Active Reading Solution: Four-Displacement

  1. The horizontal component of the vector tells us the distance traveled.

  2. The vertical component tells us the time elapsed, multiplied by c. In relativistic units c=1 so this is numerically equivalent to the time elapsed in whatever units you are measuring. For example, if the vertical component of DR is 4 light-years, then the journey took four years.

  3. The direction of that vector relates to the speed of the journey. As we have discussed before, speed=1/slope, ranging from a vertical line (speed=0) to a 45o line (light). No journey could have a slope below that 45o line.
Note that all of these components are measured in your coordinate frame (presumably the one in which you drew the x and t axes). Observers in different reference frames would measure different components for DR because they would measure different distances and times for the journey.