AND THEN THERE WAS LIGHT MAXWELL EQUATION FULL
The full six page story is here: Commentary 2.9 Maxwell equation with 3 forms. But it was worth it, because as Carroll said, I needed practice converting from differential form notation to ordinary index notation and moreover practice with manipulating indexed equations. Having done all that I did discover the easy way to get there without all the plodding tables and paper work. \mathrm# in the previous post also on the Levi-Civita symbol.) NUMERICAL TREATMENT OF MAXWELLS EQUATIONS For the numerical simulation of Maxwells equations (1.1)-(1.6) we will use the Finite-Difference Time-Domain (FDTD).This method was originally proposed by K.Yee in the seminar paper published in 1966 9, 19, 22. There is little doubt in my view that Maxwell’s synthesis of classical electromagnetic field theory is one of the most brilliant syntheses in all of physics. Then came Einstein with Special (1905) and General (1915) Relativity.Ĭarroll writes "The other one of Maxwell's equations, (1.96) can be expressed as an equation between three-forms: And so the four, the tapestry of jigsaw of four Maxwell’s equations can be combined into a single equation that shows that light is electromagnetic radiation.
Soon after his equations were known, radio waves (1887, Hertz) and X-rays (1895, Roentgen ) were discovered. It was thought that the light waves we derived above must be. I remember being astonished when we did Maxwell's equations and proved it at university. Historically, the Maxwell equations were discovered before the theory of special rel- ativity. It must have made physicists feel queasy. Therefore light had to be electromagnetic waves. Quite a bit was known about electricity and magnetism and the relationships between them at the time but he spotted a missing component and was able to show that electromagnetic waves must exist and moreover travel at the speed of light, which was already known. He published his famous equations in about 1865.
He was up there with Newton and Einstein. James Clerk Maxwell was one of the greatest theoretical physicists of all time.
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