A bug sits at the bottom of a hole; a rivet with a shaft longer than the hole flies in at relativistic speed. In the plate frame the shaft is contracted and seems too short to reach the bug; in the rivet frame the hole is even shallower. The resolution: no object is perfectly rigid, so the shaft tip keeps moving after the head stops – the bug is squashed in every frame.
How to use the Bug–Rivet Paradox Calculator
- Rivet shaft rest length
- Hole rest depth
- Speed β = v/c
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the rivet shaft length, the hole depth and the speed.
Inputs explained
| Field | What to enter |
|---|---|
| Rivet shaft rest length | Units: cm, mm, m, in, ft |
| Hole rest depth | Units: cm, mm, m, in, ft |
| Speed β = v/c | A number |
What each result means
- Lorentz factor γ = 1÷sqrt(1 – [Speed β = v÷c]^2)
- Shaft length in the plate frame = [Rivet shaft rest length]×sqrt(1 – [Speed β = v÷c]^2)
- Hole depth in the rivet frame = [Hole rest depth]×sqrt(1 – [Speed β = v÷c]^2)
Example values
How the main result changes when Rivet shaft rest length changes and everything else stays at the example values above:
| Rivet shaft rest length (cm) | Shaft length in the plate frame (cm) |
|---|---|
| 0.5 | 0.3 |
| 0.75 | 0.45 |
| 1 | 0.6 |
| 1.25 | 0.75 |
| 1.5 | 0.9 |
| 2 | 1.2 |
Formula
γ = 1/√(1 − v²/c²), shaft (plate frame) = L_shaft/γ, hole (rivet frame) = L_hole/γ
Worked example
Inputs — Rivet shaft rest length: 1 cm; Hole rest depth: 0.8 cm; Speed β = v/c: 0.8.
Results — Lorentz factor γ = 1.66667; Shaft length in the plate frame = 0.6 cm; Hole depth in the rivet frame = 0.48 cm; Naive plate-frame answer = Shaft seems too short – bug "survives"; Correct answer (both frames) = The bug is squashed.
Key terms
- Rigid body
- An object that cannot deform – impossible in relativity.
Frequently asked questions
Why is the bug squashed in the plate frame too?
The shaft tip can't learn that the head has stopped faster than light, so it keeps going.
Does relativity forbid rigid bodies?
Yes – a perfectly rigid body would transmit signals instantly.
Is this a real experiment?
It is a thought experiment illustrating simultaneity and causality.
Where does the paradox come from?
Assuming the whole rivet stops at once.