The reading project explores two fundamental approaches, geometric and algebraic, used in the Special Theory of Relativity.
Geometric Approach: The geometric approach to Special Relativity is based on the concept of four-dimensional spacetime. It involves representing physical phenomena, such as events, particles, and fields, using mathematical objects in a four-dimensional spacetime framework. The key mathematical tool used in this approach is tensor calculus, which enables the formulation of equations that remain invariant under Lorentz transformations.
Algebraic Approach: The algebraic approach to Special Relativity focuses on the mathematical formalism of relativistic equations using matrices and vectors. It involves expressing physical quantities, such as energy, momentum, and transformations, using algebraic equations and matrices. This approach relies on the Lorentz transformation matrix, which describes how physical quantities transform under relativistic effects like time dilation and length contraction.