Antiparticles

An antiparticle is the topological mirror of its partner: T(p,q) ↔ T(q,p) with reversed Hopf fibre orientation. The live pair vertex is the instantaneous placement.

Reading this entry

An antiparticle is the topological mirror of its partner. The map T(p,q) ↔ T(q,p) reverses Hopf orientation, so charge flips while the shared self-linking number pq = qp keeps the two masses equal, and the live pair vertex is the instantaneous placement.

What this is used for

Use this page to read charge reversal, parity, and time reversal as geometric operations on a torus knot. It pairs the electron with the positron and the proton seat T(2,3) with the antiproton winding T(3,2), and it points the live vertex to bubble nucleation.

Walk through

The mirror relation exchanges winding numbers, T(p,q) with T(q,p). The electron T(1,1) meets the positron as the same knot with reversed fibre orientation, and the proton seat T(2,3) meets the antiproton as T(3,2), the neutron winding read with opposite charge orientation. Charge reversal is the winding-orientation flip, parity is reflection in S³, and time reversal is the Hopf fibre direction. Pair creation is written γ + γ → T(p,q) + T(q,p) when ℏω > 2 m_particle c², with Q(T(q,p)) = −Q(T(p,q)) and m(T(p,q)) = m(T(q,p)) because self-link(p,q) = self-link(q,p). The live pair vertex is the instantaneous placement on bubble nucleation.

Structure package: Claims here are geometric/packaging results under named premises. They do not by themselves close absolute α, continuum hold, or the full SM mass spectrum. See /status.

The mirror knot

T(p,q) and T(q,p) are distinct knots (in general) but related by the exchange of winding numbers — this is the CPT discrete symmetry.

Key pairs

Electron T(1,1) ↔ Positron T(1,1): with reversed orientation (since p=q=1, the knot is the same but the fibre orientation reverses).
Proton T(2,3) ↔ Antiproton T(3,2): (same as neutron winding but with opposite charge orientation).

CPT symmetry

The framework realises the discrete CPT symmetry geometrically — Charge reversal = winding orientation flip, Parity = reflection in S³, Time reversal = Hopf fibre direction.

Pair production

Particle + antiparticle pair are created together because you cannot create a topological knot without simultaneously creating its mirror — topology conservation.

Pair annihilation

When T(p,q) and its mirror meet, the total winding number cancels → the energy is released as free (unconfined) photons.

Antiparticle masses

T(p,q) and T(q,p) have the same self-linking number pq = qp → same mass ✓

The live pair vertex

The live pair vertex is the instantaneous placement on bubble nucleation. The older bubble sketch on pair production is not that vertex. The manifold spawner stays open.

Key Equations

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.