At any time and place (, event A in Fig.
)
we can picture a flash bulb going off.
The light from the flash travels away in every direction
at the same speed c, making a spherical shell of radius r = ct.
The history of this shell's outward propagation
forms a 4-dimensional ``hypersurface" known as a LIGHT CONE,
whose simplest projection (onto x and ct)
is shown in Fig.
.
The proper time
of any event on the light cone is zero.
Events inside the light cone are called
``TIMELIKE" --
they are further away from A in time than they are in space,
and therefore can be reached from A by travel at speeds
less than c (possible) -- whereas events outside
the light cone are called ``SPACELIKE"
because their distance from A is too great
for even light to travel between them and A
in the time available. Events separated from A
by spacelike intervals of Minkowski space cannot have
any causal relationship (either cause or effect) with A,
Star Trek notwithstanding.
The WORLDLINE of any object moving at a constant physical speed (u<c) relative to A will appear as a straight line closer to the vertical than the line cone.
The lightcone of another event (such as B) can be drawn on the diagram as an extra pair of diagonal lines at ±45° to the x and ct axes, intersecting at B. Note that we have picked one particular rest frame in which to describe all the events; this is the best graphical strategy to avoid confusion. The next step is to see how such pictures (and the mathematics of the Lorentz transformation) can be used to actually solve problems within the .