Bug-Rivet Paradox Calculator
Explore special relativity through the Bug-Rivet Paradox - analyze length contraction and simultaneity
Calculate Bug-Rivet Paradox
Rest length of the rivet shaft
Length of the hole where bug sits
Speed at which rivet approaches the hole (β = v/c = 0.5000)
Preset Scenarios
Bug-Rivet Paradox Analysis
Bug Safety Analysis
Critical Velocity β₁
Critical Velocity β₂
🐛 Bug Frame Analysis
Physics Interpretation
Classic Example
Standard Textbook Setup
Rivet length (a): 5 cm
Hole length (L): 7 cm
Length ratio (a/L): 5/7 ≈ 0.714
Bug position: Bottom of hole
Critical Velocities
β₁ = (1-(5/7)²)/(1+(5/7)²) = 0.3243
β₂ = √(1-(5/7)²) = 0.7000
At v = 0.3243c: Bug just gets squished
At v = 0.7000c: Event order becomes ambiguous
The Paradox Explained
Setup
A rivet shorter than a hole moves at relativistic speed toward the hole
Bug Frame
Rivet appears contracted but tip continues after head stops
Rivet Frame
Hole appears contracted, events may seem simultaneous
Resolution
No paradox - information takes time to travel in rigid bodies
Key Physics Concepts
Length Contraction
L' = L/γ = L√(1-β²)
Lorentz Factor
γ = 1/√(1-β²)
Simultaneity
Events simultaneous in one frame may not be in another
Information Speed
Limited by speed of light c
Understanding the Bug-Rivet Paradox
What is the Bug-Rivet Paradox?
The Bug-Rivet Paradox is a thought experiment in special relativity that explores the consequences of length contraction and the relativity of simultaneity. A rivet, initially shorter than a hole, moves at relativistic speeds toward the hole where a bug sits at the bottom.
The Physics Challenge
Due to length contraction, the rivet appears even shorter in the bug's frame. However, when the rivet's head hits the wall, the information about this impact takes time to reach the tip. During this time, the tip continues moving and may reach the bug.
Critical Velocities
β₁ = (1-(a/L)²)/(1+(a/L)²)
Above this velocity, the bug gets squished in both frames
β₂ = √(1-(a/L)²)
Above this velocity, event order appears reversed between frames
Resolution
The paradox is resolved by understanding that perfect rigidity doesn't exist in relativity. Information about the head's impact travels at finite speed through the rivet material, preserving causality while explaining the apparent contradictions.
Three Velocity Regimes
v < β₁c (Safe Zone)
Bug survives in both reference frames. The rivet tip stops before reaching the bug after receiving information about the head's impact.
β₁c ≤ v < β₂c (Danger Zone)
Bug gets squished, but both frames agree on the sequence: head hits wall first, then tip reaches bug before stopping.
v ≥ β₂c (Paradox Zone)
Frames disagree on event order due to relativity of simultaneity. The rivet frame sees tip hit first, but causality is preserved.