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Energy, Mass, Momentum: Instructor's Guide

Main Ideas

  1. Momentum, energy, mass behave like space, time, proper time.
  2. These quantities are geometrically related to each other, using hyperbolic triangle trig.

Students' Task

Estimated Time: 10 minutes, including wrap-up

Students should be asked to answer the following questions on their whiteboards:
Draw a hyperbolic triangle showing energy, mass, momentum.

Prerequisite Knowledge

  • Basics of hyperbola geometry.
  • Proper time, 4-velocity, 4-momentum.



  • Derive the relationship E2−p2c2=m2c4.
  • Point out that this relationship holds even when m=0, so that massless particles can also be analyzed this way.

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