30 DOC.

9

FORMAL FOUNDATION

OF

RELATIVITY

Doc.

9

The Formal Foundation of the General

Theory

of

Relativity

Plenary

Session

of

Nov.

19,

1914-Communications

of

the

phys.-math

section of Oct.

29

A. Einstein

(Submitted

on

October

29, 1914

[see

p.

965

above])

[p.

1030]

In recent

years

I

have

worked,

in

part together

with

my

friend

Grossman,

on

a

[1] generalization

of

the

theory

of

relativity.

During

these

investigations, a kaleidoscopic

mixture

of

postulates

from

physics

and

mathematics has

been introduced and used

as

heuristical

tools;

as a consequence

it is not

easy

to

see through

and characterize the

theory

from

a

formal mathematical

point

of

view,

that

is,

only

based

upon

these

papers.

The

primary objective

of the

present paper

is to close this

gap.

In

particular,

it has been

possible

to obtain the

equations

of

the

gravitational

field in

a purely

covariance-theoretical

manner (section

D).

I also tried to

give simple

derivations

of

the basic laws

of

absolute differential

calculus-in

part, they are probably

new

ones

(section

B)-in

order to allow the reader to

get

a

complete grasp

of

the

theory

without

having

to read

other,

purely

mathematical

tracts. As

an

illustration

of

the

mathematical

methods,

I derived the

(Eulerian) equations

of

hydrodynamics

and the

field

equations

of

the

electrodynamics

of

moving

bodies

(section

C).

Section

E

shows

that Newton's

theory

of

gravitation

follows from the

general theory as

an

approxima-

tion. The most

elementary

features

of

the

present theory are

also derived inasfar

as

[2]

they

are

characteristic

of

a

Newtonian

(static)

gravitational

field

(curvature

of

light

rays,

shift

of

spectral lines).

A.

The

Basic

Idea of the

Theory

§1.

Introductory

Considerations

The

original theory

of

relativity

is based

upon

the

premise

that all coordinate

systems

in relative uniform

translatory

motion to each other

are equally

valid and

equivalent

[p.

1031]

for the

description

of

the laws of nature. When viewed from

experience,

this

theory

gains

its

main

support

from the fact that when

we carry

out

experiments

on

earth

we

Translator's

note.

Corrections have

been

made here to

typographical errors

that

occurred

in

the

original

document. This

applies

to corrections mentioned in editorial

notes

[6], [7],

[9]-[14], [19]-[22], [25]-[31],

[38], [40], [41],

[43]-[46],

[49], [50],

and to

additional

notes

{5}-{20}

at

the

end

of

this document.