Summarizing Length Contraction

Summary

• All observers agree upon relative speed.
• Distance depends on an observer’s motion. Proper length \({L}_{0}\) is the distance between two points measured by an observer who is at rest relative to both of the points. Earth-bound observers measure proper length when measuring the distance between two points that are stationary relative to the Earth.
• Length contraction \(L\) is the shortening of the measured length of an object moving relative to the observer’s frame:
  \({\text{L=L}}_{0}\sqrt{1-\cfrac{{v}^{2}}{{c}^{2}}}=\cfrac{{L}_{0}}{\gamma }.\)

Glossary

proper length

\({L}_{0}\); the distance between two points measured by an observer who is at rest relative to both of the points; Earth-bound observers measure proper length when measuring the distance between two points that are stationary relative to the Earth

length contraction

\(L\), the shortening of the measured length of an object moving relative to the observer’s frame: \({\text{L=L}}_{0}\sqrt{1-\cfrac{{v}^{2}}{{c}^{2}}}=\cfrac{{L}_{0}}{\gamma }\)