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# 17: Relativistic Mechanics

• 17.1: Introduction to Relativistic Mechanics
Einstein's Special theory of Relativity (1905) and General Theory of Relativity (1916) are revolutionary advances that have had a profound impact on the evolution and understanding of both classical mechanics and modern physics.
• 17.2: Galilean Invariance
Space and time are separable.
• 17.3: Special Theory of Relativity
Einstein's Special Theory of Relativity.
• 17.4: Relativistic Kinematics
Relative differences between Newtonian and relativistic kinematics.
• 17.5: Geometry of Space-time
Four dimensional space-time.
• 17.6: Lorentz-Invariant Formulation of Lagrangian Mechanics
The Lagrangian and Hamiltonian formalisms in classical mechanics are based on the Newtonian concept of absolute time t which serves as the system evolution parameter in Hamilton’s Principle. This approach violates the Special Theory of Relativity. The extended Lagrangian and Hamiltonian formalism is a parametric approach, pioneered by Lanczos, that renders it to a form that is compatible with the Special Theory of Relativity.
• 17.7: Lorentz-invariant formulations of Hamiltonian Mechanics
Extended canonical formation for relativistic mechanics.
• 17.8: The General Theory of Relativity
Einstein’s General Theory of Relativity expands the scope of relativistic mechanics to include non-inertial accelerating frames plus a unified theory of gravitation. That is, the General Theory of Relativity incorporates both the Special Theory of Relativity as well as Newton’s Law of Universal Gravitation. It provides a unified theory of gravitation that is a geometric property of space and time. In particular, the curvature of space-time is directly related to the four-momentum of matter and r
• 17.9: Implications of Relativistic Theory to Classical Mechanics
The Special Theory of Relativity replaces Newton’s Laws of motion; i.e. Newton’s law is only an approximation applicable for low velocities. The General Theory of Relativity replaces Newton’s Law of Gravitation and provides a natural explanation of the equivalence principle. Einstein’s theories of relativity imply a profound and fundamental change in the view of the separation of space, time, and mass, that contradicts the basic tenets that are the foundation of Newtonian mechanics.
• 17.E: Relativistic Mechanics (Exercises)
• 17.S: Relativistic Mechanics (Summary)

Thumbnail: Momenta are conserved within a closed system and the laws of conservation of momenta applies. Consider the special case of identical particles colliding symmetrically. (CC BY-SA; RobinH via Wikipedia)