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\title{Frame Display Law for TLM v2.0:\\
EA-conditioned Rendering in a Single Spacetime Deployment Frame}
\author{John C. W. McKinley \\ Independent Researcher \\
\href{https://orcid.org/0009-0005-7097-5035}{0009-0005-7097-5035}}
\date{August 24, 2025}
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\begin{document}
\maketitle
\begingroup\renewcommand\thefootnote{}\footnotetext{This version published at
\href{https://doi.org/10.5281/zenodo.16936105}{https://doi.org/10.5281/zenodo.16936105}.}\endgroup
\begin{abstract}
In the Timeless Light Model v2.0, quanta are frameless ticks and the wavefunction belongs to the observer frame. This short paper states a precise \emph{Frame Display Law} for rendering emitter-absorber movies once the absorber \( A^* \) is ontically fixed in the Quantum Platform. The law uses only standard frame-side propagators, a time-symmetric conditioning on \( (E,A^*) \), and a display rule that draws \( c \)-limited rays along stationary-phase ridges of the EA amplitude. Pacing is governed by the bridge laws \( T\,m=\hbar/c^2 \) and \( T\,C_s=1 \). The result preserves no-retrocausal signaling while matching ordinary optics \cite{BornWolf,FeynmanHibbs}, post-selection statistics via ABL \cite{Aharonov1964}, and the time-symmetric use of advanced solutions familiar from Wheeler-Feynman \cite{WheelerFeynman1945,WheelerFeynman1949}.
\end{abstract}
\section{Introduction and stance}
\label{sec:intro}
TLM v2.0 separates ontology and rendering. Quanta are frameless state-change ticks recorded in a timeless Quantum Platform (QP). Movies, paths, and probabilities are properties of a \emph{Spacetime Deployment Frame} (SDF). In this stance the wavefunction is a \emph{frame amplitude}, not a photon property. When an emission \( E \) and a realized absorber \( A^* \) are a completed pair, the frame renders a causal movie consistent with geometry and records. This paper codifies that rendering as a frame-side law and contrasts it with standard time-symmetric machinery \cite{Aharonov1964,WheelerFeynman1945,WheelerFeynman1949} while remaining compatible with SR and GR pacing \cite{Einstein1905,WaldGR} and with the author’s prior TLM statements \cite{McKinleyQuantaGlobal2025,McKinleyQTransfer2025,McKinleyPairingLaw2025,McKinleyQPlatformFrame2025,McKinleyWFDisambig2025}.
\clearpage
\begin{notebox}{Notation}
\begin{itemize}
\item \( G \): geometry in the SDF, including metric, boundaries, media, apertures.
\item \( |E\rangle \) at time \( t_E \): source state that seeds the forward field.
\item \( |A^*\rangle \) at time \( t_A \): realized absorber state that seeds the backward field.
\item \( R^* \): recorded tags such as polarization, timing windows, which-way flags.
\item \( U(t,t_0) \): standard frame-side propagator for the chosen dynamics.
\item Bridge laws: \( T\,m=\hbar/c^2 \) and \( T\,C_s=1 \) pace the rendered movie \cite{McKinleyQTransfer2025,McKinleyQuantaGlobal2025}.
\end{itemize}
\end{notebox}
\section{Ontic pairing and domain of the law}
\label{sec:setup}
\textbf{Pairing axiom.} Only completed pairs \( (E,A^*) \) are written to QP. Once written, the always-was consistency applies. The SDF never needs to choose an outcome; it conditions on \( A^* \) already realized in QP, then renders the unique movie consistent with \( G \) and \( R^* \) \cite{McKinleyPairingLaw2025,McKinleyQPlatformFrame2025}.
\section{Frame Display Law}
\label{sec:law}
\begin{lawbox}{{Frame Display Law (EA-conditioned rendering)}}
\textbf{Setup in a single SDF that spans \( E \) and \( A^* \).} Inputs: geometry \( G \), source state \( |E\rangle \) at \( t_E \), realized absorber \( |A^*\rangle \) at \( t_A \), and record sector \( R^* \).
\medskip
\textbf{1. Forward field (retarded).}
\[
\psi_f(x,t)=U(t,t_E)\,|E\rangle.
\]
Solve with the standard SDF propagator over \( G \) for the relevant equation set \cite{BornWolf,FeynmanHibbs}.
\medskip
\textbf{2. Backward field (advanced or adjoint).}
\[
\psi_b(x,t)=U(t,t_A)^{\dagger}\,|A^*\rangle.
\]
Time-symmetric use of adjoint solutions is standard in pre- and post-selected formalisms and absorber-style constructions \cite{Aharonov1964,WheelerFeynman1945,WheelerFeynman1949}.
