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## Paradoxes I: Instructor's Guide

### Main Ideas

- Most “paradoxes” result from poorly-posed questions.
- All observers must agree!
- Special relativity changes our understanding of matter.

### Students' Task

*Estimated Time: 45–80 minutes, including wrap-up*

Groups are asked to analyze one of two standard paradoxes:

##### Pole & Barn

A 20 foot pole is moving towards a 10 foot barn fast enough that the pole appears to be only 10 feet long. As soon as both ends of the pole are in the barn, slam the doors. How can a 20 foot pole fit into a 10 foot barn? From the point of view of the pole, how long is the barn? What does the pole see?

##### Space War

Two rockets of equal rest length pass each other. Rocket A fires a gun mounted in its tail at Rocket B when the tip of Rocket A reaches the tail of Rocket B. Does the bullet hit or miss Rocket B?

- Have each group select one of these paradoxes.
- Half the group should choose the lab frame; the other half the rocket frame.
- Each subgroup should determine what they observe in their chosen frame.
- Each group should then reconcile their two descriptions.

### Prerequisite Knowledge

- at least a qualitative understanding of length contraction
- basic understanding of spacetime diagrams

*These paradoxes are very effective when used early in the course, before
students have spent much or any time studying spacetime diagrams. In this
case, it is useful to revisit these paradoxes later in the course using
spacetime diagrams; see this activity.*

### Props/Equipment

- Table top whiteboards and markers

### Wrap-Up

- Discuss these two paradoxes (15 minutes)
- Consider manhole and detonator animations (20 minutes)

OSU has a copy of the software RelLab, originally written for old Macs, but which works fine in an emulator such as Mini vMac. This software converts animated scenarios between reference frames. If a copy is available, use animations to discuss these two paradoxes.

If time permits, continue the discussion by having the entire class analyze further paradoxes, namely the two manhole paradoxes and the detonator paradox.