The light cone of an observer on a world line.

    Caption: A spacetime diagram (but NOT a Minkowski diagram (a special case spacetime diagram)) showing the light cones of an observer on a world line.

    Features:

    1. A world line is a trajectory through spacetime: the 3 dimensions of space and the 1 dimension of time.

    2. In the diagram, 3-dimensional space is represented as stacked 2-dimenional planes each of which is a time slice. For clarity, only one plane is explicitly shown---it has little stars and goes right through the observer.

      The vertical direction is time dimension.

    3. In the diagram, the observer is at rest relative to their own local inertial frame, and so does NOT move in 3-dimensional space.

    4. The observer is at the relativistic present---the apex of the light cones.

    5. The past light cone is all of spacetime events that could affect the observer; the future light cone is all of spacetime events that the observer could affect.

    6. The light cones as we say are all causally connected or, to be finicky, all potentially causally connected to the observer.

    7. Events outside the light cones are NOT causally connected to the observer---nothing there can affect or be affected by the observer.

      At least NOT in special relativity. In the more general general relativity, there is a possibility of connection via the very hypothetical wormholes which also may allow time travel to the past.

    8. Outside the light cone is elsewhere.

      Any events in elsewhere could be past, present, or future relative to the observer (at their point in spacetime) as measured by a second observer depending on motion of second observer.

      But it does NOT matter when those events are measured to be (i.e., past, present, or future) because of the lack of causal connection. No paradoxes (e.g., events happening before their causes) can occur.

    9. In elsewhere, past, present, and future depend on the motion (i.e., reference-frame) of the second oberver.

    10. In particular, simultaneity is reference-frame dependent.

      Two things happening at one instant for me do NOT necessarily happen at one instant for you.

    11. Time does flow at different rates in different reference frames in general.

    12. For those of you of a certain age:

        "I demand the light cones of silence, Chief."
        "Max, you know those never work."
        "I insist."
        Whirr.
        "What did you say?

      You had to have been there in the 1960s.

    Credit/Permission: © User:MissMJ, 2008 / Creative Commons CC BY-SA 3.0.
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