QED Prerequisites Geometric Algebra: Spacetime.

In this lesson we continue our reading of an excellent paper on Geometric Algebra and spacetime algebra. The paper can be found here:

We will cover section 3.1 and begin section 3.2. This material includes our first expansion of the vector space of spacetime to include objects that are NOT the familiar 4-vectors of relativity. Also, we spend some time trying to clear up ambiguous usage of the word "vector" which often appears whenever we try to discuss vector spaces in a purely mathematical way.

The software I usually use to produce the lectures is:

[enterprisesoftwarearchitect]

Can’t believe learning that’s so valuable is so accessible!! Thank you, dear author!

[riakm]

I’m definitely looking forward to continuing this lecture series, fascinating stuff!! I thought the move of promoting the vector space’s scalars to be vectors themselves was intriguing... by doing so, isn’t the vector space’s scalar product now just a special case of the algebra’s vector product (and likewise with the scalar field’s multiplication)? So we’ve got one over-arching type of “multiplication” and all our previous notions of multiplication are merely special cases thereof...

[SomeMrMindism]

Well, the largest associative algebra is the infinite-dimensional tensor algebra, but possibly the authors meant "that is still contained in M1, 3", and indeed the Clifford algebra is a quotient of the tensor algebra

[alecchalmers]

When you mentioned this topic in a previous video, I read a couple of papers and the Wikipedia article only to come to the conclusion that this further complicated the analysis.

[davidhand]

Describing the STA is so much simpler when you don't start with the traditional mathematical treatment. This video could have been 2 minutes long if we just said:

Our basis starts with e_i for i 0 to 3.
e_0 is the unit vector of time in the rest frame, the others are unit vectors of space.
e_0 squared is 1. e_1 and above squared is -1.
The basis also includes all products of those vectors.

Bang. Done.

[Nickle]

Gauge Theory Gravity is a theory of gravitation cast in the mathematical language of geometric algebra