354

DOC.

18

DISCUSSION OF DOC.

17

detail.

The ether

was

of real

value

for the

intuitive

representation

of

optical processes

only

as

long

as one

actually

reduced these

processes,

with all

their

peculiarities,

to

mechanical

processes.

After the

concept

of

fields

of

lines

of

force

had been

put

into

the

foreground,

the ether

hypothesis

has

come

in fact to

play only a

fictitious

role.

[3]

Fritz Müller:

If there

are

two

synchronous

clocks at

point A,

and

one

of them

is

moved with

a given

velocity

from this

point

to

point

B,

then,

according

to

the

reasoning

of

the

speaker,

this

second

clock will

run slower,

if

only by a tiny

fraction.

What

happens

now

if this clock returns

by

a

polygonal

or

circular

path

to

point

A?

According

to

the

reasoning

given

in

the

lecture,

at

the

moment

of

its meeting

with

the other

clock at

point

A,

the second

clock will not

be

running

in

synchrony again.

How

can

this be

possible,

since, on

the other

hand,

Prof.

Einstein

says

that

a

rod of

a

specific

length

L

in

a system

at rest, which

he

holds in his hand, will

become shorter

by

a

definite

amount when it

is

set

in motion? But

as soon as

the rod

is

brought

to

halt

by

a

sudden

jerk,

its

length

is

once

again

=

L,

i.e.,

the rod

is

no longer

deformed. If

this

latter

argument

holds

good

for

length, i.e.,

for

a

specific

dimension,

and

if what

the mathematician

Minkowski

asserted,

which

was

termed

acceptable

by

Prof. Einstein,

is correct,

namely,

that

we

can

speak

of

a

4-dimensional

geometry,

so

that

we can compare length

with

time,

then

how

do

things

stand

with

the

clock? Must it not

then,

exactly

like

the

rod,

run synchronously

again

from the

moment it

is brought

to rest at

point

A?

This

reasoning

would suit

me

better,

whereas

I

cannot

grasp

the other

one.

Prof.

Einstein:

It

is not

the

clock's

indication of

time

that

is

to be

likened

to

the

rod,

but

its rate.

After

having

completed

its

motion and

returned,

the rod

has

the

same

length.

In the

same

way,

the

clock has

again

the

same

rate.

We

can designate

the rod

as

the carrier of the

space

differential,

and the

clock

as

the carrier of the

time

differential.

It

is

impossible

to

assume

that,

after

having

traveled

along a polygonal

path

and

returned

to

point

A,

the

clock

will

again

be

running

synchronously

with

the

clock

that

has

been

at rest at

point

A.

The

clock

runs

slower if it

is

in

uniform

motion,

but

if it

undergoes a

change

in

direction

as a

result of

a

jolt,

then the

theory

of

relativity

does not

tell

us

what

happens.

The sudden

change

of direction

might

produce a

sudden

change

in

the

position

of the hands of the

clock.

However,

the

longer

the

clock

is

moving

rectilinearly

and

uniformly

with

a given

speed

of

forward motion,

i.e.,

the

larger

the

dimensions of the

polygon,

the smaller

must be

the

effect

of

such

a

hypothetical

sudden

change.

[4]

Prof.

Prasil:

In

his famous

essay, "Space

and

Time,"

Minkowski wrote

about the

nature

of

dilation,

that the

latter

is

a

concomitant circumstance of the

state

of

motion.

[5]

He makes it

absolutely independent

of

any physical

influence.

Lorentz,

on

the other