238

ON

THE INERTIA

OF ENERGY

Doc. 45

ON

THE

INERTIA

OF ENERGY

REQUIRED

BY

THE

RELATIVITY

PRINCIPLE

by

A.

Einstein

[Annalen

der

Physik 23

(1907):

371-384]

The

principle of

relativity,

in

combination with

Maxwell's equations,

leads

to

the conclusion that the inertia

of

a body

increases

or

decreases with

its

energy

content in

a

completely

determined

way.

That

is

to

say,

if

one

observes

a

body

that emits

a

certain radiation

energy

simultaneously

in

two

opposite

directions,

and

if

one

examines

this

process

from

two

coordinate

systems

which

move

uniformly

relative

to

each other,1

one

of which is

at

rest

relative

to

the

body,

and

if

one

applies--from both coordinate

systems--the

energy

principle

to

the

process,

one

arrives

at

the result that

to

an

increase

in

the

body's

energy AE

there

must always

correspond

an

increase in the

mass

AE/V2,

where

V

denotes the

velocity

of light.

The

circumstance

that

the special

case

discussed there necessitates

an

assumption

of

such extraordinary generality

(about

the

dependence

of the

inertia

on

the

energy) demands

that the

necessity

and

justification of this

assumption

be examined

in

a

more

general

way.

Especially, the

question

arises:

Do

not

other

special

cases

lead

to

conclusions that

are

incompatible

with the

one

mentioned above?

A

first

step in

this respect I took last

year2

by

showing

that the

above

assumption

resolves the contradiction

between

electrodynamics

and

the

principle

of the

constancy

of

the

motion of

the

center

of

gravity

(at least

as

far

as

the

terms of

first order

are

concerned).

The general

answer

to

the

question

posed

is

not yet

possible

because

we

do not yet

have

a

complete

world view

that

would correspond to

the

principle

of

relativity.

Rather,

we

must

limit ourselves

to the special

cases

that

we

can

handle

at

present without arbitrariness

from

the

standpoint

of relativis-

tic

electrodynamics.

We

are

going

to

consider

two

such

cases;

in the first of

these,

the

system

whose

inertial

mass we

shall

examine

consists of

a

rigid,

[1]

[2]

1A.

Einstein,

Ann. d.

Phys. 18

(1905):

639.

2A.

Einstein,

Ann.

d.

Phys. 20

(1906):

627.