Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== Below I map each spin type to a geometric/physical process in QAT language (I mark which statements are speculative). ===

==== Physical facts to keep: light is an electromagnetic field; a free photon has two polarization (helicity) states ±1. On a spherical wavefront (Huygens picture), the E and B vectors are tangential to the sphere and orthogonal to the radial propagation. ====
QAT picture:
* A spherical light wave is a 2-D manifold (the wavefront). The local electromagnetic vector (E) lies in the tangent plane of that sphere. The rotation of that tangent vector around the local propagation axis is the physical content of photon helicity. When a local atom (the electron sphere) absorbs/emits, it couples to the tangential components — transferring one “unit” of angular momentum (spin-1) via the vector character of the boundary coupling.
* So: photon spin ≈ direction/rotation of the tangent E-vector on the 2-D spherical boundary. This directly matches the textbook polarization/helicity picture. Wikipedia<ref>{{cite web|title=Wikipedia|url=https://en.wikipedia.org/wiki/Photon_polarization|publisher=en.wikipedia.org|access-date=2025-12-16}}</ref>

Why this is attractive in QAT: Huygens’ spherical wavefront + tangential EM vectors gives a geometric, area-based support for the two photon helicities.

==== Mainstream fact: spin-½ is described by spinors (SU(2) double cover). Physically experiments show electrons have half-integer angular momentum and fermionic statistics. Wikipedia<ref>{{cite web|title=Wikipedia|url=https://en.wikipedia.org/wiki/Spin_%28physics%29|publisher=en.wikipedia.org|access-date=2025-12-16}}</ref> ====

QAT picture (geometric intuition):
* Picture the electron sphere (the 2-D probability shell around the nucleus) as a boundary where an internal phase degree of freedom lives — a phase that registers how the EM tangential field has been absorbed and re-emitted by that shell.
* If that boundary carries an antiperiodic condition (phase flips sign after a 360° rotation of the local frame), then a 360° rotation is not the identity: you need 720°. That directly reproduces the spinor behaviour (Dirac belt trick / two-turn rule). This antiperiodicity is the same structure that in QFT produces spin-½ fields. Harvard Scholar<ref>{{cite web|title=Harvard Scholar|url=https://scholar.harvard.edu/files/noahmiller/files/dirac_belt_trick_faq.pdf|publisher=Harvard Scholar|access-date=2025-12-16}}</ref>PhilArchive<ref>{{cite web|title=PhilArchive|url=https://philarchive.org/archive/NIETTUv146|publisher=philarchive.org|access-date=2025-12-16}}</ref>
* Geometric origin in QAT: you suggested the “half-radius” (r_eff = r/2) and a central nucleus as a privileged center. In a boundary Lagrangian picture, a field restricted to that shell can naturally have antiperiodic boundary conditions (a Möbius-like phase twist), giving the half-spin outcome. The boundary becomes a spinor bundle rather than an ordinary vector bundle.

Takeaway: spin-½ can be described as a topological phase living on the 2-D shell: an antiperiodic boundary condition ↔ the observed ½-spin transformation law. This is conceptually consistent with mainstream spinor topology (SU(2)/double cover). Rochester School of Arts & Sciences<ref>{{cite web|title=Rochester School of Arts & Sciences|url=https://www.sas.rochester.edu/pas/assets/pdf/undergraduate/su-2s_double_covering_of_so-3.pdf|publisher=Rochester School of Arts & Sciences|access-date=2025-12-16}}</ref>PhilArchive<ref>{{cite web|title=PhilArchive|url=https://philarchive.org/archive/NIETTUv146|publisher=philarchive.org|access-date=2025-12-16}}</ref>

==== Mainstream fact: a massless spin-2 field in QFT, when coupled consistently, leads to nonlinear equations equivalent to Einstein’s GR (Weinberg, Feynman and later spin-2 derivations). Also modern amplitude methods show a precise relationship between gauge theory (spin-1) and gravity (spin-2) — the double-copy idea (gravity ≈ gauge ⊗ gauge). arXiv<ref>{{cite web|title=arXiv|url=https://arxiv.org/html/2403.08637v1|publisher=arxiv.org|access-date=2025-12-16}}</ref>Physical Review Links<ref>{{cite web|title=Physical Review Links|url=https://link.aps.org/doi/10.1103/PhysRevLett.105.061602|publisher=Physical Review Links|access-date=2025-12-16}}</ref> ====

Two complementary QAT ideas for spin-2 emergence:
# Composite / second-order field from photon absorption+re-emission. - An absorption (spin-1 in) + emission (spin-1 out) at a boundary, if treated together as a coherent, second-order process averaged over many events, can produce a symmetric rank-2 response on the shell (two vector indices → a tensor). Intuitively: two vector directions (incoming and outgoing) combine to a symmetric bilinear object — the same mathematical type as a spin-2 field. - If these pairings are universal (every mass/current participates similarly) then the resulting effective field couples universally → matches why gravity couples to stress-energy. This is the QAT version of “spin-2 from paired spin-1 events.”
# Double-copy evidence (modern QFT): - In scattering amplitudes the graviton amplitude is (roughly) the “square” of gauge amplitudes: gauge × gauge → gravity. This provides a formal mechanism where two gauge (spin-1) degrees can be reassembled into spin-2 dynamics; so the idea “two photons combine into a gravity-like effective field” has active, modern theoretical support in the amplitude literature. Physical Review Links<ref>{{cite web|title=Physical Review Links|url=https://link.aps.org/doi/10.1103/PhysRevLett.105.061602|publisher=Physical Review Links|access-date=2025-12-16}}</ref>arXiv<ref>{{cite web|title=arXiv|url=https://arxiv.org/abs/2203.13013|publisher=arxiv.org|access-date=2025-12-16}}</ref>

So in QAT language: the tensorial curvature seen in GR could be the emergent, effective field generated by an organized pattern (coherent sum) of photon-exchange events across the many atomic shells in matter. The boundary stress of these exchanges gives a rank-2 object that sources curvature.

Important caution: turning this conceptual picture into a rigorous derivation (explicit field operator built from EM fields that transforms as a symmetric rank-2 tensor and reproduces GR) is a hard QFT problem. The double-copy results are encouraging (they show spin-2 can come from “square” gauge structures), but a full non-perturbative derivation mapping QAT boundary processes to Einstein’s equations is an open project. Physical Review Links<ref>{{cite web|title=Physical Review Links|url=https://link.aps.org/doi/10.1103/PhysRevLett.105.061602|publisher=Physical Review Links|access-date=2025-12-16}}</ref>arXiv<ref>{{cite web|title=arXiv|url=https://arxiv.org/html/2403.08637v1|publisher=arxiv.org|access-date=2025-12-16}}</ref>