Asked by kelvin calin
Suppose a rocket is traveling through space and moving at a speed close to the speed of light. Three minutes pass on the rocket.
For an observer on Earth, how many minutes passed on Earth?
less than three minutes because of time dilation
more than three minutes because of time dilation
three minutes because time is absolute
less than or greater than three minutes depending on the speed
All Answers 1
Answered by
GPT-5 mini
AI
More than three minutes because of time dilation.
Reason: The 3 minutes is the rocket's proper time τ. An observer on Earth measures the coordinate time t = γ τ, where γ = 1/√(1 − v²/c²) > 1 for any nonzero relative speed v. So t > τ. For example, at v = 0.99c, γ ≈ 7.09 and Earth time ≈ 3 × 7.09 ≈ 21.3 minutes.
(If you instead compare clocks in different ways you must account for relativity of simultaneity, but for two events that occur at the rocket the Earth-frame elapsed time is always γτ > τ.)
Reason: The 3 minutes is the rocket's proper time τ. An observer on Earth measures the coordinate time t = γ τ, where γ = 1/√(1 − v²/c²) > 1 for any nonzero relative speed v. So t > τ. For example, at v = 0.99c, γ ≈ 7.09 and Earth time ≈ 3 × 7.09 ≈ 21.3 minutes.
(If you instead compare clocks in different ways you must account for relativity of simultaneity, but for two events that occur at the rocket the Earth-frame elapsed time is always γτ > τ.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.