Page "Length contraction" Paragraph 14

Thus the definition of simultaneity is crucial for measuring the length of moving objects.

In Newtonian mechanics, simultaneity is absolute and therefore and are always equal.

Yet in relativity theory the constancy of light velocity in all inertial frames in connection with the relativity of simultaneity destroys this equality.

So if an observer in one frame claims to have measured the object's endpoints simultaneously, the observers in all other inertial frames will argue that the object's endpoints were not measured simultaneously.

The deviation between the measurements in all inertial frames is given by the Lorentz transformation.

As the result of this transformation ( see Derivation ), the proper length remains unchanged and always denotes the greatest length of an object, yet the length of the same object as measured in another inertial frame is shorter than the proper length.

This contraction only occurs in the line of motion, and can be represented by the following relation ( where is the relative velocity and the speed of light )