AFAICT you can do all of physics without cross products.
IMHO it's easier and better without cross products.
Use /wedge products/ instead.
---------------
Oh ok. Yes, I'm definitely on your side there. I'm currently teaching
myself Geometric Algebra (the term usually used for the 'physical'
Clifford Algebras), mostly through Hestenes's books. I particularly love
the extra insight one gets from SpaceTime Algebra, which was Hestenes's
PhD thesis all the way back in the 60s!
I'm not competent at it all yet, as it really does take some getting
used to. But gee, why on earth aren't they taking that approach in
schools and universities for crying out loud?!
As far as Electromagnetism is concerned, I wasn't sure whether or not
you could get by with just wedge-products, so that's good news if it's
right. I'll let you know what I think in a couple of years when my
opinion is worth something.
Actually, I was thinking of starting a thread about this topic as I am
so taken with the subject, and so flabbergasted that in 4 years of pure
mathematics nobody ever mentioned it to me. <insert shocked emoji>
Derek McKenzie
PhysicsFootnotes.com
-------- Original Message --------
Subject: [Phys-L] physics without cross products
From: John Denker <jsd@av8n.com>
Date: Sun, August 21, 2016 7:37 pm
To: Phys-L@Phys-L.org
On 08/21/2016 10:35 AM, Derek McKenzie wrote:
I'm not sure what you're referring to about a 'different model'?
AFAICT you can do all of physics without cross products.
IMHO it's easier and better without cross products.
Use /wedge products/ instead.
The cross product only makes sense in three dimensions.
The wedge product is well behaved in any number
of dimensions, from zero on up.
The cross product is defined in terms of a “right hand rule”.
A wedge product is defined without any notion of handedness,
without any notion of chirality. This is more important
than it might seem, because it changes how we perceive
the apparent symmetry of the laws of physics.