Principle of relativity: Encyclopedia II - Principle of relativity - Galilean relativity

Principle of relativity - Galilean relativity

Historically, the first principle of relativity that was formulated was a principle of relativity of uniform motion suggested by the observation that there doesn't seem to be a phenomenon in dynamics that will allow an observer to establish a zero point of velocity, nor a preferred direction.

Every choice of a zero point of velocity, a choice necessary in order to perform a calculation, constitutes a choice of reference frame. All reference frames that move with respect to each other with constant velocity and in a straight line are called inertial reference frames. The circularity of this definition is a necessity, since there is no preferred inertial reference frame.

In Galilean relativity, reference frames are related to each other in an intuitive way: to transform the velocity of an object from one frame to another, the vector representing the velocity of the object is added to the vector representing the velocity difference between the two reference frames. Such a transformation is called a Galilean transformation. The geometry of space is assumed to be Euclidian, and the measurement of time is assumed to be the same for all observers.

Another way of formulating the observation that there is no phenomenon in dynamics that will allow an observer to establish a zero point of uniform velocity, is to state that the laws of motion are equally valid in all inertial reference frames. For example the following property of motion: the common center of mass of two objects will move in uniform motion and it will also remain in uniform motion when the two objects collide or bounce against each other. This is valid in all inertial reference frames.

Adapted from the Wikipedia article "Galilean relativity", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki