EINSTEIN

ON

THE

STATIC

FIELD 125

up

Einstein's idea of

a

variable

speed

of

light.[18]

Abraham

employed

Minkowski's

four-dimensional

representation

of

space-time introducing

an

imaginary

time coordi-

nate

u

=

ict.

The

core

of

his

theory

was a

four-dimensional

generalization

of Poisson's

equation

for the

gravitational potential O:[19]

£

=

4tt&P.

Abraham also derived

a

relation between the

velocity

of

light

and

the

gravitational

potential

which for small

O/c2

reduces

to

the relation of Einstein

1911h

(Vol.

3,

Doc.

23).[20]

Abraham's

approach

was a

natural

one

to

take

and

initially appealed

very

much

to

Einstein.[21]

Even before

publishing

his

papers

on

the

static

field,

which

do not

use

Minkowski's

formalism,

Einstein himself

had

discussed

with

Max Laue the

possibility

of

representing

the

gravitational potential

by a

four-dimensional

quantity.[22]

No later

than the end of

January,

however,

Einstein became convinced that Abraham had

com-

mitted serious

errors[23]

and

began

to

correspond

with him about

his

theory.[24]

Two

weeks later

he

referred

to

Abraham's

theory

as

"completely

untenable,"[25] a

charge

he

repeated

in

letters

to

various

correspondents

in

the

following

weeks.[26]

Einstein

publicly

criticized Abraham's

theory

in

Einstein 1912c

(Doc.

3),[27]

arguing

that

it

contradicts the

hypothesis

of

equivalence

and

that

it

was

untenable from "a

purely

formal mathematical

point

of

view."[28]

The issue under

dispute

was

whether Abra-

ham's

use

of Minkowski's four-dimensional

representation

of

space-time

was

justified

if

c

is

no

longer

constant.[29]

Contrary

to his

original view,

Abraham had

already

[18]See

Abraham

1912a, 1912b.

He further elaborated

his theory in

Abraham 1912d and

1912e.

[19]See

Abraham

1912a,

p. 1.

In

the

equation

denotes

the

d'Alembertian

operator.

[20]See

Abraham

1912a,

p.

2.

[21]See

Einstein

to

Michele

Besso, 26

March

1912

(Vol. 5,

Doc.

377).

[22]See

Max Laue

to Einstein, 27

December

1911

(Vol. 5,

Doc.

333).

See

also Einstein 1912h

(Doc. 8), pp.

1062-1063,

for

a

later reference

to

the

problem

addressed

in

Laue's

letter.

[23]See

Einstein

to

Heinrich

Zangger,

27

January

1912

(Vol. 5,

Doc.

344).

This letter

and

another

to

Wilhelm

Wien,

written

on

the

same

day (Vol. 5,

Doc.

343),

contain Einstein's earliest

comments

on

Abraham's

theory.

[24]For

evidence that Einstein

corresponded

with

Abraham,

see

Einstein

to

Michele

Besso,

4

February

1912

(Vol. 5,

Doc.

354),

and

Abraham

1912c.

[25]"ganz

unhaltbar"

(Einstein to

Paul Ehrenfest,

12 February

1912

[Vol.

5,

Doc.

357]).

[26]See,

e.g.,

Einstein

to H. A. Lorentz,

18 February

1912

(Vol.

5,

Doc.

360);

Einstein

to

Wilhelm

Wien, 24

February

1912

(Vol. 5,

Doc.

365);

and Einstein

to

Heinrich

Zangger,

before

29 February

1912

(Vol.

5,

Doc.

366).

[27]See

Einstein 1912c

(Doc. 3),

pp.

355

and

368.

[28]"rein mathematisch formalen

Standpunkt"

(Einstein

1912c

[Doc. 3],

p.

355).

[29]In

a

contemporary

letter,

Einstein remarked: "The issue

is not

as

simple

as

Abraham

thinks.

In

particular

the

principle

of

constant

c

and hence the

equivalence

of

the

four dimensions

are

lost"

("So

einfach,

wie Abraham

meint,

ist die

Angelegenheit

aber nicht. Insbesondere

geht

das

Prinzip

des konstanten

c

und damit die

Gleichwertigkeit

der vier Dimensionen

verloren") (Einstein

to

Wilhelm

Wien,

11

March

1912

[Vol. 5,

Doc.

371]).