Born M., Einstein's Theory of Relativity, 1962.pdf

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EINSTEIN’S
THEORY
OF
RELATIVITY
BY
MAX
BORN
PNOPBMON
O»
TUOUTKAL
PHYBICI
IN
THN
UNIVSHCTY
OP
OOTTINSCM
TJIANSLATKD
BY
HENRY
L.
BROSE,
M.A.
CHftlST
CHURCH
OXFORD
WITH
135
DI>
OF
AMS
AND
A
FORTMAH
FROM
THE
PREFACE
TO
THF
FIRST
EDITION
HIS
book
is
an
elaboration
of
certain
lectures
which
were
given
last
winter
to
a
somewhat
con­
siderable
audience.
The
difficulty
which
persons
not
conversant
with
mathematics
and
physics
experien
in
understanding
the
theory
of
relativity
seems
to
me
to
be
due
for
the
most
part
to
the
circumstance
that
they
are
not
familiar
with
the
fundamental
conceptions
and
facts
of
physics,
in
particular
of
mechanics.
During
the
lectures
I
therefore
showed
some
quite
simple
qualitative
experiments
to
serve
as
an
introduction
to
such
concep­
tions
as
velocity,
acceleration,
mass,
force,
intensity
of
field,
and.
so
forth.
In
m/•
endeavour
to
find
a
similar
means,
adapted
to
book
purposes,
the
semi-historical
method
of
representation
here
chosen
occurred
to
me,
and
I
hope
I
have
succeeded
in
avoiding
the
uninspiring
method
of
the
elementary
text
books
of
physics.
But
it
must
be
em­
phasised
that
the
historical
arrangement
has
been
selected
only
as
a
cloak
which
is
to
bring
into
stronger
relief
the
outline
of
the
main
theme,
the
logical
relationship.
Having
once
started
this
process
I
found
myself
compelled
to
con­
tinue,
and
in
this
way
my
undertaking
increased
to
the
dimensions
of
this
book.
The
reader
is
assumed
to
have
but
little
mathematical
knowledge.
I
have
attempted
to
avoid
not
only
the
higher
mathematics
but
even
the
use
of
elementary
functions,
such
as
logarithms,
trigonometrical
functions,
and
so
forth.
Nevertheless,
proportions,
linear
equations,
and
occasionally
squares
and
square
roots
had
to
be
intro­
duced.
I
advise
the
reader
who
is
troubled
with
the
formulae
to
pass
them
by
on
the
first
reading
and
to
seek
io
arrive
at
an
understanding
of
the
mathematical
symbols
T
vi
THE
THEORY
OF
RELATIVITY
from
the
text
itself.
I
have
made
abundant
use
of figures
and
graphical
representations.
Even
those
who
are
un­
practised
in
the
use
of
co-ordinates
will
learn
to
read
the
curves
easily.
The
philosophical
questions
to
which
the
theory
ot
relativity
gives
rise
will
only
be
touched
on
in
this
book.
Nevertheless
a
definite
logical
point
of view
is
maintained
throughout
I
believe
I
am
right
in
asserting
that
this
view
agrees
in
the
main
with
Einstein’s
own
opinion.
Moritz
Schlick
takes
up
a
similar
view
in
his
valuable
work
“Allgemeine
Erkenntislehre”
(The
General
Theory
of
Knowledge).
Of
the
other
books
which
I
have
used
I
should
like
to
quote,
above
all,
Ernst
Mach’s
classical
“Mechanics”
(which
has
appeared
in
English),
and
then
the
very
lucidly
written
volume
by
E.
T.
Whittaker,
“
A
History
of
the
Theories
of
Aether
and
Electricity
’
(London,
Longmans,
Green
&
Co.,
1910),
and
the
comprehensive
account
of
the
Theory
of
Relativity
given
by
Hermann
Weyl
in
his
“Space,
Time,
Matter”
(English
translation
published
by
Messrs.
Methuen
&
Co.,
Ltd.,
1922).
Anyone
who
wishes
to
penetrate
further
into
Einstein’s
doctrines
must
study
the
latter
work.
It
is
impossible
to
enumerate the
countless
books
and
essays
from
which
I
have
drawn
more
or
less directly.
In
conformity
with
the
character
of
the
book
I
have
refrained
from
giving
references.
