300

EINSTEIN

IN COLLABORATION WITH GROSSMANN

reference

in such

a

way

that the

velocity

of

light

is

a

constant.[32]

The

point

of Einstein

and Fokker's

paper

was

to

demonstrate how the

powerful machinery

of the absolute

differential calculus allows

one

to

reduce

to

a

minimum the

physical

assumptions

required

for

deriving

Nordstrom's

theory.

In

the

final

paragraph

of their

paper they

express

the

hope

that

a

similar derivation

might

be

found for the "Entwurf"

field

equations.

In

a

footnote

to

this

paragraph, they

revoke the earlier

rejection

of

a con-

nection between the Riemann

tensor

and the

gravitational

field

equations

in

Einstein

and

Grossmann 1913

(Doc. 13). Unfortunately they

do not

go

into

any

detailed

expla-

nation of

why they

found the earlier

argument

wanting.[33]

V

In

his final

collaboration with

Grossmann,

Einstein returned

to

the

question

of the

covariance

properties

of

the

"Entwurf"

field

equations.[34]

As

discussed

in

sec.

III

above,

an

argument involving

the form of

the

conservation laws seemed

to

imply

that

the "Entwurf"

theory

is covariant

with

respect

to

general

linear transformations

only.

But this

argument against general

covariance

was contingent on

the

assumption

that

the

stress-energy

tensors

of the

gravitational

field and

of

matter

are

both

generally

covariant.

In

the

course

of

his 1914

collaboration with

Grossmann, however,

Einstein

realized that the

assumption

of the

general

covariance of the former

expression

was

not

justified.[35]

In

the

paper

resulting

from the

collaboration,

Einstein and Grossmann

1914b, it

is

shown that the "Entwurf"

theory

has the maximum covariance allowed

by

the condition that the metric

tensor is

uniquely

determined

by

the

gravitational

field

equations.

The crucial

ingredients

in this

demonstration

are

the "hole

argument,"

another version of which

is

presented

in

the

paper,

and

a

formulation of

the

gravitational

field

equation

in terms

of

a

variational

principle.

Einstein described

his

accomplishments

in

a

contemporary

letter:

"Now

I

am

completely

satisfied and

no

longer

doubt the

correctness

of the whole

system,

whether the observation of the

solar

eclipse

succeeds

or

not.

The

sense

of the

matter is too evident."[36]

Einstein's

[32]This

result

is

also contained

in

Walter Dällenbach's

notes

for Einstein's lecture

course

on electricity

and

magnetism, given

at

the ETH

in

winter

semester

1913/1914

(see Appendix

A).

[33]For

attempts

to

interpret

the footnote,

see

Stachel

1989,

pp.

82-83,

and

Norton

1984,

fn.

61.

[34]For

discussions of Einstein and Grossmann

1914b,

see

Stachel

1989,

pp.

84-85,

and

Norton

1984, sec.

6.

[35]See

Einstein and Grossmann

1914b,

p.

218, fn.

1.

The

recognition

of

this

problem

is

probably

also

responsible

for the fact that

in

Einstein 1914h

(Doc. 31)

a

passage occurring

in

the

manuscript

of

this

paper

and related

to

his

arguments against general

covariance

is

omitted

(see

the annotation

to this document).

[36]"Nun bin ich vollkommen

befriedigt

und

zweifele nicht mehr

an

der

Richtigkeit

des

ganzen Systems, mag

die

Beobachtung

der Sonnenfinsternis

gelingen

oder nicht. Die Vernunft

der Sache ist

zu

evident"

(Einstein to

Michele

Besso,

ca. 10

March

1914

[Vol. 5,

Doc.

514]).