## What to Remember from Lesson 17

### Lorentz Transformations

The way to recast space and time variables between two inertial frames is by the "Lorentz Transformations." In the limit where the relative speeds are small as compared with the speed of light, the transformations reduce to the "airport" conversion for space and there is no transformation for time coordinates. 

### Speeds In Relativity

Because a speed is a space coordinate interval divided by a time coordinate interval, an object that is moving inside one inertial frame will be observed to have a different speed in a co-moving frame. The manner in which this happens shows that nothing can move faster than the speed of light:

$$
v_H = \frac{v_A+u}{1+\dfrac{u}{c^2}v_A} \nonumber
$$

Here, $u$ is the relative speed of the inertial frames while $v_A$ and $v_H$ are the speeds of the object moving inside of the away and home frames respectively.