200

MOTION OF CENTER OF GRAVITY

Doc. 35

THE

PRINCIPLE

OF

CONSERVATION OF MOTION OF THE CENTER

OF GRAVITY

AND

THE

INERTIA

OF ENERGY

by

A.

Einstein

[Annalen

der

Physik 20

(1906):

627-633]

In

a

paper

published

last

year1

I

showed

that Maxwell's

electromagnetic

equations

in

conjunction

with the principle of

relativity

and the principle of

energy

conservation led

to

the conclusion that the

mass

of

a body

changes

with

the

change

in its

energy

content,

no

matter

what

kind

of

change

of

energy

this

may

be.

It turned

out

that

to

an

energy change

of

magnitude

AE

there

must

correspond

a

change

of

mass

of the

same

sign and

of

magnitude

AE/V2,

where

V

denotes the

velocity

of light.

In

the

present

paper

I

want

to

show

that the

above theorem

is the

necessary

and

sufficient condition for the

law

of the conservation

of

motion

of

the

center

of gravity

to

be

valid

(at least

in

first

approximation)

also

for

systems

in

which not

only

mechanical, but also

electromagnetic

processes

take place.

Although

the

simple

formal considerations that

have

to

be

carried

out to

prove

this

statement

are

in the

main already

contained in

a

work

by

H.

Poincare2,

for

the sake of

clarity

I

shall

not

base

myself

upon

that

work.

§1.

A

special

case

Let

K

be

a

stationary

rigid

hollow

cylinder

freely

floating in

space.

Let

there

be

in

A

an

arrangement

for

sending

a

certain

amount S

of radiat-

ing energy

through

the

cavity to

B. During

the emission of this

quantity of

radiation

a

radiation

pressure

acts

upon

the left interior wall of

the tube

K,

imparting to

the latter

a

certain

velocity

that is directed

to

the left.

If the

hollow cylinder's

mass

is

M,

then this

velocity

equals

1/V

•

S/M

,

as can

be

proved

easily from

the

laws of

radiation

pressure,

where

V

denotes the

1A.

Einstein,

Ann.

d.

Phys. 18

(1905):

639.

2H.

Poincare, in Lorentz-Festschrift

(1900):

252-278.

[1]

[2]