342

DOC. 13 GENERALIZED THEORY OF RELATIVITY

[35]For

Einstein's earlier discussion of the effect of

a

static gravitational field

on

electro-

magnetic processes,

see

Einstein 1912d

(Doc. 4),

§§1

and

2.

[36]See note 25 above.

[37]Kottler

1912,

§3. Following

the earlier work of

Minkowski,

Sommerfeld,

and

Laue

on

four-dimensional

electrodynamics,

Kottler

was

the first to

use

the

absolute differential

calculus

of Ricci and Levi-Civita

to express

Maxwell's

equations

in

generalized

coordinates-without,

however,

relating

this

work

to the

problem

of

gravitation.

For

a

later evaluation of

his

own

work,

see

Kottler

1922,

pp.

189-190.

[38]See

also the introduction of these

quantities

in

Einstein's research

notes

on a

generalized

theory

of

relativity (Doc. 10),

[p.

53].

[39]Einstein

discusses covariant

electrodynamics

in his

unpublished manuscript

on

special

relativity

(Doc.

1),

[pp.

55-70];

see

also

[p.

48]

for

Einstein's introduction of the

term

"six–

vector"

("Sechservektor"), following Sommerfeld

1910a,

p.

753. Calculations related

to

the

equations

below

are

found

on

[pp.

53-57]

of Einstein's research

notes

on a

generalized

theory

of

relativity

(Doc. 10).

[40]Equations

similar

to the

following

ones

appear

on [p. 57]

of

Einstein's research

notes on

a

generalized theory

of

relativity

(Doc. 10).

[41]dt

in

the second

term

should

be

dy.

[42]As

is

evident from

subsequent

discussions,

the

following argument against

a

scalar

theory

of

gravitation

was

mainly

directed

against

Nordström's

theory (Nordström 1912). Shortly

after

the

publication

of the

present

paper,

Einstein retracted the

argument (see

Einstein 1913c

[Doc.

17],

p.

1253,

and Einstein 1914d

[Doc. 26], p.

261).

For Nordström's reaction

to

Einstein's

argument,

see

Nordström 1913b,

pp.

544-546. For historical discussions of Nordström's scalar

theory

of

gravitation,

see

Isaksson

1985,

Norton

1992b,

and the

editorial

note,

"Einstein

on

Gravitation and

Relativity:

The Collaboration with Marcel

Grossmann,"

pp.

298-300.

[43]See

Laue

1911a,

p.

74.

Einstein had mentioned

this

scalar earlier

in

his

manuscript

on

special relativity (Doc.

1), [p.

50].

[44]Nordström discussed

the

implications

of the

equality

of inertial and

gravitational

mass

for his scalar

theory

of

gravitation in

Nordström

1913a.

[45]Christoffel

1869.

[46]Ricci

and Levi-Civita

1901.

[47]In

chaps. 5

and 6

of

Ricci

and Levi-Civita

1901

the absolute differential calculus

is

applied

to

various

examples

from

physics,

such

as

dynamics, electrodynamics,

heat

conduction, and

elasticity.

[48]See,

e.g.,

Minkowski

1908, Sommerfeld 1910a, 1910b,

Laue

1911a,

1913.

[49]Kottler

1912.

[50]For

a

discussion of the influence of the

algebraic

tradition

in

the

study

of differential

forms

on

Grossmann's

presentation,

see

Reich

1994,

sec.

4. For

a

history

of

the

later

geometrical

interpretation

of fundamental

concepts

of

general relativity,

see

Reich 1994,

sec.

5.3.

[51]For evidence that the

general

definition of

a

tensor

given

in

the

following

was new

in

the

mathematical literature of

the

time,

see

Budde

1914,

p.

246;

see

also the editorial

note,

"Einstein

on

Gravitation

and

Relativity:

The Collaboration with Marcel

Grossmann,"

p.

296.

[52]See

Ricci and Levi-Civita

1901,

p.

131.

[53]For

this

terminology,

see

Ricci and Levi-Civita

1901,

p.

134.

[54]Minkowski

1908.

[55]Sommerfeld

1910a,

1910b.

[56]Laue 1913.

[57]Christoffel

1869,

p.

57.

Christoffel

did

not,

however,

use

the

terminology

of

tensors and

covariant differentiation

but

referred

only to

the transformation

properties

of differential forms.

See

also Einstein's

manuscript

on

special relativity

(Doc.

1), [p.

53],

and

his research

notes

on

a

generalized theory

of

relativity (Doc. 10),

[p.

15],

for earlier introductions of similar

operations.

[58]See

Ricci and Levi-Civita

1901,

p.

138,

where

they

also

refer

to

the earlier work

by

Christoffel

(Christoffel

1869).