\medskip
\textbf{3. EA amplitude conditioned on \( A^* \) and records.}
\[
\psi_{EA}(x,t)\propto\big(\psi_b(x,t)\big)\,\big(\psi_f(x,t)\big)\quad\text{restricted to sector } R^*.
\]
Interpretation: \( \psi_{EA} \) is a frame amplitude used for rendering. It is not a physical field carried by the photon.
\medskip
\textbf{4. Display rule.}
\begin{itemize}
\item \emph{Display events, photon-like:} draw \( c \)-limited ray segments along the ridge or stationary-phase curves of \( |\psi_{EA}(x,t)| \). If multiple stationary branches exist, the rendered branch must be consistent with \( R^* \) \cite{BornWolf,FeynmanHibbs}.
\item \emph{Non-display events, entanglement or tunneling:} show only correlated endpoints. No trajectory is rendered.
\end{itemize}
Rendered paths are movie artifacts inside the SDF. The frameless tick has no path.
\medskip
\textbf{5. Tomography consistency.}
For hypothetical intermediate projectors \( \{\Pi_k\} \),
\[
P(k\,|\,E,A^*)\propto|\langle A^*|\,\Pi_k\,|E\rangle|^2.
\]
This is the ABL conditional; any probe would register conditional frequencies consistent with the EA amplitude without enabling retro-signaling \cite{Aharonov1964}.
\medskip
\textbf{6. Pacing by bridge laws.}
Displayed delays, phases, and energy bookkeeping obey
\[
T\,m=\hbar/c^2,\qquad T\,C_s=1,
\]
so that SR or GR timing, redshift, and eikonal optics along the rendered branch are reproduced \cite{Einstein1905,WaldGR,McKinleyQTransfer2025,McKinleyQuantaGlobal2025}.
\end{lawbox}
\section{Worked micro-examples}
\label{sec:examples}
\paragraph{Double-slit with post-selected pixel.}
Let \( |E\rangle \) seed a Huygens forward field through two slits, and let \( |A^*\rangle \) be the realized pixel on the screen. The product \( \psi_{EA} \) exhibits fringes. The movie draws a \( c \)-limited ray along a stationary-phase ridge that reaches the pixel, consistent with any polarization or timing tags in \( R^* \). Which-way records collapse cross-terms by sector restriction \cite{BornWolf,FeynmanHibbs}.
\paragraph{Gravitational lens with multi-branch geometry.}
With lensing geometry \( G \) that allows several stationary optical paths, \( |\psi_{EA}| \) has multiple ridges. The display renders the branch consistent with \( R^* \) and paces relative delays by the bridge laws, matching time-delay lens phenomenology \cite{WaldGR}.
\begin{figure}[t]
\centering
\begin{tikzpicture}[scale=1.0,>=Latex]
% Axes
\draw[->] (-0.2,0) -- (8,0) node[right]{screen coordinate};
\draw[->] (0,-0.2) -- (0,4) node[above]{intensity schematic};
% Two-slit envelope (schematic fringes)
\foreach \x in {0.5,1.0,...,7.5}{
\pgfmathsetmacro{\y}{2.2 + 1.6*sin(360*(\x/1.5))}
\fill (\x, 0) circle (0.015);
\draw[opacity=0.25] (\x,0) -- (\x, {0.2+0.8*max(0,\y)});
}
% Mark a realized pixel A*
\draw[red,very thick] (6.0,0) -- (6.0,3.0);
\node[red] at (6.0,3.3) {$A^*$};
% Stationary-phase branch as a ray segment
\draw[blue,thick,->] (1.0,0.5) .. controls (2.0,1.2) and (4.0,2.2) .. (6.0,3.0);
\node[blue] at (4.0,2.6) {stationary-phase ridge};
% Labels
\node at (1.0,-0.4) {slits};
\node at (6.0,-0.4) {screen};
\end{tikzpicture}
\caption{EA-conditioned rendering for a post-selected pixel \( A^* \). The frame draws a \( c \)-limited ray along a stationary-phase ridge of \( |\psi_{EA}| \). The tick itself has no path.}
\label{fig:ea}
\end{figure}
\section{Consistency and no-retro signaling}
\label{sec:consistency}
The time-symmetric construction is strictly frame-side and conditional on the completed pair \( (E,A^*) \). The ABL frequency law in Section \ref{sec:law} ensures that any inserted tomography would have produced statistics consistent with \( |\psi_{EA}|^2 \) without enabling retrocausal communication \cite{Aharonov1964}. The QP provides ontic completeness, while the SDF provides causal deployment \cite{McKinleyQPlatformFrame2025}.
