Special 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.
http://home.comcast.net/%7ecmdaven/special.htm

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]
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.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]
http://www.everythingimportant.org/relativity/special.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.
http://lanl.arxiv.org/abs/physics/0402024

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.
http://lanl.arxiv.org/abs/physics/0504095

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.
http://www.everythingimportant.org/SDA/viewtopic.php?f=14&t=969

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.
http://www.phys.unsw.edu.au/einsteinlight/

E=mc²
An article from the Wikipedia encyclopedia.
http://en.wikipedia.org/wiki/E%3Dmc%C2%B2

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]
http://arxiv.org/ftp/physics/papers/0511/0511247.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]
http://assets.cambridge.org/052148/0221/sample/0521480221WS.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.
http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

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.
http://www.howstuffworks.com/relativity.htm

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]
http://arxiv.org/abs/math-ph/0309061

Jim Doyle's Special Relativity Pages
A growing collection of pages on special relativity, including Special Relativity in under 15 Minutes!
http://www.btinternet.com/~j.doyle/SR/sr1.htm

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.
http://www.phys.ufl.edu/~rfield/PHY3063/

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]
http://arxiv.org/abs/gr-qc/0301050

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]
http://lanl.arxiv.org/abs/physics/0302045

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.
http://www.fourmilab.ch/etexts/einstein/specrel/www/

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]
http://www.sigmapisigma.org/radiations/2005/electrodynamics_fall05.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]
http://o.castera.free.fr/pdf/onemorederivation.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]
http://arxiv.org/ftp/physics/papers/0308/0308017.pdf

Relatively Simple
Special Relativity made Relatively Simple offers information and experiments about special relativity.
http://web.wt.net/~cbenton/relativity.htm

Relativistic Contraction
Relativists consider it a very important exercise to have students decide how to measure the length of a rapidly moving object.
http://www.ux1.eiu.edu/~cfadd/1160/Ch27SpRl/ApLrntz.html

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]
http://arxiv.org/abs/physics/0507099

Relativistic Kinematics
This is how special relativity is taught by Dr. David Morin at Harvard University. 72 pages. [PDF]
http://isites.harvard.edu/fs/docs/icb.topic245778.files/ICM_chap11.pdf

Relativity Tutorial
An introduction to relativity using space-time diagrams.
http://www.astro.ucla.edu/~wright/relatvty.htm

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.
http://arxiv.org/abs/gr-qc/0403111

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.
http://www.fnal.gov/pub/ferminews/santa/

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.
http://arxiv.org/abs/0710.3398

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]
http://arxiv.org/abs/gr-qc/0309020

Special Relativity
A unit for an online relativity textbook explaining special relativistic mathematical physics.
http://www.geocities.com/zcphysicsms/sr.htm

Special Relativity
A brief overview of the theory of special relativity, and how it pertains to particles at SLAC (Stanford Linear Accelerator)
http://www2.slac.stanford.edu/vvc/theory/relativity.html

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]
http://www.motionmountain.net/C-2-CLSC.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.
http://casa.colorado.edu/~ajsh/sr/sr.shtml

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]
http://www.csit.fsu.edu/~berg/teach/phy4241/Lectures/relativity1.pdf

Special Relativity Lecture Notes
A standard introduction to special relativity where explanations are based on pictures called spacetime diagrams.
http://www.phys.vt.edu/~takeuchi/relativity/notes

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.
http://www.math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html

The Special Theory of Relativity
Self-tutorial with short essays, questions and answers.
http://astro.physics.sc.edu/selfpacedunits/Unit56.html

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).
http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.cmp/1103858408

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]
http://arxiv.org/abs/gr-qc/0409105

Time Dilation
The gamma factor and time dilation can be derived using a very simple clock.
http://www.pa.msu.edu/courses/2000spring/PHY232/lectures/relativity/dilation.html

The Twin Paradox in a Spatially Closed and Bounded Universe
Spatially compact spacetimes break global Lorentz invariance and define absolute inertial frames of reference.
http://www.everythingimportant.org/relativity/general.htm

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.
http://www.rafimoor.com/english/SRE.htm

Uniform Acceleration
This paper analyzes several simple uniform acceleration problems, including the paradox of John Bell. [PDF]
http://www.ph.utexas.edu/~gleeson/NotesChapter13.pdf

University Lectures on Special Relativity
Lecture notes on Special Relativity, prepared by J. D. Cresser, Department of Physics, Macquarie University. 44 pages. [PDF]
http://www.physics.mq.edu.au/~jcresser/Phys378/LectureNotes/SpecialRelativityNotes.pdf

Wikipedia: Introduction to Special Relativity
Encyclopedia article giving a brief outline of the basic concepts of special relativity (including simple formulas).
http://en.wikipedia.org/wiki/Introduction_to_special_relativity

Wikipedia: Special Relativity
Online encyclopedia article.
http://en.wikipedia.org/wiki/Special_relativity