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\title{Gravitons as Quantum Platform Geometry Instructions: A Timeless-Light Interpretation of Gravitational Wave Quanta}
\author{John C. W. McKinley \\ Independent Researcher \\ \href{https://orcid.org/0009-0005-7097-5035}{0009-0005-7097-5035}}
\date{August 10, 2025}
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\begin{document}
\maketitle
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\footnotetext[1]{This version published at \href{https://doi.org/10.5281/zenodo.16788039}{doi.org/10.5281/zenodo.16788039.}}
\begin{abstract}
In standard quantum field theory, the \emph{graviton} is a hypothetical massless spin-2 boson mediating gravity. In the Timeless Light Model (TLM), within its Quantum Platform (QP) framework, gravitational waves are not ripples \emph{in} spacetime but the spacetime-deployment trace of a timelessly resolved geometric change. We propose a reinterpretation: the ``graviton'' corresponds not to a propagating particle, but to the minimum indivisible \emph{geometry-change instruction unit} recorded in the QP after successful event resolution. This preserves observational signatures of gravitational waves while replacing transmission with deployment, easing conceptual tensions between General Relativity (GR) and quantum theory and yielding discrete, testable predictions via residual analysis of LIGO-Virgo-KAGRA (LVK) data.
\end{abstract}
\section{Introduction}\label{sec:intro}
In quantum field theory, forces are often modeled via particle-like excitations: photons for electromagnetism, gluons for the strong force, and \( W \), \( Z \) bosons for the weak interaction. Gravity, when approached via linearized quantization of metric perturbations, is assigned a massless spin-2 boson dubbed the \emph{graviton} \cite{weinberg1972gravitation,maggiore2007gravitational}. To date, no experiment has directly detected gravitons, and reconciling a quantum particle picture with GR's smooth curvature remains conceptually strained.
Within the Timeless Light Model (TLM) and its Quantum Platform (QP) framing \cite{mckinley2025tlmcore}, events are resolved timelessly; only successful resolutions are written to the QP, and the observed world is a Spacetime Deployment Frame (SDF)---a delayed rendering of those instructions. Prior TLM work reinterprets gravitational waves as SDF manifestations of QP geometry realignments. Here we advance a specific claim: the graviton is not a spacetime traveler but an indivisible \emph{geometry instruction} recorded in the QP, whose SDF rollout collectively appears as a gravitational wave.
\section{Related Work}\label{sec:related}
Standard searches for gravitons are limited by the extreme weakness of gravitational coupling. A single graviton would carry energy \( E = h f \), with \( f \) the wave frequency; at astrophysical frequencies (\(\sim 100\ \text{Hz}\)), this energy is so small that direct detection would require a detector of planetary mass operating for cosmic timescales \cite{dyson2013gravitonlimits}. For this reason, graviton searches in practice rely on indirect constraints, such as limits on the dispersion of gravitational waves from LIGO-Virgo-KAGRA observations, which bound any graviton mass to \( m_g < 1.73 \times 10^{-23} \, \text{eV}/c^2 \) (from recent 2025 analyses of farthest BBHs) \cite{Mastrogiovanni2025}. These constraints assume a spacetime-propagating particle. The QP reinterpretation advanced here avoids the infeasibility of direct detection by recasting the ``graviton'' as a quantized deployment unit whose aggregate SDF manifestation is already within the reach of current detectors.
\section{Standard View of Gravitons}\label{sec:standard}
In linearized GR, small perturbations \( h_{\mu\nu} \) to the Minkowski background propagate at \( c \) as waves. Canonical quantization of these perturbations yields quanta with:
\begin{itemize}
\item Zero rest mass,
\item Spin 2 with two helicity states,
\item Energy and momentum consistent with propagation at \( c \).
\end{itemize}
On this view, gravitational radiation carries energy through spacetime continuously, and in principle consists of many gravitons whose coherent superposition yields the classical wave.
\section{TLM/QP Reinterpretation}\label{sec:tlm}
The TLM posits:
\begin{enumerate}
\item All outcomes are resolved timelessly in the QP.
