The Fascinating perspective of Geometric Algebra #SoMEpi

What's actually a magnetic monopole? Here we take a look at the mathematics of Electromagnetism and Gravitoelectromagnetism to see what kind of answer we can give to that question.

Links:

#SoMEpi #SoMEπ result:

Magnetic monopoles + duality transformation:

Gravitoelectromagnetism:

Mathematical descriptions of the electromagnetic field:

Great introduction to Geometric Algebra:

Excelent answer about Geometric Algebra:

Excelent answer about duality:

Music:
Cool Revenge - Jeremy Blake

VO:

[math.]

Errata: From 13:33 to 13:59 I forgot to multiply by c both magnetic fields in the geometric representation.

[larzcaetano]

Amazing!!! Loved the take on the GEM!

Just a useless suggestion: make sure you write \cos and \sin instead of cos and sin directly in LaTeX. Otherwise they’ll look italicized and unaligned vertically.

[angeldude]

The change in the field is equal to the source density.

In further branches of Geometric Algebra, "paravectors", which are grade 1 elements added to grade 2 elements, tend to be discouraged in favor of going up a dimension. This turns the electromagnetic version of the equations from a relation between a grade 1 field added to a grade 2 field with a scalar plus a grade 1 field, and into a relation between just a grade 2 field and a grade 1 field in 3+1D space-time.

I'll need to rewatch to check if the gravitational+electromagnetic version uses complex scalars, or if it was just a conversation factor. If it's the former, it should still be possible to turn it into a version with Real scalars and single-grade elements, but it would be trickier.

[sinuture]

This is exactly what I have wanted to know for a few months! It accelerated my interest in gravity much more. Thanks for this greatest video!!!

[selfsaboteursounds]

These equations imply that magnetic monopoles would carry a mass of ~m_S (the Stoney mass), and thus a quantum field of said monopoles would have a maximum interaction distance of hbar/(m_S * c) = L_P /(srt(alpha_EM)) = ~11 Planck lengths. Such a small field interaction cross section implies the half life of such monopoles would be ~12 Planck times, which is highly unstable to say the least. Such a quantum field would get lost in the quantum vacuum foam if it exists at all

[veteatomarporculo]

Very high quality in this video. Goes to the point. Explains a lot. Thank you for this master piece

[dean]

Very exciting to someone who has had an exposure to Telecommunications and Electromagnetism and then moving on to his dream of Astrophysics. Nice..

[mathunt]

Geometric algebra is a wonderful topic. I did it for one of my postdocs.

[sakuhoa]

I was literally watching your videos last night and was thinking when is the next video

[crownlands]

Beautiful exercise, and wonderfully conveyed

[KevinZomberTV]

Im doing a PhD on physics and I love your video! So Beautiful, Thanks !

[alejrandom]

Bro this is so good it almost seems forbidden math

[padraiggluck]

I enjoyed this presentation very much. Well done. ⭐️

[tw]

Interesting video. I've been thinking about looking into kaluza klein for a while. Definitely a rewatcher for sure.

[davidhand]

It seems like you've read some of the papers but not bothered with the rest. The STA has an even more mind-blowing perspective on EM, but instead of extending to 4 dimensions, you've decided to first go visit Newtonian gravity, which we all know:

- Isn't all of the forces.
- Does not really work.

Don't think about gravity just yet. I know it has an inverse square law, and it seems like a weird coincidence, but please believe me, there's so much more out there. Study STA (G(1, 3)) and see how much more beauty there is in E&M - they're just one thing! Then you will have the framework to explore the Dirac equation and begin to apply GA to modern physics.

[fromage]

Great video. Allowed me to finally grok a few key concepts. Please keep this up!

[JohnSmall]

Very interesting. Thank you for making this video

[RadoslavFicko]

The electrostatic force can be written as [Fe=(1/4.π.e)(Q^2/R^2).G/G=G.(Q/√(4.π.e.G))(Q/√(4.π.e.G)(1/R^2)], where mass M=∆Q/√(4. π.e.G) and gravitational force as [F=(G.M.M/R^2).(4.π.e/4.π. e)=(1/4. π.e)√(4.π.e.G)M.√(4.π.e.G)M(1/R^2)], where charge is equal to Q=√(4.π.e. G)∆m and ∆m can be the particle's mass loss or the binding energy between the charge and the particle ∆E=c^2.Q/√(4.π.e.G)=∆m.c^2

[Khashayarissi-obyj]

With luck and more power to you.
Hoping for more videos

[Dismythed]

This was mind-blowing, but where can we get a physicist's explanation of what is happening so that someone still learning physics can understand how we get to electromagnetism from gravity? (or is it the other way around?)