Energy, Mass, Momentum

Prompt

“Draw a hyperbolic triangle showing energy, mass, and momentum.”

Context

Estimated Time: 10 minutes, including wrap-up

This SWBQ unifies the concepts of energy and momentum and provides a geometric tool for computing energy, momentum, and mass from each other.

Students should know the basics of hyperbola geometry, and be familiar with proper time, 4-velocity, 4-momentum.

Wrap Up

• Momentum, energy, mass behave like space, time, proper time.
• These quantities are geometrically related to each other, using hyperbolic triangle trig.
• Derive the relationship $E^2-p^2c^2=m^2c^4$.
• Point out that this relationship holds even when $m=0$, so that massless particles can also be analyzed this way.

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