342 DOC.

71

PRINCETON LECTURES

THE GENERAL

THEORY

inertia and

gravitation

is formally expressed by

the

fact

that the

whole

left-hand

side of

(90)

has

the character

of

a

tensor

(with

respect to any

transformation

of

co-ordinates),

but

the

two terms

taken

separately

do

not

have

tensor

character.

In

analogy

with

Newton’s

equations,

the

first

term

would be

regarded

as

the

expression

for

inertia,

and the

second

as

the

expression

for

the

gravitational

force.

We

must next

attempt

to

find

the laws of

the

gravita-

tional

field.

For

this

purpose,

Poisson’s

equation,

Af =

4rKp

of

the Newtonian

theory must

serve as a

model. This

equation

has

its

foundation

in

the idea that

the

gravita-

tional

field arises from

the

density

p

of

ponderable matter.

It

must

also be

so

in

the

general

theory

of

relativity.

But

our investigations

of the

special

theory

of

relativity

have

shown

that

in

place

of

the

scalar

density

of

matter

we

have

the

tensor

of

energy per

unit

volume.

In the latter

is

included

not only

the

tensor

of the

energy

of

ponderable

matter,

but

also

that

of

the

electromagnetic

energy.

We

have

seen,

indeed,

that

in

a

more

complete

analysis

the

energy tensor

can

be

regarded only

as a provisional

means

of

representing matter.

In

reality,

matter

consists of

electrically charged particles,

and

is to

be

regarded

itself

as a

part,

in

fact,

the

principal part,

of the

electromagnetic

[99]

field.

It

is

only

the circumstance that

we

have

no

suffi-

cient

knowledge

of the

electromagnetic

field of

concentrated

charges

that

compels us, provisionally,

to

leave

undeter-

mined in

presenting

the

theory,

the

true

form of this

tensor.

From

this

point

of view it

is at present appropriate to

introduce

a

tensor

Tuv

of the second

rank

of

as

yet

unknown

structure,

which

provisionally

combines the

energy

density

of

the

electromagnetic

field

and that

of

ponderable

matter;

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