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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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Clock Synchronization and GPS

### Clock Synchronization and GPS

Credit: NASA
Source: http://en.wikipedia.org/wiki/File:GPS_Satellite_NASA_art-iif.jpg

One of the observations of special relativity is that for clocks to be synchronized, the time it takes for the image to reach your eyes must be taken into account when trying to set two clocks in sync.

#### Amazing But True

Credit: Arjan Richtor
Source: http://www.flickr.com/photos/42102924@N02/3884450844

Two clocks snyched to the same time [Figure2]

• Imagine there are two clocks, call them #1 and #2. Assume the distance between each clock is separated by the distance x\begin{align*}x\end{align*} in a reference frame labeled as S. If you were to attempt to set the clocks at the same time by setting at clock #1, reading the time on clock #2, then setting the time at clock #1, you would be unsuccessfully in correctly synchronizing the two clocks. This is because when you are reading the time that is on clock #2, you didn't account for the amount of time that passed for the light to reach your eyes, t=xc\begin{align*}t = \frac{x}{c}\end{align*}, where x\begin{align*}x\end{align*} is the distance between the two clocks and c\begin{align*}c\end{align*} is the speed of light. Therefore, any observer that is not equidistant from the two clocks will read a different time being displayed.
• The importance of synchronization becomes apparent in regards to concepts relating to global positioning systems. At orbital altitudes, clocks will tick faster by tens of thousands of nanoseconds per day because of a weaker gravitational field. Therefore, to ensure that the clocks are synchronized, before the orbiting clock is launched into orbit, the times need to be offset to account for the difference in the gravitational field.

#### Show What You Know

Using the information provided above, answer the following questions.

1. What are the two postulates of special relativity?
2. What does special relativity say about how time behaves when you are traveling at speeds near the speed of light?

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