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# Special Theory of Relativity

## Interpret motion between different objects that are moving at constant speeds relative to each other.

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Credit: Gareth Williams
Source: http://www.flickr.com/photos/gareth1953/6012290797

One of the many thought experiments in physics, the twin paradox discusses what would happen when one of two twins goes on a trip at relativistic speeds.

#### Amazing But True

Credit: Les Bossinas (Cortez III Service Corp
Source: http://en.wikipedia.org/wiki/File:Wormhole_travel_as_envisioned_by_Les_Bossinas_for_NASA.jpg

The twin that traveled into space at very high speeds has aged much slower then the twin on Earth [Figure2]

• Imagine the following: Billy and Jimmy are identical twins. One day Billy jumps into a space ship and travels off at very high speeds; assume Billy travels at a speed that is 80% the speed of light towards an object that is 8 light years away. According to Jimmy, it will take Billy 20 years to make the round trip. If we calculate the time that will elapse on the ships clocks during this trip it will be

tt=tγ=(0.6)(20 years)=12 years\begin{align*}t^{\prime} &= \frac{t}{\gamma}\\ t^{\prime} &= \frac{(0.6)}{(20 \ \text{years})} = 12 \ \text{years} \end{align*}

• Therefore, when Jimmy returns he will have aged only 12 years while his twin Billy will have aged 20 years.
• The paradox is a result of each twin seeing the other traveling. Therefore, Billy and Jimmy should find the other twin to have aged more slowly. This paradox is resolved when it is realized that there is no symmetry in the problem because only one of the twins, Billy, undergoes acceleration and deceleration.

#### Show What You Know

Using the information provided above, answer the following questions.

1. If Billy traveled at only 10% the speed of light for the trip described, how long would time elapse for Jimmy?
2. How much time would elapse for the twin that is on the ship? (Assume he was able to live that long).
3. Why are the previous answers so close? Is something wrong with relativity?

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