DOC.
632
OCTOBER
1918 665
The
same
must have
happened
with
the
relativity
brochure announced in
it,
for
it has
not
come
in,
to
this
day.[2]
I
suspect
it constitutes
a
third
edition
of
the
writing
from
the
Vieweg
collection.
Although
I
have
the
first
edition,
I naturally
would be
very
interested
to know what
new things
were
added.
If
you
can
make
use
of
my example
with
the
contact
rods,
it would
please
me
very
much.[4] I just
want to add
that
if
the
rods
lie
in two
equivalent systems
and,
seen
from
their
“symmetry
system”[4]-with
which
is
meant
a
system
that
is
purely kinematically symmetrical
to
them-the
contact takes
place
simultane-
ously
for
both
ends,
which
is
immediately
clear
from the
consideration
without
need for
calculation,
of
course,
then both
rods
are
subject
to the
same
Lorentz
contraction,
seen
from
the
symmetry system,
hence
are
“equally
long,”
which
is
naturally
confirmed
by
the
calculations. The intersection of
the
[two][5]
edges
x2
and
x'2
occurs
earlier, later,
and
simultaneously,
just
as
for
the
edges
x1
and
x'1,
depending on
whether observed
from
system
S
or
S'
or
from
symmetry system
K.
The
question
is,
from which
system
does
the
simplest description
result? From
the
symmetry system,
we can
retain the
old
theory
of closed currents. For
the
system
times in
S
and
S',
we are
impelled
to
a
theory
of unclosed currents. There
is
a
good analogy
to this from the
spatial
perspective.
We
have
three
equally long
rods
a,
b,
c
which
we
arrange
parallel
to
one
another
on a
plane
so
that the
dis-
tance between
any
two
is d.
Then for
the
observer who
stands
at
a,
c
is
shorter
than
b,
and
this latter
is
shorter than
a.
For the observer at
c,
on
the
contrary,
c
is
the
longest
rod and
a
the
shortest. For
the
observer
on
the
symmetrical
plane
at
b,
a
and
c are
equally long.
These facts from
the
spatial
perspective
are
“real”
and
incontestable.
Nevertheless,
I
can
list
a
series
of
physical exper-
iments, according
to which
the three
rods
are
of
equal length.
This
is
entirely
analogously
valid for
the
consideration
of
your theory
of relativity from
the
tem-
poral perspective.
The
propagation
velocity
of
electrical
waves
can
be
taken
into
account
without
altering
the
crucial
symmetry argument,
although
it
does
get
a
bit
more
complicated.
It then
depends
on
the
theories from which
one
sets out.
Let
us
very simply assume,
for
inst.,
that
an
electrified
particle
is
moving
from
the
positive pole
of
the
element to
the
negative one
at
velocity
c;
the
“circuit”
must
thus
be closed for
at least
the
time
3L/2c
so
that this
particle
can
pass by
both
contacts.
(Where
L
is
the
length
of
the
rods.)
If D
is
the width
of
the
contact,
then
necessarily
D
= 3L/2

v/c,
hence the contact width
is
of
the
order of
magnitude
v/c,
whereas
the
shortening owing
to
the
Lorentz
contraction
is
of
the
order of
magnitude
(v/2)2.
It
can now
be shown that,
seen
from
the
symmetry
system,
a
current is
formed with this minimum contact width
but
not
when
seen
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