Doing Physics with
t + x i + i j + z k
Quaternions
doug <sweetser@alum.mit.edu>

 
Intro, Classical, SR, EM, QM, G, Conclusions
Introduction
An overview (3k)
A brief history of quaternions (9k)
Multiplying quaternions the easy way (17k)
Inner and outer products (66k)
Scalars, vectors, tensors and all that (40k)
Topological properties (a work in progress)
Tools for algebra, trig, logs... (6.5k)  and a Quaternion calculator (in Java)
Understanding these web pages (52k)
in scalar/vector notation (default) or Mathematica notation

F = m a
F = m a, in an inertial frame, in polar coordinates, and in a rotating reference frame (160k)
The simple harmonic oscillator and wave equation (68k)
4 tests for a conservative force (98k)


E = m c^2
Doing the work of the Lorentz group with rotations and dilations (25k)
An alternative algebra for boosts (105k)

Problem set questions and solutions from MIT's 8.033, Classical and Relativistic Mechanics
Index and links to solved problems (25k)
PS 1: Kinematic effects of relativity (96k)
PS 2: More kinematic effects (320k)
PS 3: The Lorentz transformation and the addition of velocities (323k)
PS 4: The Doppler effect, 4- vector invariants, and the twin paradox (552k)
PS 5: Energy, Mass and Momentum (386k)
PS 6: The Compton effect and threshold collision problems (315k)


Curl B = 0
Classical electrodynamics (136k)
Electromagnetic field guages (80k)
The Maxwell equations in the Lorenz gauge (66k)
The Maxwell equations in the light gauge: QED? (135k)
The Lorentz force (17k)
The stress-energy-momentum 2-tensor of the electromagnetic field (25K)


<phi|psi>
Bracket notation & quaternions: quaternions as a complete inner product space (156k)
Polar representations (42k)
Multiplying quaternion exponentials (without Campbell-Hausdorff!) (100k)
Commutators and the uncertainty principle (74k)
The Schrödinger equation (106k)
The Klein- Gordon equation (52k)
Time reversal (65k)


F = G M m/r^2
An area of active research...(translation: some of this stuff is off the mark, but interesting   :-)
Answering prima facie questions in quantum gravity using quaternions (post to s.p.r)
The Lorentz granvitational force and Maxwell gravitational equations (post to s.p.r)
The length of a quaternion in curved spacetime: a close relative of the affine parameter of general relativity (67k)
General metrics (50k)
Gravitational redshift experiments (50k)



A summary of physics equations written as quaternions (174k)
Conclusions (5k)
 

Other stuff