700 DOC.

661

NOVEMBER

1918

I

have

studied

your paper

but

am more

than

ever

convinced

that

you

have

gotten

onto

a

very

dubious

track[4]

which

is

regrettably

costing you your

valuable

energy.

I

believe

you

are

placing

too much

importance

on

the beautiful

conserva-

tion

laws to which the

gauge

invariance[5] leads.[6]

It

is not

so surprising

that the

form of Maxwellian

electromagnetism

comes

out of it,

since

it

is

known

a

priori

that the

Maxwell

equations satisfy

the

gauge

invariance.[7]

The

question

is,

how-

ever,

whether the other

parts

of

the

action function

are gauge

invariant

as

well.

The

existence of

spectral

lines

(electrons

of

a

specific size), etc., speaks very

much

against it,

as

I

already

said

earlier.[8]

But

now

I

would

like

to

present you

with

another

counterargument

that

suggests

itself

from

your

latest

considerations.

I

make

the

following

preamble.

If

we

want to retain

the

common

units

for

mass

and

length

and

define

the

infinitesimal

displacement

in

your

geometric theory,

we

must

write,

instead

of

1

+

dQ,[9]

1

+

7dQ,

where

7

is

a

universal constant.

We

must do

this

if

we

set

dQ

=

Qvdxv,

where

Qv

signifies

the

four vector of

the

el[ectric]

potential

in

standard

units

(cm,

gr).[10]

In the Hamilton function

given on page

8

of

your paper,

which should be valid

at

least

outside

of electrons and

atoms,

we

must

then

write

72QiQi

instead of

QiQi,

and

on page (9), as

the

equation

for

the

electromagnetic

field,

dfik

_

3

Vff72

dxk 2

A

-p

.

In

this

connection

7

means

the

gravitational

constant.

(-

10-27.)[11]

This

field

equation is

easily

integrated

to determine

the

field

outside of

an

electron, whereby

it

is

legitimate

to select

guv

=

-1

0 0

0

0

-1

0

0

0

0

-1

0

0

0 0

1.

One

is

then

simply

led

to

the

equation[12]

AQ

=

-const

Q,

the

solution of which

is

e-r/r.[13]

For

Q4

to

come

out

practically

=

const/r,

[14]

l-

A-r

must

be

a

very large length (approximately

the

world

radius?) (measured