EINSTEIN'S RESEARCH NOTES

ON

A

GENERALIZED

THEORY

OF RELATIVITY

I

Einstein's research notebook contains

two

larger

sections

on

gravitation,

in

addition

to

a

variety

of entries related

to

thermodynamics,

radiation

theory,

and

electrodynam-

ics.

All entries

are

related

to

Einstein's scientific interests

or

to

his

teaching

duties

in

the

years

1912 and 1913.

Those

parts pertaining

to

gravitation

are

presented

here

as

Doc.

10.[1] They

derive from the transition between Einstein's

theory

of static

gravi-

tational

fields

of

1912 (Docs.

3, 4,

and

7)[2]

and the "Entwurf"

theory presented

in

Einstein and Grossmann

1913 (Doc.

13).[3]

These calculations

on

gravitation

must

have been

undertaken after Einstein's

move

from

Prague

to

Zurich

in

August

1912

because

they already assume

that

gravitation

is to

be

represented by

the metric

tensor

of

space-time. They were complete by May

1913

with the submission of Einstein

and

Grossmann

1913

(Doc.

13).

The

notes fall into three

parts.

The

first,

referred

to

as

Part

I

in

the

following, covers

[pp.

1-9].

The

next two

parts,

[pp.

10-26]

and

[pp.

27-

58],

start

from the other end of the notebook.

In the

course

of these

calculations,

Einstein

proceeds

from

a

recapitulation

of ele-

mentary properties

of

the

metric

tensor to

sophisticated computations using

the abso-

lute differential calculus

set

forth

in

Ricci and

Levi-Civita

1901.

It

is not

clear

why

Einstein did

many

of these

calculations,

even though

most

of them

can

be

recon-

structed

unambiguously. Major portions

of

Einstein's

notes, however,

are

attempts

to

devise the

gravitational

field

equations

that

are

presented

in Einstein and Grossmann

1913

(Doc. 13).

As

a

result,

Doc.

10

is

able

to

throw considerable

light

onto

the

historical

development

of Einstein's

general theory

of

relativity.

With

the

completion

of Einstein and Grossmann

1913

(Doc. 13),

the

two

authors had laid

out virtually

all

the elements of the

general theory

of

relativity,

which

at

this

point

lacked

only

the

gravitational

field

equations

that Einstein would

finally

adopt

in

November

1915.

These latter

field

equations,

now

part

of

the

accepted general theory

of

relativity,

are

generally

covariant.

In

1913,

however,

Einstein and Grossmann had

to

report

their

failure

to find

acceptable generally

covariant

field

equations

and their decision

to

settle

for

gravitational

field

equations

of limited covariance. This decision

cost

Einstein three

years

of

painful struggle

as

he

tried

first to

reconcile himself

to

the limited covariance

of

his

theory

and then retracted

it.

The

text

of Einstein and Grossmann

1913

(Doc.

[1]Materials

unrelated

to gravitation

are

characterized in the

descriptive note to

Doc.

10.

The

division of these materials into

parts A, B,

and

C

should

not be

confused with the division of

the research

notes

on gravitation

which follows.

[2]See

the editorial

note,

"Einstein

on

Gravitation and

Relativity:

The Static

Field,"

pp.

122-

128.

[3]For

further discussion of Einstein's collaboration with

Grossmann,

see

the editorial

note,

"Einstein

on

Gravitation and

Relativity:

The Collaboration with Marcel

Grossmann,"

pp.

294-

301.