*Note: Click-drag to measure coordinates. The rest (moving) frame uses the
gray (blue) coordinates.
The speed is presented as a fraction of c.*

The Lorentz transformation shown above is the coordinate transformation predicted by Einstein's Special Theory of Relativity. The horizontal axis measures the x position of an event and the vertical axis measures the time of an event.

**Section 4 Exercises:**

- Click on the Galilean transformation and vary the velocity. Give an explanation for the manner in which the blue lines change.
- Do the same as in Exercise 1 for the Lorentz transformation.
- Demonstrate that the Lorentz transformation is being used here by adding an event at {2,2} in the rest frame and measuring it's coordinates in the moving frame. Do these coordinates agree with your calculation using the Lorentz transformation? Show your calculation.
- Add a second event in the rest frame at {1,-2}. Does
**(delta s)**? Is the separation between these two events space-like, light-like or time-like?^{2}= (delta s')^{2} - Pick any two events in the rest frame that are space-like in separation. Adjust the velocity to find the velocity the moving frame must have in order for these events to be simultaneous? (Pick events that represent a non-trivial example.) Confirm your result using the Lorentz transformation.