I've been studying it more throughly these last months. Since then, I've come to the conclusion that STA is an overwhelming structure, as it is kinda redundant, given that only it's even sub-algebra is of any meaning (well, at least to our current understanding of the theory and phenomenology). So, I have a hunch that APS, re-written as complex paravector algebra is enough and complete to either differentiate the types, simplify calculations and describe space-time phenomena in SR/QFT settings. Though, I hadn't gone so far, currently I'm more focused on the devise of a complex newtonian mechanics based on Hestenes books/articles. Sadly, is a rather overlooked application of GA, as we have much more material for modern physics.
I will agree that the APS is underused, but the STA is far from redundant in my opinion. Have you read "Spacetime Algebra as a Powerful Tool for Electromagnetism" ? Every aspect of the STA has meaning, not just the even subalgebra!
@@EccentricTuber I haven't read it, yet. I didn't know it has meaning. The sources I've found said that only the even part is useful. I'll check it out.
@@linuxp00 Great to hear! It's really a cool paper. In the end, relative frame measurements are described using the even subalgebra, but they are more easily manipulated using the whole STA than in the APS. It's just because there are more tools in the STA than the APS! Things that look heterogeneous in the APS are homogeneous in the STA, etc.
![The most beautiful equation in math, explained visually [Euler’s Formula]](/img/n.gif)
4 dimensional spacetime is more fundamental than 3 dimension + time.
so nice!
I've been studying it more throughly these last months. Since then, I've come to the conclusion that STA is an overwhelming structure, as it is kinda redundant, given that only it's even sub-algebra is of any meaning (well, at least to our current understanding of the theory and phenomenology). So, I have a hunch that APS, re-written as complex paravector algebra is enough and complete to either differentiate the types, simplify calculations and describe space-time phenomena in SR/QFT settings. Though, I hadn't gone so far, currently I'm more focused on the devise of a complex newtonian mechanics based on Hestenes books/articles. Sadly, is a rather overlooked application of GA, as we have much more material for modern physics.
I will agree that the APS is underused, but the STA is far from redundant in my opinion. Have you read "Spacetime Algebra as a Powerful Tool for Electromagnetism" ? Every aspect of the STA has meaning, not just the even subalgebra!
@@EccentricTuber I haven't read it, yet. I didn't know it has meaning. The sources I've found said that only the even part is useful. I'll check it out.
@@linuxp00 Great to hear! It's really a cool paper. In the end, relative frame measurements are described using the even subalgebra, but they are more easily manipulated using the whole STA than in the APS. It's just because there are more tools in the STA than the APS! Things that look heterogeneous in the APS are homogeneous in the STA, etc.