The idea that events in the future may or may not affect you. If an event is not in your event cone, it will not affect you.
T| X...X 
I|  X.X  b
M|   X
E|  X.X
 | X...X
The "shaded" region inside the X's is your event cone. Events within this area can possibly affect you. Anything outside that cone cannot.
Example: A can possibly affect you. It has the time needed to cover the space to affect you. C has already affected you and is in your past. B cannot affect you, since it does not have the time to cover the distance needed.

I learned this all in physics the other day and thought it was pretty darn neato.
Just to clarify: In the above diagram, The central X of the cone is an event (An event is just a set of four-dimensional coordinates: length, width, height, and time. It's probably more helpful to think of this as a star or another heavenly body than as you specifically, as the construct has a lot to do with the speed of light and other universal matters.) The Xs above are defined by the maximum speed of anything that can affect the event at the central X (in other words, the speed of light.)

Anything within the upper region of the cone lies within the future cone of the central X. The event at the central X can affect any event in its future cone. In the diagram above, the 'a' could be affected by the event at the central X. Anything within the lower region of the cone lies within the past cone of the central X. Any events that have occured in the past cone of the central X can reach the space and time of the central X. The 'c' in the above diagram can affect the event at the central X.

It is important to note that it is not the event itself that travels through its event cone. The event is not a 'real' object; it exists at only one point in time. Instead, it refers to radiation of particles (whether they are visible light waves, x-rays, microwaves, or others) that will reach other events in the event cone. An event in the past cone of another event ('c' in the above diagram) will radiate some particles that will be present at the second event (the central X,) just as that event will radiate praticles that will arrive at any of the events in its future cone ('a' in the above diagram.)

The best real world example of an event cone is astronomy. Say the central X in the above diagram represents the moment that humanity turns on a beacon from Earth for all extra-terrestrial civilizations to detect. The past cone of the event represents every event that has ever been detectable from Earth. If anybody was trying to contact us, the message would have had to originated within this past cone for it to have arrived by the time of this event. The future cone of this event represents everybody that can receive our message. The message can only reach events that lie within this cone. Assuming 'b' and 'a' in the diagram are alien civilizations. The civilization at 'b' lies in the "elsewhere" of the event at the central X. This means that 'b' cannot affect X and X cannot affect 'b'. The civilization at 'a', on the other hand, lies within the future cone of the event at the central X. They will receive our message in the future; however, the message they send will not be able to reach the event at X because it lies in their past cone (unless they are considerably more advanced that us and are capable of time travel.)

The main confusing thing about event cones is that they are two-dimensional (like the diagram above) or somtimes three-dimensional representations of a four-dimensional graph. Also, one of the dimensions in the diagram is time, which behaves very differently from the other three. For example, in the diagram above, 'a', 'b', and 'c' represent events. However, events are usually just physical objects at one instant in time. If you took 'a', 'b', and 'c' to represent other planets, they would make vertical columns in the above diagram (since they remain constant over time.) To put it another way, if 'b' really did represent an alien civilization at one point in time, they would get our message eventually, as they would eventually move into the future cone of the event (assuming they lasted until then.) This also means that all bodies in the diagram are moving upwards (though not neccesarily at a constant rate, once you account for the theory of relativity. But that's a whole different headache.)

There are two types of event cone - self-orientated and event-orientated (the object at the point of the cones). The difference is merely one of perception.

The best way of visualising an event cone is to imagine a star going nova, shooting off interstellar matter (and light) in all directions. These can be visualised as spheres around the star expanding at different speeds. The light event cone is expanding fastest (at 3x108 ms-1, the speed of light). When this sphere reaches a point, at that point of time that place can recognise the event... that the star has gone nova. Before this happens, they have no idea.

Wormholes tend to mess event cones up... imagine a wormhole labelled $-$..

    |\       /   \ 2 /
    | \     /     \ /   
    |  \  $/       $
    |   \ /       / \ 
time|    X       /   \    
    |   / \     /     \   
    |  /   \   /       \ 
    | /     \ /         \  
    |/       \  
Area 2 is outside of X's main event cone, but any light coming through the wormhole is visible here... they can detect that it has gone nova. If the wormhole has different entry and exit times then it is possible to give people hints that the star is going to go nova (if the wormhole's exit is in the star's history event cone...
    |\       /
    | \     /
    |  \  $/
    |\  \ /  /
    | \  X  /
    |  \/ \/
    |  /\3/\
    | /  $  \
    |/  / \  \
In region 3 they have information from the wormhole that the star will go nova and can evacuate...
Is the correct name hypercone?

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