I had a bit of computer problems lately, my oldest computer did not allow me to enter the BIOS and as such I could not tell from what hard disk to boot and that was the end of the motherboard in that old computer. It was my last Windows XP computer and looking at the latest Windows 7, 10 or 11 stuff there is not that much progress. Windows OS systems become more and more a fashion thing because most of it is outdeveloped and hard to improve upon… But lets go to this small post about the long title above: total angular momentum.

To put it simple: In an atom or molecule with unpaired electrons in it physics people often think of the spin of the unpaired electrons as vectors that get projected against the vertical direction if a magnetic field is applied. Those projections are treated as scalars and as you might have guessed it is either +1/2 or -1/2. (Here I leave the constant of Planck out for simplicity.)

Ok my version of magnetism is that electrons are magnetic monopoles so they have either a north pole charge or a south pole magnetic charge. Adding these up works just like adding up the electrical charges in an atom or a molecule; because after the humble opinion of your servant electron magnetism looks just like electron electricity: permanent and monopole.
So that is all to know, basically it is very simple once you have seen a few times what they do and mean with that “Total angular momentum in the x-direction” because that sounds so complicated. But all in all the calculations they do are just like adding up monopole magnetic charges so they were on the right track more or less a long time ago.
This post is four pictures and for me that is a bit hard because I always made the backgrounds on the computer that broke down. And that old graphics program can’t run on Windows 7 or higher while modern graphics programs like GIMP just don’t have the features to make such a background in a few clicks. Of course a long time ago this doomsday day was foreseen and I saved a lot of backgrounds as png files. So I opened that folder and what? It’s fucking empty…:(
Well lets go to the pictures:

The most hilaric picture is the fourth one where two electrons with opposite spins are in different energy levels in an atom or molecule. And if you want your electron spin as a vector, how the hell should you get opposite pointing vectors while the electrons are in different parts of the atom or molecule? That is very weird behavior and as such it always goes unexplained to the extend it is never mentioned as a problem. Just like all that other stuff that is wrong with electron magnetism as you view them as tiny magnets and not as magnetic monopoles.

Well thanks for your attention and see you in another post.

This is a 56 year old documentary about the machine depicted below and imitates the original Stern-Gerlach experiment in many ways. Now in the year 1967 (I became 4 years old that year) you could also have used any television they had in those long lost years and split the electron beam with a magnetic field like I once did.
It is all done beautiful, there is even an oven to vaporise the metal, in this case cesium. All these decades the explanation of the result of this experiment has not changed: Everything is explained by tiny magnets that align or anti-align with the applied magnetic field. And, just like at present day, the anti-alignment is not explained at all. How can that happen in the first place and how can it be stable?
From five screenshots I made four pictures and after that I will link to the video that has a length of about 25 minutes.

In the next picture you see the oven, I did not know you could vaporise metal so easily.

Professor Jerrold R. Zacharias is going to do some explanation of how this all is supposed to work and as such you see the well known iron filings and a magnetic field made by these two coils you see below.

As usual a lot of the explanation is swiped under the carpet (just like in 2023) and at the bottom of the picture you see that magnet being alligned or anti-aligned with the magnetic field. But why does that piece of cardboard hang from four lines or four thin ropes? What would happen if he just glued two of the lines at the north and south pole of the magnet? In that case it would be very very hard to get an anti-alignment of the bar magnet with the magnetic field. Just as impossible as balancing a pencil on it’s top for say a few minutes of time. But the physics professors just never talk about stuff like that, it is only “The standard model of particles physics is so amazingly correct” and more of that nonsense. Well I agree that if you swipe all this stuff under the carpet it all looks tidy..

The cesium used has atomic number 55 and a mass of say 133 atomic units. If here just like in the original SG experiment it is only one unpaired electron that causes the effects observed, in that case the electron moves a mass about 250 thousand it’s own electron mass.
On top of that, the electron is very tiny and it is supposed that a magnetic field with a gradient can give a force on the electron. In my opinion that is where fantasyland begins. Viewing electrons as magnetic monopoles removes a lot of what so hard is to understand, like the anti-alignment thing.

As picture number four you see the results of different field strengths of the magnetic field, it is a lovely old fashioned machine.

Here is the video:

The video is only posted on Youtube about 9 months ago, that is why I missed it in the past. After all you don’t go out every month looking for the lastest video about the SG experiment!
Let me end this post with a comical note. For a picture on the other website I combined an idea about electron spin with that old painting known as “The Scream”. Here it is:

That was it for this post. May be it is time to do some math again, now it looks as if I only discuss video’s. Thanks for your attention.