346
DOC.
17
THE THEORY OF RELATIVITY
But
this does not
say
at all
a priori that,
when two events
are
simultaneous
with
respect
to
the reference
system
k-by
that
I
mean
the coordinate
system
together
with
the
clocks-they
are
also
simultaneous
as
understood
with
respect
to
the
system
k'.
This does not
say
that time
has
an
absolute
meaning,
i.e., a meaning independent
of
the
state
of motion of the reference
system.
This
is
an
arbitrariness that
was
contained
in
our
kinematics.
And
now we come
to
a
second
factor that
was
also
arbitrary
in kinematics
up
until
now.
We
speak
about the
shape
of
a body,
the
length
of
a
rod,
for
example,
and believe
that
we
know
exactly
what
the
length
of
the
rod
is,
even
when it
is
in
motion
with
respect
to
the reference
system
from
which
we are describing
the
events.
A brief reflection
shows,
however,
that these
concepts
are
not at all
as simple as
we
instinctively
believe
them
to
be.
Consider
a
rod
moving
in
the direction of
its
axis
relative to
the reference
system
k.
We
ask:
What
is
the
length
of
this
rod?
This
question
can
have
only
the
following meaning:
What
experiments
do
we
have
to
perform
in
order
to
learn
what
the
length
of
the
rod
is?
We
can
take
a man
with
a
measuring
rod and
give
him such
a push
that he
assumes
the
same
velocity
as
the
rod;
in
that
case
he
will be at rest relative to
the
rod,
and
will
be
able to
determine its
length
by
repeated
application
of
his
measuring rod,
in
the
same way
the
lengths
of
bodies at rest
are
actually
determined. He
will
obtain
a
perfectly
definite number and
will
be
able to
declare
with
some
degree
of
justification
that he
has
measured the
length
of
this
rod.
However,
if
only
such
observers
are
available who
do
not
move along
with
the
rod,
but instead
all
of them
are
at rest
relative
to
a
reference
system
k,
we can
proceed
in
the
following manner:
We
imagine
that
very many
clocks,
with
an
observer
assigned
to
each of
them,
are
distributed
along
the
route
traveled
by
the
axially moving
rod.
The
clocks
are regulated
by
means
of
light
signals according
to
the
procedure
described
before, such
that
in
their
totality they
indicate the time associated with
the reference
system
k.
These observers determine the
two
positions
with
respect
to
the
system
k at
which
the
beginning
and the end of the rod
are
found
at
a given
time
t,
or,
what
amounts to
the
same,
those
two clocks
that the
beginning
and the end of
the
rod
just
pass
by
when
the
clock in
question
indicates
the
time
t.
The
distance
between the
two
positions (or
clocks) so
obtained
is
then measured
by
repeatedly
applying a
measuring
rod,
which
is
at rest
relative
to
the reference
system
k,
along
the
connecting
line.
The
results of the
two
procedures
can
justly
be
designated
as
the
length
of the
moving
rod.
However,
it
should
be
noted that these
two
manipulations
do not
necessarily
lead
to
the
same
result,
or,
in
other
words,
the
geometrical
dimensions
of
a body
do
not
need
to
be
independent
of the
state
of motion of the reference
system
with
respect
to which
the
dimensions
are
determined.
If
we
do
not
make these
two
arbitrary
assumptions,
then
we are
at first
no
longer
capable
of
solving
the
following
problem:
Given
are
the coordinates
x, y,
z
and
the
time
t
of
an
event with
respect
to
the
system
k;
find
the
space-time
coordinates
x',