find here (almost) all the formulae with which
they are familiar;but in many cases the interpretations
given to the terms in these formulae will surprise them.
I doubt if this is the last word about these inter
pretations:but I believe that the book is valuable in
ix
x Foreword
drawing attention to the possibility of more open dis
cussion in general, and in particular to the fact that
acceptance of the theory of relativity need not commit
one to every detail of conventional interpretation of
its terms.
King's College London C. W. KILMISTER