[SpaceProgram] Maxwell's Equations expressed in Quaternions for FTL Research

[Jerry Isdale]

At the 100YSS Symposium today, Buck Field, gave a talk on "Developing Faster Than Light Technology - A Project Management Institute Based Approach".  The PMBook of Knowledge approach interested me so I went to hear him.
He talked about using PM to set and persue goals needed to advance physics in critical areas.

One story he related was that back in late 1800s, Maxwell came out with his theories and equations on Electro-Magentics (light as magnetic, etc). THe work was originally done using the new math of Quaternions and was quite elegant and complete. However a vicious flame war ensued in NATURE mag - The Heaviside-Tait Debates - over whether to use the vector approximation equations, or the more complete Quaternion based solution.  Vectors were well known and understood math & notation. Q was very new and hardly known.  Vectors won even though the approximation introduces lots of difficulties (rotations in euclidian 3d vectors give zero crossings and infinity results).  Quaternions were left on the shelf and forgotten (indeed major textbooks on Maxwell theory totally ignore quaternions).  
Q was resurrected in late 80s or early 90s by the 3d modeling and animation world (video games) as a way to do rotations without messy zero crossings (divide by zero errors are not something you want in middle of a melee).

Buck Field noted that there are a lot of interesting physics of time/space that could be explored with Q interpretations of Maxwell... such as the fields around molecules used by molecular biologists for docking molecules.   That field loves Q for the rotations, etc but dont dig into the how and why of the field theory.  Physicists are stuck in their Vector Interpretation and not interested in simple rotations -- and seemingly unaware of original Q derivations by Maxwell.

Buck postulated that for a small amount ($10k) you could fund some grad students for a year of labor into re-evaluating the Quaternion Models of Electro-Magnetics, and possibly uncovering some very interesting and new applications of physics that are lost using the vector approximations.

This sounds like a challenge to our math hackers.

I'm going to dig back into Quaternions for rotations
   http://www.cprogramming.com/tutorial/3d/quaternions.html
  http://blog.wolframalpha.com/2011/08/25/quaternion-properties-and-interactive-rotations-with-wolframalpha/
to try and grok the math, and then dig back for the original Maxwell models.

Anyone with me? Want to forge ahead and tell me what lies there?

Jerry Isdale
isdale at spacegambit.org
USA Program Lead, SpaceGAMBIT
Global Alliance of Makers Building Interstellar Technology
http://SpaceGAMBIT.org

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