Taking any two events in the universe, there are two different
possibilities as to the relation between them. It may be physically
possible for a body to travel so as to be present at both events, or it
may not. This depends upon the fact that no body can travel as fast as
light. Suppose, for example, that it were possible to send out a flash
of light from the earth and have it reflected back from the moon. The
time between the sending of the flash and the return of the reflection
would be about two and a half seconds. No body could travel so fast
as to be present on the earth during any part of those two and a half
seconds and also present on the moon at the moment of the arrival of
the flash, because in order to do so the body would have to travel
faster than light. But theoretically a body could be present on the
earth at any time before or after those two and a half seconds and also
present on the moon at the time when the flash arrived. When it is
physically impossible for a body to travel so as to be present at both
events, we shall say that the interval[2] between the two events is
“space-like”; when it is physically possible for a body to be present
at both events, we shall say that the interval between the two events
is “time-like.” When the interval is “space-like,” it is possible for
a body to move in such a way that an observer on the body will judge
the two events to be simultaneous. In that case, the “interval” between
the two events is what such an observer will judge to be the distance
in space between them. When the interval is “time-like,” a body can
be present at both events; in that case, the “interval” between the
two events is what an observer on the body will judge to be the time
between them, that is to say, it is his “proper” time between the two
events. There is a limiting case between the two, when the two events
are parts of one light flash—or, as we might say, when the one event
is the seeing of the other. In that case, the interval between the two
events is zero.
[2] I shall define “interval” in a moment.
There are thus three cases. (1) It may be possible for a ray of light
to be present at both events; this happens whenever one of them is the
seeing of the other. In this case the interval between the two events
is zero. (2) It may happen that no body can travel from one event to
the other, because in order to do so it would have to travel faster
than light. In that case, it is always physically possible for a body
to travel in such a way that an observer on the body would judge the
two events to be simultaneous. The interval is what he would judge to
be the distance in space between the two events. Such an interval is
called “space-like.” (3) It may be physically possible for a body to
travel so as to be present at both events; in that case, the interval
between them is what an observer on such a body will judge to be the
time between them. Such an interval is called “time-like.”
Public-domain text, read in full here on John Shaqi.
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