Spacetime
Spacetime Mechanics
3D Diagrams
Zero Intervals
Proper Time
The Two Towers
Spacetime & Reality
3D Diagrams
In Spacetime Mechanics we've shown the spacetime diagram two dimensionally, but it is often represented three dimensionally, with time shown as the vertical (z) axis and space represented by the horizontal (x and y) axes. I.e. One of the spatial dimensions is suppressed to allow time to be included in the 3D representation.
In this 3D diagram, the line dividing the timelike and spacelike intervals becomes a double cone. The front cone stands point downwards on top of the 2D plane representing 3D space. The back cone stands with its point upwards, below the plane. Event A is at the point where the two cones meet the plane.
Events within the front cone are timelike (with respect to A) and could be caused by event A. Events in the back cone are also timelike (with respect to A) and are past events that could have caused event A. Events outside the cones are spacelike (with respect to A) and can neither cause, nor be caused by, event A.
The surface of the two cones represent the spacetime points where the spatial and time intervals are exactly the same (with respect to event A). We noted above, that the spatial distance is subtracted from the time interval to arrive at the spacetime interval. Hence, this has the strange effect that, the spacetime interval at each point on the surface of the cones is zero.
