DOC.

628

SEPTEMBER

1918 659

You

unjustifiably

contest

the

accuracy

of

my

rod consideration.

It

is

com-

pletely

correct when

the

two

assumptions

1)

principle

of

relativity

2)

isotropy

of

the

physical space

are

taken

as a

basis.

I

do

seem

to have

forgotten, though,

to

emphasize

in

the

first

explanation

that

the

principle

of

relativity

must be

applied

again

at

this

place.

The

consideration

is

best

clothed in this form:

A

sphere

that

when measured at

rest

has

the

radius R

must

always

have

the

same

shape

&

size,

measured from

a

coordinate

system

K

relative to which it is

moving

at

the

velocity u, independently

of

the

choice of

system

K.

The

static

sphere

relative

to

K'

with

the

equation

x'2

+

y'2

+

Y2

=

R2

must

therefore have

the

same

shape

and

size, seen

from

K,

as

the

sphere

at

relative rest

to

K with the

equation

x2

+

y2

+

z2

=

R2,

seen

from

K'.

This,

translated

into formulas with

the

aid of

equations (1),

nec-

essarily requires l

=

1.

The consid.

yields

l2

=

1/l2,

whereby

l

should be

positive.)

The situation

naturally is

different

if

you

do

not

want to

presuppose

the

principle

of relativity

or

the

law of

isotropy.

Then the

problem

reads

as

follows:

Are

there

known

observations,

or are

observations

conceivable

that

can

clarify

this? In

any

event

it

is

clear

that

the

choice

of

l

is

not

merely

a

matter of formal

convention but

is

a

realistic

hypothesis.

This

hypothesis

determines,

for

ex.,

the

form of the electron in connection with

velocity

and

thus

also

the

dependence

of

electromagnetic

mass on velocity.

Thus,

for

instance,

for

a

while Bucherer

advocated

a

theory

that

boils down

to

another

choice of

l.[4]

But

now

that the

laws of motion of

the

electron have been verified with

great precision,

a

different

choice

of

l

is out of

the

question

today.[5]

A

decision between

Lorentz and Einstein

is

impossible,

anyway,

since

factually

Lorentz’s

theory agrees entirely

with

the

special

th.

of

rel.;

it

is just

a more

specialized

(exclusively

electromagnetic)

theory.-

Now to

the

clock

problem.

This

paradox

is

solved,

from

the

point

of view

of

special

relativity

theory,

as

follows.

If

U is

permanently

at rest relative to

a

Galilean reference

system

while U'

is

describing a

circle relative to

it,

then

U'

lapses

behind

U

even

though

the

clocks

are

of

the

same

construction and

even

though-looked

at

kinematically-U

thus

likewise

describes

a

circle relative to

a