## The Anomalous Zeeman Effect: Zeeman and Preston

#### By Barbara Dooley

Throughout this article, I will begin by describing the Zeeman Effect, as well as the history of the discovery of the effect, and different people, notably Thomas Preston, who contributed greatly to the effect and discovered the Anomalous Zeeman Effect. In this article, I will be addressing the scientific side of the effect, rather than the mathematical, so for readers who are seeking a mathematical approach, I am afraid that this is not the article for you.

Some of you may have heard of Zeeman, but may not know what he is famous for and how he stumbled upon this discovery. Well, fear not, for hopefully all your questions are going to be answered. Pieter Zeeman was born in Zonnemaire, a small town in the Netherlands, on 25t​h​ May 1865. He studied Physics at the University of Leiden under Hendrik Lorentz, who will be mentioned in more depth later on.

Firstly, before I move onto Zeeman’s findings, I will briefly describe what a spectroscope is and how it works. A spectroscope is an instrument that allows scientists to determine the chemical makeup of a visible source of light. Spectroscopes may also operate over a wide range of non-optical wavelengths, from gamma rays and X-rays into the far infrared. Light is focused into a thin beam of parallel rays by a lense, then passed through a prism or diffraction grating that separates the light into a frequency spectrum, ranging from the smaller frequency to the bigger frequency wavelengths.

In 1896, Zeeman measured the splitting of spectral lines by a strong magnetic field. However, at the time, he did not realize that the lines were splitting, but instead believed that they simply became broader when a strong magnetic field was formed near the light source under which the spectral lines were observed. He also observed polarisation effects that indicated that the line was split in a manner consistent with the electron theory of Lorentz (which posited that in matter there are charged particles, electrons, that conduct electric current and whose oscillations give rise to light), but he did not realize this until later on.

He decided to continue the discovery and under closer inspection found that the spectral lines separated into either doublets or triplets when a strong magnetic force was placed near.

But Zeeman got no further in his discovery. In 1897, he was appointed as a lecturer at the University of Amsterdam and the disruption to his work caused by the move from Leiden was only increased by the inferior facilities he was forced to work with. He now had a smaller spectroscope, which lacked the sophistication and accuracy of his previous one. He printed thirty photographs of the splitting of the lines, but the quality of the photos was so bad that only one was deemed suitable.

However, around this time, an Irishman named Thomas Preston had heard of Zeeman’s discovery and wanted to investigate it in more depth. He decided to conduct the exact

experiment which Zeeman had done in 1896 in order to determine the accuracy of his theory.

First, before I launch into another description, now some background of Preston’s life. Preston was born on 23r​d​ May 1860 in County Armagh. He graduated from Trinity College Dublin in 1885 in Mathematics and Experimental Science.

Preston learnt of the Zeeman Effect through​ ​G.F Fitzgerald, a fellow scientist at Trinity. He obtained a spectroscope from the Royal University and a strong electro-magnet, also from the Royal University. (Later he ordered his own magnet which was constructed to his own special design by the Dublin manufacturer Yeates and Co. This is probably why he remained in debt until his untimely death). Please note that these instruments were, in fact, of better quality and standard than the apparatus used in Zeeman’s conduction of the experiment. Preston was also offered use of the laboratories at the Royal University, where he installed his apparatus.

Thus, in December 1897, he presented his experimental results, stating that he had indeed observed the triplet nature of line splitting as reported by Zeeman. However, due to his higher quality apparatus, he had also reported that he had observed four-fold and six-fold splitting for two significant lines respectively. His photographs were of much higher quality than Zeeman’s and the four fold and six fold splitting of the lines was evident in these photos.

However, there was a catch. As this latter observation was something never seen before, Preston admitted that both these splits did not follow any simple law. A more powerful magnet was needed if he was to pursue his declared aim of seeking a law governing the magnetic splittings. After numerous months of trying to produce a hypothesis, Preston came up with his rule, now known as Preston’s rule. This rule states that all the lines of a spectral series have exactly the same pattern. Preston suggested that the Zeeman pattern was the same in all respects for all the corresponding lines of a given series and that this similarity carried over from one element to another where such elements had similar types of series.

