Alice underground: the door, the quaternion and the relativity

Alice underground is the first version of Aline in the wonderland by Lewis Carroll. The original manuscript, illustrated by Carroll himself, was given to the little Alice Liddell for Christmas in 1864 and picked up the story that he had told to Alice and her sisters Lorina and Edith during a summer's afternoon, precisely on July the 4th, 1862. This first version of the carrollian fantasy novel is, ultimately, a restricted version of Alice, where various characters and episodes completely absent in Underground are added, such as the Duchess or the team composed by the Mad Hatter, the March Hare and the Dormouse.
The intial, interesting considerations about underground is about the importance of the trees and the doors: following the suggestion by Adele Cammarata⁽³⁾, we can assume that the tree and the door that Alice cross to enter the garden of the Queen of Hearts, completely absent in Wonderland, is linked with the Celtic tradition. Indeed the oak is one of the sacred trees of the druids, symbolizing a link between heaven and earth⁽¹⁾. In this way the oak, which in Celtic was called duir, is a real door that connects people with the gods, but also ourselves with our inner part. So, from an etymological point of view, a carved door in a tree trunk is a Celtic symbol used to identify the Alice's passage towards a more stable phase after the size's changes of the previous scenes.
These changes in size, alluding both to the transition to adulthood, in perfect connection with the Druidic symbolism, and with the more classic homothetic transformations, i.e. the transformations which, without changing the proportions of a geometric figure, change its size. All these changes remain unchanged in the transition to the second version, including the meeting with the Caterpillar, who continues to ask Alice:

Who are you?

The first atomic clock

The first atomic frequency standard, based on the ammonia molecule (1949).
Inventor Harold Lyons is on the right; Edward Condon, at the age the director of NBS, is on the left.

The story of the atomic clock is really interesting, because starts from a pure research and arrives to an incredible application. First of all we must start from Isidor Isaac Rabi, who started the studies about the atomic transitions, and we must arrive to Harold Lyons, who applied the devices developed during 1930s-1940s by Rabi's team⁽²⁾, who awarded the Nobel Prize for these studies in 1944⁽¹⁾, in order to construct an atomic clock.
In particular the key paper is published in 1938, A new method of measuring nuclear magnetic moment⁽³⁾

It is the purpose of this note to describe an experiment in which nuclear magnetic moment is measured very directly. The method is capable of very high precision and extension to a large number and variety of nuclei.

A beam of particles, in the case of the first experiment they used molecules of LiCl, passed through a group of magnets, so that the nuclear spins is decoupled from each other and from the molecular rotation. At this point an additional magnetic field, this time slightly oscillating, is applied such that the spin and the nuclear magnetic moment are redirected, obtaining at the end a sort of frequency's precession⁽³⁾.
At the end, Rabi and his colleagues were able to observe perfectly the separated resonance peaks of the two nuclei of lithium and chlorine and just a year later, as also promised in the conclusions of the first article, they were able to update the method using some new atoms, describing with more details the experimental apparatus used by the team:⁽⁴⁾: