238 DOC. 40 ON KOTTLER'S PAPER

being

at

rest,

such that

no

law

of

nature fails to be satisfied

relative to K'.

3.

The

Gravitational Field Not

Only Kinematically

Caused. The

previous

consideration

can

also be inverted. Let the

system

K' with the

gravitational field,

which

we

considered

above,

be the

original system.

One

can

then introduce

a

new

system

K that is accelerated with

respect

to K' such that

(isolated)

masses move

uniformly

in

straight

lines

(within

the domain of

consideration).

But

one

must not

go

beyond

this and

say:

If

K'

is

a

reference

system

with

an

arbitrary

gravitational field,

then

one can always

find

a system

K relative to which isolated

masses move

uniformly

in

straight

lines, i.e.,

relative to which

no gravitational

field exists. The

absurdity

of

such

a hypothesis

is

plainly

obvious.

If

the

gravitational

field relative

to

K'

is,

for

example,

that

of

a mass

point

at

rest,

then

not

even

the most refined trick

of

transformation

can

transform the field

away

in the entire

neighborhood

of

the

mass

point.

Therefore,

one

may

never

maintain that

a gravitational

field could be

explained, so

to

speak, by pure kinematics;

a

"kinematic, nondynamic interpretation

[4]

of

gravitation"

is

not

possible. By mere

transformation from

a

Galilean

system

into

[p.

641]

another

one by means

of

an

acceleration

transformation,

we

do not learn about

arbitrary

gravitational

fields

but

only

about

some

of

a very special

kind;

but these

too

must-of

course-obey

the

same

laws

as

all other fields of

gravitation.

This is

again

just

another formulation

of

the

principle

of

equivalence (specialized

in its

application

to

gravitation).

A

theory

of

gravitation

violates the

principle

of

equivalence-in

the

sense

as

I

understand

it-only if

the

equations

of

gravitation are

not

satisfied

in

any system

K'

of

reference which

moves nonuniformly

relative

to

a

Galilean

system.

It is

evident

that this accusation cannot be raised

against my theory

of

generally

covariant

equations,

because the

equations

are

here satisfied in

every system

of

reference.

The

postulate

for

general

covariance

of

the

equations

embraces the

principle of

equivalence as

a

special

case.

4.

Are

the

Forces

of

a

Field

of

Gravitation "Real" Forces?

Kottler

censures

that I

interpret

the second term in the

equations

of motion

d2xv +

E

aB

dXa

dxB

=0

aBdS

ds

as

an expression

of

the influence

of

the

gravitational

field

upon

the

mass point,

and

the first

term

more

or

less

as

the

expression

of

the Galilean inertia.

Allegedly

this

would introduce "real forces

of

the

gravitational

field" and this would not

comply

with the

spirit

of

the

principle

of

equivalence. My answer

to this is that this

equation

as a

whole is

generally

covariant,

and therefore is

quite

in

compliance

with the

hypothesis

of

equivalence.

The

naming

of the

parts,

which I have

introduced,

is in

principle meaningless

and

only

meant to

appeal

to

our physical

habit

of

thinking.