Published online by Cambridge University Press: 16 October 2026
This chapter introduces special relativity as a unifying framework for mechanics and electromagnetism. It starts from the principles of relativity and retardation, showing that a universal signal speed c is incompatible with Galilean transformations and motivates Lorentz covariance. Space and time are combined into four-vectors with an invariant spacetime interval defined by the Minkowski metric, and the Lorentz transformation is derived from the requirement that this interval be the same in all inertial frames. The chapter then develops contravariant and covariant vectors and tensors, leading to a geometric view of scalar, vector, and tensor laws. Relativistic dynamics is formulated using proper time, four-velocity, four-momentum, and the invariant energy–momentum relation. Finally, Maxwell’s equations are rewritten in covariant form using the four-potential, the four-current, and the electromagnetic field tensor, and the Lorentz force law is cast as a four-vector equation for charged particle motion.
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