Particles

ModelledOlder sketch. Live vertex: /cosmology/bubble-nucleation. Manifold spawner stays [O]. Token BN1 stays unissued.

Pair Production

Older sketch of a knot and its mirror. The live pair vertex is the instantaneous placement. This page is not that vertex.

Reading this entry

This page keeps the older bubble sketch of a knot and its mirror, and it points the live pair vertex to the instantaneous placement. The banner records shared radius, length, and pitch for the (1,1) and (−1,1) rulings as algebra of the input R₀, packaged as a model.

What this is used for

Use this page for the older threshold, confinement energy, and nucleation-rate sketch. The live vertex, with its shared radius, length, and pitch, is the placed jump named on bubble nucleation.

Walk through

The banner records the live pair vertex as the placed jump: equal-pitch helices and the (1,1) and (−1,1) rulings share radius, length, and pitch as [E algebra] of the input R₀, placed as [M packaging]. The older sketch writes γ + γ → e⁺ + e⁻ when the photon energy reaches 2 m_e c² (1.022 MeV), with threshold hν ≥ 2 m_{T(p,q)} c². On compact S³ the curvature absorbs recoil, and nucleation begins once the photon energy exceeds E_conf = ℏc / R_Compton = m_e c². The sketched rate is Γ_nucleation ∝ exp(−E_barrier / kT). For E ≫ 2 m_e c² the page marks a deviation window E ≫ m_e c²/α ≈ 70 MeV.

Doctrine v1.1.13: The live pair vertex is the placed jump on bubble nucleation. Equal-pitch helices and the

and

rulings share radius, length, and pitch [E algebra] of the input

. No transition equation is solved. That placement is [M packaging]. The cut, charge, Hopf labels,

, and the manifold spawner stay [O residual]. Token BN1 stays unissued. A continuum bulk PDE is not that vertex. The explicit bulk field equation stays open. The sketch below is the older bubble picture. It is not the live vertex.

Older bubble sketch

In the standard picture, occurs when photon energy (1.022 MeV), requiring a nucleus for momentum conservation.

An older CPT sketch wrote pair production as nucleation of a bubble from the vacuum. That sketch is not the placed vertex. The live sentence is the placed jump, with and still inputs.

Threshold Condition

Momentum and the Vacuum

In , momentum is defined on a compact space. The spatial curvature provides the equivalent of nuclear recoil — momentum is absorbed directly by the curvature, satisfying conservation laws.

Nucleation occurs when the photon energy exceeds the Weber confinement energy . Two photons are required for charge conservation.

Nucleation Rate

The nucleation rate from the BN programme depends on a topological barrier:

Nucleation Rate

where is the bubble nucleation barrier from the BN3 programme.

High-Energy Momentum Non-Conservation

At very high energies (), the ability of the curvature to absorb recoil momentum comes into question. CPT predicts deviations from QED at energies . This testable prediction is currently classed as [O].

Furthermore, a slight pair production rate asymmetry between matter and antimatter directly connects to baryogenesis.

Source Documents

The primary research documents underlying this page. All files are freely viewable and downloadable. They represent the working research as written — including integrity tags, equations, and finding IDs.

Documents open in the CPT Research Library — a formatted viewer for all source research files.