Re:What is the inverse of a vector?
by Grustaf on Wednesday November 03, 2021 @05:22PM
(#29100436)
That looks pretty much equivalent, and they even have a version where F = E + B, just like in the youtube video. But my question is if this F, or the tensor version for that matter, has any physical meaning?
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Yes, F is the electromagnetic field whose laws of motion generate the E/M dynamics.
https://en.wikipedia.org/wiki/Electromagnetic_tensor
(This assumes you believe a "Field" has a physical meaning.)
I think the point is that when learning EM, it's a lot about developing intuition by visualizing in your head how the E and B fields behave in different situations, and how charges interact with them etc. You know, a lot of holding your right hand in the "physicist handshake" position and twisting it.
Sure, the same information is contained in the F tensor, but it doesn't have a similar straightforward geometric intuition.
It’s pretty easy to think about a normal three dimensional vector field representing the magnetic field, the trouble for me is when you combine the two into one tensor field.
Looking at the link reminds me that this entity is used outside of GA, but it still feels a bit weird. More weird than say complex currents, but maybe it actually isn’t.