\section{Bridge laws and pacing}
\label{sec:bridge}
The bridge laws
\[
T\,m=\hbar/c^2,\qquad T\,C_s=1
\]
fix pacing. They underwrite the observed clocking of the rendered movie, including Doppler and gravitational redshifts and the eikonal phase picked by stationary-phase selection \cite{Einstein1905,WaldGR,McKinleyQTransfer2025,McKinleyQuantaGlobal2025}. The laws do not modify standard equations of motion; they constrain how the SDF deploys them as a movie.
\section{Falsifiable consequences}
\label{sec:falsifiable}
\begin{itemize}
\item \textbf{Display versus non-display.} Experiments that toggle which-way records \( R^* \) must convert rendered-path movies into endpoint-only displays with no residual sub-trajectory artifacts. Residuals would falsify the display rule \cite{BornWolf}.
\item \textbf{Tomography neutrality.} Inserting weak or partial tomography upstream must yield conditional frequencies consistent with the ABL law when post-selecting \( A^* \), and no change in unconditional upstream rates \cite{Aharonov1964}.
\item \textbf{Stationary-phase rendering.} In multi-branch optics and lensing, the rendered branch statistics must match stationary-phase ridges of \( |\psi_{EA}| \) subject to sector restrictions \( R^* \) \cite{BornWolf}.
\end{itemize}
\section{Discussion and conclusion}
\label{sec:conclusion}
The Frame Display Law is not new dynamics. Steps 1 to 2 use ordinary SDF propagators. Step 3 is a time-symmetric conditioning on the realized absorber and records. Step 4 translates amplitude terrain into movies by a stationary-phase display rule. Step 5 guarantees tomography consistency without retrocausal signaling. Step 6 paces the movie with bridge laws. In sum: pre-resolve by constraints -> compute forward and back -> multiply and condition -> render ridges -> pace by the bridges.
\bigskip
\noindent\textbf{One-line slogan.} Pre-resolve by constraints -> compute forward and back -> multiply and condition -> render ridges -> pace by the bridges.
\bigskip
\noindent\textbf{Acknowledgments.} Thanks to readers of the TLM v2.0 series for requesting a compact statement of the frame-side display rule.
\begin{thebibliography}{99}
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Y. Aharonov, P. G. Bergmann, and J. L. Lebowitz,
Time Symmetry in the Quantum Process of Measurement,
\emph{Physical Review} 134 (1964): B1410--B1416.
\href{https://doi.org/10.1103/PhysRev.134.B1410}{doi:10.1103/PhysRev.134.B1410}.
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\href{https://doi.org/10.1103/RevModPhys.21.425}{doi:10.1103/RevModPhys.21.425}.
\bibitem{BornWolf}
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\bibitem{FeynmanHibbs}
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\bibitem{Einstein1905}
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(English translations widely available.)
\bibitem{WaldGR}
R. M. Wald,
\emph{General Relativity},
University of Chicago Press, 1984.
% ----- Author's TLM papers with DOIs -----
\bibitem{McKinleyQuantaGlobal2025}
J. C. W. McKinley,
Quanta are Global, Frames are Local: A Rosetta Statement of the Timeless Light Model (v1.0),
Zenodo (2025).
\href{https://doi.org/10.5281/zenodo.16917106}{doi:10.5281/zenodo.16917106}.
\bibitem{McKinleyQTransfer2025}
J. C. W. McKinley,
The Quanta Transfer Law (v1.0),
Zenodo (2025).
\href{https://doi.org/10.5281/zenodo.16897573}{doi:10.5281/zenodo.16897573}.
\bibitem{McKinleyPairingLaw2025}
J. C. W. McKinley,
Generalized Pairing Law: No Quantum Emission Without an Absorber,
Zenodo (2025).
\href{https://doi.org/10.5281/zenodo.16892099}{doi:10.5281/zenodo.16892099}.
\bibitem{McKinleyQPlatformFrame2025}
J. C. W. McKinley,
Quantum Platform as Frame Generator,
Zenodo (2025).
\href{https://doi.org/10.5281/zenodo.16788735}{doi:10.5281/zenodo.16788735}.
\bibitem{McKinleyWFDisambig2025}
J. C. W. McKinley,
Timeless Light Model vs Wheeler–Feynman Absorber Theory: A Disambiguation (v5.0),
Zenodo (2025).
\href{https://doi.org/10.5281/zenodo.16924316}{doi:10.5281/zenodo.16924316}.
\end{thebibliography}
\end{document}