Teaching Relativity Using Spacetime Graphs

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Teaching Relativity Using Spacetime Graphs

• Dr. Michael E. Huster
• Simpson University
• Redding, CA
• 9 April, 2005

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Outline

• Students have a difficulty understanding or
  calculating concepts in relativity
• Time dilation
• Length contraction
• Spacetime interval
• Students can learn to use spacetime graphs to
  calculate and understand these effects

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Introducing Spacetime Graphs

• These are used as classroom activities, homework
  evaluation
• Spacetime graphs are introduced using a simple
  example
• Emphasize time runs vertically
• Students work through two examples

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The First Spacetime Graph

• Draw worldlines for two different trips
• Different speeds have different slopes
• Standing still is a vertical line

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Second Graphs A Planet

• More of a challenge

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Student Input

• One pointed out the charts for Jupiters Moons in
  astronomy magazines are spacetime graphs!

Day of the month
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Time Dilation

• The usual thought experiments are used to
  introduce
• time dilation
• length contraction
• Introduce the formulas

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Moving Rocket Experiment
Larry sees the light flash start by him, bounce
to the ceiling and back down
Mary sees the light travel a diagonal path
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Introduce Relativistic Axes

• feet and nanoseconds are used
• Speed of light 1 ft / ns
• Light always travels in lines at 45º
• Some instructors introduce a meter as a unit of
  time instead

The light cone
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Time Dilation Activity

• The students are guided through graphing the
  following experiment in two different reference
  frames
• Three events A, B, C

C
B
A
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Rest Frame of the Rod
Draw rod
Draw worldlines of ends of rod
C
Label events draw worldlines of light flash
B
Ask for the time interval A ? C
A
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Reference Frame Moving at 0.6 c
Draw length contracted rod
C
Draw worldlines of ends of rod
Label events draw worldlines of light flash
B
Ask for the time space interval A ? C
A
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Important Points

• Students calculate time dilation by constructing
  the graph
• Compare with formula tM g t0
• The invariant slope of 1 for light is the
  relativity postulate

A rich set of concepts are associated with these
graphs
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Loss of Simultaneity

• A similar activity with a light flash going to
  the front and back of a rocket shows loss of
  simultaneity

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The Pole Vaulter and the Barn Paradox

• This paradox addresses how both observers can see
  the other as length contracted
• A very rich scenario to graph
• Two proper lengths pole barn
• Proper times
• Ends of pole entering barn
• Doors opening
• Spacelike timelike intervals

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Farmers Athletes Graphs
Farmerss View
Athletes View
spacelike
timelike
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More Questions

• What are the proper lengths of the shed and the
  pole?
• What is the spacetime interval between events
• A B
• A C
• B D
• C D
• A D
• B C

The students have to wrestle with spacelike
versus timelike separation
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The Twin Paradox

• Set up the story so each twin sends equally
  spaced light messages to the other
• Students can calculate the time each one
  experiences

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Traveling Twin
Stay-at-Home Twin
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Summary

• Spacetime graphing is used to help students
  visualize relativistic effects
• Students graph examples
• Time dilation
• Length paradoxes
• Twin paradox
• Students can calculate effects using spacetime
  graphs