Applications and Paradoxes
PHYS 401 · Module 6
This module applies special relativity to famous thought experiments and real technologies. Students resolve the twin paradox, barn-pole paradox, Doppler shifts, and the relativistic corrections needed for GPS.
Lessons in this module
The twin paradox
The twin paradox compares different worldlines between the same events. This lesson resolves the apparent symmetry and explains why the traveling twin ages less.
The barn-pole paradox
The barn-pole paradox shows how length contraction and relativity of simultaneity fit together. This lesson resolves the apparent contradiction about whether a fast pole fits inside a barn.
Relativistic Doppler effect
The relativistic Doppler effect combines wavefront arrival changes with time dilation. This lesson derives longitudinal shifts and explains redshift, blueshift, and transverse Doppler effect.
GPS satellites and general relativistic corrections
GPS requires relativistic timing corrections to work accurately. This lesson explains special relativistic satellite motion, gravitational time dilation, and why full GPS timing uses general relativity.
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