Space-time (Minkowski) Diagrams

Galilean Transformation Lorentz Transformation

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:

  1. Click on the Galilean transformation and vary the velocity.  Give an explanation for the manner in which the blue lines change.
  2. Do the same as in Exercise 1 for the Lorentz transformation.
  3. 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.
  4. Add a second event in the rest frame at {1,-2}.  Does (delta s)2 = (delta s') 2?  Is the separation between these two events space-like, light-like or time-like?
  5. 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.