Consider a plane polarized electromagnetic wave in the vacuum described by the vector and scalar potentials, A(r, t) Ae(kr-wt) D(r, t) = Poe(kr-wt) where the orientation of the vector Ao is arbitrary. a) Using Maxwell's equations, find the relationship that must hold between Ao and po b) Using the principal of gauge invariance, show that one can transform to a new but physically equivalent vector potential which is transversely polarized, i.e. Ao k-0. Explicitly find the gauge transformation function x that does this. c) What is the scalar potential p(r, t) in the gauge of part (b)?

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Special Relativity

The theory of special relativity discusses how space and time are related to objects traveling along a straight line at a constant speed. Simply stated, as an object reaches the speed of light, its mass becomes infinite and it is unable to move faster than light. This interstellar speed limit has been the topic of much debate in astronomy, and also in science fiction when people consider how to fly over large distances.