Maxwell's equation in geometric algebra

In this video, we perform a superposition of Maxwell's equations to find an equivalent single equation multivector geometric algebra form. Once assembled, we will demonstrate, using grade selection, that all of the original Maxwell's equations can be extracted from our new multivector Maxwell's equation (i.e. that no information was lost performing this superposition.)
Prerequisites: familiarity with Maxwell's equations, geometric algebra basics (vector multiplication, grade selection, 3D pseudoscalar, vector/bivector products, wedge and cross product duality, bivector products and dot products, ...), , and calculus (partial differentials, gradient, curl, divergence)
If you liked this video, you may be interested in my book, Geometric Algebra for Electrical Engineers, available in hardcover or softcover on amazon:
amzn.to/49hplMm
An electronic (PDF) version of the book is available on my blog here:
peeterjoot.com...

[@PeeterJoot]

typos @5:58, in the "Check Recovering Maxwell's equations" slide. I write out a set of grade selection operations, one for each grade, but all the grade selections on the left are written as scalar selections.

[@errantis]

Great video. Can you recommend a book for further exploration of geometric Algebra that also includes physical applications?"

[@PeeterJoot]

For some very theoretical applications, the Doran and Lasenby's book "Geometric Algebra for Physicists" is unparalleled. Hestenes' book "New Foundations for classical mechanics" has many applications spelled out. The Hestenes book is very expensive, but you can probably find a copy at a university library if you have access to one.

[@riadhalrabeh3783]

Great effort.. best wishes for you and the family.

[@erykpakula]

Thank you for video

[@andy_lamax]

why does my man sound like Wilson Fix from marvel's daredevil??

[@PeeterJoot]

I did get a better microphone after some complaints. Maybe I won't be emulating Fisk in future videos

[@itswakke]

love this!!

[@leokovacic707]

Do you have some insights into a geometric algebra interpretatioon of the aharonov bohm effect in any formulation .

[@PeeterJoot]

Understanding the connections between quantum theory and electromagnetism is one of the things I'd really like to understand, but I don't currently have any good insights for you. In particular, the Aharonov-Bohm effect appears to make the vector potential a first hand citizen, but I don't understand how that effect isn't perturbed by a gauge transformation of the potential. I once asked my Professor in an engineering electromagnetism class about this, and only got a startled blank stare. I haven't tried to do a literature search for an answer, but expect there is one or many available. If somebody could point me to one, I'd appreciate it.

[@leokovacic707]

@@PeeterJoot I mentioned this to my CED prof and he was bewildered as well never heard of it . I think the catch is that irrotational fields need not be integrable (gradients/ conservative) . The basic calculation uses the Schrödinger eq , plugging in a trial solution of the form e^ig where g is the path integral of A - the vector potential which is curl free but not conservative and even though it's curl( the magnetic field is zero ) you get a different value for different path and hence a phase shift . Basically the point being that the potential although only determined up to a gauge , is more real than the concep of a field. But I'm sure GA could give a different SPIN on this pun intended, especially in something akin to hestenes approach to electron theory m

[@jackdragon5353]

Is I (capital i) the unit pseudoscalar?

[@PeeterJoot]

Yes

[@Pluralist]

[@samin3997]

MHD is the way

[@PeeterJoot]

Magneto-Hydro-Dynamics?

[@alexeyl22]

Good effort )). But you obviously had to skip a lot of explaining to fit this in 10 min. Impossible to follow as is.

[@PeeterJoot]

Sorry about that. I have some other videos that describe the background material, and I had assumed those would have been watched first. Or see my book, available in pdf form for free here: peeterjoot.com/gaee/