DOC.

21

THEORY OF RELATIVITY 259

magnitude

Mc2.

We do

not

yet

have

a

direct

experimental

confirmation of this

[15]

important

result;

but

we

do know

special

cases

for which the

validity

of

the "law of

the inertia of

energy"

can

be deduced

even

without the

theory

of

relativity.

[16]

Minkowski's Mathematical Treatment

of the

Theory

of

Relativity

The

development

of the

theory

of

relativity

was

furthered

greatly by

H.

Minkowski's

mathematical formulation of

its

foundations. Minkowski started

out

from the

premise

[17]

that the "time coordinate"

enters

the fundamental

equations

of

the

theory

of

relativity

in

exactly

the

same

way

as

the

spatial

coordinates if

t is

replaced by

the

imaginary

quantity

V-1ct,

which

is

proportional

to

it.

The

equations

of the

theory

of

relativity

thereby

become

equations

in

a

four-dimensional

space;

and

only

in

the number of

dimensions

are

the formal

properties

of this four-dimensional

space distinguished

from the formal

properties

of the

space

of Euclidean

geometry.

Remark

on

the

Presumptive

Limit

of

the

Range

of

Validity

of the

Theory

Finally,

one more

important question:

Does the

theory

of

relativity possess

unlimited

[18]

validity?

Even the

supporters

of the

theory

of

relativity

have different views

on

this

question.

The

majority

are

of the

opinion

that the

propositions

of

the

theory

of

relativity-especially

its

conception

of time and

space-can

claim unlimited

validity.

However,

the writer of these lines

is

of the

opinion

that the

theory

of

relativity

is

still

in

need of

a generalization,

in

the

sense

that the

principle

of the

constancy

of

the

velocity

of

light

is to

be abandoned.

According

to

this

opinion,

this

principle

is

[19]

to

be retained

only

for

regions

of

practically

constant

gravitational potential.

The

future

must

show whether this

view,

which

is

based

mainly

on

epistemological

grounds,

will

prove

to

be

right.

Literature

An excellent

presentation

of this

subject

is

contained

in

Physikalisches

über

Raum

und Zeit

by

E.

Cohn,

2d

ed.

(B.

G. Teubner,

1913).

[20]