416

DOC.

42

SPECIAL AND GENERAL RELATIVITY

Relativity

and

the Problem of

Space

177

Thus

Descartes

was

not

so

far

from

the truth

when he

believed he

must

exclude the existence

of

an

empty space.

The

notion indeed

appears

absurd,

as long

as

physical

reality

is

seen

exclusively

in

ponderable

bodies.

It

requires

the

idea

of

the

field

as

the

representative

of

reality,

in combination

with the

general principle

of

relativity,

to

show the

true

kernel

of Descartes'

idea;

there

exists

no

space

"empty

of field."

Generalised

Theory

of

Gravitation

The

theory

of

the

pure

gravitational

field

on

the

basis

of

the

general theory

of

relativity

is

therefore

readily

obtainable,

be-

cause we

may

be confident

that the

"field-free" Minkowski

space

with its metric in

conformity

with

(1) must satisfy

the

general

laws

of

field.

From this

special

case

the

law

of

gravi-

tation

follows

by

a

generalisation

which

is practically

free from

arbitrariness.

The

further

development

of

the

theory

is

not

so

unequivocally

determined

by

the

general principle

of

relativ-

ity;

it has been

attempted

in

various directions

during

the

last

few decades. It

is

common

to

all

these

attempts, to

conceive

physical reality

as a

field,

and

moreover,

one

which

is

a

gen-

eralisation

of

the

gravitational

field,

and in which the field

law

is

a

generalisation

of

the

law for

the

pure gravitational

field.

After

long probing

I

believe

that

I

have

now

found1

the

most

1

The

generalisation

can

be characterised

in

the

following way.

In accordance with its derivation

from

empty

"Minkowski

space,"

the

pure gravitational

field

of the functions

gik

has the

property

of

symmetry given by

gik = gki (g12 =

g21,

etc.).

The

generalised field

is

of

the

same

kind, but

without this

property

of

symmetry.

The

derivation

of

the

field

law

is completely analogous

to

that

of the

special case

of

pure gravitation.