DOCS.

661,

662 NOVEMBER-DECEMBER

1918 701

in

cm,

a

very large

number

indeed!).

The order of

magnitude

of

1/r

is

hence in

any

case

well

over

1/A ~

1013.

This universal

constant

has

the dimension of

an

electricity

quantity and must be

of

immense

size if

the

theory is

not to violate

the

known laws of electrostatics. Not

the

slightest

hint

of

this

can

be

found in

the

known laws of nature.

It

therefore

seems downright

insane to introduce

such

a

thing

for

the

sake of

the

gauge

invariance! This

surely

is

a

very

serious

objection.

Moreover,

I

absolutely

cannot

concede

that

your

theory

leads to

the

equation

of motion

d{mui)

ds

1

dgaß

2 dxi

muau13

=

0

because

this

expression,

in which

m

is

supposed

to be

constant,

of

course,

is

invariant neither

against

coordinate

nor gauge

transformation.[15] In

your

consid-

eration

you

cannot

assume a

priori

that the

Qi’s

do not

yield any moving

forces.

The

special

role of

the

electrically uncharged point-mass

consists in

that

its

path

does not

depend on

the

electrical

field

fik.

I

am

convinced,

now as

before,

that

from

the

aspect of invariance and

gauge invariance,

the

geodesic

line

is

the

only

one

that

can come

into consideration at

all.-[16]

Furthermore, I

do

not

see

how

the introduction

of

a gauge according

to

F

=

a

is

possible,

even

though

one can

make free

use

of

a

gauge

factor.[17]

It

may very

well

be

possible,

for

inst.,

that

any

attempt

at

imposing

such

a

gauge

would

bring

about

singularities.-

My

first

objection

seems

to

me

by

far

the

most

substantial: the

gauge

invari-

ance

leads to

a

modification

of

the

laws,

which not

a

single

fact

supports,

and

also

leads to

a new

natural

constant

that

is

meaningless, according

to

current

knowledge.

Added

to

this

is

that

the

existence

of

spectral lines, i.e.,

of clocks

independent of their

prehistory,

makes the

only

natural

way

seem

to

be

treating

ds

as an

invariant

from

the

beginning.

I

am

already looking

forward

to

being

able to

chat-and

argue-with

you

in

February.

Until

then, cordial

regards, yours,

Einstein.

662. From Arnold Sommerfeld

[Munich,] 3

December

1918

Dear

Einstein,

For

a

particular

purpose (a

popular

book

on

atomic

models)

I

need

a

simple

description

of

the

foundations

of

quantum

statistics.[1] For

that

I

must make