98

DOC. 21 GENERAL RELATIVITY

Doc.

21

On

the

General

Theory

of

Relativity

Plenary

Session of November

4,

1915

[p.

778]

My

efforts in

recent

years

were

directed toward

basing

a

general theory

of

relativity,

[1]

also for nonuniform

motion, upon

the

supposition

of

relativity.

I believed indeed

to

have found the

only

law of

gravitation

that

complies

with

a reasonably

formulated

postulate

of

general relativity;

and

I

tried to demonstrate the truth of

precisely

this

solution in

a paper1

that

appeared

last

year

in

the

Sitzungsberichte.

Renewed criticism showed to

me

that this truth is

absolutely impossible

to show

in the

manner suggested.

That this seemed to be the

case

was

based

upon

a

misjudgment.

The

postulate

of relativity-as

far

as

I

demanded it

there-is

always

satisfied

if

the Hamiltonian

principle

is chosen

as a

basis.

But

in

reality,

it

provides

no

tool

to

establish the Hamiltonian function H of the

gravitational

field.

Indeed,

equation (77)

l.c.

which limits the choice of H

says only

that

H

has

to

be

an

invariant

toward linear

transformations,

a

demand that has

nothing

to do with the

relativity

of

accelerations.

Furthermore,

the choice determined

by equation

(78)

l.c. does not

[3]

determine

equation

(77)

in

any

way.

For these

reasons

I

lost trust in the field

equations

I

had

derived,

and instead

looked for

a

way

to

limit the

possibilities

in

a

natural

manner.

In this

pursuit

I

arrived

at

the demand

of

general

covariance,

a

demand from which

I

parted, though

with

a

heavy

heart,

three

years ago

when

I

worked

together

with

my

friend

Grossmann.

As

a

matter

of

fact,

we were

then

quite

close

to

that solution

of

the

problem,

which will

be

given

in the

following.

Just

as

the

special theory

of

relativity

is

based

upon

the

postulate

that all

equations

have

to

be covariant relative

to

linear

orthogonal

transformations,

so

the

[p.

779] theory developed

here

rests

upon

the

postulate

of the covariance

of

all

systems

of

equations

relative

to

transformations

with

the substitution determinant

1.

Nobody

who

really grasped

it

can

escape

from its

charm,

because it

signifies

a

real

triumph

of

the

general

differential calculus

as

founded

by

Gauss, Riemann,

Christoffel,

Ricci,

and

Levi-Civita.

[2]

1"Die formale

Grundlage

der

Relativitätstheorie," Sitzungsberichte

41

(1914), pp.

1066-1077.

Equations

of

this paper

are

quoted

in

the

following

with the additional note

"l.c." in order to

keep

them distinct from those in the

present paper.