Special Relativity: Length Contraction

Length Contraction Diagram

Introduction

Another intriguing consequence of Einstein's theory of special relativity is the phenomenon of length contraction.
When objects move at extremely high speeds, particularly close to the speed of light (c), their length appears shortened when observed by a stationary observer.

To visualise length contraction, imagine a fictional cyclist moving very close to the speed of light towards two stationary observers.
From the perspective of the stationary observers, the cyclist appears contracted, but this contraction occurs only in the dimension in which she is moving.

The contracted length (L') observed by a stationary observer can be calculated using the following equation:
L' = L/(1 - v²/c²)
Where:
- L' is the contracted length as seen by the stationary observer.
- L is the proper length of the object measured by the moving object itself.
- v is the relative velocity between the moving object and the stationary observer.
- c is the speed of light.

The Voyager space probe, with a proper length of four meters, is the fastest man-made object, travelling at 17,260 m/s.
We can calculate the contracted length of the Voyager probe as observed by Earth-based observers.

Length Contraction Diagram

Plug in the known values into the length contraction formula:
l' = 4 m × (1 - (17,260² / 299,792,458²))
Calculate this equation to find the contracted length.
In this example, the four-meter-long Voyager space probe appears shortened by just under 7 nanometers when travelling at such high speeds.

It's important to note that relativistic effects, such as length contraction, are generally not noticeable in our everyday experiences.
Even though the contraction is real, it becomes significant only at speeds close to the speed of light, and objects we encounter in our daily lives do not move at such extreme velocities.

bookmarkSummary

Length contraction is a consequence of special relativity, where the length of a moving object appears shortened when observed by a stationary observer.
The length contraction formula relates the contracted length observed by the stationary observer to the proper length measured by the moving object.
The example of the Voyager space probe demonstrates that even at the highest speeds achieved by mankind, the length contraction effect is minuscule and generally not noticeable in practical scenarios.