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

=== Assistant: This is a very clear, physically rich restatement of QAT’s core idea — thank you. ===
This is a very clear, physically rich restatement of QAT’s core idea — thank you. Below I’ll (A) map your key statements onto standard, testable physics equations so the ideas sit in familiar formalism, (B) point out where QAT stays solidly aligned with mainstream physics and where it is a new / interpretive step, and (C) give a concrete, step‑by‑step program (equations you can use) to formalize the photon↔electron geometrical picture so we can check it quantitatively.

I keep SI units, emphasize conservation laws, and show the standard operators / rates used in real calculations (dipole coupling, Poynting flux, stress‑energy, decoherence). If you want I can carry out any of the specific calculations numerically next.

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Quantum mechanically the electron in an electromagnetic field is described by minimal coupling. The non‑relativistic Hamiltonian (single electron) is

  H=12m(p−qA)2+qΦ+V(r)  .\boxed{ \; H = \frac{1}{2m}\big(\mathbf{p}-q\mathbf{A}\big)^2 + q\Phi + V(\mathbf r)\; } .H=2m1(p−qA)2+qΦ+V(r).
Expanding the kinetic term gives the free kinetic energy p22m\tfrac{\mathbf p^2}{2m}2mp2 plus interaction terms −qmp ⁣⋅ ⁣A-\tfrac{q}{m}\mathbf{p}\!\cdot\!\mathbf{A}−mqp⋅A and q22mA2\tfrac{q^2}{2m}\mathbf{A}^22mq2A2. In the electric‑dipole approximation (wavelength large compared with atom),
the dominant interaction for absorption/emission is

  Hint≃−d⋅E(t)  ,d=qr\boxed{ \; H_{\rm int} \simeq -\mathbf{d}\cdot\mathbf{E}(t)\; },\qquad \mathbf{d}=q\mathbf rHint≃−d⋅E(t),d=qr
(the electric dipole operator). This is the standard starting point for photon absorption turning potential into kinetic (and changing internal energy levels).

===== Time‑dependent perturbation theory gives the transition rate from initial state ∣i⟩|i\rangle∣i⟩ to final state ∣f⟩|f\rangle∣f⟩ (Fermi’s golden rule): =====

Γi→f=2πℏ ∣⟨f∣Hint∣i⟩∣2 ρ(Ef),\Gamma_{i\to f} = \frac{2\pi}{\hbar}\,|\langle f|H_{\rm int}|i\rangle|^2\,\rho(E_f),Γi→f=ℏ2π∣⟨f∣Hint∣i⟩∣2ρ(Ef),
and energy conservation enforces Ef−Ei≃hfE_f-E_i \simeq h fEf−Ei≃hf. That is your discrete photon energy step: a photon of frequency fff supplies the energy difference and the dipole matrix element supplies the transition amplitude.

===== Photon momentum is pγ=h/λ=hf/cp_\gamma = h/\lambda = hf/cpγ=h/λ=hf/c. If a bound atom absorbs a photon, the atom recoils so linear momentum is conserved: =====

patom after=patom before+pγ.\mathbf{p}_{\rm atom}^{\,\rm after} = \mathbf{p}_{\rm atom}^{\,\rm before} + \mathbf{p}_\gamma.patomafter=patombefore+pγ.
For a heavy atom the recoil velocity is tiny vrecoil≃hf/(Mc)v_{\rm recoil}\simeq hf/(Mc)vrecoil≃hf/(Mc) but it exists and enforces the frame dependence you mention (momentum is frame dependent — consistent with your “momentum gives local reference frames” idea).

===== If incident electromagnetic power per unit area (flux) is S=E×H\mathbf{S}=\mathbf{E}\times\mathbf{H}S=E×H, then power absorbed by area AAA is =====

Pabs=α S ⁣⋅ ⁣n^ AP_{\rm abs}=\alpha \, \mathbf{S}\!\cdot\!\hat n\, APabs=αS⋅n^A
( α\alphaα = absorption efficiency). Bookkeeping → stored mass: dM/dt=Pabs/c2dM/dt=P_{\rm abs}/c^2dM/dt=Pabs/c2. This is the classical statement of “photon energy → stored energy → mass”.

