DOC.

18

DISCUSSION OF DOC.

16 223

Doc.

18

"Discussion"

Following

Lecture Version of

"On the

Present State of the Problem of Gravitation"

[Physikalische Zeitschrift

14

(1913):

1262-1266]

Mie:

First

of

all,

I would like

to

round

out

Mr. Einstein's

interesting

lecture

by adding

a

few words

on

the historical

development

of the

theory.

Mr.

Einstein

passed over

this

very

briefly.

Nordström's

theory

takes off from Abraham's

investigations.

I

find

it

necessary

to

have it said here

that Abraham

was

the first

to

set

up

somewhat

reasonable

equations

for

gravitation.

While scientists before

him-after

all,

there do

exist several older

theories of

gravitation-always

tried

to

represent

the

gravitational

field much like the

electromagnetic

one,

Abraham found

a new

possibility.

For the

older

attempts

are

impossible

to

reconcile with the

principle

of

relativity;

because

if

the

principle

of

equality

of inertial and

gravitational mass

is to

be satisfied with

sufficient

exactness,

then the

gravitational

field

cannot

be

represented by a

six-vector.

For that

reason

Abraham first

put

forth

a

theory

with

a

scalar

gravitational potential.

I

would like

to write down the field

equations

with the scalar

potential

in the

somewhat

simplified

form that

I gave

them later. The

gravitational

field is described

with the aid

of

a

four-vector

(gx, gy, gz,

i

•

u),

which

one

can, however,

as

well

replace

by

another

one

(kx,

ky,

kv

i.w).

These

two

four-vectors

are

related

to

one

another in

a

fashion similar

to,

say,

the relation between the field

strength

and the electric

displacement

in the electric

field,

or

between the

stress

and deformation in

an

elastic

body.

In

addition,

the

description

of the

gravitational

field also includes

a

four-dimensional scalar

w,

which

may

be called the

gravitational potential.

The field

equations

then

appear

as

follows:

dtta_dw a«

_3G

*x=

dx'*y

dy'*z

dz'

dx'

dkx

^

dky

^

dkz

,

dw

=

"VP

dx

dy

dz

dt

where

y

denotes

a

universal

constant

and

p

the

density

of

the

gravitational

mass.

If

one

identifies

the two

vectors

(g,

i

•

u)

and

(k,

i

•

w),

one gets

the

equations

that

Abraham has

already

been

using. However,

he made the mistake

of

setting p

identical with the

density

of

the inertial

mass,

which, according

to the

theory

of

relativity is,

in

turn,

identical with the

energy density. However,

the left-hand side

of

the last

equation

is

a

four-dimensional

scalar,

an

invariant for the Lorentz transforma-

tion,

whereas

the

energy density

is

not

an

invariant, so,

of

course,

the

principle

of

relativity

cannot

be

satisfied in this

manner.

Nordström

improved

on

this

theory by substituting

for

p

a

quantity

that

is

invariant for the Lorentz transformation. At

about

the

same

time

as

he

did

so,

I also

[1]

[2]

[3]