146

DOC. 30 FOUNDATION OF GENERAL RELATIVITY

[p. 769]

Doc. 30

The Foundation of the General Theory of Relativity

by

A.

Einstein

[This

first

page

was missing

in the

existing translation.]

[1]

[2]

[3]

[4]

[5]

[6]

The

theory

which is

presented

in the

following pages conceivably

constitutes the

farthest-reaching generalization

of

a

theory

which,

today,

is

generally

called the

"theory

of

relativity";

I will call

the

latter

one-in

order to

distinguish

it from

the

first named-the

"special theory

of

relativity,"

which I

assume

to

be

known. The

generalization

of

the

theory

of

relativity

has been facilitated

considerably by

Minkowski,

a

mathematician who

was

the first

one

to

recognize

the formal

equivalence

of

space

coordinates and the time

coordinate,

and utilized this in the

construction of the

theory.

The mathematical tools that

are necessary

for

general

relativity were readily

available in the "absolute differential

calculus,"

which is based

upon

the research

on

non-Euclidean manifolds

by

Gauss, Riemann,

and

Christoffel,

and which has been

systematized by

Ricci and Levi-Civita and has

already

been

applied

to

problems

of

theoretical

physics.

In section B

of

the

present paper

I

developed

all the

necessary

mathematical

tools-which

cannot be assumed to be

known

to

every

physicist-and

I tried to do it in

as simple

and

transparent a manner

as

possible, so

that

a special

study

of

the mathematical literature is

not

required

for

the

understanding

of

the

present paper. Finally,

I want to

acknowledge gratefully my

friend,

the mathematician

Grossmann,

whose

help

not

only

saved

me

the effort of

studying

the

pertinent

mathematical

literature,

but who also

helped me

in

my

search

for the field

equations

of

gravitation.

[The

balance

of

this translation is

reprinted

from

H.

A.

Lorentz et

al.,

The

Principle of Relativity,

trans.

W. Perrett and

G. B.

Jeffery (Methuen, 1923;

Dover

rpt., 1952).]