194
RESEARCH
NOTES
ON
RELATIVITY
where
t,
x, y,
z are
the
usual time and
space
coordinates,
and
c(x,
y, z)
is the
variable
speed
of
light
of
the 1912
theory. Although
his
equation
immediately suggests
the
geodesics
of Gauss's
theory,
which
are
defined
by
the extremum
principle
8fds
=
0,
and
also
picks
out the
geodesics
of
a
curved
spacetime
with
line elements
ds2
=
c2
(x, y,
z)dt2

dx2

dy2

dz2,
Einstein
did not
report
any
connection
to
the
geodesic
equation
in his note. On the
other
hand, he
did notice that
this extremum
principle
could
be
written
in the
form of Hamilton's
principle
8jHdt
=
0, suggesting
once
again
that
the
equations
of
analytic
mechanics
had
a
significance
that extended
well
beyond
Newtonian
mechanics. This Hamiltonian form of
the
equations
of motion
persists
in
Einstein's
early
work
on
general relativity, appearing
in Doc.
10, [p. 10],
and
Einstein
and Grossmann
1913
(Doc. 13), §1,
for
example.
Einstein's
note
was
written
no
later than
May 1912,
the
month of
publication
of
Einstein 1912d
and at
least three months
prior
to the
discovery
of
the
decisive
analogy
to
Gauss's
theory.
In
March
he had
already
announced
to his
correspondents
his
intention
of
proceeding
from
the static
to
the
dynamical
case
in his
study
of
gravita
tion.[9]
Einstein
subsequently reported
on
many
occasions
the
difficulty
he
encountered
in
the
task
of
generalizing the 1912 static
theory.[10]
In
June,
for
example,
he wrote
that
he
remained
perplexed
that
his
principle
of
equivalence
holds
only infinitesimally,
so
that
the field
of uniform Born acceleration could
not be
a
static
field
of
the
type
produced
by masses
at
rest.[11]
There
were,
he
continued,
other
types
of
timeinde
pendent
fields
that could
not be
produced
in this
way.
Such
was
the field
produced
by
a
rotating ring,
in
which reflected
light rays
did
not retrace the
same
trajectory
upon
their
return.[12]
This
new case
corresponded
to
a
static
magnetic
field in the
theory
of
electricity,
whereas
the
former
cases
corresponded
to
electrostatic
fields.
Einstein's interest
in the fields
produced
by
rotation
was
part
of
his
effort
to
gen
eralize
the
principle
of
relativity,
which included
the
project
of
"conceiving
rotation
as
rest."[13]
The
primary
burden of Einstein 1912e
(Doc.
7),
published
in
July,
was
to
establish that there
are
dynamical
effects within
his 1912
theory
of static
gravitational
fields
compatible
with
what
he
would later
call the
"hypothesis
of
the
relativity
of
inertia"
(Einstein
1913c
[Doc. 17],
pp.
12601262).
According
to this
hypothesis,
which
he
had taken from Mach's
writings,
the
inertial forces
acting
on an
accelerated
mass are
not
indicators of
its
absolute acceleration
as
Newton
had
argued
but
merely
[9]See
Einstein
to
Paul Ehrenfest, 10
March
1912
(Vol.
5,
Doc.
369);
Einstein
to
Wilhelm
Wien,
11
March
1912
(Vol. 5,
Doc. 371);
Einstein
to
Wilhelm
Wien,
20
March
1912
(Vol.
5,
Doc. 375);
and Einstein
to
Marian
von
Smoluchowski,
24
March
1912
(Vol. 5,
Doc.
376).
[10]See,
e.g.,
Einstein
to
Heinrich
Zangger,
20
May
1912
(Vol.
5,
Doc.
398);
Einstein
to
Heinrich
Zangger,
after
5
June
1912
(Vol.
5,
Doc.
406);
and
Einstein
to
Ludwig Hopf, 12
June
1912
(Vol. 5,
Doc. 408).
[11]Einstein to
Paul
Ehrenfest,
20 June
1912
(Vol. 5,
Doc. 409).
[12]This effect arises
in
the
fields
induced
by
rotating
frames of
reference,
as was
found
by
Frank
1912.
Frank's work
was
described
to
Einstein
by
Ehrenfest
in
a
letter from before
9
April
1912
(Vol. 5,
Doc.
380).
[13]Einstein
to
Michele
Besso, 26
March 1912
(Vol.
5,
Doc.
377).