## Exploration 2: The Twin "Paradox"

*Please wait for the animation to completely load.*

In this Exploration we will be 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
View from Earth-Bound Twin and play.

- How fast is the moving twin traveling relative to the stationary twin
(measured in c)?
- What is 1/slope of the red and green worldlines, respectively?

Select
Pulses from Earth-Bound Twin and
play. The two twins agree to send each other a light pulse once a year on the
anniversary of the traveling twin's departure. Also shown is the
stationary observer's clock.

- What is the frequency of the stationary twin's light pulse?
- How many light pulses reach the moving twin during her outbound
trip? During her inbound trip?
- At the end of the trip how old is the stationary twin and how old
is the traveling twin? Why this discrepancy?

One of the most important concepts in special relativity is the idea of the
spacetime interval. The spacetime interval is (Δs)^{2} =
(Δ ct)^{2} - (Δx)^{2 }which is the Pythagorean theorem of
spacetime.

Select
View from Earth-Bound Twin and play.

- Calculate the spacetime interval for the stationary
observer during the animation.
- Calculate the spacetime interval for the traveling twin's
outbound trip.
- Calculate the spacetime interval for the traveling twin's inbound
trip.
- Compare the sum of (g) and (h) to (f). Why is there this
difference?