DOC.
42
SPECIAL AND GENERAL RELATIVITY 275
30
Relativity
also
simultaneous
relatively
to the
train?
We shall
show
directly
that the
answer
must
be
in
the
negative.
When
we
say
that the
lightning
strokes
A
and
B
are
simul-
taneous
with
respect
to
the
embankment,
we
mean:
the
rays
of
light
emitted
at
the
places
A
and
B,
where the
lightning
occurs,
meet
each other
at
the
mid-point
M of the
length
A
-
B of
the
embankment. But
the
events
A
and
B also
cor-
respond
to
positions A
and
B
on
the train.
Let
M' be the
mid-point
of the distance
A -
B
on
the
travelling
train. Just
when the
flashes1
of
lightning occur,
this
point
M'
naturally
coincides with the
point M,
but
it
moves
towards the
right
in
the
diagram
with the
velocity
v
of
the train.
If
an
observer
sitting
in
the
position
M'
in
the train did
not possess
this
velocity,
then
he would remain
permanently
at
M,
and the
light
rays
emitted
by
the
flashes
of
lightning A
and
B would
reach him
simultaneously, i.e. they
would
meet
just
where he
is
situated. Now
in
reality
(considered
with reference
to
the
railway
embankment) he
is hastening
towards the beam of
light coming
from
B,
whilst he
is riding
on
ahead of the beam
of
light coming
from
A.
Hence the observer will
see
the
beam
of
light
emitted
from B
earlier than he
will
see
that emitted
from
A.
Observers who take
the
railway
train
as
their
reference-body must
therefore
come
to
the conclusion that
the
lightning
flash B
took
place
earlier than the
lightning
flash
A.
We thus arrive
at
the
important
result:
Events which
are
simultaneous with reference
to
the
em-
bankment
are
not
simultaneous with
respect to
the
train,
and
1 As
judged
from
the embankment.