Relative Time And Space Intervals

Davies & Gribbin (1992: 70, 71, 73-4):

In other words, the simultaneity of events that are separated in space is relative. Different observers in different states of motion measure different durations between the same pair of events. In a similar fashion, it turns out that different observers in different states of motion will measure different distances between the same pair of events. …

When an observer changes his or her state of motion, the relationship between space and time is altered, so that distances and durations are perceived differently. …

To achieve a noticeable effect, the motion must be at a sizeable fraction of the speed of light. The effect is once again to alter the apparent length of the broom handle, making it appear shorter in the direction of motion. This is simply the length-contraction effect we mentioned earlier. Conversely, time intervals are stretched, or dilated by the motion. In a sense, an interval of space is traded for an interval of time. 

So how much space is each unit of time worth? Since the conversion factor is the speed of light, one second is worth the distance light travels in one second — about 300,000 km, or one light-second.

 

Blogger Comments:

To be clear, this is Special Relativity. Compared with a slower moving body, for a faster moving body, time intervals are relatively expanded and space intervals in the direction of motion are relatively contracted. This means that, for the faster moving body, processes unfold relatively more slowly — the interval between each tick of a clock is longer — and the body traverses more space intervals per unit of time in the direction of motion.

This is the same effect as gravity in General Relativity. Time intervals are relatively more expanded, and space intervals are relatively more contracted with proximity to the centre of mass. A falling body traverses increasingly more intervals of space per unit of time as it falls — i.e. accelerates — but the process itself unfolds increasingly more slowly — i.e. time units 'stretch' — as the body approaches the centre of mass.

To be clear, it is not so much that time and space intervals are "traded", but that the relative extent of time intervals and space intervals is inversely proportional.