Monthly Archives: June 2023

Spin selection rules and the permanency of magnetic charge of the electron.

The official version aka the standard model of particle physics says there is only one kind of electron, all electrons are the same, and their magnetic properties like spin are only a matter of alignment cq anti-alignment with the magnetic field. The standar model treats electrons as tiny magnets.
I think that electrons are magnetic monopoles and as such there are two kinds; a north pole and a south pole kind. But can electrons flip their spin? After all a lot of quantum computing is based on the idea that indeed electrons can flip their spin even stronger: the electron can be in a super position of spin un and down.
Over the years I slowly evolved to the position that the magnetic charge of electrons is permanent. And if the magnetic charge is permanent in that case in the electron cloud of an atom or a molecule, al lot of transitions cannot be done. During those transitions the spin of an electron cannot flip simply because it’s charge is just like the electric charge: permanent.

Now I did not know it but inside a lot of chemistry files you can find a thing known as ‘Spin selection rules’ that give a good description of how an electron can jump up and down the diverse orbitals when it comes to it’s spin. You can also find it under ‘Forbidden transitions’ but also stuff like radioactive decay has forbidden transitions.

An important feature of a forbidden jump in electron transitions is that ther assiciated energy can be observed but that is always on a longer timescale. My impression is that the chemical people don’t understand very good as why this is: Well an electron in some atom or molecule can only ‘flip’ it’s spin as it gets replaced by another electron.

Example: The 21 cm radio frequency in radio astronomy. Photons with a wavelength of 21 cm come from atomic hydrogen that undergoes a spin flip to it’s lowest potential energy configuration when it comes to magentism.
But if that can only be done by other electrons bumping into that hydrogen atom, that says something about the electron streams in vacuum from where the 21 cm radiation is coming.

Here a simple picture of what is allowed and what not:

Basically it says: Spin flip is not allowed.

It is very well known inside the science of chemistry that energy states like those singlet and triplet stuff above are very close to each other. So how it is possible that just some thermal shaking or good old molecular vibrations do never flip the spin of an electron?

If all that mumbo jumbo about electrons was true, why can’t some heat or some vibrations make that sole electron flip it’s spin? Do we get that nonsense like “If you think you understand quantum mechancis, in that case you don’t understand quantum mechanics” one more time?

And I admit that too: If you are that stupid to view the electron as a tiny magnet, yes indeed the science of particle physics but also chemistry becomes very hard to understand. It’s loaded with weird stuff all over the place. In chemical bonding the electrons in a pair must always have opposite spins but in permanent magnets the spins must always be aligned.

May be it is time to split my dear reader. See you in the next post.

Proof that Z^2 = -1 cannot be solved on real spaces with an odd dimension. (General theory part 1.)

Finally after all those years something of a more general approach to multiplication in higher dimensions? Yes but at the same time I remark you should not learn or study higher dimensional numbers that way. You better pick a particular space like 3D complex numbers and find a lot out about them and then move on to say 4D or 5D complex numbers and repeat that process.
Problem with a more general approach is that those spaces are just too different from each other so it is hard to find some stuff all of those spaces have. It is like making theory for the complex plane and the split complex numbers at the same time: It is not a good idea because they behave very differently.
The math in this post is utterly simple, basically I use only that the square of a real number, this time a determinant, cannot be negative. The most complicated thing I use of the rule that says the determinant of a square is the square of the determinant like in det(Z^2) = det(Z)^2.

This post is only 3.5 pictures long so I added some extra stuff like the number tau for the 4D complex numbers and my old proof from 2015 that on the space of 3D complex numbers you can’t solve X^2 = -1.

I hope it’s all a bit readable so here we go:

Oops, this is the circular multiplication… Well replace j^3 = 1 by
j^3 = -1 and do it yourself if you want to.

So all in all my goal was to use the impossibility of x^2 being negative on the real line to the more general setting of n-dimensional numbers. As such the math in this post is not very deep, it is as shallow as possible. Ok ok may be that 4D tau is some stuff that makes math professors see water burning because they only have the complex plane.
Let me end this post with thanking you to make it till the end, you have endured weird looking robots without getting mentally ill! Congratulations!
At the end a link to that old file from 2015: