DOC. 9 FORMAL FOUNDATION OF RELATIVITY

31

do not have the

slightest

indication that the earth

moves

around the

sun

with

a

considerable

velocity.

But the confidence

we

have in

relativity theory

also has another root. One cannot

easily

close one's mind to the

following

consideration. When K' and K

are

two

coordinate

systems

in

relative uniform

translatory

motion to each

other,

then these

systems

are

completely

equivalent

from

a

kinematic

point

of

view.

We, therefore,

look in vain to find

a

sufficient

reason why one system

should be

more

suitable

as

a

system

of

reference for the formulation

of

laws

of

nature than another.

Instead,

we

feel

urged

to

postulate

the

equivalence

of

both

systems.

But this

argument immediately spawns

a

counterargument.

The kinematic

equivalence

of

these two coordinate

systems

is

by no means

limited to the

case

where

the two

systems

K and K'

are

in

uniform translatory

motion to each other.

From

the

kinematic

aspect,

this

equivalence

also

obtains, i.e.,

just

as well,

when both

systems

rotate

uniformly

relative to each other. One feels

pressed

toward the idea that the

existing theory

of

relativity

is in need

of

a

considerable

generalization

such that the

apparently unjust preference

for uniform

translatory

motion

over

other relative

motions has

to

be eliminated from the

theory. Everyone

who studied this

subject

in

detail must feel the desire for such

an

extension of the

theory.

[3]

At first

glance

it

appears

that such extension

of

the

theory

of

relativity

would

have to be

rejected on physical grounds.

Because: let there be

a

coordinate

system

K that is admissible

in

the

sense

of

Galilei-Newton,

and another

system

K' which is

in uniform rotation relative to

K; centrifugal

forces will then

act

on masses

which

are

at rest relative to

K' while

the

masses

which

are

at rest

relative

to K do

not suffer

such forces.

Already

Newton viewed this

as

proof

that the rotation

of

K' had to be

interpreted as

"absolute";

in other

words,

that K' cannot claim the

same right as

K

to

be considered

"at

rest." This

argument, however,

is-as

especially

E. Mach has

shown-not

cogent.

This is because

we

need not

necessarily

derive the existence

of

[4]

centrifugal

forces

from

a

motion of

K'; instead,

we can

just

as

well derive them from

the

averaged

rotational movement

of

distant

ponderable

masses

in the

environment,

but

relative

to

K',

thereby treating

K'

as

"at rest."

If

the Newtonian laws

of

[p.

1032]

mechanics and

gravitation

do not allow for such

interpretation,

it

may

well be

founded

in

deficiencies

of

this

theory.

The

following important

argument

also

speaks

in favor

of

a

relativistic

interpretation.

The

centrifugal

force which

acts

under

given

conditions

upon

a

body

is determined

by precisely

the

same

natural constant that

also

gives

its action in

a

gravitational

field. In

fact,

we

have

no means

to

distinguish

a

"centrifugal

field" from

a gravitational

field.

We

thus

always measure as

the

weight

of

a

body

on

the surface

of

the earth the

superposed

action

of

both fields named

above;

and

we

cannot

separate

their actions. In this

manner,

the

point

of

view to

interpret

the

rotating system

K'

as

at rest

and the

centrifugal

field

as

a

gravitational