10- The relativity of length

What happens to the length of an object moving relative to an observer?

What happens to the length of an object moving relative to an observer?

It contracts along the direction of motion; this is called length contraction.

What is the formula for length contraction?

• L₀ = the proper length (length in the object's rest frame)

• L = the contracted length observed in a moving frame.

What is proper length (L₀)?

The length of an object measured in its own rest frame (where it is stationary).

What happens to the length of an object as its speed approaches the speed of light (v → c)?

The length contracts to zero in the direction of motion!

What happens to length contraction at low speeds (v ≪ c)?

γ ≈ 1, so L ≈ L₀, meaning the contraction effect is negligible.

Graph of 1/γ against β.

Does an object contract in all directions?

No, only along the direction of motion; perpendicular dimensions remain unchanged.