276 DOC. 42 SPECIAL AND GENERAL
RELATIVITY
The
Relativity
of
Simultaneity
31
vice
versa
(relativity
of
simultaneity). Every reference-body
(co-ordinate
system)
has
its
own
particular
time;
unless
we
are
told the
reference-body to
which the
statement
of time
refers,
there
is
no
meaning
in
a
statement
of the
time
of
an
event.
Now before the advent of the
theory
of
relativity
it had
always
tacitly
been
assumed in
physics
that the
statement
of
time had
an
absolute
significance,
i.e.
that
it
is independent
of
the
state
of
motion of the
body
of reference. But
we
have
just
seen
that this
assumption is incompatible
with the
most
nat-
ural
definition of
simultaneity;
if
we
discard this
assumption,
then
the conflict between the
law
of
the
propagation
of
light
in
vacuo
and the
principle
of
relativity (developed
in Section
7)
disappears.
We
were
led
to
that
conflict
by
the considerations
of
Section
6,
which
are
now no
longer
tenable.
In that section
we con-
cluded
that
the
man
in
the
carriage,
who
traverses
the distance
w
per
second
relative
to
the
carriage,
traverses
the
same
dis-
tance
also
with
respect to
the
embankment
in
each
second
of
time.
But,
according to
the
foregoing
considerations,
the
time
required by
a
particular
occurrence
with
respect to
the
carriage
must not
be considered
equal to
the duration of
the
same
occurrence as
judged
from the
embankment
(as
reference-
body).
Hence it
cannot
be contended that the
man
in
walking
travels the distance
w
relative
to
the
railway
line
in
a
time
which
is
equal to
one
second
as
judged
from
the
embankment.
Moreover,
the considerations of Section
6
are
based
on
yet
a
second
assumption,
which,
in the
light
of
a
strict consider-
ation,
appears
to
be
arbitrary,
although
it
was always
tacitly
made
even
before the introduction
of
the
theory
of
relativity.