\item Only successful outcomes are recorded; unresolved possibilities leave no record.
\item The SDF is a delayed, causal deployment (rendering) of QP instructions.
\end{enumerate}
From this vantage:
\begin{itemize}
\item A ``graviton'' is the minimal QP \emph{geometry-change instruction} that alters curvature relations among SDF frames.
\item It does not propagate \emph{in} spacetime; e.g., its apparent arrival is the SDF's local deployment of a pre-resolved QP state.
\item Observed gravitational waves are the aggregate SDF playback of many such indivisible instruction units, which can approximate smooth waveforms at macroscopic scales.
\end{itemize}
\section{Implications}\label{sec:implications}
\subsection{Discrete Geometry Changes}\label{subsec:discrete}
If the QP encodes curvature realignments as indivisible units, then a gravitational wave should exhibit a lower bound on detectable strain increments---a quantization threshold \(\Delta h\). In the continuum limit (many units), observed signals appear smooth; but sufficiently precise data may reveal stepwise microstructure.
\subsection{Energy Accounting}\label{subsec:energy}
In GR, gravitational-wave energy is continuous. In the QP view, energy quanta correspond to instruction units and may connect to discrete microstate accounting at horizons \cite{bekenstein1973bhentropy}. This suggests a bridge from geometry-instruction counts to entropy bounds (e.g., with instruction counts analogous to black hole microstates).
\section{Observational Program and Falsifiability}\label{sec:tests}
A concrete test with existing detectors (LIGO/Virgo/KAGRA), including recent O4 data, is:
\begin{enumerate}
\item Select a high-SNR compact-binary coalescence, e.g., using publicly available GWTC data.
\item Fit the best continuous GR waveform.
\item Subtract to obtain a residual \( r(t) \) in strain.
\item Apply step-detection (CUSUM, matched step banks, or Bayesian changepoint) to search for statistically significant plateaus of height \( \Delta h \) persisting over coherent intervals.
\end{enumerate}
A reproducible detection of non-instrumental, stepwise strain increments consistent across detectors and polarization reconstructions would support the instruction-quantization hypothesis; conversely, strong upper bounds on \( \Delta h \) would constrain or refute it.
\section{Visualization}\label{sec:viz}
\begin{figure}[h!]
\centering
\begin{tikzpicture}[scale=1.0]
% QP node
\node[draw, thick, fill=blue!10, rounded corners, minimum width=4.8cm, minimum height=1.8cm] (qp) at (0,+2)
{Quantum Platform (QP)\\ \small Timeless instruction record};
% Graviton unit
\node[draw, thick, fill=yellow!25, rounded corners, minimum width=3.2cm, minimum height=1.0cm] (unit) at (0,-0.5)
{Graviton (TLM)\\ \small geometry-change unit};
% SDF node
\node[draw, thick, fill=green!10, rounded corners, minimum width=7.2cm, minimum height=1.8cm] (sdf) at (0,-3)
{Spacetime Deployment Frame (SDF)\\ \footnotesize Wave = deployed geometry instructions};
% Arrows with labels
\draw[->, thick] (qp.south) -- (unit.north) node[midway, right] {deployment};
\draw[->, thick] (unit.south) -- (sdf.north);
\end{tikzpicture}
\caption{Schematic: QP records indivisible geometry-change instructions; the SDF renders them as an apparently continuous gravitational wave.}
\label{fig:qp-sdf}
\end{figure}
\section{Conclusion}\label{sec:conclusion}
This reinterpretation of gravitons as timeless QP geometry instructions resolves key tensions in quantum gravity while preserving GR phenomenology. By predicting discrete strain microstructures in LVK data, it offers falsifiable tests that could validate or refine the TLM. Future work may explore links to entropy and deployment bounds in broader unification efforts.
