416

DOC.

41

HAMILTON'S

PRINCIPLE

Published

in

Königlich Preußische

Akademie

der

Wissenschaften (Berlin). Sitzungsberichte

(1916):

1111-1116. Submitted

26

October

1916, published

2

November

1916. A

fragmentary

three-page manuscript

version of

all

but the last

two paragraphs

of

§3

of the

paper

and

an

ad-

ditional

page

of related calculations

[5

034]

are

preserved.

[1]See

also Doc.

31

for

an

earlier

manuscript

on

the

same

topic

that shows

some

similarities

with this

paper;

a

major

difference

is

that here the form

of the

Hamiltonian

is

left

completely

unspecified,

whereas

in

Doc.

31

a

specific

form

is

chosen.

[2]See

Lorentz

1915,

1916b, 1916c,

1916d

and

Hilbert

1915. See

also Cattani and

De

Maria

1993 and Kichenassamy 1993

for historical discussions of variational

principles

in

general

rel-

ativity.

[3]Hilbert's

theory

was

based

on

Gustav Mie's

theory

of

matter,

which

implied

in

particular

that the

energy-momentum

tensor

of

matter

should

be

a

function of

electromagnetic quantities

only

(see

Mehra

1973 and

Earman and

Glymour

1978b for historical discussions of Hilbert's

and

Einstein's

theories).

See also Einstein's

more

explicit comment

on

the

shortcomings

of

Hilbert's

theory

in

a

footnote

on [p. 1]

of Doc.

31

(see its

note 3

for the

text) and in

a

letter

in

which

he

called Hilbert's

assumptions

for the Hamiltonian "infantile"

("kindlich."

Einstein

to

Hermann

Weyl,

23

November

1916).

[4]See

Einstein 1916e

(Doc. 30),

where the additional condition

V-g

=

1

was

imposed.

[5]"abhängig"

should

be

"unabhängig."

[6]"quvoT"

should be

"guvoT."

[7]"quv"

should

be "guv."

[8]"(13)

und

(14)"

should be

"(11)

und

(12)."

[9]The

quantity

S first

occurred

in

Einstein 1914o

(Doc.

9),

p.

1075.

There the condition that

it

vanishes

identically

(see

eq.

(15) below) is

used

to

determine the

explicit

form of

the

Hamil-

tonian used

in

that

paper.

[10]"(14),

(15)

und

(16)"

should be

"(13), (14)

und

(15)."

[11]"(16)"

should

be (15)."

[12]The

minus

sign

should

be

a

plus sign.

[13]In

a

contemporary

letter Einstein

expressed

his satisfaction

at having

derived

eq.

(17)

(and

thus

the

conservation laws

(21))

from invariance considerations instead of from

the

explicit

form of

the field

equations through

direct

calculation,

as

he had

done

in

Einstein 1916e

(Doc.

30), pp.

808-809

(see

Einstein

to

Paul

Ehrenfest,

7

November

1916).

The conservation

laws

being independent

of the

particular

form of

9)?,

Einstein also

argued

a

week later that Hil-

bert's

assumptions concerning

the

energy-momentum tensor

of

matter

were

unjustified

(see

Einstein

to

H. A. Lorentz,

13

November

1916).