130

DOC.

8

REPLY TO A COMMENT BY

M.

ABRAHAM

Doc.

8

Relativity

and

Gravitation

Reply

to

a

Comment

by

M.

Abraham

by

A.

Einstein

[Annalen

der

Physik

38

(1912):

1059-1064]

In

a

note

appearing

in these

Annalen,

M.

Abraham has

responded

to

some

critical

remarks that

I

made about his

investigations

on

gravitation,

and

has,

in

turn,

criticized

[1]

my

papers on

this

subject.

In what

follows, I

wish

to

take

up,

one

by

one,

the

points

he touched

upon,

and in

particular,

I

wish

to

contrast

my

views

on

the

current state

of

the

theory

of

relativity

with those

expressed by

him.

Abraham

notes

that

I

have delivered the

coup

de

grace

to

the

relativity theory by

abandoning

the

postulate

of the

constancy

of the

velocity

of

light

and

by

the

therewith connected

relinquishment

of

the

invariance of

the

systems

of

equations

with

[2]

respect

to

the

Lorentz transformations. A

reply

to

this necessitates

a

consideration of

the foundations of the

theory

of

relativity.

[3]

The

theory presently designated

as

"the

theory

of

relativity"

rests

on

two

principles

that

are

totally independent

of

one

another,

namely

1.

the

principle

of

relativity (with

respect

to

uniform

translation),

2.

the

principle

of the

constancy

of the

velocity

of

light.

I want to formulate both

principles

more

precisely,

not

in the belief that

I

am

bringing up

something

new,

but

only

so as

to

be able

to

express myself

more

comfortably

at

a

later

point.

Let

us

contrast two

formulations

of

the

principle

of

relativity

with each

other:

1.

If

we

refer

the

physical system

to

a

coordinate

system

K that is such that the

laws of

nature

become

as simple

as

possible,

then there exist

infinitely many

coordinate

systems

with

respect

to

which these laws

are

the

same, namely,

all of

those coordinate

systems

that

are

in uniform translation relative

to K.

2.

Let E be

a

system

isolated from all other

physical systems (in

the

customary

physical

sense

of

the

term),

and let E be referred

to

a

coordinate

system

K that is

such that the laws

to which

the

spatial-temporal changes

of

E conform be

as

simple

as

possible;

then there exist

infinitely many

coordinate

systems

with

respect

to

which

these laws

are

the

same, namely,

all of those coordinate

systems

that

are

in uniform

translation relative

to K.

It is

easy

to

see

that it

is

only

the

relativity principle

in

form

2

that is

urged upon

us

by

the available

experiments.

For let E

again

denote the "isolated"

system

under

consideration and

U

the

totality

of

all

of

the other

systems

in the world. To

test

the

relativity principle

in form

1,

one

would

have

to

conduct

two

experiments,

in the first