298 DOC. 71 PRINCETON LECTURES
SPECIAL
RELATIVITY
fall
together;
the
vanishing
of
this
quantity
s2,
is
the invari-
ant
condition that the
two
space-time points
can
be
con-
nected
by
a
light
signal
in
vacuo.
If P
is
a
point
(event)
represented
in
the
four-dimensional
space
of
the
x1, x2, x3,
l,
then all the
“points”
which
can
be
connected
to
P
by
means
[41]
of
a
light signal
lie
upon
the
cone
s2
=
0
(compare
Fig.
1,
in
which the dimension
x3
is suppressed).
The
“upper”
FIG. 1.
half of the
cone
may
contain the
“points” to
which
light
signals
can
be
sent
from
P;
then the “lower” half of the
cone
will
contain the
“points”
from
which
light
signals can
be
sent to
P.
The
points
P'
enclosed
by
the conical surface
furnish,
with
P,
a
negative
s2;
PP',
as
well
as
P'P
is then,
according
to
Minkowski,
time-like.
Such
intervals
repre-
sent
elements
of
possible
paths
of
motion,
the
velocity
being less
than that
of
light.*
In
this
case
the
l-axis
*That
material
velocities
exceeding
that of
light are
not
possible,
follows
from the
appearance
of the radical
"\/1
-
v2
in the
special
Lorentz
trans-
formation
(29).
[38]