846 DOCUMENT

594 AUGUST 1918

[23]Pp.

78-79.

[24]The

purported gap

is that

Einstein

only synchronizes

clocks

with

respect to the time that

they

indicate,

not with

respect

to

the unit

of

time

they use.

[25]According

to Adler,

the unit

of

time

of

a

clock

depends on

its construction

(clockwork

and

clock

dial)

as

well

as on

external

conditions,

such

as a

gravitational

field.

[26]Pp.

81-82.

[27]Einstein

refers

to

Adler’s

proposed

method for

comparing

the

lengths

of

rods that

move

with

respect

to

each other. Each rod is

provided

with

two

electric

contacts,

one

at

each

end. The contacts

of

one

rod

are

connected

by a

wire

to

the

poles

of

a battery,

the

contacts

of

the other rod

are

connected

to

a galvanometer.

If

the rods

pass

each other and

their

contacts

touch in such

a way

that

a

current is

indicated

by

the

galvanometer, they are

considered

to

be

of

equal length.

[28]P.

83.

[29]Adler

criticizes the lack

of

such

a

definition.

[30]Adler

indicates three

possible

methods

to

define the relative

speed

of

two

systems.

The method

leading to

what

he calls

v1

consists

of

the measurement

of

the

length

of

a

stretch

AB

in

S

by an

ob-

server

at

rest in

S

and the determination

of

the

times

at

which

a point

P'

of

a moving system

S'

passes

A and

B.

The

speed

is

given by

the

quotient

of

AB and the time interval.

[31]Pp.

89-91. On

these

pages,

Adler

argues

that

a

clock has

to

be read

by

an

observer that has the

same position as

the

clock,

that

only

clocks

at

the

same

position

can

be

compared,

and that the result

of

the

reading

of

a

clock is

independent

of

the

speed

of

the observer.

[32]In chap.

3,

Adler takes

as

his

point

of

departure

the

general validity

of

the Lorentz transforma-

tion and

of

the relativistic addition theorem

for

velocities.

[33]P.

95.

[34]Adler

considers three

systems K,

S,

and

S'

that

are

first

at rest (with

coinciding

coordinate

axes

and

origins)

and then

move

with

respect

to

each

other in the

way

indicated in

note

2

(the

motion takes

place along

the

x-axis).

A

measuring

rod lies in each

system along

the

x-axis,

in such

a way

that the

three rods coincide while the

systems are

still

at rest.

Adler claims that the instant that motion

begins,

rods M in S and

M'

in

S'

still

fully

coincide,

irrespective

of

whether there is

a

Lorentz contraction

or

not.

A

point

of

M with coordinate

x

in S will thus coincide with

a point

of M'

with coordinate

x'

=

x

in

S'.

[35]P.

96.

[36]“greifen" (see p. 96).

[37]Adler

poses

the

question

whether the

separation

of the

three

systems

takes

place

at time t

=

0

or

at

time

t'

=

0,

where

t

and

t'

are

the

system

times

of

S

and

S',

respectively.

Because the

systems

are equivalent,

t

=

0 will

imply

t'

=

0. On

the other

hand,

t

and

t'

are

connected

by a

Lorentz

transformation with the relative

speed

of

S

and

S',

which

implies

that t’

=

0

if

t

=

0

(and

vice

ver-

sa).

Thus the clocks will have

to

show

two

different times

at

the instant

of

separation,

unless the

out-

come

of

the

reading

of

a

clock

depends

on

the

state

of

motion

of

the observer

(which

is the "absurd

view"

referred

to by Einstein).

[38]P.

98.

[39]Einstein

refers

to

the result that the time

of

separation

differs for different values

of

x or

x'.

[40]On pp.

99-101,

Adler

gives

an

alternative derivation

of

the result mentioned

in

the

preceding

note.

[41]Pp.

102-103.

[42]The

clocks

are

the clocks in S and

S'

;

T

is the time in the

symmetry system

K.

[43]The

manuscript pages

from the middle

of

p.

91 to

the middle

of

p.

95

are

omitted in Adler 1920.

[44]P.

106.

[45]On

this

page,

Adler claims that Einstein does

not

realize that the

separation

of the

two

systems

takes

place

at

different

times, not

only

for

different

systems,

but also

at different

points

within

one

system.

[46]P.

109.

[47]Adler omitted

this

page

in Adler 1920.