Conscious Relativity: A Geometric Framework for Subjective Continuity

ConsciousRelativityAGeometricFrameworkforSubjectiveContinuity.tex

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\title{Towards a Theory of Conscious Relativity}
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\begin{abstract}
We propose that subjective experience possesses a unique dimensional coordinate \$\mathrm{\[con]}\$ alongside spacetime, forming a five-coordinate reality $\[x, y, z, t, \mathrm{con}]\$. We distinguish between raw subjective experience (the fact that there is \`something it is like' to be) and its contents (memories, personality, beliefs stored physically). Within the Many-Worlds interpretation (MWI) of quantum mechanics, all quantum branches exist simultaneously in the universal wavefunction. However, each observer experiences only one definite path through this branching structure, determined by their unique \$\mathrm{\[con]}\$ trajectory. This framework introduces a geometric constraint that explains why observers experience single outcomes despite the existence of all branches. The \$\mathrm{\[con]}\$ parameter remains invariant under Lorentz transformations, analogous to proper time, and gives rise to what we term a "\$\mathrm{\[con]}\$ field" through holographic projection into spacetime. We present formal structure and thought experiments to illustrate how this dimensional approach resolves the preferred basis problem while maintaining consistency with known physics.
\end{abstract}

\section{Introduction}
The Many-Worlds interpretation preserves quantum unitarity but faces a central explanatory challenge: why do observers experience only one definite outcome if all quantum branches exist? This is the preferred basis problem. Existing interpretations include wavefunction collapse (Copenhagen), subjective probabilism (QBism), or decoherence without subjective explanation (Everettian MWI).

This paper proposes that subjective experience constitutes a fifth coordinate \$\mathrm{\[con]}\$ that selects a unique path through the branching wavefunction. This trajectory intersects exactly one decoherent history, while all other branches persist but are not experienced. The \$\mathrm{\[con]}\$ coordinate does not require altering quantum dynamics—rather, it defines which branch of the evolving universal wavefunction is experienced.

\section{Mathematical Framework}

\subsection{Dimensional Emergence}
We propose that $\[x, y, z, t, \mathrm{con}]\$ emerge from a lower-dimensional information-theoretic substrate, in analogy to the AdS/CFT correspondence:
\begin{equation}
\Psi(x,y,z,t,\mathrm{con}) = T\[I(u^1, u^2, ..., u^n)]
\end{equation}
where \$I\$ is the boundary information density, \$u^i\$ are encoding coordinates, and \$T\$ is the emergence map projecting encoded information into physical and experiential dimensions. The \$\mathrm{\[con]}\$ coordinate specifies the presence and continuity of subjective experience, independently of physical content.

\subsection{Invariance Under Lorentz Transformations}
We postulate that \$\mathrm{\[con]}\$ remains invariant under Lorentz transformations:
\begin{align}
x' &= \gamma(x - vt) \\
y' &= y \\
z' &= z \\
t' &= \gamma(t - vx/c^2) \\
\mathrm{con}' &= \mathrm{con}
\end{align}
This is analogous to proper time \$\tau\$ and ensures continuity of experience across reference frames.

\subsection{Holographic Projection of the \$\mathrm{\[con]}\$ Field}
The \$\mathrm{\[con]}\$ field \$\varphi\$ is projected into spacetime as:
\begin{equation}
\varphi(x,y,z,t) = \int \Psi(x,y,z,t,\mathrm{con}) , \delta(\mathrm{con} - \mathrm{con}\_0) , d\mathrm{con}
\end{equation}
Systems with high integrated information \$\Phi\$ (e.g., as in IIT) support strong projection of the \$\mathrm{\[con]}\$ field.

\subsection{Propagation and Causal Limits}
We propose that the \$\mathrm{\[con]}\$ field propagates with velocity \$v\_{\mathrm{con}} \leq c\$. Thus:
\begin{equation}
\frac{\partial \varphi}{\partial t} + \vec{v} \cdot \nabla \varphi = f(\varphi, \Psi)
\end{equation}
This restricts conscious continuity to causal paths and excludes instantaneous duplication or teleportation.

\section{Thought Experiments}
\textbf{Amnesia Test:} Memory loss does not disrupt continuity of experience, showing \$\mathrm{\[con]}\$ is not content-dependent.\\
\textbf{Transporter Paradox:} Identical copies result in different \$\mathrm{\[con]}\$ trajectories.\\
\textbf{Relativistic Travel:} Near-\$c\$ motion stretches the \$\mathrm{\[con]}\$ field, but continuity is maintained.\\
\textbf{Quantum Coin Flip:} Only one outcome intersects a given \$\mathrm{\[con]}\$ trajectory despite both existing in the wavefunction.

\section{Empirical Consequences}
\begin{enumerate}
\item High-\$\Phi\$ systems correlate with \$\mathrm{\[con]}\$ presence
\item Coherence patterns may reflect active \$\mathrm{\[con]}\$ fields
\item Field boundaries should be spatially continuous
\end{enumerate}

\section{Philosophical Implications}
\begin{itemize}
\item Identity persists via \$\mathrm{\[con]}\$ continuity
\item Death terminates the trajectory; birth initiates a new one when \$\Phi \geq \Phi\_c\$
\item Free will reflects subjective selection among quantum-compatible paths
\end{itemize}

\section{Open Questions}
\begin{itemize}
\item Can \$\varphi\$ be integrated into Hilbert space formalisms?
\item Are \$\mathrm{\[con]}\$ values conserved?
\item How does \$\mathrm{\[con]}\$ interact with artificial systems?
\end{itemize}

\section{Conclusion}
We introduce \$\mathrm{\[con]}\$ as a coordinate of subjective continuity, defining a unique trajectory through the universal wavefunction. This model maintains unitarity while resolving the experiential definiteness of quantum outcomes. The framework suggests testable predictions and reframes consciousness as a geometric, non-duplicable feature of reality.

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