Deprecated site

I am keeping this old version up for historical reasons. The text html files were not easy to maintain. The current site is available on github, either the easy to remember: or The new version is more modern, using a program called mkdocs to make it more friendly to a wider range of devices. More importantly, my new proposal for gravity is there, space-times-time invariance. Also there is a far better presentation of how to derive the Mawwell field equations from scratch. Enjoy the new site which I can update as needed.

analytical animations at Visual

GEM t-shirt

Buy a Unified Standard Model t-shirt! $18 total

Video Ed

Technical shows, Not-so-technical, quaternion animations, all served up from YouTube. Watch and learn!


A community research web site centered on visualing quaternions, often motivated by physics.

Math (pdf)


Force equals mass times acceleration

Classical Physics (pdf)

F equals minus G M m over R squared

Unifying Gravity and EM

I am rescinding my efforts to unify gravity and EM using quaternions and hypercomplex numbers. The quaternions do the work of EM fine and that part of this work is still of value. The hypercomplex numbers were given the chore of doing gravity. Under a rotation, the square of a hypercomplex number changes. As such, when used in a Lagrangian, angular momentum will not be conserved. Gravity most definitely conserves angular momentum. There may be things people can learn (how to derive field equations using Lagrange densities, the precession of the perihelion of Mercury, ...).

Simply put, all of the work, claims, and even the t-shirt, that touch on hypercomplex numbers are WRONG. I learned a huge amount of real physics anyway. You might also. Good luck in your studies of this flawed work.

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)

GEM action

Slides from talks


Mathematica notebooks


--boxed The curl of the B field is zero

Electromagnetism (pdf)

energy equals gamma m c squared

Special Relativity (pdf)

The norm of the wave function phi

Quantum Mechanics (pdf)

Let's Talk

Get Stuff

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).

Books Buttons Turquoise Einstein t-shirts No Stinkin' Higgs t-shirts

A few good papers:

  1. Sudbery's first paper (memo, 1977, 44 pages) on why quaternion analysis is no good.
  2. Sudbery's second paper (1979, 28 pages) on the topic. Please look to my work above on quaternion analysis for a much better alternative!.
  3. 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.
  4. Salamin's paper (1979, 9 pages) on rotations.
  5. Howell and Lafon's paper (1975, 13 pages) on the efficiency of quaternion multiplication.
  6. 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.
  7. 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.


All work done/financed in my free time. Woof!

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