Introducing light cones

The region of space from which events can influence you, or which you can influence, depends on the universal speed(often referred to as the speed of light) and the duration for which the light has been on its way or the duration for which the light is allowed to head out into the future.

From now on, only having three dimensions to represent in, and allocating one of those to time, restrict space to two dimensions. So what were spheres of influence become discs of influence – events happening on these discs can influence Alice.

Stack the (thinly sliced) discs, and you get a cone. This one shows the past influence: Combine it with another (flipped in the x-y plane, so reaching into the future) to show events that you could influence, and you get a light cone.

This set of stacked discs, assembled into a cone, are for Alice. She is the witness: the time and space so restricted are personal — valid for her. Alice is the local witness to this light cone.

Alice, Bob and Charlie all have their light cones – there are only local witnesses – and these may or may not notice the same happenings, depending on the separations of Alice, Charlie and Bob and on the duration you consider.