314 DOC.

31

ON THE RELATIVITY PROBLEM

=

E

/XV

which

is

an

invariant, i.e.,

a

quantity independent

of the choice of the reference

system

(i.e.,

of the choice of the four

space-time

coordinates).

The

quantities

guv are

functions

of

x1

..

x4

and

serve

to

represent

the

gravitational

field.

With the

help

of

the

absolute differential

calculus,

which

was

developed by

Ricci

[23]

and Levi-Civita

on

the basis of Christoffel's mathematical

investigations,

it

is

possible,

based

on

the existence of the above

invariant, to

replace

the familiar

systems

of

equations

of theoretical

physics by

such

equivalent systems (in

the

case

of

constancy

of all of the

guv)

that hold

totally independently

of the choice of the

space-time

coordinates

xv.

All such

systems

of

equations

contain the

quantities guv,

i.e.,

the

quantities

that determine the

gravitational

field. The latter therefore have

an

influence

on

all

physical processes.

Conversely,

the

physical processes

must

also determine the

gravitational field,

i.e.,

the

quantities guv.

One arrives

at

the differential

equations

that determine these

[24] quantities by means

of the

hypothesis

that the

momentum and

energy

conservation

[25]

laws

must

hold for the material

processes

and the

gravitational

field taken

together.

[26]

This

hypothesis

also

restricts,

after the

fact,

the choice of the

space-time

variables

x,

[27]

without, however,

arousing again

the

epistemological

doubts

analyzed

earlier.

Because

according

to

this

generalized

theory

of

relativity,

physical properties peculiar

to

privileged spaces

no

longer

exist.

The

course

of all

processes

is

governed by

the

quantities guv,

which

are

in

turn

determined

by

the

physical happenings

in

all

of the

rest

of the universe.

The

principle

of the inertia and the

gravitation

of

energy

is

completely

satisfied

in this

theory.

Further,

the laws of motion of

gravitational

masses are

such that

it is

not

absolute acceleration

(acceleration

with

respect

to

"space")

that

appears

as

that

which

is

decisive for the

occurrence

of inertial

resistance,

but

instead-as

must

be

demanded

on

the basis of

the

above

considerations-acceleration

with

respect

to other

[28]

bodies.

The

theory

of

relativity

in the broader

sense

does

not

signify

the abandonment

of the earlier

theory

of

relativity,

but rather

a

further

development

of the latter that

seems

to

me

necessary

for the

epistemological

reasons I

pointed

out.

Zurich, Polytechnic.

A.

Einstein