628
APPENDIX
A
tation
and
Relativity:
The Collaboration
with
Marcel
Grossmann,"
pp.
294-301).
An
example is
the notation used for
the
gravitational
field
equations,
which
is
that of
Einstein 1913c
(Doc.
17).
Einstein
began
with
the
question: Why
can one
not
simply
apply
the Lorentz transformations
to
gravitation?
His
answer was
that
it is
impossible
because the inertia of
a
body depends
on
its
energy
content,
and because inertial
mass
is,
on
the other
hand,
equal
to
gravitational
mass
according
to
Eötvös. Einstein
next
stated that the
principle
of
the
constancy
of the
speed
of
light
is not correct;
by con-
sidering light
emitted from
an
accelerated
frame of reference and
using
the
principle
of
equivalence
he
then derived
a
formula for
the
gravitational
redshift.
He
briefly
remarked that Nordström had found the
same
result. Einstein introduced
the distinction
between
local
time
and
coordinate time
and
derived
the bending
of
light
as a conse-
quence
of the
variability
of the
speed
of
light expressed
in coordinate time. He thus
concluded what the
notes
refer
to
as
the
first
part
of his considerations.
He
began
the second
part
by
summarizing
Mach's
critique
of Newton's
principle
of
inertia,
which
he
characterized
as a major
factor
in
motivating
his
search for
a
theory
of
gravitation.
The
subsequent
section bears the
heading
"the mathematical
method of the
theory
of
gravitation" ("Die mathem[atische]
Methode der Gravi-
tationstheorie").
Einstein
first
introduced Hamilton's
principle
and derived from
it
the
equations
of motion of
a
point
mass.
He
then
argued
that the
theory
of covariance
no
longer applied
to
these
equations
because of the
nonconstancy
of the
speed
of
light.
Next
he
introduced transformations
to arbitrary
coordinates and
rewrote
the earlier
variational
principle
in
general
coordinates
using
the
metric
tensor.
After
posing
the
question
of
how to construct
a
theory
of covariance
on
the
basis of the scalar
four–
dimensional line element ("the father of
all
scalars"
["der
Vater aller
Skalare"]), he
referred
to
the works of
Christoffel, Ricci, and
Levi-Civita.
The remainder of Einstein's lectures
were
devoted
to
a
further
development
of the
tensor concept
introduced earlier in
the
course.
In
particular
he
stressed the distinction
between
covariant
and
contravariant
quantities,
and
explained
the
concept
of covariant
differentiation,
which
he
characterized
as a
very complicated operation.
The
starting
point
for the further discussion of the
physics
of Einstein's
gravitation theory
are
the
conservation
laws,
expressed
in
terms
of the
vanishing divergence
of
a
stress-energy
tensor.
After
emphasizing
that the conservation laws of the
new theory
should
com-
prise
a
term
for the
gravitational field,
Einstein turned
to
the "accursed task"
("ver-
fluchte
Aufg[abe]")
of
constructing
the
field
equations.
He first wrote
Poisson's
equa-
tion
which, he claimed,
should
be
recovered in
first
order from the
gravitational
field
equations.
He
also claimed that
the
validity
of the conservation
laws
requires
the
possibility
of
rewriting
the
expression
for the
vanishing
of the covariant
divergence
of the
source
term
of the
field
equations
by
using an ordinary divergence.
He noted
that Nordström's
field
equations
follow
immediately
from
his
argument
if
the
speed
of
light
is
presumed
to be constant
(see
Einstein and Fokker
1914
[Doc. 28]).
Coming
back
to the
approximate validity
of Poisson's
equation,
Einstein stated that
the
first term
of the
generally
covariant differential
operator
which
generalizes
the