# Lesson Plan: Events in Minkowski Diagrams Physics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to determine the order of events as perceived from different inertial reference frames and determine whether events are simultaneous.

#### Objectives

Students will be able to

- determine which event occurs first out of several in a Minkowski diagram of the rest frame of an observer,
- determine which two events are closest to each other out of several in a Minkowski diagram of the rest frame of an observer,
- realize that there is a difference between seeing an event—that is, the light emitted from the event reaching you, the observer, so that you can see it—and measuring the time at which an event happens, which is independent of the travel time of the light,
- realize that an observer will see two events at the same time if they lie on a line because the light from those events travels along the line but that this is different from those two events occurring at the same time in a given reference frame,
- determine which event occurs first out of several in a Minkowski diagram of nonrest frames,
- determine which event an observer sees first out of several in a Minkowski diagram of nonrest frames,
- determine which two events are closest to each other out of several in a Minkowski diagram of nonrest frames,
- realize that events that are simultaneous in one reference frame may not be simultaneous in another (simultaneity refers to when an event occurs, not when it is seen),
- draw lines of constant time, lines of constant position, and grids of lines of constant time and position for any frame on a Minkowski diagram,
- use lines of constant time and lines of constant position to determine whether two events are simultaneous and the order of occurrence of multiple events,
- use lines of constant position to show how length contraction occurs,
- use lines of constant time to show how time dilation occurs,
- be aware that Minkowski diagrams must be drawn very precisely in order to show relativistic effects correctly.

#### Prerequisites

Students should already be familiar with

- what reference frames are,
- what Minkowski diagrams are,
- drawing nonrest frames on Minkowski diagrams,
- drawing and interpreting world lines on Minkowski diagrams,
- what a line of constant time is in a Minkowski diagram,
- what a line of constant position is in a Minkowski diagram.

#### Exclusions

Students will not cover

- events associated with objects or people that change reference frames (i.e., acceleration, even if it is instantaneous acceleration),
- calculating time dilation or length contraction.