Line of Simultaniety
Line of Simultaneity - A line in spacetime connecting the all the events simultaneous with now.
Consider the animated spacetime diagram shown below (Courtesy of
Wikipedia Commons, ).
It depicts a spacetime diagram with three
events, A, B and C, as seen by three different observers. The animation replays the same span of time from the point of view of each observer. One observer is at rest in the reference frame, the speed v=0 case. Another observer is traveling to the right along the x-axis at 0.3 times the speed of light, the speed v=.3c case. The third observer is traveling to the left along the x axis at .5 times the speed of light, the v=-.5c case. All three observers arrive at the intersection of the x-axis and t-axis simultaneously.
The grid lines that intercept the t-axis are lines of constant time. Those that intercept the x-axis are lines of constant location. The white line sweeping up the t-axis represents the line of simultaneity for each observer, the line connecting all the events simultaneous with now.
For the v=0 observer the events A, B and C are simultaneous. For the v=3c observer events A, B and C occur in order C, B, A. For the v=-.5c observer the order of events is A, B, C. Notice that the event B happens at the same now instant for all three observers. It is only events that are separated by space-like
that have their order changed by relative motion. All events lying within the shaded areas, events separated by a time-like interval, occur in a fixed order for all observers.
Notice that volume of spacetime in the shaded area, between the white now line and and the spacetime point where B is located shrinks to zero as now approaches that point from below. It is from this volume of spacetime that any event impacting the state of a system at B's location must originate.