Trying to be a semi-pro amateur physicist (yes I accept special relativity is right!). I _had_ my own effort to unify gravity with other forces in Nature. It ran into quite a number of technically... Read More »
Nature abhors a magnetic monopole, although she adores gravitational and electric monopoles. The homogeneous Maxwell equations are the ones that need no currents, known as the no magnetic monopoles and Faraday's laws. There are three ways to derive the homogeneous Maxwell equations. The first way is to use vector identities. This is the simplest approach, the one most widely used. Pick out a particular way to write the electric and magnetic field, and the job is done. The divergence of a curl is a long way to say zero. Define the magnetic field as a curl, then its divergence is zero, and there are no magnetic monopoles hiding behind the couch.
The Maxwell source equations will be derived using quaternions - an approach James Clerk Maxwell himself tried and yet failed to do. As far as I am aware, this technique is not in the literature, up to an isomorphism (meaning actually it is there but under a different name, math in disguise). By using quaternions, the approach can be extended to generate field equations for particles with the weak and strong force symmetries, SU(2) and SU(3). The extension is a technical speculation, which I define as precise math whose applicability to Nature I have not a clue :-)
Warning: doing a classic field theory calculation in detail requires far more math than is customary on this site. The blog is my longest so far...
The Maxwell equations govern light, electricity and magnetism as a trinity. The Big Goal for the next five weeks is to understand my variations on those equations. I want readers to see both the forest and the trees, the planet and the subatomic particles, the math behind the curtain.
Many may fear they don't have the math chops to follow this five week march. The names of the players and their jobs will be explained. There is repetition in this process which may make the steps start to sound familiar. After three weeks, the diligent reader will be rewarded with a deeper understanding of the mathematical intricacies of light, unknowable to poets or priests. My variations are nothing more than that, variations.
Asking a specific question which has a specific answer is the sign of fertile soil instead of another shovel full of fertilizer. One question leads to variations on that query. Even dull looking questions can be informative. Snarky puzzle answers usually has four problems, but the fifth installment has a bonus fifth problem.
To celebrate a half year of effort, this is a blog on weekly blogging. Three tangibles are created by the process: the Science20 blog, a YouTube videoblog, and a chapter in a book of blogs (still under development). I will go through my technical suite used in production. The 20-25 hours per week will be broken down. Some data on the level of interest will be shown. Finally, the rewards of this work will be reviewed.