define a stationary observer as one for whom Maxwell's Equations (and their prediction for the speed of light) hold. This would give a practical distinction between moving observers and stationary observers, and an absolute notion of velocity. If this sounds fishy, then you're right! Some new approach was needed to solve this puzzle. Einstein's resolution: special relativity Einstein didn't like the conclusion described above for how exlectromagnatism is connected to Newtonian relativity. Various experiments, notably one performed by Michelson and Morley, could find no evidence that the speed of light was different for different observers. So Einstein proposed that the principle of relativity does indeed hold for electricity and magnetism. He realised that this postulate is self-consistent, but that it requires some profound revisions of our understanding of space and time. Einstein's theory, now known as Special Relativity, implies that two observers moving at some large relative velocity will not agree on the time intervals or distances between events, or even whether two events occur at the same time or at different times. To understand this, we'll have to think carefully about how distances and times are measured and how the measurements as performed by one observer are related to those performed by another observer moving at some constant relative velocity. With the basic assumption that all observers should agree on the speed of light (in a vacuum), we'll see that there are unique, mathematically precise rules for relating measurements made by observers moving at different velocities. These agree with our ordinary intuition in the case where all velocities are much less than the speed of light, but give rise to the startling consequences we have mentioned in cases where velocities become large. Despite these counterintuitive results, the new rules provide a consistent framework for physics involving arbitrary velocities, and are supported by a huge amount of compelling experimental evidence, which we will discuss. Relativistic invariants In order to talk about physics in the new framework, we'll find it useful to think about what quantities will be agreed upon by two observers moving with some relative velocity. These are important, since they are the quantities that the observers can sensibly compare with each other. We'll see that there are invariant (i.e. the same for all observers) notions of distance, time and simultaneity (called "proper distance", "proper time", and "spacelike separation", respectively) that generalize our usual notions. We'll see that many of these new concepts can be understood in a pictorial way using spacetime diagrams. Relativistic energy and momentum After understanding the new framework for measuring and comparing lengths and times we'll see that the usual definitions of momentum and energy will have to be modified in order that the conservation of energy and momentum still hold. We'll see that the correct definition of energy