DOC. 22 ADDENDUM TO DOC.

21 109

Whoever

does

not

categorically

reject

the

possibility

that

gravitational

fields

could constitute

an

essential

part

of

matter

will find

powerful support

for this

conception

in

the

following.2

Derivation

of

the Field

Equations

Our

hypothesis

allows

us

to take the last

step

that the idea of

general relativity may

consider

as

desirable. It allows

us,

namely,

also to write the field

equations

of

gravitation

in

a

general

covariant form. I have shown in the

previous paper (equation

(13))

that

Gim

=

£

(il, lm)

= Rim

+

Sim

I

(13)

is

a

covariant tensor. And

we

had

im)

*»--E

a

«

p m

/

dX[

I

(13a)

S:im

(13b)

This tensor

Gim

is the

only

tensor available

for

the establishment of

generally

covariant

equations

of

gravitation.

We have

won

generally

covariant field

equations

if

we agree

that the field

equations

of

gravitation

should be

Guv = -KTuv.

(16b)

These,

together

with the

generally

covariant

laws,

provided

for

by

the absolute

differential

calculus, express

the causal

nexus

for "material"

processes

in

nature;

and

they express

it in

a

form that

emphasizes

the fact that

any special

choice of

coordinate

system-which

logically

has

nothing

to do with nature's law anyway-is

[p. 801]

not

used in the formulation

of

these laws.

2In

writing

this

paper

I

was

not

yet

aware

that

the

hypothesis

^

T*

=

0

is,

in

principle,

admissible.