Some time back I was looking at a few recently published posts and I started scribbling a few calculations. And all of a sudden I realized something has gone wrong. Now that full normal vector does what it was supposed to do: Always return a normal vector even if there is only one minor matrix that is not singular. But sometimes you get a zero vector and that is not what you want of course. You can always work around it if it happens to you, so it is not a serous fault or so. But it’s all a tiny bit less perfect as I thought.
That full normal vector is something you can use if you want to make a non square matrix into a square one. In doing so you must craft new columns perpendicular to all previous columns and normalize them. And there is the problem of course: If you get a zero vector, you cannot normalize it to length one.
The reason I decided to write this post is that during my scribbling I soon got one of those cylinder equations that don’t look at all like the equation of a cylinder. But in the 3D numbers, both complex and circular, you can factorize the determinant with a plane and a cylinder equation. So in that sense it is very vaguely related to the 3D numbers. For 3D numbers you can factorize the determinant using it’s eigenvalues and stuff like that I always name “Eigenvalue functions” because you just plug in the coordinates of a number and voila: There are your eigenvalues. It’s much easier compared to every time by hand calculating the 3 eigenvalues every 3D number has.
This post is four images long and an extra graph in a so called “Figure 01“. With the 3D version of Desmos, a free browser based app for drawing graphs, you can try a bit for yourself. I used two versions of the cylinder equation, don’t get confused by that because the one is only the minus of the other. That’s why in Desmos you sometimes must equal the cylinder equation to a positive number or a negative number. Here we go:
Again: If you try it in Desmos you must either use positive or negative numbers for your cylinder equation.
In case you want to know a bit more about the eigenvalue functions, just use the search function of this website and you will find plenty of stuff to think about. Ok, I hope you learned something and if not lets hope you are not one hundred % bored because math is just a boring thing or not? The next post is likely about magnetism but it is also tempting to write one more post on all the possible factorizations you can do with the determinant of 3D numbers and the many ways there are to find the 3D complex exponential as the intersection of a whole lot of geometrical objects. We’ll see.
A few years back Nobel prizes were rewarded for all that ‘faster than light’ stuff related to entangled particles (or photons) and the weird belief that particles far apart can more or less instantly communicate with each other.
Last year 2025 (by the way happy new year) we looked in details to the first experiment from John Clauser who used cascading electrons to generate pairs of photons and he got the Nobel prize because he showed that those photons always have the same linear polarization.
Since the year 2015 I started seriously doubting that electrons are indeed tiny bipolar magnets as a possibility to explain the results from the Stern-Gerlach experiment from the year 1922. Back in the time when people tried to explain this result of Otto Stern and Walter Gerlach in the letters they did send to each other it often started with the Gauss law for magnetism and that they ‘should find a solution within this framework of the Gauss law’.
So it never dawned on them that instead of finding a solution within this Gauss framework (magnetic monopoles do not exist) their scientific task should have been: Checking if the Gauss law for magnetism is indeed valid for unpaired electrons. After all, electrons being magnetic monopoles is indeed a perfect explanation for the Stern-Gerlach experiment. But no they did not do it, no one dared to take on the Gauss law that after all is just a fancy piece of math not rooted in any experimental evidence.
That is why even today in this new year 2026 we have crazy stuff like electrons that anti-align themselves with an applied external magnetic field like they did in the SG experiment explanation. And the most crazy thing in my view is the official version of the electron pair where the present day belief is still that because of the Pauli exclusion principle the electrons must have different spin numbers while in practice this simply means the two tiny magnets somehow must be anti-aligned to form a pair while from chemistry we know that electron pairs are very important in keeping molecules together.
But let me stop ranting against the belief that magnetic monopoles do not exist and turn to the beef of why I selected this video: It is all that Bell theorem stuff that says or validates all those ‘faster than light’ kind of collapsing of the wave function that they think actually happens. There is an old proof out that proves that Einstein’s idea’s of so called hidden variables cannot be true. It was only last year in 2025 that I looked into that and guess what? This proof uses the results of a repeated or sequential Stern-Gerlach experiment that gives all those probabilities for measuring electron spin. There is only one little pesky detail: In a century of time there has never ever such an experiment done. And if my idea’s of simply electrons having a permanent magnetic charge, just like their electric charge, are true, in that case measuring electron spin is the same as measuring the electric charge of the electron: It will always be the same no matter what. So that is why John Clauser always had the same linear polarization in his pairs of photons, the root cause or the ‘hidden variable’ if you want to frame it that way of finding always equal linear polarity is that the photons are made by the same electron. You really don’t need all this ‘faster as light’ crazy stuff to explain the outcome of the experiment John Clauser did.
I am more or less planning to look in this new year a bit deeper into all those other experiments done that show the ‘faster than light’ weirdo stuff but almost all experiments use crystals that do the parametric down conversing thing and break down one photon into two lower photons with opposite linear polarization. In my view the only logical explanation using electron permanent monopole properties is that an electron pair gets ejected into a higher energy state and later falls down and as such it will always generate an electron pair with opposite linear polarization.
But lets turn to the video: If electron spin is just a permanent monopole magnetic charge, in that case measuring electron spin is not probabilistic at all and as such the ‘proof’ as presented in the video is clear cut wrong. You can find the video at the end, this post is 3 images and one extra so called Figure 1. Here we go:
Furthermore if electron spin is a permanent monopole feature and depending on the kind of magnetic charge is what gives the two opposite polarization states of the photons they produce. As such the photon pairs as mentioned in the video are never in a superposition let alone that measuring one photon’s polarization leads to a collapse of the wave function and forces the other photon to take on the opposite (linear) polarization. And as such there is no ‘faster than light’ stuff going on at all.
And finally the video:
It has to be remarked that both Mithuna Yoagnathan and Derek Muller do nothing strange here. All physics professionals believe this kind of weird stuff to the extend there are even Nobel prizes handed out for this kind of crap. So both Mithuna and Derik are nice people and do only what is accepted as truth. Even the usage of these faulty probabilities related to a sequential or repeated Stern-Gerlach experiment is what they all do while bragging that physics is the only five-sigma science… Well no it just isn’t, never ever a sequential Stern-Gerlach experiment was performed there is also zero experimental validation for their fantasy that monopoles are tiny bipolar magnets. Another very fundamental piece of experimental validation that is missing is that if it was true that electrons are tiny magnets, in that case they will not be accelerated by a constant homogeneous magnetic field. That is a cornerstone of their thinking but once more: Where is that fucking experimental validation for this?
