## Exercise 2: More on the Twin "Paradox"

*Please wait for the animation to completely load.*

In this Exploration we will continue considering different aspects of the so-called
twin paradox. Restart. At t =
0 years the traveling twin (represented by the green circle) heads out on her
journey and then returns at t = 10 years **(position given in lightyears)**.
In the top panel the spacetime diagram for the stationary frame is shown.

Select
Pulses from Traveling Twin and play.
Also shown are the stationary observer's clock and the clock that the moving
observer's clock as seen by the stationary observer.

- What is the frequency of the moving twin's light pulse in the moving frame?
- What are the frequencies of the moving twin's light pulses as measured in the stationary twin's frame? Over what time intervals are these frequencies observed? What is the
average frequency?
- How do the
*measured* frequencies compare with the frequencies of the
stationary twin's pulses as measured in the moving twin's frame (from
Exercise 1)? Explain.
- Now compare the
*average* frequency measurements of the stationary (from
Exercise 1) and moving twins and explain.

Select Pulses from Traveling Twin: ST and play.
One way to see what is going on with the twin's pulses is to see the pulses
depicted as blue lines on the spacetime diagram.

- Where was pulse A (received at t = 2 years) emitted?
- Where was pulse B (received at t = 4 years) emitted?
- What can you say from (e) and (f) regarding how the stationary twin
*actually sees*
the motion of the moving twin? The phrase "actually sees" means what a
real (not omnipresent) stationary observer would see including delays due to
light travel time.

Select Stationary Twin Actually Sees This
and play. The orange circle and the orange trajectory on the spacetime
diagram represent what the stationary twin would actually see. (Therefore the orange trajectory on the spacetime diagram is not a
true worldline).

- How fast does the moving twin appear to be moving on her outbound trip (measured in c)?
- How fast does the moving twin appear to be moving on her return trip (measured in c)?
Explain.

Original Physlet-based material authored by Mario Belloni and Wolfgang
Christian and appears in the paper,

"Teaching Special Relativity Using Physlets," *The Physics Teacher*, May
2004.

Narrative of the laboratory exercises authored by Tim Gfroerer.

© 2007 by Mario Belloni, Wolfgang Christian, and Tim Gfroerer.