30 DOC.
9
FORMAL FOUNDATION
OF
RELATIVITY
Doc.
9
The Formal Foundation of the General
Theory
of
Relativity
Plenary
Session
of
Nov.
19,
1914-Communications
of
the
phys.-math
section of Oct.
29
A. Einstein
(Submitted
on
October
29, 1914
[see
p.
965
above])
[p.
1030]
In recent
years
I
have
worked,
in
part together
with
my
friend
Grossman,
on
a
[1] generalization
of
the
theory
of
relativity.
During
these
investigations, a kaleidoscopic
mixture
of
postulates
from
physics
and
mathematics has
been introduced and used
as
heuristical
tools;
as a consequence
it is not
easy
to
see through
and characterize the
theory
from
a
formal mathematical
point
of
view,
that
is,
only
based
upon
these
papers.
The
primary objective
of the
present paper
is to close this
gap.
In
particular,
it has been
possible
to obtain the
equations
of
the
gravitational
field in
a purely
covariance-theoretical
manner (section
D).
I also tried to
give simple
derivations
of
the basic laws
of
absolute differential
calculus-in
part, they are probably
new
ones
(section
B)-in
order to allow the reader to
get
a
complete grasp
of
the
theory
without
having
other,
purely
mathematical
tracts. As
an
illustration
of
the
mathematical
methods,
I derived the
(Eulerian) equations
of
hydrodynamics
and the
field
equations
of
the
electrodynamics
of
moving
bodies
(section
C).
Section
E
shows
that Newton's
theory
of
gravitation
follows from the
general theory as
an
approxima-
tion. The most
elementary
features
of
the
present theory are
also derived inasfar
as
[2]
they
are
characteristic
of
a
Newtonian
(static)
gravitational
field
(curvature
of
light
rays,
shift
of
spectral lines).
A.
The
Basic
Idea of the
Theory
§1.
Introductory
Considerations
The
original theory
of
relativity
is based
upon
the
premise
that all coordinate
systems
in relative uniform
translatory
motion to each other
are equally
valid and
equivalent
[p.
1031]
for the
description
of
the laws of nature. When viewed from
experience,
this
theory
gains
its
main
support
from the fact that when
we carry
out
experiments
on
earth
we
Translator's
note.
Corrections have
been
typographical errors
that
occurred
in
the
original
document. This
applies
to corrections mentioned in editorial
notes
[6], [7],
[9]-[14], [19]-[22], [25]-[31],
[38], [40], [41],
[43]-[46],
[49], [50],
and to