Inertial frames of reference

A frame of reference provides a coordinate system for describing where events happen and a clock for describing when they happen. The motion of an object is described relative to that frame.

An inertial frame of reference is one in which a free object—an object with no resultant force acting on it—remains at rest or moves with constant velocity. Its velocity does not change in speed or direction. An object can therefore be moving and still be described from an inertial frame.

A frame moving without rotating at constant velocity relative to an inertial frame is also inertial. For example, a free object at rest in one inertial frame may be moving at constant velocity in another.

A frame accelerating relative to an inertial frame is not inertial. For example, if a spacecraft accelerates relative to an inertial frame, a free object that remains at rest in that inertial frame changes velocity relative to the spacecraft. The object therefore does not move at constant velocity in the spacecraft’s frame, even though no resultant force acts on it.

Postulates of special relativity

Special relativity is built on two postulates about observers who are not accelerating. Each observer describes events from an inertial frame of reference: a frame in which objects with no resultant force acting on them move at constant velocity. Inertial frames can move at constant velocity relative to one another.

The principle of relativity

The laws of physics have the same form in every inertial frame. An experiment governed by those laws works in the same way whether it is performed in one inertial frame or another. No inertial frame is singled out as the preferred frame by the form of the laws.

This does not mean that observers in different frames must measure the same values for every quantity. It means that they use the same physical laws to describe their measurements.

The speed of light in free space

Light travelling in free space has the same speed, $$c$$, in every inertial frame. This speed is approximately $$3.00 \times 10^8\ \mathrm{m,s^{-1}}$$.

The measured speed of light is the same regardless of the motion of either the light source or the observer. For example, two observers moving at constant velocity relative to each other both measure a light pulse in free space to travel at speed $$c$$.