148

DOC. 30 FOUNDATION

OF GENERAL RELATIVITY

For

the

laws

of

geometry, even

according

to the

special theory

of relativity,

are

to

be

interpreted directly

as

laws

relating

to

the

possible

relative

positions

of solid bodies

at rest;

and, in

a

more

general way,

the

laws of

kinematics

are

to be inter-

preted

as

laws

which

describe

the relations

of

measuring

bodies

and

clocks.

To two

selected

material

points

of

a

stationary rigid body

there

always corresponds

a

distance

of

quite

definite

length,

which

is

independent of

the

locality

and

orientation of

the

body,

and is also

independent

of

the time.

To

two selected

positions

of

the hands

of

a

clock at

rest

relatively

to

the

privileged

system

of

reference there

always

corresponds

an

interval

of

time

of

a

definite

length,

which

is

independent

of

place

and

time.

We

shall

soon

see

that the

general theory

of

relativity

cannot

adhere

to

this

simple

physical interpretation

of

space

and

time.

§

2.

The Need

for

an

Extension

of

the Postulate

of

Relativity

[7]

In

classical mechanics,

and

no

less

in the

special theory

of

relativity,

there

is

an

inherent

epistemological

defect which

was,

perhaps

for

the first

time,

clearly

pointed

out

by

Ernst

Mach. We

will

elucidate it

by

the

following

example:-Two

fluid

bodies

of

the

same

size

and nature hover

freely

in

space

at

so great

a

distance

from

each other and

from all

other

masses

that

only

those

gravitational

forces need be

taken into

account

which arise

from the interaction

of different

parts

of

the

same

body.

Let the

distance between

the

two

bodies be

invariable, and

in

neither

of

the

bodies

let there be

any

relative

movements of

the

parts

with

respect

to

one

another.

But let either

mass,

as judged by an

observer

at

rest

relatively

to

the other

mass,

rotate

with

constant

angular

velocity

about the

line

joining

the

masses.

This is

a

verifi-

able

relative motion

of

the two

bodies. Now

let

us

imagine

that

each

of

the

bodies has been

surveyed by

means

of

measuring

instruments

at rest

relatively

to

itself,

and let the

surface of

S1

prove

to

be

a sphere,

and that

of

S2

an ellipsoid

of

revolution.

Thereupon

we

put

the

question-What

is

the

reason

for this

difference

in the

two

bodies?

No

answer can