Spacetime
Spacetime Mechanics
3D Diagrams
Zero Intervals
Proper Time
The Two Towers
Spacetime & Reality
Spacetime Mechanics
The mechanics of spacetime is fundamentally based on the concept of the spacetime interval. This may be described loosely as the "distance" in four dimensional spacetime between one event and another.
Spacetime diagrams are used to express spacetime relationships. The simplest way of showing this is with time shown as the vetical axis and spatial distances horizontally. The time interval and spatial distance can then be combined if we use appropriate units. One way to do this is by measuring time in seconds, and distances in light-seconds (i.e. the distance that light travels in a second).
An event A (person A clapping) is separated in space and time from person B clapping, and from person C clapping. In the case of B, the time interval is larger than the spatial distance, but for C the spatial distance is larger than the time interval, as shown on the diagram. However, this does not properly represent the relationship because spatial distances and time intervals do not combine in the manner that you might expect:
- Spatial distances combine according to the Pythagorean theorem.
- So, mathematically: d2 = x2 + y2 + z2
Where:
d is the spatial distance (in light-seconds).
x, y and z are the distances in the three spatial dimensions (in light-seconds). - But, spatial distances are subtracted from the time intervals to derive the spacetime interval.
- So: s2 = t2 - d2
Where:
s is the spacetime interval (in seconds or light-seconds).
t is the time interval (in seconds).
d is the spatial distance (in light-seconds).
So the relationship between event A and B, for which the time interval is greater than the spatial interval, is said to be "timelike", because, when the spatial interval is subtracted from the time interval, a time interval (AB') remains. Whereas the relationship between event A and C, for which the spatial interval is greater than the time interval, is said to be "spacelike", as a spatial interval remains when they are combined (the distance AC').
Between the timelike and spacelike areas lies a line at 45o for which the time interval and spatial interval is the same at each point. This marks the boundary between the timelike and spacelike intervals.
