Hi woneill1701 (star trek reference?)

Yup!

I don't know much about geometric algebra. I've looked at some stuff and read some of the Wikipedia page and I'd like to learn.

For me, the only place to go to in order to understand the implications of Geometric Algebra is the book by David Hestenes - "

*New Foundations for Classical Mechanics*"

It's hard to buy, but easy to download... I'm sure you would devour it in a couple of days.

He actually created a full series of books applying it to conventional Physics - and in doing so, simplifying everything from Maxwell's equations to SR/GR...

For context, while still at school I had mastered the use of Homogeneous Matrix Operations on 2D and 3D Vectors in the context of Computer Graphics using the book "

*Mathematical Elements for Computer Graphics"* by David Rogers. It was good about explaining what to do, but delivered none of the whys...

I am OCD, and my learning style is based on understanding - not memory, so I hoped that when I went to University they would enlighten me as to the fundamental reasons why of the Universe (this being one of them)...

To my horror, it was just as bad as being at school... We were given an even more primitive toolkit of vector operations to use than I had already got from my computer graphics book, and when I asked them why things were the way they were, they got

**very** testy!

Anyway, it was only when I read the Geometric Algebra book 10 years later that everything became so obvious and clear! The stuff they wouldn't/couldn't explain about vector/matrix operations just fell out of a very simple mathematical construct.

In short, by adopting the Vector format we all know today, they had excluded 80% of the mechanisms behind dimensional transformations/interactions from view. Geometric Algebra, by adding in the complete formulation, makes it SOOOOO much simpler while at the same time actually reducing mathematical complexity.

To me, it was one of the most important "lost" aspects of physics that prevents any aspiring physicist from being able to derive their own understanding from basic principles. You are just given a toolkit and graded on your ability to use it constructively...

I also disagree with the Minkowski stuff. I think it'd be correct if we replaced all the η's with δ's and used O(4) or SO(4) (4-dim rotation group) instead of the Poincare group (Lorentz transformations). I'd like to know why you don't like the Minkowski stuff. I think it's possible to understand the physics to some degree without formalizing it, so perhaps we can discuss this parallel to the maths.

In terms of Spacetime, I think it is a great modeling tool, and simply extends the usual graphical representation of anything against time into 4D. Nothing wrong with that! Just like any other representation that juxtaposes some function against time, it makes visualization possible and easy!

My problem comes when they say that this is reality, and that time is the 4th dimension!

I believe this was a deliberate attempt to prevent any further legitimate research into additional dimensions because the folks in the establishment already understood the implications of anyone being able to manipulate dimensional transforms that could affect external dimensions...

To me, Time cannot be a dimension because it is impossible to move through it. To me it is an artifact - an emergent property - of the Lorentz transformation. (In my original work with vectors for Computer Graphics I did a lot of work with perspective transformations, and the Lorentz Transformation, to me, is nothing more than a perspective transform.

But, as of today, I do not have the maths to either prove or dis-prove it. I feel like a chimp digging into an ant-hill with an old twig compared to the tools you guys have!

Anyway, I will follow your suggestions - Lie groups do seem directly related to GA - and I will get to them once my core Maths is back up to speed.

I was originally taught Maths as a process toolkit. This time I'm going to learn it as a language from basic principles!

Here's a video from the Electric Universe people on the logical inconsistency of special relativity,

The EU folks definitely have a lot of stuff right! Plasma is definitely the driving force behind most of Cosmology! But, I think they have over-reached with their formulation of Electric Gravity (things in a Faraday Cage would all be weightless if they were correct)...

I'm still not 100% sold on what to think about SR vs. the AEther.

SR does seem to have withstood many of its tests - and there have been

**many**!

At the same time, SR could explain why EM waves have physical presence and momentum, but no physical matter or mass in our universe.

If it wasn't for Quantum Physics, I would probably still be challenging SR the same way I challenge Minkowski, but given that Quantum Physics has to be right for any of our Solid State technology to work, I see SR as the mechanism why we cannot detect any materialistic waves associated with Quantum Physics.

(I see Quantum waves traveling at the speed of light through a universe that has collapsed in size down to nothing, with no observable time on the part of the wave. I imagine other denizens of that universe having the same conversation that we are today, but with our quantum waves behaving like E/M in that universe...)