258 DOC.

21

THEORY OF RELATIVITY

Heuristic

Value of the

Theory

of

Relativity

Is

the

theory

of

relativity

of

significance

for the further

development

of

physics apart

from

the fact that

it solves

the dilemma

analyzed

above? This

question must

be

answered in the affirmative for the

following

reason:

According

to

the

theory

of

relativity,

the

systems

K and K'

are

equivalent,

and

the

coordinates and time values

of the

two

systems

are

connected

by

the

equations presented

above. If

a

general

physical theory

is

formulated with

respect

to

K,

then,

with the

help

of the transforma-

tion

equations t,

one can

introduce the

quantities

x',

y',

z', t' into the

equations

instead of the

quantities

x,

y, z,

t.

This results

in

a

system

of formulas referred

to

K'.

According

to

the

relativity principle,

the latter

must

coincide

exactly

with the

system

of

formulas formulated with

respect

to

K,

the

only

difference

being

that

x,

y,

z,

t

are

replaced by

x',

y',

z',

t'.

Thus,

the

theory

of

relativity provides

a

general

criterion of

[13]

admissibility

for

a

physical theory.

Some

Accomplishments

of the

Theory

of

Relativity

Let

us

briefly

enumerate

the individual results owed

so

far

to

the

theory

of

relativity.

It

yields

a

simple theory

of the

Doppler principle,

of

aberration,

of Fizeau's

experiment.

It

proves

that the Maxwell-Lorentz field

equations

are

also admissible in

the

electrodynamics

of

moving

bodies. The laws of deflection of fast cathode

rays

and of the

ß-rays

of radioactive

substances,

which

are

essentially

identical with the

former,

in fact the laws of motion of

rapidly moving

material

points

in

general,

can

be established with the

help

of the

theory

of

relativity

without

invoking special

[14]

hypotheses.

Inertia

and

Energy

But the

most

important

result

produced by

the

theory

of

relativity

thus far is

a

relation between the inertial

mass

of

physical systems

and their

energy

content.

Let

a

body

in

a

certain

state

possess

the inertial

mass

M.

If the

quantity

of

energy

E

is

supplied

to it

in

any way whatsoever, then,

according

to

the

theory

of

relativity,

its

E

inertial

mass

increases

thereby

to

M

+

E/c2,

where

c

denotes the

velocity

of

light.

The

the

law

of conservation

of

mass

that

we

have retained

up

to

now

is

thereby

modified

and

merged

with the

energy principle

into

one

law.

The result

suggests

that the

inertial

mass

M

of

a body

is to

be conceived of

as

an energy

content

of the