DOCUMENT 627 SEPTEMBER 1918 895

[1]Weyl

1918d,

in which the author

systematically

developed

the mathematical foundation

of

the

unified

theory

of

gravity

and

electromagnetism

first

presented

in

Weyl

1918b

(see

Doc.

472,

note

3,

for

more

details

on

this

theory).

[2]Doc.

619.

[3]In

Weyl

1918d,

geometry

is

developed

in three

stages

(as

Weyl explained

in Doc.

619). First,

a

manifold with

just a topology

is

considered,

then

an

affine connection is added, and

finally a

metric.

[4]Einstein had raised this

objection

in Doc. 551

(for

a

brief

discussion,

see

Doc.

551, note 9).

[5]See

Docs. 507 and 512

for

Einstein’s fundamental

objection

to

Weyl’s theory.

[6]A

month

earlier,

Einstein had written

to

Michele Besso

that

one

cannot formulate

a

sensible

energy

conservation law in

Weyl’s theory (see

Doc.

604).

[7]In Doc.

619,

Weyl suggested

this

gauge

invariant definition

of

length

in

response

to the

objection

that the line

element

loses its

physical

significance

in his

theory.

[8]Which

means

that

Weyl’s theory

would still

run

into the

problem

that the

rate

of

a

clock is

dependent upon

its

prehistory

and would thus

be incompatible

with the existence

of

spectral

lines.

[9]In response

to

Einstein’s criticism,

in

Doc. 579,

that

the

electromagnetic

four-vector

potential

affects

the motion

of

uncharged particles, Weyl pointed out,

in Doc.

619,

that

it is

not

clear whether

the

trajectories

of

uncharged

particles

are

geodesics

in his

theory.

[10]Einstein’s

argument appears

to be the

following.

The

geodesic equation

in

Weyl’s theory con-

tains force

terms

proportional

to

the

vector

potential

(Q1, Q2,

Q3).

Consider

an uncharged particle

moving along a

closed field line

of

the

vector

potential,

and

assume

that the

space-time trajectory

of

this

particle

is

a geodesic

in

Weyl’s theory.

For

every

revolution

of

the

particle

around the closed

loop,

an

amount of work is

done

that is

given by

the

loop integral

of the vector

potential.

After

every revo-

lution, the initial situation will be

restored, yet

the

system

has

gained energy.

[11]One of

the

attempts

to

give a

unified treatment of the

"gravitation

terms" and the "A-terms" that

Einstein

may

have had in mind here is the

suggestion

that he made in Doc. 591 and retracted in

Doc. 604:

to

introduce the

cosmological

constant

as a

constant

of

integration

rather

than

as a

universal

constant

of

nature.

[12]On

Charles St. John’s

measurements,

see

Doc.

619, note 19.

[13]Erwin

Freundlich

inspected

the construction

of

such

an oven

at

the firm Badische Anilin- und

Sodafabrik in

Ludwigshafen a

year

later

(see

Erwin

Freundlich

to Einstein, 15

September

1919 and

3

October

1919).

[14]Einstein

had informed Heinrich

Zangger

and

Edgar Meyer

of

his refusal in

mid-August

(see

Docs. 601 and

602).

[15]Weyl

had,

in

mid-September, explained

that he had declined the

position

at

the

University

of

Breslau for

reasons

of

health

(see

Doc.

619).

[16]A

month

earlier,

Einstein had written that he considered

Weyl

the

superior

lecturer

(see

Doc.

597).

[17]The

winter

semester at

the

University

of

Berlin

began on

30

September

(see

Doc.

631, note

2).

627.

From Eduard

Study

Bonn,

Argelanderstrasse

126 27. 9. 1918

Hochgeehrter

Herr

College,

Ihr niedlcher

zweiter Brief

hat

mir

ebenfalls viel

Vergnügen

bereitet.[1] Vielen

Dank

dafür,

wie

auch

für die freundliche

Übersendung

Ihres

Büchleins,

das ich

gleich gelesen

habe.[2]

Das Meiste kannte ich

schon,

muss es

aber natürlich

später

noch

gründlicher

studieren.

Aber

warum

fürchteten

Sie,

mir wehe

zu

thun?

Jeder

vernünftige

Autor

freut sich doch

einer

vernünftigen

Kritik,

aus

der

er

lernen kann.