Length depends on the reference frame
When an object moves at a speed close to relative to an observer, its measured length in the direction of motion is shorter than the length measured in the object's own rest frame.
Proper length, , is the length measured in the reference frame in which the object being measured is stationary.
An observer moving relative to that object measures a shorter value, denoted .
| Length | How it is measured |
|---|---|
| Proper length, | The object is stationary relative to the observer. |
| Observed length, | The object is moving relative to the observer. |
Since the proper length is measured in the object's rest frame, it is the largest measured length.
Measuring the endpoints
The length of an object is the separation between its two ends. For an observer who sees the object moving, the positions of both ends must be recorded at the same time in that observer's frame.
If the endpoints are at positions and , the observed length is
In the object's own rest frame, with endpoint coordinates and ,
Exam Tip: Identify the proper length by asking which observer is at rest relative to the object or distance being measured. Do not automatically assume that the Earth observer measures the proper length.