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.