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Doing Physics with
t + x i + i j + z k
doug <>
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of this site!  (I prefer it :-) 
Intro, Mathematics, Classical, SR, EM, QM, G, Conclusions
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)
Tools for algebra, trig, logs... and a Quaternion calculator (in Java)
An OPEN SOURCE project QEMation to develop Quaternion Equation driven aniMation!

F = m a: Classical Mechanics(.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

E = m c squared: Special Relativity(.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

Curl B = 0: Electromagnetism(.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

<phi|psi> Quantum Mechanics(.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

F = G M m/r squared: Gravity(.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

Other stuff

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

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