\appendix
\section{Derivation of a Discrete Strain Signature}\label{app:discrete}
\subsection{Linearized GR Baseline}\label{app:baseline}
Write the metric as
\begin{equation}
g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}, \quad \lvert h_{\mu\nu} \rvert \ll 1,
\end{equation}
with the transverse-traceless (TT) gauge waveform
\begin{equation}
h_{ij}(t) = h_0 \cos\!\big( \omega t + \phi \big)\, e_{ij},
\end{equation}
where \( e_{ij} \) is the polarization tensor.
\subsection{Quantized Deployment Model}\label{app:model}
Assume the SDF renders geometry-change instructions as indivisible increments of size \( \Delta h \) applied at deployment times \( t_n \). Then
\begin{equation}
h_{ij}(t) = \sum_{n=1}^{N} \Delta h \; e_{ij} \; \Theta(t - t_n),
\end{equation}
where \( \Theta \) is the Heaviside function. For large \( N \) with appropriately spaced \( t_n \), this approximates a smooth waveform; for sufficiently fine data, step structure may be resolvable.
\subsection{Minimum Detectable Step}\label{app:mds}
Let \( \sigma_{\text{noise}} \) denote the detector RMS strain noise in the relevant band and \( M \) the number of coherent cycles integrated. A rough detectability bound is
\begin{equation}
\Delta h_{\min} \gtrsim \frac{\sigma_{\text{noise}}}{\sqrt{M}}.
\end{equation}
In optimal LIGO bands, \( \sigma_{\text{noise}} \sim 10^{-22} \). High-SNR events increase \( M \), lowering detectable \( \Delta h_{\min} \).
\subsection{Search Procedure}\label{app:search}
Given data \( d(t) \), fit a continuous GR waveform \( h_{\text{GR}}(t) \), compute the residual \( r(t) = d(t) - h_{\text{GR}}(t) \), and test for stepwise behavior via:
\begin{itemize}
\item CUSUM or Bayesian changepoint analysis for amplitude plateaus,
\item Matched filtering against a bank of quantized step templates,
\item Cross-detector coincidence in step times \( t_n \) and heights \( \Delta h \).
\end{itemize}
Instrumental artifacts must be vetoed via standard detector characterization.
\section{Figure: Continuous vs Stepwise Waveform}\label{app:figure}
\begin{figure}[h!]
\centering
\resizebox{0.95\linewidth}{!}{%
\begin{tikzpicture}
\begin{axis}[
width=12cm,
height=6cm,
xlabel={Time \( t \)},
ylabel={Strain \( h(t) \)},
axis lines=left,
legend style={at={(0.5,-0.2)},anchor=north,legend columns=-1},
ymin=-1.2, ymax=1.2,
xmin=0, xmax=6.5,
xtick=\empty, ytick=\empty,
domain=0:6.28,
samples=200,
grid=minor
]
% GR smooth waveform
\addplot[blue, thick] {sin(deg(x))};
\addlegendentry{GR: Continuous Wave}
% TLM stepwise waveform (refined for better sin approximation)
\addplot[red, thick, mark=*, mark options={scale=0.4, fill=red}]
coordinates {
(0,0) (0.52,0) (0.52,0.5) (1.05,0.5) (1.05,0.866) (1.57,0.866) (1.57,1.0) (2.09,1.0) (2.09,0.866) (2.62,0.866) (2.62,0.5) (3.14,0.5)
(3.14,0) (3.67,0) (3.67,-0.5) (4.19,-0.5) (4.19,-0.866) (4.71,-0.866) (4.71,-1.0) (5.24,-1.0) (5.24,-0.866) (5.76,-0.866) (5.76,-0.5) (6.28,-0.5)
};
\addlegendentry{TLM: Stepwise Deployment}
\end{axis}
\end{tikzpicture}%
}% <-- close resizebox here
\caption{Continuous (GR) versus stepwise (TLM) gravitational waveforms. The step height \( \Delta h \) represents an indivisible geometry-change instruction.}
\label{fig:step-vs-sine}
\end{figure}
\section*{Acknowledgments}
The author thanks readers of prior TLM manuscripts for feedback connecting gravitational-wave phenomenology to deployment granularity.
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\end{thebibliography}
\end{document}