DOC.
620
SEPTEMBER
1918 645
among others,
conforms
just
as
well
to
experience.
Which
hypotheses
one
adds
for
experience is merely
a
matter
of
taste.
I
therefore do
not deny
at
all that the
hypotheses
can
be chosen
so
that
l
has
to
be
=
1,
thus that
one
arrives
at
your
transformation;
I
just
contest
(1)
that
experience
virtually compels
l
=
1, (2)
that the
derivation in
your
first
paper
is correct.[5]
For
the
problem
of
interest
to
me
it does not
help
me
in
the
least to avoid
your
first
paper
&
to take
another
descriptive
method
as a
basis for
the
discussion.
I
see
in
your
first derivation
an
error
that
is admittedly
somewhat difficult to
recognize
but that
is
completely
clear
to
me now.
I could
question
the
correction
of
this consideration if
you
would
demonstrate
to
me
that there
is
an error
in
my
deduction
(§38,
eqs. 114-126) as
well.
For
only
either[6]
t
= (113)
or
t
=
a(t~
(126)
can come
out;
if
my
result
(126)
is
right,
then
yours
(113)
must
be
wrong.-
The
case l
=
7,
which
I
treat in
the 4th
chapter,
is
interesting
particularly
because
it determines
only
Lorentz
deformations,
but has
no
influence
on
the
running
speed
of
the
clocks.
(Albeit,
Lorentz contractions in
the
direction
of
motion
&
perpendicular
to
it,
which
are
in
a
relation of
ß
to each
other.[7])
Chap.
II
merely
offers preparatory
considerations for sections
II-IV
(chap.
III),
which
are
the
main issue for
me.
There
you
can see
that
I
did
not
overlook
your
“standard
clock,”
rather that
it
is
the actual
point
of
departure
of
my
reflections.
I
have been
making
a
serious effort for
a
year
now
to
understand
it,
but
an
insurmountable
logical
contradiction in
your
assertions remains for
me:
a)
The
clocks U
and
U'
are
of
the same construction.
b)
The two systems in which these
clocks
are at rest are equivalent.
c)
The two
clocks
display varying differences
in
hand position, when compared
to
each
other at
relative rest, when
one
has described a circular
path
relative
to the other
(comp. end
of
§4
of
your
1st
pap[er]).
For, according
to
the
general
laws
of relative
motion,
U, seen
from
U',
describes
a
circle when
U',
seen
from
U,
describes
one.
Hence each of
the
two clocks
must have
lagged
behind
the
other. There
is just
the
logical
possibility
that,
upon meeting up
with
each
other
again, a
difference in
hand
position
is
the
more
probable
situation
(comp.
§31-32
of
my paper).
This
logical
contradiction
is
admitted also
by
supporters
of
your
theory
(Berg, Petzoldt),
but
judged merely
as a
false
consequence.[8]
If
you
could
clarify
this
point, very
much would indeed
have been
gained,
since
then
you
would have to look
differently
at
the
entire
problem
of differences in
the
running
rates.
Something quite analogous
to this