108

DOC. 22 ADDENDUM TO DOC.

21

[p.

799]

[p. 800]

Doc. 22

On the General

Theory

of

Relativity

(Addendum)

by

A. Einstein

In

a

recent

investigation1

I have shown how

Riemann’s

theory

of

covariants

in

multidimensional manifolds

can

be utilized

as a

basis for

a theory

of

the

gravitational

field. I

now

want to show here that

an even more

concise and

logical

structure of the

theory can

be achieved

by introducing an admittedly

bold additional

hypothesis on

the

structure

of

matter.

The

hypothesis

whose

justification we

want

to

consider relates to the

following

topic.

The

energy

tensor

of

"matter"

Tyu

has

a

scalar

^

Tff,

whose

vanishing

for

the

electromagnetic

field is well known. In

contrast,

it

seems

to

differ from

zero

for

matter

proper.

Because,

if

we

consider the

most

simple special

case,

that

of

an

"incoherent" continuous fluid

(with pressure

neglected),

then

we are

used to

writing

.-

dx" dxv

T•"

=

\f~gPo~7^

~7~",ds

ds

and

we

have

£

K

=

£sMVr-

=

Po^-

n

Iiv.

The scalar

of

the

energy

tensor

does

not

vanish in this

approach.

One

now

has to remember that

by our knowledge

"matter" is not to be

perceived

as

something primitively given or physically plain.

There

even

are

those,

and

not

just

a

few,

who

hope

to

reduce

matter

to

purely electrodynamic processes,

which

of

course

would have to be done

in

a

theory more completed

than

Maxwell’s

electrodynamics.

Now

let

us just assume

that

in such

completed electrodynamics

the

scalar

of

the

energy

tensor also would vanish! Would the

result,

shown

above, prove

that matter cannot be constructed in this

theory?

I

think I

can answer

this

question

in the

negative,

because it

might very

well be that in

"matter,"

to which the

previous

expression relates, gravitational

fields

do

form

an

important

constituent.

In

that

case,

^

TMM

can appear positive

for the entire structure while in

reality only

£

(Tj¡

+

t¡f)

is

positive

and

]jT

T£

vanishes

everywhere.

In the

following we assume

the

conditions

^7Tmm

=

0

really to

be

generally true.

1These

Sitzungsberichte, p.

778.