The 126 Dimensions of Benzene
A recent Nature Communications article has touted the discovery of a novel electronic structure for benzene, which consists of a 126-dimensional wavefunction. What does this actually mean?
It turns out that wavefunction tiling is a very useful method of establishing the probable boundaries of electrons within a molecule.
The basic idea is that we suss-out the extent to which an electron might be discovered at a particular location and add in the knowledge that this instance necessitates an opposing spin electron in that same orbital, at a predictable location. This stems from the Pauli Exclusion Principle, which we will examine momentarily.
Benzene was first described by Faraday in 1825. Electrically, benzene can be described as having 42 electrons, for which there are three spatial descriptors concerning location. 42x3 is 126. That’s 126 interactive coordinates that describe the electrical “structure” of benzene. These are the dimensions. But is this really a physical structure? In other words, is a molecule really a hyperdimensional object or is this pure indexing? Also, is an electron really an material with a surface and location or is it rather a description of a probable dynamic interaction?
If the electron is actually a predictable interaction rather than an material itself, then this new description of benzene, though no doubt astonishingly accurate, is incomplete since we do not yet understand what exactly is interacting. Brad Morton has written extensively on the notion that a wavefunction is a property rather than a physical material, here. In this case we ought consider candidate actors in the description that constitutes the electron.
Perhaps the electron is, in fact, a reified measurement of the location and directional momentum of the outer surface of an atom.
This would make sense, because the atomic surface can be thought of as in feverish rotational motion. In this manner, each lobe of surface can rotate one way or the other but never both simultaneously. This helps us begin to rationalize what Pauli Exclusion actually means. As the atomic material is excited, new surfaces are presented to the experimentalist and modeled accordingly by the mathematician with locations and directionality of spin (up or down). Since each of these surfaces gets a particle title, N, with three location coordinates, the 3N dimensions can pile up pretty quick.
We understand from hybridization theory that these atomic surfaces, called orbitals, are produced by atomic excitations and appear consecutively in polar pairs. Often orbitals will fill one by one with a particular spin. Consider this to mean that those surfaces each rotate in the same direction. Depending on the hybridization,
orbitals will eventually expand or ‘fill’ with opposite spin electrons per Pauli’s principle. Structurally, this could indicate that an additional, electrically useable, surface appears at the opposite pole for that orbital.
This makes sense: If you measure one orbital surface from a clockwise hemisphere, then you will necessarily find counterclockwise motion (opposite spin) at the antipodal hemisphere once it appears, functionally. Functional in this case mean electrically interactive. You are viewing lobes of the same structure undergoing the same rotation but from opposite ends of the atom.
If the earth was an atom, you could measure spin direction at the North pole and if allowed, another opposite spin at the South pole. If you measure the Northernxf hemisphere, you instantly know the state of the Southern.
But let’s say you only get that second measurement if the south pole interacts electrically with your detector. In the case of atoms, such filled valence orbitals become apparent and interactive only under certain excitations or bonding-arrangements, as well as in the noble gases. Having unpaired valence electrons might be visualized as having directional surface rotation on balance, which predisposes those atoms to electrochemical surface-enmeshments.
The excitation-dependent shapes of atomic surfaces (orbitals) may in this manner outline the physical mechanism behind the Pauli Exclusion Principle. At least insomuch as we understand the electron to be an indexed property of the atom’s motive surface rather than a physical material in and of itself.
