TABLE OF CONTENTS Physical phenomena are conventionally described relative to some frame of reference which allows us to define fundamental quantities such as position and time. Of course, there are very many different ways of choosing a reference frame, but it is generally convenient to restrict our choice to the set of rigid inertial frames. A classical rigid reference frame is the imagined extension of a rigid body. For instance, the Earth determines a rigid frame throughout all space, consisting of all those points which remain rigidly at rest relative to the Earth, and to one another. We can associate an orthogonal Cartesian coordinate system S with such a frame, by choosing three mutually orthogonal planes within it, and measuring x, y, and z as perpendicular distances from these planes. A time coordinate must also be defined, in order that the system can be used to specify events. A rigid frame, endowed with such properties, is called a Cartesian frame. The description given above presupposes that the underlying geometry of space is Euclidian, which is reasonable provided that gravitational effects are negligible (we shall assume that this is the case). An inertial frame is a Cartesian frame in which free particles move without acceleration, in accordance with Newton's first law of motion. There are an infinite number of different inertial frames, moving with some constant velocity with respect to one another.
The key to understanding Special Relativity is Einstein's Relativity Principle, which...
