## Q-Algebra

The following 4_XOR_16 matrix may define an algebra.

This matrix determines in which dimension we end up when multiplying vector components.

The result of multiplying vectors and can obviously be written as a 4x4 matrix!

We honor this finding by defining

 (1) (2)

 (3)

Looking rigorously at Eq. 2 yields

We can therefore write

 (4)

This also gives us the following sums and differences:

 (5) (6)

## Pythagorean Theorem

Let's say we have two arbitrary verctors and and the sum of these two vectors

With our new algebra we can square this equation without producing ambiguities.

This turns out to be the well known cosinus relationship for arbitrary triangles.

## New Electromagnetism

We have found the following three equations (gateway model) for new electromagnetism:

 (7)

 (8) (9)

Let's look at Eq. 7 first.

Our model for an electron is two pretonic charges rotating around each other with speed . This gives us the following for Eq. 7.

In the special case of the two pretonic charges constituting an electron and are parallel with opposite direction and perpendicular to at all times. We can therefore simplify to

 (10)

So Eq. 7 gives us Coulombs law if we look at two pretonic charges rotating with around each other. In the general case (two arbitrary charges with arbitrary velocities) we end up with an additional term

 (11)

Let's look at Eq. 8 and Eq. 9 now.

A moving charge generates a field at distance. A target charge feels a force if this field (at the location of ) changes. The field at the location may change due to a change of (limited propagation speed) but the more probable reason is that moved to another location with a different .

 (12)

Equations Eq. 10, Eq. 11 and Eq. 12 describe all known electromagnetic phenomena (Lorentz Force, Biot-Savat, Lenz Law,...).

Source: Robert Distinti (www.distinti.com)

## News

 23.04.2023 Cassiopeia 2.9.0 released 05.10.2022 Cassiopeia 2.8.3 released 29.09.2022 Cassiopeia 2.8.0 released 08.07.2022 Cassiopeia 2.7.0 released 14.04.2021 Cassiopeia 2.6.5 released 10.02.2021 Cassiopeia 2.6.1 released 26.06.2015 Word Processor Comparison 24.06.2015 Updated Documentation 23.06.2015 Cassiopeia Yahoo Group 18.06.2015 Advanced Data Security 11.05.2015 Cassiopeia Overview 08.05.2015 Exporting to files 14.05.2013 LaTeX and HTML Generation 08.05.2013 Example Paper released 26.04.2013 Co-editing in a workgroup 16.04.2013 Equation Editor Quick Reference 12.04.2013 Equation Editor 04.04.2013 Links and Bibliography 01.04.2013 Books 30.03.2013 Documents 28.03.2013 Simulations 16.03.2013 2D Graphs 10.03.2013 Symbolic Algebra 08.03.2013 Getting Started 07.03.2013 Installation and Setup

## White Papers

 13.10.2015 01 Writing documents 15.10.2015 02 Using the equation editor