One of the ideas that Einstein’s Theory of Relativity is based upon is the Galilean transformation. This was an attempt by Galileo to create a set of rules that could be applied to moving and stationary frames of reference. The idea was a simple one.

Figure 2 explains the Galilean transformation. Imagine we have two observers named Jack and Jill. Jill is our stationary observer (red). Jack moves at velocity v away from Jill (blue). As he is moving he sends out a beam of light. This beam of light travels at c (300,000km per second) towards Jill. Jill measures the velocity of the light wave. Most people, including Galileo, believed that the velocity of the light wave would be 300,000km per second plus the velocity that Jack was travelling at. This is wrong as the light wave sent to Jill was travelling at c not c + v. Therefore it is not the same light wave (c’ is not equal to c). Einstein concluded from this idea that the problem of time was how it was measured. The light wave in this experiment seems to travel at two different velocities depending on which observer you are. The same is true for time. Einstein saw this problem and discovered the solution. A constant was needed for all observers that did not change when viewed from different points of reference. This was later to become the basis for Einstein’s Special and General theories of relativity.