Foundations of Physics

322 Pages·1967·11.299 MB·English

by  Dr. Mario Bunge (auth.)

Springer Tracts in Natural Philosophy
Volume
10
Edited by C. Truesdell
Co-Editors: R. Aris . L. Collatz . G. Fichera· P. Germain
J.
Keller . M. M. Schiffer . A. Seeger
Mario Bunge
Foundations of Physics
With 5 Figures
Springer-Verlag New York Inc. 1967
Dr. Mario Bunge
Professor of Philosophy
MeGill Univel'Sity, Montreal
ISBN 978-3-642-49289-1 ISBN 978-3-642-49287-7 (eBook)
DOIIO.1007/978-3-64249287-7
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TItle-No. 6738
Preface
This is not an introduction to physics but an analysis of its founda
tions. Indeed, the aims of this book are: (1) to analyze the form and
content of some of the key ideas of physics; (2) to formulate several
basic physical theories in an explicit and orderly (i.e., axiomatic) fashion;
(3) to exhibit their presuppositions and discuss some of their philosoph
ical implications; (4) to discuss some of the controversial issues, and
(5) to debunk certain dusty philosophical tenets that obscure the under
standing of physics and hinder its progress. To the extent to which
these goals are attained, the volume can serve as a companion to studies
in theoretical physics aiming at deepening the understanding of the
logical structure and the physical meaning of our science.
In order to keep the book slender, whole fields of basic physical
research had to be excluded - chiefly many-body physics, quantum
field theories, and elementary particle theories. A large coverage was
believed to be less important than a comparatively detailed analysis
and reconstruction of three representative monuments: classical mechan
ics, general relativity, and quantum mechanics, as well as their usually
unrecognized presuppositions. The reader is invited to join the project
and supply some of the many missing chapters - or to rewrite the
present ones entirely.
Foundations research is not popUlar: most philosophers shrink at
its technicalities and most scientists feel the urge to go forward rather
than retrace their steps, understand what they have gone through, analyze
it critically and thereby be in a better position to plan what to do next.
Only a few physicists have been allowed to work in the foundations of
physics: GALILEI, KEPLER, LEIBNIZ, HUYGHENS, NEWTON, EULER,
D'A LEMBERT, AMPERE, HELMHOLTZ, HERTZ, MACH, DUHEM, BOLTZ
MANN, OSTWALD, POINCARE, PLANCK, EINSTEIN, BOHR, BORN, SCHRO
DINGER, DE BROGLIE, HEISENBERG, and not many more. They could
afford it because they had done "hard" work. The rest must pretend
that there are no foundation problems. Yet no one can help asking and
answering questions belonging to foundations research - only, this is
usually done with some shame and therefore hurriedly and sloppily.
Even those eminent scientists were amateurs in the field of foundations
research if judged by the current standards prevailing in the discipline:
when it came to dissect their own creatures they did not avail them-
VI Preface
selves of the necessary tools - mathematical logic, metamathematics,
scientific semantics, methodology, and other disciplines which, after all,
have attained maturity only in recent times.
Foundations research in physics compares unfavorably with its
partner the foundations of mathematics. While practically no physicist
knows what 'foundations research' means, mathematicians have learned
to esteem it because it contributes to clarifying and organizing the body
of acquired knowledge and, by showing its presuppositions and limita
tions, it suggests new research lines: in short it contributes to the matura
tion of their science. Why not learn from mathematicians, pushing
foundations research ahead and advancing it far enough that it may
play a creative role and contribute to the maturation, not just the
swelling, of physical science? There is little excuse for failing to attempt
it, as all physical theories teem with logical and semantical difficulties,
and the great majority of them are in their infancy as regards logical
organization and physical interpretation. The prime matter - supplied
by the physicist - and the tools - wrought by the mathematician,
the logician and the philosopher of science - are there. The problems
are exciting and many of them brand new: why should they not attract
a good many thoughtful physicists, whether young or experienced, and
become an established branch of physics?
I am grateful to
Professors PETER G. BERGMANN, PETER HAVAS and WALTER NOLL,
and Doctors BERNARD COLEMAN, JOHN L. MARTIN and E. J. POST, each
of which criticized some fragments of the manuscript;
my wife Dr. MARTA C. BUNGE and my son Dr. CARLOS F. BpNGE,
Professor MILLARD BEATTY and several former students, particularly
Professor ANDRES J. KALNAY and Mr. WILLIAM G. SUTCLIFFE, all of
whom made me aware of several difficulties;
the Physics Departments of the Universities of Buenos Aires, La
Plata, Delaware and Freiburg, which gave me the opportunity to teach
seminars on the subject, to students who had not surrendered their
right to understand and criticize;
the far-sighted and liberal Alexander-von-Humboldt-Stiftung, for a
research fellowship at the Albert-Ludwigs-Universitat in Freiburg i. Br.
during the last stage of this research;
Professors S. FLtiGGE and H. HONL for their cordial hospitality at the
Freiburg University;
and above all Professor CLIFFORD TRUESDELL for urging me to under
take this project.
Physikalisches Institut der Universitat
Freiburg i. Br. , November, 1966 MARIO BUNGE
Table of Contents
Introduction
Foundations Research
1. Object: Fundamental Theories
2. Aims: Analysis and Synthesis
3. VVhyFoundations? 2
4. HowFR? 4
5. Present State of FR 5
6. Outlook ..... 6
Chapter 1
Toolbox
1. Form and Content 9
1.1. Language . 9
1.2. Logic ... 11
1.3. Semantics. 18
2. Predicates 30
2.1. Magnitudes 30
2.2. Constants . 34
2.3. Semantical and Methodological Status 35
2.4. Dimensions . . . 37
2.5. Scales and Units. 38
3. Hypotheses . .. . 40
3.1. Assumptions 41
3.2. Law Statements 44
3.3. Variational Principles 46
3.4. Conservation Laws 47
4. Theories . . . . . . 51
4.1. Form and Content 52
4.2. Physical Axiomatics 61
4.3. Theory Construction 70
5. Theory Checking 73
5.1. Testability . 74
5.2. Explanation and Prediction 78
5.3. Rival Theories and Programmes 83
VIII Table of Contents
Chapter 2
Protophysics
1. Zerological Principles . 86
2. Physical Probabilities 89
3· Chronology . . . . . 93
4. Physical Geometry. . 101
5. General Systems Theory 108
6. Analytical "Dynamics" . 112
6.1. General "Dynamics" . 113
6.2. Excursus: Independent Axiomatization of Hamilton's "Dynamics" . 116
6.3. Transition from G to Lagrange's "Dynamics" . . . . . . . .. 118
6.4. Excursus: Independent Axiomatization of Lagrange's "Dynamics" 119
6.5. Transition from G to Hamilton-Jacobi's "Dynamics" 121
6.6. Extensions to Continuous Systems 122
6.7. Intertheory Relations . . . . . . . . . . . 123
Chapter 3
Classical Mechanics
Introduction 127
1. Particle Mechanics . . . . 129
1.1. Background and Primitives 130
1.2. Axioms ..... . 131
1.3. Sample of Theorems 136
1.4. Analysis ... . . 139
2. Continuum Mechanics 143
2.1. Background and Building Blocks 145
2.2. Axioms ...... . 148
2.3. Typical Consequences 152
2.4. Tests ....... . 155
Chapter 4
Classical Field Theories
Introduction. . . . . . . 157
1. Classical Electromagnetism . . . . . . . . . . 159
1.1. Microelectromagnetism . . . . . . . . . . 161
1.2. Alternative Formulations of Microelectromagnetism 166
1.3. Some Typical Theorems ... . . . . . 171
1.4. Classical Electrodynamics . . . . . . . . 174
1.5. Phenomenological Macroelectromagnetism . 177
1.6. Representational Macroelectromagnetism 178
1.7. Nonfield Theories of E.M. 179
1.8. Testability of CEM. . . . . . 180
2. Special Relativity . . . . . . . . 182
2.1. Background and Heuristic Cue 182
2.2. Basis of Relativistic Kinematics 183
2.3. Some Logical Consequences 187
2.4. Relativistic Physics 195
2.5. Disputed Questions 200
Table of Contents IX
3. General Relativity. . . . . . 207
3.1. Heuristic Components 207
3.2. Basis of General Relativity 218
3.3. Comments .. . . . . . 222
3.4. Some Representative Theorems 228
3.5. Empirical Tests . . . . . 232
Chapter 5
Quantum Mechanics
Introduction 235
1. Quantum Heuristics 239
2. Background and Building Blocks 241
3. Comprehensive Postulates 245
4. Comprehensive Theorems 252
5. Specific Postulates . 259
6. Specific Theorems . 262
7. Measurement Theory 274
8. Debated Questions. 287
Epilogue .. 296
Bibliography 298
Subject Index 307
Special Symbols
Names of subjects
CED Classical electrodynamics
CEM Classical electromagnetism = MAXWELL'S theory
CM Continuum mechanics = Classical mechanics
CP Calculus of Probability
EG Euclidean Geometry
B.m. electromagnetic
FR Foundations research
G General "dynamics"
GO Geometrical optics
GR General relativity = EINSTEIN'S gravitation theory
H HAMILTON'S "dynamics"
HJ HAMILTON-JACOBI'S" dynamics"
L LAGRANGE'S" dynamics"
LT Local time theory
NP Newton-Poisson theory of gravitation
n.r. nonrelativistic
PC= Predicate calculus with identity = ordinary logic
PEG Physical Euclidean geometry
PM Particle mechanics
OED Quantum electrodynamics
OFT Quantum field theory
q.m. quantum mechanical
OM Quantum mechanics
OMM Quantum mechanics of measurement
3 General theory of systems
3M Statistical mechanics
3R Special relativity
3RK Special relativistic kinematics
UT Universal time theory
Logical symbols
.., not
A and
v or
=;> implies = if ... then ... = sufficient condition
~ equivalence = if and only if (iff) = necessary and sufficient condition
3 x there is at least one x
31 there is exactly one
"Ix for all x
Metatheoretical symbols
w·f·f· well formed formula.
A axiom, postulate, assumption, hypothesis, premise
t, Thm. theorem, logical consequence
XII Special Symbols
I- entails
Cn(A) set of consequences of the assumption(s) A
df equal by definition
Df. definition
>
T = <A, I- theory based on the axiom set A
Semantical symbols
designates, names
refers to, represents
mirrors, models
Iff extension
J intension
vltean meaning
g equal by referition
Mathematical symbols
u logical sum (union)
n logical product (intersection)
( is included in
E is a member of
I such that, given that
{xl Px} the set of all x such that P x
<x, y) ordered pair of individuals x and y
XxY Cartesian product of the sets X and Y = {<x, y) I xEX AyE Y}
f: X-+ Y f maps X into Y
('j the empty set
C the set of complex numbers
I the set of integers
N the set of natural numbers
R the set of real numbers
R+ the set of nonnegative reals
Protophysical symbols
set of physical systems (J
is a proper part of
+ physical addition
physical product
gives rise to
system of N physical parts (JiE;[;
the null individual of the kind ;[;