First a short magnetic update:
In reason 66 as why electrons cannot be magnetic dipoles I tried to find a lower bound for the sideway acceleration the electrons have in the simple television experiment.
To put it simple: How much sideway acceleration must the electrons have to explain the dark spots on the screen where no electrons land?
The answer is amazing at first sight: about 2.5 times 10^15 m/sec^2.
This acceleration lasts only at most two nano seconds and in the end the minimum sideway speed is about 5000 km/sec so while the acceleration is such a giant number it does not break relativity rules or so…
Here is the link:
16 Aug 2018: Reason 66: Side-way electron acceleration as in the television experiment.
You know I took all kinds of assurances that it is only a lower bound on the actual acceleration that takes place. For example I took the maximal sideway distance as only 0.5 cm. Here is a photo that shows a far bigger black spot where no electrons land, so the actual sideway distance if definitely more than 0.5 cm.
The math part of this post is not extremely thick in the sense you can find the results for yourself with the applet as shown below. Or by pencil & paper find some 4D eigenvalues and the corresponding eigenvectors for yourself.
But we need them in order to craft the so called eigenvalue functions and also for the diagonal matrices that come along with all of the matrix representations of the 4D complex numbers Z.
I hope I wrote it down pretty straightforward, this post is five pictures long. And if you like these kind of mathematical little puzzles: Try, given one of the eigenvalues like omega or omega^3, find such an eigenvector for yourself. It is really cute to write them down, multiply them by the eigenvalue and observe with your own eyes that indeed we have all that rotation over the dimensions included that omega^4 = -1 behavior.
This post is five pictures long, it is all rather basic I hope.
The applet used is from the WIMS server (https://wims.sesamath.net/), look for the Matrix calculator in the section on Online calculators and plotters.
For the time being I think that in Part 12 we will craft the eigenvalue functions for any 4D complex number Z. Ok, that was it for this update.