Timeline for Why is the Hodge dual so essential?
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| Mar 23, 2014 at 6:15 | comment | added | Stan Liou | @ZachMcDargh: Yes and no. It's not needed for Maxwell's equations, but the info it incorporates is necessary for EM to be fully predictive--$H\propto\star F$ of standard EM relates $(\mathbf{E},\mathbf{B})$ with $(\mathbf{D},\mathbf{H})$, which is necessary, and as an important side-effect, connects the light cone with the causal structure of spacetime. In H&O's book, they investigate a general $H_{ab}\propto\kappa_{ab}{}^{cd}F_{cd}$ and some of the assumptions on $\kappa$ for which the light cone even exists, and for which which metric could be derived from it, up to some conformal factor. | |
| Mar 23, 2014 at 0:07 | comment | added | ZachMcDargh | Thank you for this fantastic answer! It seems from what you've said here that the answer to the title question is that the Hodge dual is not completely necessary, but it is often convenient, and can be a useful way to incorporate additional information, e.g. about the metric. | |
| Mar 23, 2014 at 0:00 | vote | accept | ZachMcDargh | ||
| Mar 22, 2014 at 19:49 | history | answered | Stan Liou | CC BY-SA 3.0 |