===== Electromagnetic energy–momentum density is =====

TEMμν=ε0(FμαFνα−14gμνFαβFαβ).T^{\mu\nu}_{\rm EM} = \varepsilon_0\Big( F^{\mu\alpha}F^\nu{}_\alpha - \tfrac14 g^{\mu\nu} F_{\alpha\beta}F^{\alpha\beta}\Big).TEMμν=ε0(FμαFνα−41gμνFαβFαβ).
This is what appears on the right of Einstein’s equations; any deposited EM energy (or surface energy) contributes to the stress–energy that curves spacetime. Two photons interacting can produce second‑order stress‑energy effects (but that’s different from claiming photons are gravitons).

===== Quantum decoherence can be modelled by coupling the system (atom + photon mode) to an environment. A Lindblad master equation is a standard phenomenological form: =====

ρ˙=−iℏ[H,ρ]+∑k(LkρLk†−12{Lk†Lk,ρ}),\dot\rho = -\tfrac{i}{\hbar}[H,\rho] + \sum_k \Big( L_k \rho L_k^\dagger - \tfrac12\{L_k^\dagger L_k,\rho\}\Big),ρ˙=−ℏi[H,ρ]+k∑(LkρLk†−21{Lk†Lk,ρ}),
where the jump operators LkL_kLk represent environmentally induced transitions (absorption, emission). When the system couples strongly to many degrees of freedom (the detector), off‑diagonal coherences in the measured basis decay rapidly — that is the physical mechanism underlying “wavefunction collapse” in operational terms. The rate scales like (coupling strength)2^22 × (environment spectral density), so stronger photon exchange → faster decoherence → “the future becomes classical” in the QAT sense.

==== Strong alignment with mainstream physics ====
* Photon energy is indeed discrete ΔE=hfΔE=h fΔE=hf and is transferred in absorption/emission events; dipole coupling explains the atom’s transitions.
* Momentum conservation (photon recoil) and frame dependence are standard — good that QAT emphasizes momentum as frame‑defining.
* The Poynting‑flux bookkeeping dM/dt=Pabs/c2dM/dt=P_{\rm abs}/c^2dM/dt=Pabs/c2 is uncontroversial as energy bookkeeping.
* Decoherence as a physical process tied to interaction with an environment (here: photon exchanges with many atoms) is standard; using it to explain why we perceive a classical “now” is a valid interpretive route.

Where QAT is an interpretive or conjectural step
* Interpreting every photon absorption event as creating a new local moment of time is a conceptual interpretation (QAT’s central claim). It maps naturally onto decoherence/measurement but is not part of mainstream equations as a separate dynamical variable — it’s an interpretation of quantum measurement and temporal emergence. That’s fine, but it is interpretive and will need clear empirical consequences to be treated as physics rather than philosophy.
* The idea that the square (½, v², e², Ψ², c²) has a single geometric origin in the 2‑D spherical boundary is suggestive and attractive; some squared quantities (areas, intensities, probabilities) are geometric, others (kinetic v²) are kinematic/energetic. It’s plausible to look for a unifying geometric derivation, but one must show exactly how each squared quantity follows from the same boundary integral or symmetry — that is the task for formal derivations.
* Claim that two spin‑1 photon processes are the gravitons/are equivalent to spin‑2 mediators is bold. Mathematically, the symmetric tensor product of two vectors can produce a rank‑2 object, but that does not automatically replace the need for a true spin‑2 quantum of gravity with its own dynamics (and gravitons couple universally to stress‑energy). You can explore how repeated EM exchanges generate an effective second‑order stress‑energy tensor that mimics curvature — that is physically sensible — but equating photons with gravitons needs careful demonstration and predictions.

