A Grand Illusion

A figurative depiction of the helium-4 atom with the electron cloud in shades of gray.
In the nucleus, the two protons and two neutrons are depicted in red and blue.
Not to scale - The nucleus is approximately 1/100,000 the size of the atom.

It's nearly empty space or, in other words, reality is but a grand illusion of solidity based on the fact the nucleus of a given atom is 1/100,000 the size of the atom itself while at the same time, said nucleus comprises 99.9% of the atom's mass so ... why does reality feel solid to us rubes? :)

My trip on this prepandemic morning in November 2018 is to visit the place that, precisely a century before February 8, 2022, saw one of the most pivotal events for the nascent quantum physics. Without quite realizing what they were seeing, Stern and his fellow physicist and collaborator Walther Gerlach discovered quantum spin: an eternal rotational motion that is intrinsic to elementary particles and that, when measured, only comes in two possible versions—“up” or “down,” say, or “left” or “right”—with no other options in between.

Before the Roaring Twenties were over, physicists would reveal spin to be the key to understanding an endless range of everyday phenomena, from the structure of the periodic table to the fact that matter is stable—in other words, the fact that we don’t fall through our chair.

But the reason why I have a personal obsession with the Stern-Gerlach experiment—and why I am here in Frankfurt—is that it provided nothing less than a portal for accessing a hidden layer of reality. As physicist Wolfgang Pauli would explain in 1927, spin is quite unlike other physical concepts such as velocities or electric fields. Like those quantities, the spin of an electron is often portrayed as an arrow, but it is an arrow that does not exist in our three dimensions of space. Instead it is found in a 4-D mathematical entity called a Hilbert space.

It's all about spins & fields is it not?

The state of a vibrating string can be modeled as a point in a Hilbert space. The decomposition of a vibrating string into its vibrations in distinct overtones is given by the projection of the point onto the coordinate axes in the space.

Seen below is an explanation of how quantum computers work. Indirectly, it also shows how spin and fields make up, in part, the quantum mechanical reality in which we all inhabit.