As a spacecraft moving at 0.92 c travels past an observer on Earth, the Earthbound observer and

step 1 As a spacecraft, moving at 0 .9 .9 .C. travels past an observer on Earth, the Earth -bound obser

As a spacecraft moving at 0.92 c travels past an observer on...

As a spacecraft moving at $0.92 \mathrm{c}$ travels past an observer on Earth, the Earthbound observer and the occupants of the craft each start identical alarm clocks that are set to ring after $6.0 \mathrm{~h}$ have passed. According to the Earthling, what does the Earth clock read when the spacecraft clock rings?

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Key Concepts

Time Dilation

This is a fundamental aspect of special relativity where time intervals measured by clocks in motion relative to an observer appear longer than those measured by clocks at rest with respect to that observer. In problems like these, the moving clock (measured in its own frame) experiences proper time, while an observer in another inertial frame sees the moving clock as running slower, necessitating a comparison of different time intervals due to relativistic effects.

Lorentz Factor

The Lorentz factor, often denoted by gamma (?), quantifies the amount of time dilation (and length contraction) experienced due to relative motion at significant fractions of the speed of light. It is calculated as 1/sqrt(1 - v²/c²), where v is the relative velocity and c is the speed of light. This factor is essential when determining how observed times compare between different inertial frames.

Proper Time

Proper time is the time interval measured by an observer who is at rest relative to the event being timed. In the context of the problem, the spacecraft's own clock measures the proper time, meaning it records the time elapsed in its rest frame, which is then compared to the dilated time seen by an Earth-bound observer.

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