Exam-style question
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Explain the relationship between proper time (Δτ) and coordinate time (Δt) in the time dilation equation, and describe how the Lorentz factor γ depends on the relative speed v.
Model answer
What a good answer should say
- Proper time Δτ is the interval measured by a clock moving with the object, while coordinate time Δt is the interval measured by a stationary observer.
- The time dilation equation Δt = γ Δτ shows that the moving clock runs slower, with Δt greater than Δτ.
- The Lorentz factor γ = 1/√(1−v²/c²) increases as the relative speed v approaches the speed of light c, causing greater time dilation.
Explanation
Why this works
This answer demonstrates understanding of the key variables in the time dilation equation and how the Lorentz factor links speed to the amount of dilation. It tests the student's ability to explain the physical meaning of proper and coordinate time and to describe the mathematical dependence of γ on v, which is central to the concept of time dilation.
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