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The space time approach with E as t wedge x and B as x wedge y is purely linear algebra, not differential forms. As opposed to the weird GA form it actually ma
by Certhas 4mo ago
The space time approach with E as t wedge x and B as x wedge y is purely linear algebra, not differential forms.
As opposed to the weird GA form it actually makes the physically most meaningful symmetry (Lorentz transformations) explicit. That's why it's actually used in Physics.
Anti symmetric space time tensors are the absolute standard. Further formulations that reveal other aspects, dualities, symmetries are much more niche and specialized subjects and not how the subject should be taught when first encountering it.
https://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism https://en.wikipedia.org/wiki/Covariant_formulation_of_class...
- jsLavaGoat 4mo agoOK, well, MTW is a pretty standard GR textbook and it is often cited as a useful text on differential forms for math.
- Certhas 4mo agoDid you mean to reply to someone else? For the record, MTW by now also shows it's age. When I was doing research in GR adjacent fields the experts were rather recommending Wald. Might have just been my bubble of course...
- Loquebantur 4mo agoOne should teach the next generation the best way possible, and not turn them into conformists. "Standards" are things to be overcome when they've outlived their prime. Disparaging new ideas as "niche" and "specialised" when their explicit aspiration is to be better foundations is motivated reasoning.
- Certhas 4mo agoThe ideas of GA aren't new. As the article explains, the ideas of Clifford algebras are common place throughout research and deserve to be introduced earlier. Understanding bivectors and wedge products is much more important than, for example, Euler angles in my opinion. The geometric product on the other hand obscures much of the structure, and serves no pedagogical or fundamental purpose. Not everything that's new is better, just by virtue of being new. You might have misunderstood my point about what's niche, or I misunderstood which formulation of Maxwell the post I was replying to was referring to. Either way, it feels this discussion went off the rails rather immediately...
- Certhas 4mo agoMaybe I wasn't clear: Other formulations that reveal dualities, etc... at the cost of obscuring the fundamental covariance deserve to be treated as secondary.