This discovery was known was the Anomalous Zeeman effect, as on first observation, it did not follow any simple law. Later on, the six-fold splitting was realized as being the introduction of quantum mechanics but only after Preston’s death, when the concept of electron spin and wave mechanics was introduced.

And what an untimely death he had. In 1900, Preston died of a perforated ulcer just as he was reaching the height of his academic career. In 1902, Zeeman, together with his former mentor, Lorentz, received the Nobel prize in Physics, for the discovery of his effect, which couldn’t have been proved if Preston didn’t step in. Preston was basically forgotten until the 1920s, when his rule sparked the birth of electron spin (the quantum property of electrons, a form of angular momentum that is a fundamental, unvarying property of the electron) ;only then was his contribution to Physics realized.

## 4D Cube Explained-part 2

Hello again, this is the promised follow up, in which we dive deeper into the secrets of the 4D cube!

In the last chapter, we covered the basic ideas of a 4D cube as an introduction. In this chapter, we would explain further into the idea of 4D geometry, as well as answering the questions proposed in the last chapter.

So, we have derived what a 4D cube look like, and to view it from a 3D perspective, we have two ways of representing that image:

Wait a sec, those two look quite different, are they both correct? What’s the difference?

As we can see, in Graph 1, the two 3D cubes that are supposed to be opposite each other are of different sizes. However, in Graph 2, the two 3D cubes opposite each other are the same sizes. In the previous chapter, we explained how to intercept Graph 2, but what about Graph 1? How do we understand Graph 1?

Let’s go back to the relationship between 3D and 2D. What is the 3D equivalent of Graph 1?

We get a picture like this:

Two opposite sides of a 3D cube are two squares. One is bigger, one is smaller. They are connected at all vertices, to create the picture above. Where have I seen this picture before? Think back on the museums you’ve visited, the Renaissance paintings you’ve seen. Think about the study of perspective. Or better yet, think about the room you are in. Go to one end of this room, place your back against the wall, and look across the room at the other end. You get a picture kind of like the one below.

Is it not exactly what we drew just then? When we place ourselves inside the 3D cube, Given a variable distance, we can see the two sides opposite each other at the same time, only of different sizes.

Artists know this. They use this skill to create realistic feeling of a 3D world on a 2D plane. Take a look at this painting, School of Athens. In this famous painting, the people far from us seem smaller, whereas the people near us seem bigger. This creates the feeling of 3D world on the 2D panel.

So, if we have a 4D cube that looks like Graph 1 it means that we are placing ourselves inside a 4D space, the smaller cube farther from us and therefore looking smaller, the bigger cube nearer us, looking bigger. I’m using the term ”farther” “nearer”, but these adjectives are the adjective of a new variable, a variable that does not exist in our dimension, the 4th variable in space. What might that be? It could be anything, colour, temperature…anything will do. But for our convenience let’s consider the 4th dimension as time, which is the easiest thing to understand in our 3D world, but the one thing that we cannot control. Ok, so now our variable is time, and the cubes are just two cubes through different time lapse. We are standing at a starting position “Now”, and the smaller cube we see in the distance is the exact same cube, labelled ”a year from Now”. That cube is considerably farther from us, so it seems smaller.

hat is how we interpret the difference between Graph 1 and Graph 2. Also, we gained a brand new understanding of a cube in 4th dimension. It is a cube, consisting of several 3D cubes that are spread across a time span, but also tangible at the same time.

Check out these photographs from photographer Steven Wilkins, showing the same landscape at different times on the same panel. In these pictures, the same thing at different times coexists. These pictures amazingly share the same idea as the structure of a 4D cube.

https://www.stephenwilkes.com/fine-art/day-to-night/52fa9a11-c5e8-4048-8071-0b560af4b6c2

So through these two articles, I hope I have given you a better understanding of a 4D world, and I would be very glad if you would be more fascinated in the mysteries of the higher dimensional space. There are endless magic to that topic and still a lot to explore!