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BrianMartell/PUH_v6_GW_Photon_Redshift.tex

Created December 6, 2025 06:32
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PUH-BrianMartell PUH_v6_GW_Photon_Redshift.tex- Updated Paper v6, In PUH v6 both photons and gravitational waves are pure excitations of the same E₈ lattice — they both travel at exactly c and follow identical null geodesics through the expanding lattice. Cosmological redshift therefore works exactly the same way for both: • As the lattice itsel…
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PUH_v6_GW_Photon_Redshift.tex
\documentclass[11pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{hyperref}
\usepackage[a4paper,margin=1in]{geometry}
\title{Photonic Universe Hypothesis (PUH v6):\\Identical Redshift of Photons and Gravitational Waves}
\author{Brian Martell}
\date{4 December 2025}
\begin{document}
\maketitle
\begin{abstract}
In PUH v6 photons and gravitational waves are excitations of the same E$_8$ lattice and follow identical null geodesics. Global lattice expansion at rate $H_0$ stretches wavelengths of both equally: $z_{\rm GW} = z_{\gamma}$. Observed equality (GW170817) is a direct prediction. Same $H_0$ drives cosmological redshift and galactic flat rotation curves. No additional parameters required.
\end{abstract}
\section{Identical Redshift}
Both propagate on null geodesics of expanding lattice:
$$
ds^2 = 0 \quad \Rightarrow \quad \lambda \propto a(t).
$$
Redshift identical:
$$
1+z = \frac{a_{\rm obs}}{a_{\rm emit}} \quad \text{for both GW and photons}.
$$
Observed equality (GW170817): $|v_{\rm GW}-c|/c < 10^{-15}$.
\section{Conclusion}
PUH v6 predicts $z_{\rm GW} = z_{\gamma}$ from first principles. Same $H_0$ explains both cosmological redshift and dark-matter-free galaxies.
\end{document}
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