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