DOC.

13

GENERALIZED THEORY OF RELATIVITY

151

Doc.

13

Outline of

a

Generalized

Theory

of

Relativity

and of

a

Theory

of Gravitation

I.

Physical

Part

by

Albert Einstein

II. Mathematical Part

by

Marcel Grossmann

[Teubner,

Leipzig, 1913]

I

Physical

Part

The

theory expounded

in

what

follows derives from the conviction that the

proportionality

between the inertial and the

gravitational mass

of

bodies

is

an

exactly

valid law of

nature

that

must

already

find

expression

in

the

very

foundation of

theoretical

physics. I already sought

to

give expression

to

this conviction in several

earlier

papers by seeking

to

reduce the

gravitational

mass

to

the inertial

mass;1

this

endeavor led

me

to

the

hypothesis

that,

from

a

physical point

of

view,

an

(infinitesi-

mally

extended,

homogeneous) gravitational

field

can

be

completely replaced

by a

state

of acceleration of the reference

system.

This

hypothesis

can

be

expressed

pictorially

in

the

following

way:

An observer enclosed

in

a

box

can

in

no

way

decide

whether the box

is at rest

in

a

static

gravitational field,

or

whether

it is in

accelerated

motion,

maintained

by

forces

acting

on

the

box,

in

a

space

that

is

free of

gravitational

fields

(equivalence

hypothesis). [2]

We know the fact that the law of

proportionality

of inertial and

gravitational

mass

is

satisfied

to

an

extraordinary degree

of

accuracy

from the

fundamentally

important investigation

by

Eötvös,2

which

is

based

on

the

following argument.

A

body

at rest

on

the surface of the Earth

is

acted

upon

by

gravity

as

well

as

by

the

centrifugal

force

resulting

from Earth's rotation. The first of these forces

is

[1]

1A. Einstein,

Ann. d.

Phys.

35

(1911): 898;

38

(1912):355;

38

(1912):

443.

2B. Eötvös,

Mathematische und

naturwissenschaftliche

Berichte

aus

Ungarn

8 (1890);

Wiedemann's Beiblätter

15 (1891):

688.

[3]