The fundamental equations of special relativity are derived with only high school algebra and toy universes consisting of moving rulers.
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.
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.
Expressions for momentum and energy of a relativistic particle may be derived from the composition law for velocities along one spatial dimension.
The usual relativistic expressions for momentum and kinetic energy are generalized from the one-dimensional to the three-dimensional case.
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.
The general problem of relativistic addition of velocities – and the successive application of noncollinear Lorentz boosts – is addressed.
This is chapter 1 of a book by Chris Doran and Anthony Lasenby on geometric algebra, which is the natural mathematics of spacetime.
Here is the formula for adding velocities in special relativity when motion occurs in a single direction.
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.
There is a preferred algebra of quaternions and complex numbers that is ideally suited to express the equations of special relativity and classical electrodynamics.
Lorentz contraction in systems undergoing constant proper acceleration is proven to be completely self-consistent in the context of special 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.
Albert Einstein's first paper on relativity, translated here from Annalen der Physik vol XVII 1905 p. 891-921, is of historical interest.
The quaternions are an expansion of complex numbers and show close relations to numerous physically fundamental concepts (e.g. Pauli Matrices).
Relativists consider it a very important exercise to have students decide how to measure the length of a rapidly moving object.
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.
Chapter of a classical mechanics text describes spatiotemporal effects. Includes problems and solutions.
An introduction to relativity using space-time diagrams.
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.
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.
Special relativity may be derived just from assuming isotropy, homogeneity and a principle of relativity, without the need to consider the speed of light.
The age-old puzzling problem of Lorentz contraction on a rotating platform, i.e., Ehrenfest's paradox, is explained in its proper mathematical context.
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.
A standard introduction to special relativity where explanations are based on pictures called spacetime diagrams.
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.
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.
Self-tutorial with short essays, questions and answers.
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).
Spatially compact spacetimes break global Lorentz invariance and define absolute inertial frames of reference.
The gamma factor and time dilation can be derived using a very simple clock.
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.
Lecture notes on Special Relativity, prepared by J. D. Cresser, Department of Physics, Macquarie University. 44 pages.
Encyclopedia article giving a brief outline of the basic concepts of special relativity (including simple formulas).
Online encyclopedia article.
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