maxwell: :ablobcatbongokeyboard: gon write my equations in quaternions
:neofox_gun: that shit is for the birds rewrite it in vector calculus
:bunhd: what if we rewrote it in geometric algebra
:neofox_googly_shocked: no thats fucking the wrong way
@icedquinn quaternions for electromagnetics / 3d graphics are just geometric algebra done in an obtuse way that obscures what you're actually doing tbh
@subtype i don't think geometric algebra existed in maxwell's time.
one of the weird things i learned from the crazy people is that the original electromagnet equations are using 4D quaternions or some shit, and he was forced to rewrite the whole thing in vector calculus.
i think some other person downstream from him then amputated some of the dimensionality further, but i don't understand enough god tier math to investigate any of it.
i just know geometric algebra is fascinating and i had to write some support code for it once
@icedquinn Yeah, he probably couldn’t do it back then that way. And I might have been talking out of my ass as per Maxwell in general; I wasn’t taught his equations in the quaternion form and can’t even find that formulation right now to check.
I see quaternions pop up a lot in 3D graphics though, and you get the same math but with a cleaner explanation with GA: https://marctenbosch.com/quaternions
In particular, the weird 4D thing disappears (though quaternions used for 3D rotations aren’t really 3D, as only unit quaternions are used and thus one coordinate is redundant).
Though the real fun with GA starts when you stop aping the standard 3D transformation formulas and leave humanity behind with something like representing 3D points as vectors in a 5D space with (++++-) signature (so squared magnitue of a vector is something like x^2 + y^2 + z^2 + w^2 - u^2).
(also sorry for the late response, I was distracted by the thread that went from sideloading apps on iOS to the history of feudalism)
@subtype i don't remember most of the stuff i read about GA. i remember some basic concepts like being able to derive all the transforms from wedge operators and reflections
i know from 3d math that rotational transforms are improperly represented by euler vectors and you need that fourth dimension or else spinny shit doesn't work.
as for maxwell you have to find the original print of his book. don remember where those are rn
@subtype its mostly a curiosity for me more than anything. there was an odd chain of claims that amounts to
standard engineering goes like this
faraday does a magnets
maxwell finalizes the math
??? scientists reject it and make him rewrite it as vectors
something about the vectors is different
??? forgar the name takes the vectors and amputates half of the formulas because reasons
heaviside and poynting et all finish electrical engineering using the amputated vectors
relativity et all uses this model
supposedly tesla liked to fuck around and was using the quaternion form, which eric dollard makes some reference to.
at one point i came across an amusing argument that was saying technically some solutions to maxwells equations account for unlimited vacuum energy entering the system :blobcatgoogly: but those solutions are shelved because it makes thermodynamics unhappy
i suspect newton and tesla were probably more correct than einstein, but i'm also a weirdo who likes weird shit. and i just want to make basic circuits :blobcatlaydown:
@subtype electronics acting like a fluid is another weird thing that comes up in the weird papers. one of the actually verified weird physics (townsen-brown effect) works that way. you pump up voltage through the tubes and shoot it through an asymmetric capacitor and it makes shit fly around. deeply inefficient mode of propulsion but it shouldn't exist to begin with.
also did some tests with doing things real stupid (running a circuit off the negative poles of batteries only and having the whole thing on a negative gradient, like biology does it.)
@subtype there was an old paper out of japan where they found anomalous mass in a spinning motor (https://ui.adsabs.harvard.edu/abs/1989PhRvL..63.2701H/abstract). it spins one way and it weighs less than it spins the other way. light has been found to do the same thing (sagnac effect.)
i had found a student replicated Hayasaka a couple of years ago. it became one of those things like Fleishman-Ponz where people have seen it and then shrug it off like well that's fucking weird guess it doesn't mean anything though :youmusip:
there is a very very heavy focus on how important counterspin is in all the weird flyer papers. i find it somewhat odd how often that specifically comes up.
assuming that things are being pulled because thats what electrostatic fields do to contain energy, and since energy cares more about gradients than anything, then creating a counteracting barrier would free you from that. (we have this issue in motors where we get back emf because the magnets being pulled by one pole are trying to charge other poles which results in wasting a lot of energy as the opposing forces are trying to neutralize the others)
@icedquinn dunno about the rest, but Sagnac effect is something I've studied and it has nothing to do with mass, it's just that light sort of can't catch up if a fiber is spun with light inside it.
@subtype it depends on which way you spin it. the direction of linear motion doesn't matter (michaelson-morley) but the angular motion does. photons spinning one orientation are slower than the other or none.
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