106

DOC.

1

MANUSCRIPT ON SPECIAL

RELATIVITY

[73]See §9.

[74]The argument

of

this

paragraph

follows Einstein

1905s

(Vol. 2,

Doc.

24).

[75]At

this

point

in the

original text

Einstein indicates

a

note

he has

appended at

the foot of

the

page: "Inbezug

auf E' verschwindet die Summe der

Impulse

beider

Wellenzüge."

[76]See

Einstein

1907j

(Vol.

2,

Doc.

47),

pp.

442-443,

for similar

calculations.

[77]In

a

letter

to

Wilhelm

Wien

of

10

July 1912

(Vol. 5,

Doc. 413)

Einstein

inquired

whether

a test

of

the proportionality

of inertial

and gravitational

mass

for radioactive bodies

was

exper-

imentally

feasible. The

importance

of such

a

test is

also

emphasized

in

Einstein

1912h

(Doc.

8), p.

1062.

[78]See

the historical discussion of

contemporary experiments

in Vol.

2,

the

editorial

note,

"Einstein

on

the

Theory

of

Relativity,"

pp.

270-271.

[79]Beginning

with

the words "Vektor- und

Tensoren-Theorie," the

remainder of

this

head-

ing

is

written

in

dark

ink

and

replaces

the

deleted

word "Geometrie." For

a

discussion of the

relationship

between

geometry

and

tensor

calculus

as

tools for

Einstein's

development

of

a

generalized theory

of

relativity,

see

the

editorial note, "Einstein

on

Gravitation

and Relativity:

The

Collaboration

with Marcel Grossmann."

[80]"a31y" in the

third

equation

below should

be

"a32y."

[81]See,

e.g.,

the

discussion

in Minkowski 1909.

[82]These

questions

are

not

literal

quotations

from Minkowski's

writings.

[83]For

Minkowski's characterization of

the

laws of

physics in

a

four-dimensional world,

see

Minkowski

1908,

p.

57,

where

he

states:

"The entire world

appears to be

resolved into such

world

lines, and

I

would like

to state at

the

outset

that

in

my

view the

physical

laws should

find

their

most perfect expression

in the

interrelations

among

these world lines"

("Die ganze

Welt

erscheint

aufgelöst

in

solche

Weltlinien, und ich möchte

sogleich vorwegnehmen,

dass meiner

Meinung

nach

die

physikalischen

Gesetze

ihren

vollkommensten

Ausdruck

als

Wechselbezie-

hungen

unter

diesen Weltlinien

finden

dürften").

[84]See Einstein

and

Grossmann 1913 (Doc.

13),

part 2,

for

a

systematic treatment

of

tensor

calculus. For

a

brief discussion of

the

contemporary understanding

of

tensors

as

well

as

of Ein-

stein's

and

Grossmann's contribution

to tensor

calculus,

see

the

editorial note, "Einstein's

Research Notes

on

a

Generalized

Theory

of

Relativity,"

secs.

II and III.

[85]Einstein

follows

Sommerfeld's rather than Minkowski's

terminology (see Sommerfeld

1910a,

p.

750).

This

terminology

is

also used

in

Laue

1911a.

[86]For

Sommerfeld's

definition of

an

axial

vector,

see

Sommerfeld

1910a,

p.

750;

for

Laue's

definition,

see

Laue

1911a,

p.

60.

[87]At this

point in

the

original text

Einstein indicates

a

note

he has

appended at

the foot of

the

page:

"Wir wollen solche Vierervektoren wie Laue mit

den grossen

Buchstaben

des

griechischen Alphabeths

bezeichnen."

See

Laue

1911a,

p.

61.

[88]From

this

point

on

the

manuscript is

written

on

paper

of Swiss manufacture.

[89]Einstein's

use

of

parentheses to distinguish

between

vectors

(or tensors) and

their

com-

ponents

is

not

common

in

the

contemporary

literature,

including

Einstein's

own

writings.

For

exceptions,

see

Einstein and Fokker

1914 (Doc.

28),

pp.

322-323, and

Einstein's lecture

notes

for

his

course on

electricity

and

magnetism at

the ETH

in

winter

semester

1913/1914

(Doc.

19).

[90]Einstein's

general

definition of

a

tensor implies

the

existence of sixteen rather than of

ten independent components.

It

was,

however,

customary at

the time

to

restrict

the

notion of

a

tensor to

what

are now

called

symmetric,

second-rank

tensors (see Sommerfeld

1910a,

p.

767).

[91]Neither

Minkowski,

nor

Sommerfeld,

nor

Laue makes

use

of

a

general tensor concept

as

it

is

defined here.

[92]This

notation is

neither

common

in the

literature of the time

nor

is

it

found

in

other

con-

temporary

writings

by

Einstein.

[93]For

a

systematic

discussion

of

vectors

as

second-rank,

antisymmetric

tensors,

see

Ein-

stein and Grossmann

1913 (Doc.

13),

part 2,

§3.

[94]"ein

Tensor" should

be

"eines Tensors."

[95]See

Sommerfeld

1910a,

p.

753.