MAX
BORN
F
rankfurt
un
the
M
ain
June,
1920
PREFACE
TO
THE
THIRD
EDITION
PART
from
a
number
of
minor
alterations,
this
edition
differs
from
its
two
predecessors
in
that
the
chapter
on
Einsteinian
dynamics
has
been
revised.
Previously,
in
forming
the
acceleration,
we
did
not
d
tinguish
sharply
between
time
and
proper
time,
and
we
used
Minkowski’s
cova^iant force-vector in
place
of
ordin­
ary
force
;
this
of
cotlree'tncreased
the
difficulty
of.
under­
standing
a
chapter
which
was,
from
the
outset,
not
easy.
Dr.
W.
Pauli,
jun.,
called
my
attentiorFnia^
method
of
deriving
the
relativistic
formula
of
mass
proposed
by
Lewis
and
Tolman,
which
fitted
in
admirably
with
the
scheme
of
this
book,
as
it
linked
up
with
the
conception
of
momentum
in
the
same
way
as
the
account
of
mechanics
here
chosen.
The
chapter
on
Einsteinian
dynamics
was
revised
in
con­
formity
with
this
point
of
view:
this
also
entailed
some
alterations
in
the
manner
of
presenting
ordinary
mechanics.
It
is
hoped
that
these
changes
will
simplify
the
reading.
I
should,
not
like
to
lose
this
opportunity
of
thanking
Dr.
W.
Pauli
for
his
advice.
His
great
work
on
the
theory
of
relativity
which
has
appeared
as
Article
19
in
the
fifth
volume
of
the
“
Enzyklopädie
der
mathematischer
Wissenschaften,”
which
appeared
recently,
has
been
of
great
service
to
me.
It
is
to
be
recommended
foremost
of
all
to
those
who
wish
to
become
intimately
acquainted
with
the
theory
of
relativity.
A
MAX
BORN
G
öttinoeh
bth
March,
1922
CONTENTS
CHAPTER
I
PAOB
§
I.
The
Origin
of
the
Art
of
Measuring
Space
and
Time
$
2.
Units
of
Length
and
Time.......................................
5
3-
Origin
and
Co-ordinate
System
....
$
4.
The
Axioms
of
Geometry.................................................
..
.
9
$
5.
The
Ptolemaic
System.................................................
.10
$
6.
The
Copemican
System...........................................................
.11
S
7.
The
Elaboration
of
the
Copemican
Doctrine
....
13
G
eometry
and
C
osmology
CHAPTER
11
T
he
F
undamental
L
aws
15
i.
-$2.
$
3.
$
4.
$
5.
5
6.
$
7.
$
8.
$
9.
$10.
$
11.
$
12.
$
13.
$
14.
$15.
of
C
lassical
M
echanics
Equilibrium
and
the
Conception
of
Force.......................................
15
The
Study
of
Motions—Rectilinear
Motion
....
16
Motion
in
a
Plane..............................................................................
23
Circular
Motion..............................................................................
24
Motion
in
Space
.......................................................................
26
Dynamics—The
Law
of
Inertia..................................................................
27
Impulses...............................................................................
.22
The
Law
of
Impulses.....................................................................................
29
Mass.........................................................................................................
30
Force
and
Acceleration...........................................................................
32
Example—Elastic
Vibrations..................................................................
34
Weight
and
Mass
. .......................................................................................
36
Analytical
Mechanics.....................................................................................
39
The
Law
of
Energy.....................................................................................
41
Dynamical
Units
of
Force
and
Mass
.........................................................45
CHAPTER
III
T
he
N
ewtonian
W
orld
-S
ystem
$
i.
§2.
J
3.
$
4.
$
5.
$
6.
5
7.
$
8.
$
9.
Absolute
Space
and
Absolute
Time.................................................
48
Newton’s
Law
of
Attraction
.
'........................................51
General
Gravitation.....................................................................................
53
Celestial
Mechanics...........................................................
56
The
Relativity
Principle
of
ClassicalMechanics
.'
59
Limited
Absolute
Space............................................................................61
Galilei
Transformations............................................................................62
Inertial
Forces...............................................................................................
67
Centrifugal
Forces
and
AbsoluteSpace................................................
69
b
is
00*^

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