222 DOC.

17

PROBLEM OF GRAVITATION

§10. Concluding

Remarks

In the

foregoing

discussion

we

have sketched the

most

natural

paths

that the

theory

of

gravitation

can

follow. One either sticks with the

ordinary theory

of

relativity,

i.e.,

assumes

that the

equations expressing

the laws of

nature

remain covariant

only

with

respect

to

linear

othogonal

substitutions. In that

case one can

set

up

a

scalar

theory

of

gravitation

(the

Nordström

theory),

which is rather

simple

and which satisfies the

main

requirements

to

be

imposed upon a theory

of

gravitation

but

does

not

include

the

relativity

of inertia

among

its

consequences.

Or

one

extends the

theory

of

relativity

in the

manner

sketched here. It is

true

that in that

case one

arrives

at

equations

of

considerable

complexity;

but,

in

exchange,

the

equations

to

be

sought

follow from the basic

premises

with the

help

of

surprisingly

few

hypotheses,

and

one

satisfies the

conception

of the

relativity

of

inertia.

Whether the

first

or

the second

path corresponds

in

essence

to

nature

must

be

decided

by photographs

of

stars

appearing

close

to

the

sun during

solar

eclipses.

Let

us hope

that the solar

eclipse

of

1914

will

already bring

about this

important

decision.

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