Activity Structure

This is a kinesthetic activity to help derive the expression for time dilation.

2 people are needed for this skit. It helpts to have each person toss a small ball in the air to represent a photon in the light clock.

Prompt

Have one person walking with their light clock and one person standing still with their light clock.

“For each light clock, consider two events: the photon is emitted and the photon is detected. How would each person describe these events for a tick of my light clock? For hers?

How do the time intervals for your light clock in (1) your reference frame \(\Delta t\) and (2) your friend's reference frame \(\Delta t'\) compare?

Student Conversations

• Symmetry: "My photon is emitted and detected at the same horizontal coordinate in my reference frame. From her reference frame, my light clock travels a distance between emission and detection of the photon. Similarly, her photon is emitted and detected at the same horizontal coordinate in her reference frame. From my reference frame, her light clock travels a distance between emission and detection of the photon. They situations are exactly symmetric."
• When 2 events happen at the same spatial coordinate (colocated) My clock measures the proper time interval because the emission and detection events happen at the same spatial (\(x\)) coordinate in my reference frame. Since \(\gamma \gt 1\), that the time interval I observe for my own clock is shorter than the time interval for my clock measured in any other reference frame. I measure a special time interval, the proper time. The proper time is the time measured by a clock moving with the events. That clock measures the shortest time between the events.