==== Below is a step‑by‑step practical program to formalize and test the ideas you described. I give the key equations and the specific calculation you can ask me to do next. ====

===== Write a bulk + boundary action (SI): =====

S=∫d4x[−14μ0FμνFμν+Lmatter]  +  ∫Σd3y −h Lbdy(ψ,A,h),S = \int d^4x\big[ -\tfrac{1}{4\mu_0}F_{\mu\nu}F^{\mu\nu} + \mathcal{L}_{\rm matter}\big]
\;+\; \int_{\Sigma} d^3y\,\sqrt{-h}\,\mathcal{L}_{\rm bdy}(\psi,A,h),S=∫d4x[−4μ01FμνFμν+Lmatter]+∫Σd3y−hLbdy(ψ,A,h),
with boundary coupling Lbdy\mathcal{L}_{\rm bdy}Lbdy containing AajaA_a j^aAaja. Variation gives:
* Maxwell with surface current ∇νFμν=μ0(Jbulkμ+jΣμδ(Σ))\nabla_\nu F^{\mu\nu}=\mu_0(J^\mu_{\rm bulk}+ j^\mu_\Sigma \delta(\Sigma))∇νFμν=μ0(Jbulkμ+jΣμδ(Σ)).
* Surface stress energy Sab=−2−hδSbdy/δhabS_{ab}=-\tfrac{2}{\sqrt{-h}}\delta S_{\rm bdy}/\delta h^{ab}Sab=−−h2δSbdy/δhab.

I can write this out in full and derive the boundary conditions (pillbox) for you.

===== Use electric dipole operator d=qr \mathbf d = q\mathbf rd=qr. The single‑photon absorption rate from level iii to fff: =====

Γi→f=2πℏ∣⟨f∣d⋅ϵ ∣i⟩∣2 ρ(ℏω).\Gamma_{i\to f}=\frac{2\pi}{\hbar} | \langle f |\mathbf d\cdot \mathbf\epsilon\, |i\rangle|^2 \, \rho(\hbar\omega).Γi→f=ℏ2π∣⟨f∣d⋅ϵ∣i⟩∣2ρ(ℏω).
Compute these for hydrogen (e.g., 1s→2p1s\to 2p1s→2p, Hα etc.). That gives ∆E & rates and connects to your idea of atomic-scale photon-by-photon unfolding.

I can compute the dipole matrix elements and rates for hydrogen lines (SI).

===== If an atom of mass MMM absorbs a photon of frequency fff, =====

vrecoil=pγM=hfcM.v_{\rm recoil} = \frac{p_\gamma}{M} = \frac{hf}{c M}.vrecoil=Mpγ=cMhf.
For hydrogen this recoil is tiny; for boundary shells it may be small but conceptually important (the boundary can take recoil and thus supports conservation).

I can evaluate recoil velocities for chosen transitions.

===== Model the atom‑plus‑shell as a system coupled to many degrees of freedom (photon bath, phonons). The off‑diagonal density matrix element ρij\rho_{ij}ρij decays approximately as ρij(t)∝e−Γdect \rho_{ij}(t)\propto e^{-\Gamma_{\rm dec}t}ρij(t)∝e−Γdect with =====

Γdec∼g2S(ω)\Gamma_{\rm dec}\sim g^2 S(\omega)Γdec∼g2S(ω)
where ggg is coupling, S(ω)S(\omega)S(ω) environmental spectral density. Stronger photon exchange → larger ggg or spectral intensity → faster decoherence. QAT’s “each photon → new now” is equivalent to short decoherence time per photon event.

I can set up a simple Lindblad model and compute decoherence times as function of photon flux and dipole coupling.

