\documentclass[12pt,a4paper]{article} \usepackage{fix-cm} \usepackage[T1]{fontenc} \usepackage[margin=1in]{geometry} \setlength{\headheight}{13.6pt} \addtolength{\topmargin}{-1.6pt} \usepackage{amsmath,amssymb,amsthm,mathtools} \usepackage{mathrsfs} \usepackage{xcolor} \usepackage[hypertexnames=false]{hyperref} \usepackage{fancyhdr} \usepackage{titlesec} \usepackage{enumitem} \usepackage{graphicx} \usepackage{tikz} \usetikzlibrary{arrows.meta,patterns,calc,positioning,shapes.geometric,decorations.pathmorphing,decorations.pathreplacing} \usepackage{float} \usepackage[numbers,sort&compress]{natbib} % Colors \definecolor{accent}{RGB}{139,37,0} \definecolor{linkblue}{RGB}{44,74,110} % Hyperref setup \hypersetup{ colorlinks=true, linkcolor=linkblue, citecolor=linkblue, urlcolor=linkblue, plainpages=false } \pdfstringdefDisableCommands{% \def\alpha{alpha}% \def\beta{beta}% \def\omega{omega}% \def\Delta{Delta}% \def\approx{approx }% \def\leq{<=}% \def\neq{!=}% \def\not{}% \def\mathcal#1{#1}% \def\mathfrak#1{#1}% \def\textup#1{#1}% } % Section formatting \titleformat{\section}{\Large\bfseries\scshape}{Part \Roman{section}.}{0.5em}{}[\vspace{2pt}\hrule\vspace{6pt}] \titleformat{\subsection}{\large\bfseries}{\thesubsection}{0.5em}{} \titleformat{\subsubsection}{\normalsize\bfseries\itshape}{\thesubsubsection}{0.5em}{} % Theorem environments \theoremstyle{definition} \newtheorem{axiom}{Axiom} \newtheorem{definition}{Definition}[subsection] \newtheorem{postulate}{Postulate} \theoremstyle{plain} \newtheorem{theorem}{Theorem}[subsection] \newtheorem{proposition}{Proposition}[subsection] \newtheorem{lemma}{Lemma}[subsection] \newtheorem{corollary}{Corollary}[subsection] \theoremstyle{remark} \newtheorem{remark}{Remark}[subsection] \newtheorem{consequence}{Consequence}[subsection] % Custom commands \newcommand{\vt}{v_{\text{t}}} \newcommand{\clight}{c} \newcommand{\dT}{\partial_T} \newcommand{\Lag}{\mathcal{L}} \newcommand{\Sact}{\mathcal{S}} \newcommand{\Hil}{\mathcal{H}} \newcommand{\bx}{\mathbf{x}} \newcommand{\bk}{\mathbf{k}} \newcommand{\bSigma}{\boldsymbol{\Sigma}} \newcommand{\bE}{\mathbf{E}} \newcommand{\bB}{\mathbf{B}} \newcommand{\bv}{\mathbf{v}} % Header/footer \pagestyle{fancy} \fancyhf{} \fancyhead[L]{\small\scshape Bidirectional Causality} \fancyhead[R]{\small\thepage} \renewcommand{\headrulewidth}{0.4pt} % Allow slightly loose line breaking to reduce overfull hbox warnings \emergencystretch=3em \begin{document} % ============================================================ % TITLE PAGE % ============================================================ \begin{titlepage} \centering \vspace*{1.2cm} % Top rule {\color{accent}\rule{0.6\textwidth}{1.2pt}} \vspace{1.8cm} {\fontsize{32}{38}\selectfont\bfseries\scshape Bidirectional Causality} \vspace{0.4cm} {\fontsize{18}{24}\selectfont\scshape and the Physics of} \vspace{0.4cm} {\fontsize{32}{38}\selectfont\bfseries\scshape Superluminal Propagation} \vspace{1.2cm} % Decorative separator \begin{tikzpicture} \draw[accent, thick] (-2.5,0) -- (-0.4,0); \fill[accent] (0,0) circle (2.5pt); \draw[accent, thick] (0.4,0) -- (2.5,0); \end{tikzpicture} \vspace{1.2cm} {\large\itshape\begin{minipage}[c]{0.75\textwidth}\centering A reformulation of causality, electrodynamics, gravitation, and quantum theory under a preferred frame defined by the future boundary of the universe \end{minipage}} \vspace{2.5cm} {\Large\scshape Andrew Duquette} \vfill % Bottom block {\color{accent}\rule{0.3\textwidth}{0.6pt}} \vspace{0.5cm} {\large Working Draft\,---\,February 2026} \vspace{1.2cm} \end{titlepage} \thispagestyle{empty} \vspace*{2cm} \begin{abstract} \noindent We abandon Lorentz invariance as a fundamental symmetry and replace it with a preferred frame defined by the future boundary condition of the universe. This single structural change permits stable superluminal propagation, resolves the vacuum instability of tachyonic fields, and produces a bidirectional causal structure in which effects propagate forward in preferred time by default and backward from specific spacetime events. The future boundary is an extended spacetime volume, not a surface; agents operating within this volume can send tachyonic signals into the interior history, selecting which self-consistent history--boundary pair is realised from a space of allowed solutions---including the initial conditions themselves. Interior agents are part of the determined solution and lack this causal leverage. We reformulate electrodynamics with symmetric field coupling at enhanced strength, derive a modified dispersion relation that decouples mass from velocity class, reconstruct the gravitational field equations, and examine the consequences for quantum field theory. The tachyonic particle emerges as a massive spin-1 excitation---structurally identical to the photon but with a higher speed limit---governed by the same Maxwell field architecture at enhanced coupling strength. The cosmological history partitions into four causal epochs: boundary seeding of initial conditions, forward-causal propagation, tachyonic enforcement when the selected attractor requires it, and the boundary volume itself. The framework makes specific observational predictions distinguishable from standard physics. \end{abstract} \newpage \tableofcontents \newpage % ============================================================ % PART I: FOUNDATIONS % ============================================================ % ============================================================ % CONTENT (split into separate files) % ============================================================ \input{sec01_foundations} \input{sec02_electrodynamics} \input{sec03_gravitation} \input{sec04_quantum} \input{sec05_tachyon} \input{sec06_causality} \input{sec07_cosmology} \input{sec08_algebraic} \input{sec09_enforcement} \input{sec10_model_theory} \input{sec11_predictions} \input{sec12_summary} \newpage \bibliographystyle{unsrtnat} \bibliography{unified} \end{document}