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- Intro, Mathematics, Classical, SR, EM, QM, G, Conclusions
- Introduction
- An overview
- A brief history of quaternions
- Mathematics (.ps)(.pdf)(ftp .ps)
- Multiplying quaternions the easy way
- Inner and outer products
- Scalars, vectors, tensors and all that
- Quaternion analysis (.ps)(.pdf)(ftp .ps)
- Topology
- Tools for algebra, trig, logs... and a Quaternion calculator (in Java)
- An OPEN SOURCE project QEMation to develop Quaternion Equation driven aniMation!

(.ps)(.pdf)(ftp .ps)

F = m a, in an inertial frame, in polar coordinates, and in a rotating reference frame

The simple harmonic oscillator and wave equation

4 tests for a conservative force

(.ps)(.pdf)(ftp
.ps)

Doing
the work of the Lorentz group with rotations and dilations

An alternative algebra
for boosts

Problem set questions and solutions from MIT's 8.033, Classical and
Relativistic Mechanics

Index and links to solved problems

PS 1: Kinematic effects of relativity

PS 2: More kinematic effects

PS 3: The Lorentz transformation
and the addition of velocities

PS 4: The Doppler effect, 4- vector
invariants, and the twin paradox

PS 5: Energy, Mass and Momentum

PS 6: The Compton effect and threshold
collision problems

(.ps)(.pdf)(ftp
.ps)

Classical electrodynamics

Electromagnetic field gauges

The Maxwell equations in the light
gauge: QED?

The Lorentz force

The stress-energy-momentum 2-tensor
of the electromagnetic field

(.ps)(.pdf)(ftp
.ps)

Bracket notation & quaternions:
quaternions as a complete inner product space

Multiplying polar representations (without Campbell-Hausdorff!)

Commutators and the
uncertainty principle

Unifying the representations of spin and angular momentum

The Schrödinger
equation

The Klein-Gordon
equation

Time reversal

(.ps)(.pdf)(ftp
.ps)

An area of active researchquaternions.(translation: some of this stuff may be off
the mark, but interesting :-)

Einstein's vision: unifying
gravity and electromagnetism (.ps)(.pdf)(ftp
.ps)

A more mature working draft is available
**here**
This has for example the force equations that predict equations of motion
that can be rearranged into a dynamic approximation of the Schwarzschild
metric of general relativity. There is also an explanation of the mass
distribution and rotation profiles of spiral galaxies without using
dark matter!

Strings and Relativistic Quantum Gravity

A slide presentation of string ideas, small movies, little math

Answering prima
facie questions in quantum gravity using quaternions (post to s.p.r)

The length of a quaternion
in curved spacetime: a close relative of the affine parameter of general
relativity

General metrics

Gravitational redshift
experiments

A summary of physics
equations written as quaternions

Conclusions

- Other stuff
- A bound Xerox copy of these web pages is available.
- Quaternion web boards devoted to history, math, physics, metaphysics, and programming
- Mathematica 3.0 notebooks used to create these pages, free to download & print
- The site is available via ftp (click here). It comes as a 3.4 MB file that has the Unix .tar.gz extension. In a Linux environment, after downloading, run "tar -zxf qsite.tar.gz" (in other flavors of Unix, the command is gtar not tar). For Win 95/98, download and use Winzip. It first asks to decompress, then all the files need to be extracted. After unpacking, find the file qindex.html to open this page on your local machine.
- An introduction to quaternions, rotations, and spins by Kim Bailey
- Henri Baker's ftp site containing papers by Silberstein on special relativity using complex quaternions, Sudbery on quaternion analysis, and rotations using quaternions.
- A mathematical summary of binary products, algebras and division rings (like quaternions) by Dave Rusin
- Doug's background in physics
- Feedback welcome! (Would like to know why you visited, what could be added.)
- Thanks to...

cost: $30 for "Doing physics with quaternions",

$40 for "Doing physics quaternions." + "Doing special relativity with quaternions"

Includes the button, "A brief definition of spacetime"

snail mail your request with a check to:

Doug Sweetser

5 Edge Hill Rd

Jamaica Plain, MA 02130

Intro, Mathematics, Classical, SR, EM, QM, G, Conclusions

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