Length Contraction, Worldlines, and Spacetime Diagrams
Geometry of spacetime
Length contraction
An object moving relative to an observer is measured to have a shorter length along the direction of motion: Here is the proper length measured in the object’s rest frame.
Worldlines
A worldline is the path of an object through spacetime. A stationary object has a vertical worldline on a spacetime diagram, while a moving object has a slanted worldline.
Reading spacetime diagrams
On a spacetime diagram, the light cone marks paths at speed . Events inside the cone can influence each other causally; events outside cannot be connected by slower-than-light signals.
Visualization tip
Many relativity paradoxes become easier to resolve when you draw worldlines and simultaneity slices rather than relying on verbal intuition.
Which length is proper length?
Proper length is defined in the rest frame of the object.
Correct answer: Length measured in the object's rest frame
What geometric object represents an object's history in spacetime?
A worldline traces the sequence of positions of an object through time.
Correct answer: Worldline
Spatial and spacetime intuition
Everyday intuition
- Objects move through space over time
- Time is assumed universal
Relativistic intuition
- Objects trace worldlines in spacetime
- Different observers slice spacetime differently