DOC.

3

STATICS OF GRAVITATIONAL FIELD

95

Doc.

3

The

Speed

of

Light

and the Statics of the Gravitational Field

by

A.

Einstein

[Annalen

der

Physik

38

(1912):

355-69]

In

a

paper

that

appeared

last

year,1

I

drew from the

hypothesis

that the

gravitational

field and the

state

of acceleration of the coordinate

system

are

physically equivalent

a

few

conclusions that tie in

very

well with the results of the

theory

of

relativity

(theory

of

relativity

of uniform

motion).

But

at

the

same

time it turned

out

that

one

of the basic

principles

of that

theory, namely,

the

principle

of the

constancy

of

the

velocity

of

light,

is

valid

only

for

space-time regions

of

constant

gravitational

potential.

Even

though

this result rules

out

the universal

applicability

of the Lorentz

transformation, it

should

not

frighten

us away

from the further

pursuit

of the

path we

have

taken; at

the

very

least the

hypothesis

that the "acceleration field" is

a

special

case

of

the

gravitational

field

has,

in

my opinion,

such

a

high degree

of

probability,

especially

in view of the conclusions

regarding

the

gravitational mass

of the

energy

content,

already

drawn

in

the first

paper,

that

a more

exact

consideration of the

conclusions of the above

equivalence

hypothesis

seems

indicated.

[3]

Since

then,

Abraham has

proposed

a

theory

of

gravitation2

that contains the

conclusions drawn in

my

first

paper

as

special

cases.

However,

we

shall

see

in what

follows that Abraham's

system

of

equations cannot

be reconciled with the

equiva-

lence

hypothesis,

and that his

conception

of time and

space

does

not

hold

up even

from

a purely

formal,

mathematical

point

of view.

§1. Space

and

Time in the

Acceleration Field

Let the reference

system

K

(coordinates

x,

y,

z)

be in

a

state

of

uniform acceleration

in the direction of

its

x-coordinate. Let this

acceleration

be

uniform in Born's

sense,

i.e.,

the

acceleration

of

its

origin,

referred

to

a

nonaccelerated

system

with

respect

to

which

the

points

of K

possess

no

velocity

or

infinitely

small

velocity,

shall

be

a

constant

quantity.

According

to

the

eqivalence hypothesis,

such

a

system

K

is

strictly

[4]

1A. Einstein, Ann. d.

Phys.

35

(1911): 35.

2M.

Abraham, Phys.

Zeitschr.

13

(1912).

[1]

[2]