Exercise 2: More on the Twin "Paradox"

Pulses from Traveling Twin Pulses from Traveling Twin: ST Stationary Twin Actually Sees This

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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.

  1. What is the frequency of the moving twin's light pulse in the moving frame?
  2. 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?
  3. 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.
  4. 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.

  1. Where was pulse A (received at t = 2 years) emitted?
  2. Where was pulse B (received at t = 4 years) emitted?
  3. 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).

  1. How fast does the moving twin appear to be moving on her outbound trip (measured in c)?
  2. 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.