Albert Einstein's Theory of Relativity is a set of two theories in physics, special relativity and general relativity. The core idea of both theories is that two observers who move relative to each other will often measure different 'time' and 'space' intervals for the same events, but the content of physical law will be the same for both.

Special relativity, developed in 1905, only considers observers in inertial reference frames which are in uniform motion with respect to each other. The theory postulates that the speed of light in vacuum will be the same for these observers. This leads to redefinitions of such fundamental notions as time, distance, mass, energy and momentum with wide ranging consequences. Moving objects become heavier and shorter; moving clocks go slower. Light has momentum. The speed of light emerges as an upper limit for the speed of matter and information. Mass and energy are seen as equivalent. Two events judged to be simultaneous by one observer may be seen as non-simultaneous by other observers which are in motion with respect to the first one. The theory does not account for gravitational effects. The mathematical basis of special relativity is provided by the Lorentz transformation.

General relativity was published by Einstein in 1915. It uses the mathematics of differential geometry and tensors in order to describe gravity. The laws of general relativity are the same for all observers, even if they are accelerated with respect to each other. General relativity is a geometrical theory which postulates that the presence of mass and energy "curves" space, and this curvature affects the path of free particles (and even the path of light), an effect we interpret as a gravitational force. The theory can be used to build models of the evolution of the universe and is hence a crucial tool in cosmology.

Elementary Relativistic Physics

This document describes Special Relativity in moderate detail and provides an overview of General Relativity. A familiarity with elementary algebra and elementary classical physics is assumed. Results of calculations are provided to three significant figures.

[1.0] Special Relativity

• [1.1] THE ETHER WIND / DOPPLER SHIFT
  
• [1.2] EINSTEIN'S POSTULATE
  
• [1.3] TIME DILATION
  
• [1.4] LENGTH CONTRACTION
  
• [1.5] THE TWIN PARADOX
  
• [1.6] THE TWIN PARADOX REVISITED (1)
  
• [1.7] THE TWIN PARADOX REVISITED (2)
  

[2.0] Further Concepts In Relativity

• [2.1] THE THREE-WAY PARADOX
  
• [2.2] RELATIVISTIC MASS INCREASE / MASS-ENERGY EQUIVALENCE
  
• [2.3] A FEW SUBTLETIES
  
• [2.4] RELATIVITY IN PRACTICE
  
• [2.5] GENERAL RELATIVITY
  
• [2.6] COMMENTS, SOURCES, & REVISION HISTORY
  

See also: Geometry, Mathematics, Light, Physics