Physics · University
Proper time from coordinate time
The clock moves at a constant speed between the two events; proper time is measured by that clock.
Method and conditions
The clock moves at a constant speed between the two events; proper time is measured by that clock.
Δτ = Δt/γ
Worked examples
An inertial laboratory measures 197 s between two events on a clock moving at 0.68c. What elapsed proper time does that clock record? Round the final result to 4 decimal places if needed. Answer in s.
Divide laboratory time by γ: Δτ=197√(1−0.68²).
144.4428 s
An inertial laboratory measures 122 s between two events on a clock moving at 0.04c. What elapsed proper time does that clock record? Round the final result to 4 decimal places if needed. Answer in s.
Divide laboratory time by γ: Δτ=122√(1−0.04²).
121.9024 s
Try it
An inertial laboratory measures 173 s between two events on a clock moving at 0.58c. What elapsed proper time does that clock record? Round the final result to 4 decimal places if needed. Answer in s.
An inertial laboratory measures 85 s between two events on a clock moving at 0.74c. What elapsed proper time does that clock record? Round the final result to 4 decimal places if needed. Answer in s.
Check your work
Answers and marking notes
- 140.9287 s
Divide laboratory time by γ: Δτ=173√(1−0.58²).
- 57.1716 s
Divide laboratory time by γ: Δτ=85√(1−0.74²).
Further reading and review references
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