Special relativity is 'special' in the sense that it is restricted. The principle of relativity states that the laws of physics are the same in all inertial reference frames. In such a reference frame a 'free' body will continue at rest or at constant velocity until acted upon by a resultant force. However, there also exist reference frames in which this does not appear to be the case. In these frames bodies spontaneously accelerate when released. Three obvious examples are: (i) that coffee tends to slop from a cup when the cup rests on a table in an accelerating train; (ii) that we experience a 'centrifugal force' pushing us to the outside of a vehicle when it corners; and (iii) that objects released close to the earth have a free-fall acceleration directed toward the Earth's centre. Thus acceleration, rotation and gravitational fields all produce 'non-inertial' reference frames. In these non-inertial frames the spontaneous accelerations can be accounted for using normal Newtonian mechanics if we introduce new force fields which exert 'inertial forces' on otherwise free bodies. Centrifugal force is an example of an inertial force. The classical approach to
acceleration and rotation is to describe the forces (at least in (i) and (ii)) as 'fictional', arising only because of an inappropriate choice of reference frame. If we transform to an inertial reference frame then the inertial forces are seen to be illusions. It is not that the coffee slops from the cup, the cup accelerates away from the coffee; we are not thrown outwards as the car corners, it turns inwards toward us. Gravitational fields however, are treated rather differently. The acceleration of a free-falling body is said to be 'caused' by a gravitational force arising from the real attraction of massive bodies. These contrasting explanations of apparently similar phenomena are described in more detail below.