Light cones
The figure below is a plot of the light cone of the spacetime event t=0, x=1, y=0. The light cone is the surface determined by all of the spacetime paths passing through that event. The half of the surface to the future of t=0 is called the future light cone of that event. The half to the past of t=0 is called the past light cone of that event.
Notice that the future and the past are cleanly divided by this light cone.
This clean division can be spoiled when we allow spacetime to become curved.
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