===== Compute the surface stress‑energy SabS_{ab}Sab (EM energy + tension) and plug into Israel junction conditions: =====

[Kab]−hab[K]=−8πGc4Sab.[K_{ab}]-h_{ab}[K] = -\frac{8\pi G}{c^4} S_{ab}.[Kab]−hab[K]=−c48πGSab.
Take weak‑field limit and extract the Newtonian potential produced by the surface energy density. This connects QAT’s boundary mass formation to curvature.

I can work a weak‑field example numerically (use the R=re/2R=r_e/2R=re/2 shell) and estimate the tiny GR effect.

==== 1. Decoherence vs flux — QAT says photon absorption is the generator of “now”. So decoherence rate should scale with absorbed photon flux and coupling strength. Predict a functional dependence Γdec(F)\Gamma_{\rm dec}(F)Γdec(F). Experiment: measure decoherence rates of a small mesoscopic system under controlled photon flux (e.g., trapped ion/atom in cavity) and compare to the predicted scaling. ====
# Mass increase from absorbed energy — in principle a system absorbing power PPP gains mass dM/dt=P/c2dM/dt=P/c^2dM/dt=P/c2. This is experimentally tiny, but in extreme laboratory conditions (ultra‑intense laser on micron targets) you can compute orders of magnitude. QAT suggests thinking of the boundary as storing that mass locally — predict tiny changes in gravitational field or inertia (practically extremely small).
# Transition statistics — QAT emphasizes the geometry of many repeated photon exchanges. You can predict statistical distributions of atomic transition sequences (including correlations) that could differ if the boundary geometry imposes a golden‑ratio structure on allowed couplings. This is speculative but can be framed into a spectral prediction for hydrogen lines or selection rules.
# Plasma / large‑scale — if boundary surface ideas scale to plasma double layers, QAT may predict measurable macroscopic correlations (e.g., polarization alignments, filament geometry) in plasmas that correlate with local radiation fluxes.

==== - “v² because spherical geometry” — v² in Ek=12mv2E_k=\tfrac12 m v^2Ek=21mv2 is a kinematic fact (energy scales ∝ (length/time)^2). Spherical geometry gives squared area r2r^2r2 and flux ∝1/r^2; both are squares but come from different physical dimensional reasons. The unifying route would be to show a mapping that takes boundary area elements (∝r^2) to effective kinematic variables in the emergent 3D interior — that is precisely the mathematical program I outlined above (action on the shell → effective inertial terms in the interior). ====
* “Photon and electron are two parts of same geometrical process” — this statement is an interpretive (ontological) claim that can be expressed technically by coupling fields on a boundary: treated as two excitations of the same boundary manifold, yes — write the joint boundary action and quantize it; you’ll get coupled photon/electron mode structure. That’s how to make it precise.
* “Conservation of energy, momentum, charge … linear nature of time” — conservation laws come from symmetries (Noether). For QAT: energy conservation ↔ time-translation invariance of the whole (including boundary), charge conservation ↔ U(1) invariance on boundary + bulk. Making those symmetries explicit in the action is straightforward and is the right way to anchor QAT.

==== 1. Derive the dipole transition rate for hydrogen 1s→2p1s\to2p1s→2p in SI and compute the rate & recoil, showing how a single photon changes internal energy and sends a tiny momentum to the shell. ====
# Set up a Lindblad master equation for a two‑level system coupled to a photon bath and compute decoherence rate as a function of photon flux and dipole coupling (explicit formula and numbers). This directly links “photon-by-photon → now” to measurable decoherence.
# Compute the exact surface stress SabS_{ab}Sab for a thin charged spherical shell with tension TTT (we already found TTT) and then compute the Newtonian potential jump in the weak field (approximate gravitational effect from the formed mass).
# Write the explicit boundary action Sbdy[A,ψ]S_{\rm bdy}[A,\psi]Sbdy[A,ψ] and perform variation to derive the surface Noether current and the pillbox Maxwell boundary conditions (fully worked).

Which of (1)–(4) would you like me to do now? (I recommend (2) because it connects QAT’s central interpretive claim to a directly testable decoherence scaling law.)