652 DOCUMENT 465 FEBRUARY 1918

[5]Schlick

emphasizes

the word

"willkürlichen"

in the

previous sentence.

[6]See

Doc. 456.

[7]In

the

draft,

there is

a

deleted line

at

this

point repeating

the actual

objection

that Einstein

men-

tioned in Doc. 460: "derselbe

Körper

könne nicht

zugleich

ruhend und

bewegt

sein."

[8]This

example

is also

given

in Mie

1917c,

p.

598.

[9]A

similar

argument

is

put

forward

by

Hendrik A. Lorentz in Doc. 43 and

by

Franz

Selety

in

Doc. 364. See also Einstein’s

response

to

Lorentz in Doc. 47.

[10]The

crucial difference between

going

from rest

to

uniform motion and

going

from

rest to

accel-

erated

motion in Minkowski

space-time

is that the former

case corresponds

to

a symmetry-transfor-

mation

of

the

space-time

metric,

whereas the latter does

not.

Mie would

return to

the

problem

of

an

electron in circular motion in Mie 1920b.

[11]Presumably

the discussion

following one

of

Mie’s Wolfskehl lectures

of

June

1917,

published,

in revised form and without the

discussion,

as

Mie

1917a, 1917b,

and 1917c.

[12]Erich

Justus Kretschmann (1887-1973)

was a

substitute

high

school

teacher

in

Königsberg.

In

Kretschmann

1917,

the author criticizes the notion

of

a relativity principle

used

by

Einstein,

accord-

ing

to

which

a theory

satisfies

a relativity principle

associated with

some group

of

coordinate

trans-

formations

if

its laws

are

covariant

under

those transformations.

Since,

Kretschmann

argues, any

physical

law

can

be stated in

generally

covariant

form,

any theory

can,

in this

sense,

be made to

satisfy

the broadest

possible relativity principle.

Kretschmann

proposes a

different notion

of

a relativity prin-

ciple,

which is

fully independent

of

the form in which the laws

of

a theory are

stated.

Consider

a

theory

in which the

physically possible trajectories are given by

the

geodesics

of

the

space-time

geometries

it

allows;

and consider

symmetries common

to

the

sets

of

all

geodetic trajectories

for all

allowed

space-time geometries. According

to

Kretschmann’s

definition,

the

theory

satisfies

a partic-

ular

relativity principle,

if

and

only

if

the transformations associated with that

relativity principle cor-

respond

to

such

symmetries (Kretschmann

1917,

sec. 26).

Since the set

of

geodesics

of

some

intri-

cately

curved

space-time geometry

allowed

by general relativity

will,

in

general,

have

no

nontrivial

symmetries,

Kretschmann concludes

that,

in this

new

sense,

general relativity

does

not

satisfy any

rel-

ativity principle

at

all. To arrive

at

theories that

do,

he

continues,

one

has

to

add further

requirements

to

the laws

of

general relativity

that restrict the allowed

space-time geometries

to

those with the

appropriate symmetries.

In the

concluding secs.

27-29 of

his

paper,

Kretschmann

argues

that,

in order

to

satisfy a general principle

of

relativity, a theory

would have

to

allow

arbitrary

rather

than

just geo-

detic

trajectories.

Since

such

a theory

would be

highly unrealistic,

Mie

can

refer

to

this

argument as

a

proof

of the

impossibility

of

having a general

principle

of

relativity.

A

large portion

of

Kretschmann’s

paper

(secs. 13-22)

is devoted

to

constructing special

coordi-

nate

systems

in

general relativity.

At the

beginning

of

this

discussion,

Kretschmann

acknowledges a

letter from Mie

of

February

1916 for

a

useful

suggestion

in this

context

(Kretschmann

1917,

p.

592,

fn.

1).

For Einstein’s

response

to

Kretschmann's

paper, see

Einstein

1918f

(Vol.

7,

Doc.

4).

For further

discussion

of

Kretschmann’s

paper, see

Norton

1992a,

sec.

8,

and Norton

1993,

sec.

5.

[13]Mie’s

"axiom

of

the

general relativity

of

the

gravitational

field"

("Axiom

von

der

allgemeinen

Relativität des Gravitationsfeldes"; Mie

1917c,

p.

597),

a generalization

of

his

earlier

principle

of

the

relativity

of

the

gravitational potential (see

Doc.

346,

note 3,

for

further

discussion).

[14]In

the

draft,

Mie deleted the

following passage:

"hoffentlich

...

werde ich Sie dann auch für

diese

Auffassung gewinnen."

[15]The

following part

of

the

text,

which deals with the modified field

equations

and the

cosmolog-

ical model

proposed

in Einstein 1917b

(Vol. 6,

Doc.

43)

departs substantially

from the

draft,

with the

exception

of

the first

two sentences

and the closure.

Following

the

two sentences,

the draft continues:

"Ich bin

nun

aber recht entsetzt

zu

merken,

dass in

der

neuen

Theorie

überhaupt

gar

nichts mehr

von

den

Prinzipien gilt,

die ich

bisher

als die schönsten in

Ihrer

Gravitationstheorie

angesehen

habe. Das

Prinzip

der

Relativität der

Bewegungen gilt

sicherlich nicht

mehr,

weil ja im Weltraum selber die

Zeitaxe eine andere Rolle

spielt

als die drei räumlichen

Axen,

es muss

also Versuche

geben,

die nicht

mehr wie der Michelsonsche Versuch ein

negatives

Resultat

geben, vorausgesetzt,

dass

man

die

Genauigkeit

weit

genug

treiben kann. Vor allem aber

wird,

soviel ich

sehe,

auch das

Prinzip von

der

Relativität des

Gravitationspotentials ungültig,

weil ein Teilchen

nur an

einer

Stelle

existenzfähig

ist,

wo p

und damit

zugleich

das

Gravitationspotential

einen bestimmt

vorgeschriebenen

Wert hat. An