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Were Maxwell's equations still condensed to 4 equations (Heaviside's equations in Gibb's vector notation), or something less concise, as I believe they were wit
by madengr 12y ago
Were Maxwell's equations still condensed to 4 equations (Heaviside's equations in Gibb's vector notation), or something less concise, as I believe they were with quanternions?
- phkahler 12y agoI believe they become Maxwell's Equation, and it's super simple.
- throwaway283719 12y agoExpressing Maxwell's equations using the six-component electromagnetic tensor F, they become dF = μJ d*F = 0 where μ is the magnetic permeability of the vacuum and J is the electromagnetic 4-current. The operator 'd' is the differential operator from exterior algebra, and the '*' is the Hodge dual. Using the bivector field F = E + iB from geometric algebra, they become DF = μJ where μ and J are as before, and D is the covector derivative. For comparison, using the traditional Gibbs/Heaviside notation Maxwell's equations are ∇ . E = ρ/ε ∇ . B = 0 ∇ x E = -∂B/∂t ∇ x B = μ(J + ε ∂E/∂t)