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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.
- An article from the Wikipedia encyclopedia.
- 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.
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.
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]
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.
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]
- 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]
- Chapter of a classical mechanics text describes spatiotemporal effects. Includes problems and solutions. [PDF]
- 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]
- Tutorial explains about the postulates, paradox, simulaneity, time dilation, Lorentz transformation constructions, spacetime wheel, and the Fitzgerald-Lorentz contraction. Page includes some animated illustrations.
- Download Christoph Schiller's 1612 page walk through the whole of physics, from classical mechanics to relativity, electrodynamics, thermodynamics, quantum theory, nuclear physics and unification. chapter 2 explains special relativity. [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]
- 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.
- 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.
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