An inertial observer measures a longer interval between ticks of a moving clock than that clock’s own proper time.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, consistent units, and the stated model assumptions
Source
OpenStax, College Physics 2e, §28.2 (Paul Peter Urone and Roger Hinrichs)OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example. The textbook section reference was corrected.
An inertial observer measures a longer interval between ticks of a moving clock than that clock’s own proper time. Proper time is measured in the frame where the two clock events occur at the same location.
| Symbol | Meaning | Units |
|---|---|---|
| Time (dilated) | ||
| Time (proper) | ||
| Velocity | ||
| Speed of Light |
Relate proper time to an inertial observer’s interval.
Compare clock intervals at different relative speeds.
A clock measures 1.00 s of proper time while moving at the listed speed relative to an inertial observer. Find the observer’s interval.
OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example. The textbook section reference was corrected.
Assumptions
FormuLab is a study reference. Verify formulas, units, assumptions, and course-specific conventions before relying on them.
© 2026 FormuLab. All rights reserved.