GEM Blog 29: Deriving the Maxwell Source Equations Using Quaternions (2/5)

This is a dramatic reading of "Deriving the Maxwell Source Equations Using Quaternions", a blog by the Stand-Up Physicist available at Science20.com. Start with the big picture - a definition of what the Maxwell equations do, account for all spacietime changes of spacetime change of a spacetime potential caused by a current density mediated by massless photons who have no sense of their own history.

The rules for multiplying quaternions are explained. The simplest quaternion derivative of a potential contains both the electric field E and magnetic field B. The product of the two ways to write the quaternion derivative of a potential generates the Lagrange density for the Maxwell source equations, B squared minus # squared. Much work goes into writing that out component by components, all 22 terms. The Euler-Lagrange equations are then used to generate both Gauss's and Ampere's Laws. A visualization of the two laws allows for a comparison.

The weak and strong forces are profoundly similar to EM, the key difference being the symmetry groups involved. Because quaternions have both multiplication and division, it is possible to write a form of Gauss's and Ampere's laws that have both SU(2) and SU(3) symmetries with underlies the weak and the strong forces. Whether that is at all relevant to Nature is an open question.

Category:

Science & Technology

Tags:

• Maxwell
• source
• derivation
• Gauss
• Ampere
• Law
• Euler-Lagrange
• Lagrange
• density

[yonadav3]

very interesting, keep up the good work