Bug-Rivet Paradox Calculator

Your details

Choose whether to enter lengths in meters or millimeters. Speed is always given as a fraction of the speed of light.
The rest-frame length of the rivet shank: measured when the rivet is at rest. This is the longest the shank ever appears.
m
The rest-frame depth of the blind hole in the plate where the bug sits. The bug is at the far end.
m
The speed of the rivet as a fraction of the speed of light c. Enter 0.8 for 80% of light speed.
c
Lorentz factor (gamma)Paradox zone
1.6667

The relativistic factor 1/sqrt(1 - v^2/c^2). At v = 0.8c, gamma = 1.667.

Contracted shank length (plate frame)0.36
Contracted hole depth (rivet frame)0.6
Critical speed (beta_c)0.8
Rivet speed239,833,966m/s
Time for stop-signal to reach tip (plate frame)6.0042ns
Extra distance tip travels after head hits (plate frame)1.44
OutcomeParadox zone: plate frame says safe, rivet frame says squished. The tip reaches the bug before the stop signal arrives.
Contracted shank (plate frame)0.36
Contracted hole (rivet frame)0.6

gamma = 1.6667 at 80.0% of light speed.

  • At beta = 0.800, gamma = 1.6667, so lengths contract to 1/gamma = 0.6000 of their rest values.
  • Plate frame: the moving rivet shank appears 0.3600 m (rest length 0.6 m).
  • Rivet frame: the hole appears 0.6000 m (rest depth 1 m).
  • The paradox zone begins at the critical speed beta_c = 0.8000.

Next stepThis is the classic paradox zone. The resolution is the relativity of simultaneity: in the plate frame the rivet head hits first and the tip is still moving; in the rivet frame the tip reaches the bug first. Both are correct. The tip physically reaches the bug because the stop signal from the head cannot outrun the tip at near-light speeds.

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