126

DOC.

7

GRAVITATIONAL INDUCTION

Doc.

7

Is

There

a

Gravitational Effect Which Is

Analogous

to

Electrodynamic

Induction?

by

A.

Einstein

[Vierteljahrsschrift

fur

gerichtliche

Medizin

und

öffentliches

Sanitätswesen 44

(1912):

37-40]

Taking

a

plain special

case as a

model,

one can

formulate the

question

raised in the

title

as

follows.

Consider

a system

of

ponderable

masses

consisting

of

a spherical

shell K with

mass M,

which

is

homoge-neously

distrib-

uted

over

the surface

of

the

sphere,

and the material

point

P

with

mass m,

which is

set

in the

center

of

this

sphere.

Does

a

force

act

on

the fixed material

point

P

if

I

impart an

acceleration

Y

to

the shell

K?

The

[1] following

arguments

will induce

us

to

view such

a

force effect

as

really being present

and will

give

us

its

magnitude

in first

approximation.

1. According

to

the

theory

of

relativity,

the inertial

mass

of

a

closed

physical

system depends

on

its

energy

content

in such

a

way

that

an

increase of the

energy

[2]

of the

system by

E will increase the inertial

mass by

E/c2,

where

c

denotes the

[3]

velocity

of

light

in

a vacuum.

Thus,

if M denotes the inertial

mass

of

K in the

absence

of

P,

and

m

denotes the inertial

mass

of P in the absence of

K,

or,

in other

words,

if M

+

m

denotes the inertial

mass

of

the

system consisting

of P and K

together

in the

case

where

m

is

infinitely

far from

K,

then it follows that the inertial

mass

of the

system

consisting

of

K

and

m possesses

the value

w

kMm....(1)-m

M

+,

Rc2

if

m

is

in the

center

of

K,

where k denotes the

gravitational

constant

and

R

the radius

of

K.

For

kMm/R

(at

least in first

approximation)

is the

energy

that

one

must

apply

in order

to

transport

P from the

center

of

K

to

infinity.

2.

In

a

paper

that will

shortly appear

in the Annalen

der

Physik,

I

have

shown,

[4]

based

on a hypothesis

about

the

nature

of

the

static

gravitational

field,

that

a

material

point

moves

in

a

static

gravitational

field

according

to

the

following

equations: