The Electron Does Not Exist - Curvature Identities on the AOL

Allen, James Johan Sebastian

The Electron Does Not Exist As A Physical Object

In Pattern Field Theory the electron is not a particle, not a cloud, and not a quantum object that moves around a nucleus. All electron-like behaviour is generated by curvature identities on the Allen Orbital Lattice (AOL). This page introduces that claim in three ways:

An interactive AOL overview to show the geometric substrate.
A focused curvature identity view for electron-like modes.
A shell and valence view that replaces the orbital picture with lattice geometry.

Ionization and Curvature Identities

In Pattern Field Theory, ionization energies arise from the curvature release threshold of an AOL identity. For hydrogen and helium, these thresholds match the known values (13.6 eV and 24.587 eV) as consequences of prime-indexed curvature recursion and PAL stability, without electrons as physical objects.

Detailed derivations are provided in the full paper: Ionization and Curvature Identities in PFT.

Allen Orbital Lattice - Structural Overview

The AOL is the geometric substrate in Pattern Field Theory. Stable curvature modes on this lattice produce the identities that mainstream physics labels as particles. Instead of electrons orbiting a nucleus, we have curvature identities that occupy stable configurations on this lattice.

The 3D view here shows a neutral AOL configuration with multiple layers and radius bands. You can rotate, zoom, and inspect how shells and sectors are arranged. No particles are present in the code. Everything is geometry.

Experimental ring image often described as first image of entanglement — Experimental ring pattern frequently described as the first image of quantum entanglement. Pattern Field Theory interprets this not as two photons but as a duplex curvature envelope undergoing lambda-phi shear inside an SPDC crystal. The ring is one undifferentiated identity, not two separate objects.

What The Entanglement Photograph Actually Shows

In 2019 a ring-like image was promoted as the first photograph of entanglement. The experiment and the image are real, but the usual explanation is not consistent with the geometry that is visible. The pattern is continuous and globally structured and does not support a two-particle picture.

In Pattern Field Theory the bright ring is the equilibrion boundary of a duplex curvature mode generated by lambda-phi shear in the nonlinear crystal. The central region is the identity-continuity well where the field-pattern has not yet differentiated. The two bright intensity regions on opposite sides of the ring correspond to phi-split curvature exits of one unified identity.

This makes the photograph important evidence for a field-based interpretation. It shows the geometry that exists before entanglement ends. There are no independent photons in this view, only a single duplex resonance on the lattice.

Electron As Curvature Identity On The AOL

In Pattern Field Theory an electron is represented by a curvature identity operator

℘(Z) = Λ(F_Z, k_Z, φ_Z)

where:

F_Z is the base curvature pattern for atomic number Z,
k_Z is curvature load, replacing a mass parameter,
φ_Z is the quantahex sector phase.

The 3D view here uses the same AOL geometry but is conceptually focused on a single curvature mode that would be interpreted as one electron in mainstream language. The difference is that no independent object is assumed. We only work with a geometric identity on the lattice.

Shells And Valence From Lattice Geometry

Orbital shells are usually presented as discrete electron orbits or probability clouds. Pattern Field Theory replaces that picture with curvature basins on the AOL. Shells are stable bands where the curvature identity operator has zero net gradient under the lattice constraints.

Valence emerges as a closure deficit on these shells. Instead of counting electrons, we examine how far a curvature basin is from a stable eight-state closure on the lattice. This reproduces the octet rule and periodic behaviour without invoking electron occupancy as a fundamental concept.

The 3D view here emphasises shells and sector bands. It is the same underlying lattice shown in a way that connects directly to shell structure and periodicity.

Summary - From Electron Ontology To Curvature Physics

Pattern Field Theory removes the need for electrons as physical objects. All phenomena normally attributed to electrons are re-expressed as curvature identities and shell behaviour on the Allen Orbital Lattice. The entanglement photograph is reinterpreted as a duplex curvature envelope, and atomic structure is reconstructed from geometry rather than from particle occupancy. This is controversial, but it is mechanically defined and testable.

Pattern Field Theory