A brief history of quaternions

Multiplying quaternions the easy way

Scalars, vectors, tensors and all that

Quaternion analysis (pdf, related video: "Why Quantum Mechanics is Weird")

Where quaternions fit in math, adapted from Max Tegmark, 1998.

- written in Java 1.0, so is broken :-(F = m a, in an inertial frame, in polar coordinates, and in a rotating reference frame

I think it is reasonable to believe I have found a way to unify gravity
with the forces of electromagnetism, the weak and strong forces in a way that can been quantized. Only unloved math
tools are used. The problem is a *puzzle* to be solved, not a math
problem so difficult only a few folks at the Institute for Advanced Study to
understand. At the core is the action, shown here, which requires both quaternions and hypercomplex multiplication
(indicated by the box-times), keeping only the scalar. My paper is here (
Mathematica notebook,
html,
or pdf)

Geometry + 4-Potentials = Unified Filed Theory, 2007 April APS talk available as html or YouTube video.

Unifying Gravity and EM, a Riddle You Can Solve (pdf), 9th Eastern Gravity Meeting, 2006.

Why a Rank 1 Unified Field Theory is Compelling and Its Background Mathematical Structure (pdf), 8th Eastern Gravity Meeting, 2005.

Unifying Gravity and EM by Generalizing EM (pdf), 7th Eastern Gravity Meeting, 2004.

Unifying gravity and EM by analogies with EM, MIT IAP course, Jan. 2003.

- Lagrange Densities (pdf, video 1, video 2)
- Fields and Quantum Mechanics (pdf, video 3, video 4)
- Forces, Metrics, and New Physics (pdf, video 5, video 6)

Realizing Einstein's Dreams: Unifying Gravity and Light, and Why Quantum Mechanics is Weird (pdf), Joint APS/AAPT meeting, Spring 2005.

4-potential Equations for Gravity and Electromagnetism (pdf), Joint APS/AAPT meeting, Fall, 2003.

The Cosmological Consequences of the Product Rule (pdf), Joint APS/AAPT meeting, Spring, 2004. A Universe with zero dark matter is good :-)

Picture Stories of Events in Spactime (pdf), Do While Studios, Spring 2000. The relationship between Special and General relativity using quaternions.

**A family of variations on the Maxwell action using quaternions and hypercomplex numbers contains the symmetries of the standard model and a testable gravity theory** (pdf)

(my current best effort, version 20091119)

OLDER EFFORTS... an approaching using standard tensors and differential geometry

Deducing a Unified Field Theory from Electromagnetism (pdf).

Unifying Gravity and EM by analogies to EM (pdf) (v 4.4, 13 pages).

Geometry + 4-Potential = Unified Field Theory, submission for the 2007 Essays on Gravitation, sponsored by the Gravity Research foundation (pdf)

An approach using quaternions.

Einstein's Vision I: Classical unification of gravity and electromagnetism using Riemannian quaternions (pdf)

Einstein's Vision II: Unified force with constant velocity profiles (pdf).

Unifying Gravity and EM by analogies to EM (pdf)
Brookhaven National Lab meeting.

The Maxwell equations in the light gauge: QED?

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

Paper: Maxwell's vision: electromagnetism with Hamilton's quaternions (pdf), Second Meeting on Quaternionic Structures in Mathematics and Physics, Rome, 1999.

Doing the work of the Lorentz group with rotations and dilations

An alternative algebra for boosts

Index and links to solved problems

PS 1: Kinematic effects of relativity

PS 3: The Lorentz transformation and the addition of velocities

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

- Follow on twitter, the account is "visualphysics"
- Subscribe for new videos on YouTuve, the account is "sweetser"
- Quaternion Question and Answer, a site for chatting about quaternions.
- Feedback welcome!

For a fee: Books, Buttons, Turquoise Einstien T-shirts, and No Stinking Higgs t-shirts

For free: Doing Physics with Quaternions (much of this site, 156 pages), Lectures on Dynamic Graphs and Unified Field Theory (75 pages).

A few good papers:

- Sudbery's first paper (memo, 1977, 44 pages) on why quaternion analysis is no good.
- Sudbery's second paper (1979, 28 pages) on the topic. Please look to my work above on quaternion analysis for a much better alternative!.
- C. A. Deavours paper, "The Quaternion Calculus". My critique is that using his definition of a quaternion derivative, if a function like f=q is analytic in q, f^2 is not. That indicates a better definition must be found before quaternion analysis can really begin.
- Salamin's paper (1979, 9 pages) on rotations.
- Howell and Lafon's paper (1975, 13 pages) on the efficiency of quaternion multiplication.
- Silberstein's paper (1912, 20 pages) on using biquaternions for quaternion special relativity. Biquaternions are NOT an algebraic field, and are not used in any operations on this web site.
- Resources on gimble lock, a problem that arises from
*not*using quaternions for 3D rotations, links provided by Alex Green: Apollo, A fourth gimbol for Christmas, skylab, Gimble Lock - Explained. Bottom line: always avoid Euler angles.

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