RESEARCH NOTES
ON
RELATIVITY
193
13)
contains
only
scant
clues
as
to the
reasons
for
this
decision. Doc.
10,
and
especially
its
third
part,
provide
the
most
complete
record available of the
progression
in
Ein
stein's
thinking
as
he
explored possibilities
for the
gravitational
field
equations,
con
sidered the
now
standard
choices,
but abandoned them
in
favor of the
equations
of
the
"Entwurf"theory.[4]
II
The calculations of
Doc. 10
on
gravitation
were
undertaken after Einstein had
rec
ognized
the nonEuclidean character of
the
spacetime
metric and
its
connection with
gravitation.[5]
This decisive
insight
came
to
him after
his
move
to
Zurich
in
August
1912.[6] Initially drawing only
on an
analogy
with Gauss's
theory
of
surfaces,[7]
Ein
stein
recognized
that the
arbitrary
coordinates of Gauss's
theory
could
help
him
carry
out
the
program
of research announced
five
years
earlier in Einstein
1907j (Vol. 2,
Doc.
47),
§18.
There he had
proposed using
the
theory
of
gravitation
as a means
of
extending
the
principle
of
relativity
to
accelerated frames of
reference. Two results
connect
Einstein's
1912 theory
of
static gravitational fields
with Gauss's
theory.
First,
in Einstein 1912c
(Doc. 3),
he remarked that
Euclidean
geometry
would break down
in
a uniformly
rotating
reference
system:
As
a
result of
the
Lorentz contraction of
moving rods,
the measured ratio of
the
circumference of
a
circle
to its
diameter
must
differ from the Euclidean value
tt.[8]
Second,
in
a
correction added
in
proof
to
Einstein
1912d
(Doc. 4),
p.
458,
Einstein
reported
that
he
had discovered
a very suggestive
formulation of
the
equations
of motion of
a
point
mass
falling
in
a
gravitational field.
The
equations
could be rewritten
as a
single
extremum
principle
8 {fV(c2dt2

dx2

dy2

dz2)}
=
0,
[4]For
further
discussion,
see
Norton
1984
and Stachel
1989.
[5]In
a biographical
note
of
1916,
Einstein listed this
insight
as
marking
the second
stage
in
the
development
of
general relativity.
The
note
is
11 196
in
the
Einstein Archive. See
also
Ishiwara
1971.
[6]See
Einstein
1923. A
draft version of this
preface
is
1
014
in
the Einstein Archive. See
Stachel
1989,
p.
65.
[7]As
a
student Einstein had enrolled
in
lectures
on
infinitesimal
geometry
by
C. F. Geiser,
which covered Gauss's
theory (see
Einstein
1955).
See also Einstein
to
Walter
Leich,
24
April
1950,
for Einstein's recollection of these lectures. Marcel
Grossmann's
notes
on
Geiser's
lec
tures,
which Einstein
may
have studied
as a
student
(Einstein
1955), are
preserved in
the ETH
library
as
Hs.
421:15. For
a
history
of
the
classical
theory
of surfaces
in
the
tradition of
Gauss,
see Coolidge 1940,
book
3.
Einstein had
not
known
originally
of
the
relevant works of
Riemann, Ricci,
and
LeviCivita,
only learning
of them from Marcel Grossmann after
seeking
Grossmann's
help
in
constructing
generally
covariant
quantities
from the
spacetime
metric
(see sec.
III
below).
[8]This
example
had
already
been discussed
by
Einstein
in
Einstein 1911f
(Vol.
3,
Doc.
22).
For
an
account
emphasizing
the
importance
of
this
particular
consideration,
see
Stachel
1980.
See also Pais
1982,
pp.
210216,
for further evaluation of
the
factors
guiding
Einstein's
tran
sition from his
theory
of static
fields
of
1912 to
the "Entwurf"
theory.