EINSTEIN'S RESEARCH NOTES
ON
A
GENERALIZED
THEORY
OF RELATIVITY
I
Einstein's research notebook contains
two
larger
sections
on
gravitation,
in
addition
to
a
variety
of entries related
to
thermodynamics,
radiation
theory,
and
electrodynam-
ics.
All entries
are
related
to
Einstein's scientific interests
or
to
his
teaching
duties
in
the
years
1912 and 1913.
Those
parts pertaining
to
gravitation
are
presented
here
as
Doc.
10.[1] They
derive from the transition between Einstein's
theory
of static
gravi-
tational
fields
of
1912 (Docs.
3, 4,
and
7)[2]
and the "Entwurf"
theory presented
in
Einstein and Grossmann
1913 (Doc.
13).[3]
These calculations
on
gravitation
must
have been
undertaken after Einstein's
move
from
Prague
to
Zurich
in
August
1912
because
they already assume
that
gravitation
is to
be
represented by
the metric
tensor
of
space-time. They were complete by May
1913
with the submission of Einstein
and
Grossmann
1913
(Doc.
13).
The
notes fall into three
parts.
The
first,
referred
to
as
Part
I
in
the
following, covers
[pp.
1-9].
The
next two
parts,
[pp.
10-26]
and
[pp.
27-
58],
start
from the other end of the notebook.
In the
course
of these
calculations,
Einstein
proceeds
from
a
recapitulation
of ele-
mentary properties
of
the
metric
tensor to
sophisticated computations using
the abso-
lute differential calculus
set
forth
in
Ricci and
Levi-Civita
1901.
It
is not
clear
why
Einstein did
many
of these
calculations,
even though
most
of them
can
be
recon-
structed
unambiguously. Major portions
of
Einstein's
notes, however,
are
attempts
to
devise the
gravitational
field
equations
that
are
presented
in Einstein and Grossmann
1913
(Doc. 13).
As
a
result,
Doc.
10
is
able
to
throw considerable
light
onto
the
historical
development
of Einstein's
general theory
of
relativity.
With
the
completion
of Einstein and Grossmann
1913
(Doc. 13),
the
two
authors had laid
out virtually
all
the elements of the
general theory
of
relativity,
which
at
this
point
lacked
only
the
gravitational
field
equations
that Einstein would
finally
adopt
in
November
1915.
These latter
field
equations,
now
part
of
the
accepted general theory
of
relativity,
are
generally
covariant.
In
1913,
however,
Einstein and Grossmann had
to
report
their
failure
to find
acceptable generally
covariant
field
equations
and their decision
to
settle
for
gravitational
field
equations
of limited covariance. This decision
cost
Einstein three
years
of
painful struggle
as
he
tried
first to
reconcile himself
to
the limited covariance
of
his
theory
and then retracted
it.
The
text
of Einstein and Grossmann
1913
(Doc.
[1]Materials
unrelated
to gravitation
are
characterized in the
descriptive note to
Doc.
10.
The
division of these materials into
parts A, B,
and
C
should
not be
confused with the division of
the research
notes
on gravitation
which follows.
[2]See
the editorial
note,
"Einstein
on
Gravitation and
Relativity:
The Static
Field,"
pp.
122-
128.
[3]For
further discussion of Einstein's collaboration with
Grossmann,
see
the editorial
note,
"Einstein
on
Gravitation and
Relativity:
The Collaboration with Marcel
Grossmann,"
pp.
294-
301.