Relativity

• Commutative Hypercomplex Special Relativity - Einstein's special relativity is formulated in terms of 4-D commutative hypercomplex mathematics. The traditional results are obtained, but some additional effects are suggested.
• Derivation of the Lorentz Transformation - This derivation uses the group property of the Lorentz transformations, which means that a combination of two Lorentz transformations also belongs to the class Lorentz transformations. [PDF]
• A Derivation of the Lorentz Transformation From a Simple Definition of Time - The fundamental equations of special relativity are derived with only high school algebra and toy universes consisting of moving rulers. [PDF]
• Deriving Relativistic Momentum and Energy - Expressions for momentum and energy of a relativistic particle may be derived from the composition law for velocities along one spatial dimension.
• Deriving Relativistic Momentum and Energy. II. - The usual relativistic expressions for momentum and kinetic energy are generalized from the one-dimensional to the three-dimensional case.
• The Doppler Shift Equation For An Accelerating Frame of Reference - The exact equation for the Doppler shift in a uniformly accelerating rocket is derived in two different ways. The first method depends on a functional equation and Einstein’s approximation. The second approach is a direct application of several familiar equations in the relativity of uniformly accelerated motion.
• Einstein Light - A multimedia tutorial on Special Relativity. The introductory level takes 10 minutes, but has links to over 40 explanatory pages giving greater depth and breadth.
• E=mc² - An article from the Wikipedia encyclopedia.
• Generalized Relativistic Velocity Addition with Spacetime Algebra - The general problem of relativistic addition of velocities – and the successive application of noncollinear Lorentz boosts – is addressed. [PDF]
• Geometric Algebra for Physicists - This is chapter 1 of a book by Chris Doran and Anthony Lasenby on geometric algebra, which is the natural mathematics of spacetime. [PDF]
• How Do You Add Velocities in Special Relativity? - Here is the formula for adding velocities in special relativity when motion occurs in a single direction.
• How Stuff Works: Special Relativity - The major principles of special relativity (SR) are discussed in an accessible way, via 5 segments, to help you understand the lingo and theories involved.
• Imaginary In All Directions - There is a preferred algebra of quaternions and complex numbers that is ideally suited to express the equations of special relativity and classical electrodynamics. [PDF]
• Jim Doyle's Special Relativity Pages - A growing collection of pages on special relativity, including Special Relativity in under 15 Minutes!
• The Lecture Notes of Dr. R. D. Field - The online physics course notes for Physics 3063, by Professor Rick Field, University of Florida, is a good summary of many of the useful formulas used in special relativity.
• Lorentz Contraction and Accelerated Systems - Lorentz contraction in systems undergoing constant proper acceleration is proven to be completely self-consistent in the context of special relativity. [PDF]
• Nothing but Relativity - There are many ways to derive the Lorentz transformation without invoking Einstein's constancy of light postulate. The path preferred in this paper restates a simple, established approach. [PDF]
• On the Electrodynamics of Moving Bodies - Albert Einstein's first paper on relativity, translated here from Annalen der Physik vol XVII 1905 p. 891-921, is of historical interest.
• On the Electrodynamics of Moving Bodies (Part A: Kinematics) by Albert Einstein - In this annotated version of Einstein's paper, the author attempts to express Einstein's insights in familiar notation and fills in some of Einstein's many missing intermediate steps. [PDF]
• One More Derivation of the Lorentz Transformation - The theory of relativity is constructed from four general group-theoretical assumptions on the structure of space-time: These are homogeneity, isotropy, group structure and a causality condition. [PDF]
• Quaternions in University-Level Physics Considering Special Relativity - The quaternions are an expansion of complex numbers and show close relations to numerous physically fundamental concepts (e.g. Pauli Matrices). [PDF]
• Relatively Simple - Special Relativity made Relatively Simple offers information and experiments about special relativity.
• Relativistic Contraction - Relativists consider it a very important exercise to have students decide how to measure the length of a rapidly moving object.
• Relativistic Force Transformation - Formulas relating one and the same force in two inertial frames of reference are derived directly from the Lorentz transformation of space and time coordinates. [PDF]
• Relativistic Kinematics - This is how special relativity is taught by Dr. David Morin at Harvard University. 72 pages. [PDF]
• Relativity Tutorial - An introduction to relativity using space-time diagrams.
• Sagnac Effect, Twin Paradox and Space-Time Topology - When viewed with an alternative synchronization convention, the Sagnac effect on a rotating disk is purely topological and the rim of the disk is essentially an inertial system.
• Santa at Nearly the Speed of Light - An estimate of the speed and distances covered by Santa Claus on Christmas night. The physics is unassailable. The article is hosted on the Fermi National Accelerator Laboratory website.
• Simple Derivation of the Special Theory of Relativity Without the Speed of Light Axiom - Special relativity may be derived just from assuming isotropy, homogeneity and a principle of relativity, without the need to consider the speed of light.
• Space Measurements on a Rotating Platform - The age-old puzzling problem of Lorentz contraction on a rotating platform, i.e., Ehrenfest's paradox, is explained in its proper mathematical context. [PDF]
• Special Relativity - A unit for an online relativity textbook explaining special relativistic mathematical physics.
• Special Relativity - A brief overview of the theory of special relativity, and how it pertains to particles at SLAC (Stanford Linear Accelerator)
• Special Relativity - This is chapter two of Christoph Schiller's 1000 page walk through the whole of physics, from classical mechanics to relativity, electrodynamics, thermodynamics, quantum theory, nuclear physics and unification. 61 pages. [PDF]
• Special Relativity - Tutorial explains about the postulates, paradox, simulaneity, time dilation, Lorentz transformation constructions, spacetime wheel, and the Fitzgerald-Lorentz contraction. Page includes some animated illustrations.
• Special Relativity and Maxwell Equations - A self-contained summary of the theory of special relativity is given, which provides the frame for classical electrodynamics. 26 pages. [PDF]
• Special Relativity Lecture Notes - A standard introduction to special relativity where explanations are based on pictures called spacetime diagrams.
• A Special Relativity Paradox: The Barn and the Pole - The answer to the famous barn and the pole paradox is that the two doors are never closed at the same time in the runner's frame of reference.
• The Special Theory of Relativity - Self-tutorial with short essays, questions and answers.
• The Structure of Space-Time Transformations - This theorem by H. J. Borchers and G. C. Hegerfeldt proves that the constancy of light velocity alone implies the Lorentz group (up to dilatations).
• Synchronization Gauges and the Principles of Special Relativity - Synchronization functions set the mathematical clocks represented by the Lorentz transformation and resetting these clocks mathematically only produces a theory equivalent to special relativity in predicting empirical facts. 57 pages. [PDF]
• Time Dilation - The gamma factor and time dilation can be derived using a very simple clock.
• The Twin Paradox in a Spatially Closed and Bounded Universe - Spatially compact spacetimes break global Lorentz invariance and define absolute inertial frames of reference.
• Understanding Special Relativity - Brief explanation of special relativity, using no more than high-school level mathematics; includes an account of the twin paradox, some remarks on faster-than-light travel, and some material on relativistic mechanics. By Rafi Moor.
• Uniform Acceleration - This paper analyzes several simple uniform acceleration problems, including the paradox of John Bell. [PDF]
• University Lectures on Special Relativity - Lecture notes on Special Relativity, prepared by J. D. Cresser, Department of Physics, Macquarie University. 44 pages. [PDF]
• Wikipedia: Introduction to Special Relativity - Encyclopedia article giving a brief outline of the basic concepts of special relativity (including simple formulas).
• Wikipedia: Special Relativity - Online encyclopedia article.