Explore the fascinating relativistic paradox of length contraction. Calculate how objects appear shorter when moving at high velocities and understand the relativity of simultaneity.
Last updated: March 2026 | By Summacalculator
Enter value from 0 up to but not including 1 (e.g., 0.8 = 80% speed of light)
Object's proper length in its rest frame
Lorentz Factor (γ)
1.666667
γ = 1/√(1 - v²/c²)
Contracted Length
6
meters (observer frame where object is moving)
The Paradox: In one frame, the moving object is length-contracted. In the other frame, the hole is length-contracted. The apparent contradiction is resolved by the relativity of simultaneity.
The Bug-Rivet Paradox (also called the Barn-Pole Paradox) is a thought experiment in special relativity that illustrates the counterintuitive effects of length contraction and the relativity of simultaneity. Imagine a rivet traveling at relativistic speed toward a hole of the same rest length, with a bug waiting at the bottom of the hole. Due to length contraction, each observer sees the other object as shorter.
From the hole's perspective, the moving rivet is contracted and can fit. From the rivet's perspective, the moving hole is contracted and appears too shallow. This apparent contradiction is resolved because events that are simultaneous in one frame are generally not simultaneous in another.
In the hole's frame, there can be an instant when the whole rivet is inside the hole at once. In the rivet's frame, the hole bottom moves away before the rear of the rivet reaches the entrance. Both observers agree on the physical outcome, but not on which distant events happen at the same time.
γ = 1.1547, length contracts to 86.6025% of rest length
γ = 1.6667, length contracts to 60% of rest length
γ = 2.2942, length contracts to 43.589% of rest length
γ = 7.0888, length contracts to 14.1067% of rest length
A spacecraft 100 meters long travels at 0.8c (80% the speed of light). How long does it appear to observers on Earth?
To Earth observers, the 100-meter spacecraft appears 60 meters long. That is 40% shorter than its proper length. In the spacecraft's own rest frame, it still measures 100 meters.
No—the object does not physically compress in its own rest frame. Length contraction is a frame-dependent measurement effect.
The resolution is the relativity of simultaneity. Events that are simultaneous in one frame occur at different times in another, eliminating the contradiction.
Direct visual appearance is more complicated because of light-travel-time effects. But measured lengths do contract. At 1000 km/h, the contraction is only about 4.293232 × 10^-11%.
Yes. Time dilation accompanies length contraction. Moving clocks run slow by the same Lorentz factor γ.
As velocity approaches the speed of light, γ grows without bound. Length along the direction of motion approaches zero in the limit.
No—only along the direction of motion. Transverse dimensions are unchanged.
Yes. Relativistic effects are confirmed in particle physics, accelerator experiments, and cosmic-ray muon observations.
From the traveler's frame, distances along the direction of motion are shorter. For example, at 0.99c, 4.37 light-years contracts to about 0.616464 light-years.
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