A Unified Informational Framework for Quantum and Gravitational Phenomena: A Bohmian Perspective"

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\title{A Unified Informational Framework for Quantum and Gravitational Phenomena: A Bohmian Perspective}
\author{Anonymous (Inspired by a Novel Theoretical Proposal)}
\date{May 2025}

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\maketitle

\begin{abstract}
We propose a unified theoretical framework that integrates quantum mechanics, gravitation, and cosmology through an informational interpretation of the quantum potential ($Q$) in Bohmian mechanics. Operating in configuration space, $Q$ acts as a universal informational system, instantaneously guiding all particles while preserving nonlocality, conservation laws, and entropic stability. Spacetime is treated as a derived phenomenon constrained by $Q$, with gravitation emerging as an informational manifestation that orchestrates complex particle trajectories across scales. Fundamental constants ($\hbar$, $c$, $G$) serve as control mechanisms, anchoring $Q$’s influence within spacetime. This framework critiques the Copenhagen and Many-Worlds interpretations, offering a deterministic, contradiction-free foundation for a Theory of Everything compatible with established physics. Testable predictions include gravitational entanglement experiments and cosmological signatures of $Q$’s influence.
\end{abstract}

\section{Introduction}
Unifying quantum mechanics and gravitation remains a central challenge in theoretical physics. The Copenhagen interpretation’s reliance on wave function collapse and the Many-Worlds interpretation’s proliferation of universes introduce philosophical and physical ambiguities \citep{Bell1987}. Bohmian mechanics, with its deterministic trajectories guided by the quantum potential ($Q$), offers a promising alternative \citep{Bohm1952}. This paper proposes that $Q$ serves as a universal informational system, operating outside spacetime to constrain it as a derived phenomenon. Gravitation emerges as an informational process driven by $Q$, with fundamental constants as control mechanisms. We aim to provide a contradiction-free framework compatible with quantum mechanics, relativity, and cosmology, with testable implications.

\section{Critique of Standard Interpretations}\label{sec:critique}
The Copenhagen interpretation posits wave function collapse upon measurement, raising the measurement problem and lacking a physical mechanism for collapse \citep{Heisenberg1927}. The Many-Worlds interpretation avoids collapse by postulating multiple universes, but its untestable nature and ontological complexity are problematic \citep{Everett1957}. Both fail to unify quantum mechanics with gravitation or cosmology. Bohmian mechanics, by contrast, provides a deterministic, nonlocal framework that avoids these issues \citep{Bohm1952}.

\section{Bohmian Mechanics as a Universal Framework}\label{sec:bohmian}
In Bohmian mechanics, the wave function $\psi = R e^{iS/\hbar}$ evolves via the Schrödinger equation:
\begin{equation}
i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m} \nabla^2 \psi + V \psi
\end{equation}
The quantum potential is:
\begin{equation}
Q = -\frac{\hbar^2}{2m} \frac{\nabla^2 R}{R}
\end{equation}
Particle motion is governed by:
\begin{equation}
m \frac{d^2 \mathbf{x}}{dt^2} = -\nabla (V + Q)
\end{equation}
$Q$’s nonlocality enables instantaneous correlations, as in entanglement \citep{Bell1964}. We extend this to a cosmic scale, proposing that $Q$ guides all particles via a universal wave function $\psi_{\text{universe}}$ in configuration space, unbound by spacetime.

\section{The Informational Role of $Q$}\label{sec:informational}
We hypothesize that $Q$ is a universal informational system, coordinating particle trajectories through instantaneous information exchange. This ensures:
\begin{itemize}
    \item \textbf{Nonlocality}: $Q$’s dependence on $\psi_{\text{universe}}$ enables superluminal correlations.
    \item \textbf{Conservation}: $Q$ leverages the wave function’s intrinsic energy, preserving matter and energy.
    \item \textbf{Entropic Stability}: $Q$ guides particles to maintain quantum coherence, preventing entropic collapse.
\end{itemize}
In configuration space, $Q$ operates outside spacetime, enabling coordination without violating relativity, as no physical signals are involved. In localized systems (e.g., quantum computers), a constrained ``local $Q$'' emerges, shaped by human-engineered boundary conditions but subordinate to the universal $Q$, ensuring cosmic coherence.

\section{Gravitation as an Informational Phenomenon}\label{sec:gravitation}
We propose that gravitation is an emergent informational manifestation of $Q$. In general relativity:
\begin{equation}
G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}
\end{equation}
Spacetime is derived, constrained by $Q$ in configuration space. Gravitation translates the universe’s intrinsic energy into coordinated, dynamically optimized trajectories, producing structures like galaxies. This aligns with entropic gravity \citep{Verlinde2011} and holographic principles \citep{Maldacena1998}. Gravitation preserves nonlocality, conservation, and entropic stability, acting as $Q$’s dynamical expression across scales.

\section{Fundamental Constants as Control Mechanisms}\label{sec:constants}
Constants like $\hbar$, $c$, and $G$ anchor $Q$’s influence within spacetime:
\begin{itemize}
    \item $\hbar$ defines quantum scales, constraining $Q$’s effects.
    \item $c$ limits material entities to sub-luminal speeds, preserving spacetime causality.
    \item $G$ governs gravitational strength, stabilizing cosmic structures.
\end{itemize}
As tools of $Q$, these constants enable superluminal information exchange in configuration space while restricting physical dynamics to spacetime, resolving tensions between nonlocality and relativity.

\section{Testable Predictions}\label{sec:predictions}
This framework yields testable predictions:
\begin{itemize}
    \item \textbf{Gravitational Entanglement}: Experiments measuring entanglement induced by gravitational fields could reveal $Q$’s informational role \citep{Marletto2017}.
    \item \textbf{Cosmological Signatures}: $Q$’s guidance of vacuum fluctuations during inflation may produce distinct patterns in the cosmic microwave background, detectable by future observatories.
    \item \textbf{Quantum Technologies}: Enhanced coherence in quantum systems could be achieved by optimizing local $Q$, testable in quantum computing experiments.
\end{itemize}

\section{Implications and Future Directions}\label{sec:implications}
This framework impacts:
\begin{itemize}
    \item \textbf{Quantum Technologies}: Optimizing local $Q$ could improve quantum coherence.
    \item \textbf{Cosmology}: Modeling $Q$ in $\psi_{\text{universe}}$ could explain cosmic structure formation.
    \item \textbf{Quantum Gravity}: The informational view of gravitation may bridge quantum mechanics and relativity.
    \item \textbf{Philosophy}: $Q$’s trans-spatiotemporal nature prompts questions about reality and cosmic order.
\end{itemize}
Future work includes mathematical modeling of $Q$ in cosmology, experimental tests of gravitational entanglement, and integration with holographic theories.

\section{Conclusion}\label{sec:conclusion}
We present a unified framework where $Q$ in Bohmian mechanics acts as an informational system, constraining spacetime, orchestrating gravitation, and leveraging fundamental constants. This resolves issues in standard quantum interpretations, offering a deterministic, contradiction-free foundation for a Theory of Everything. Its compatibility with established physics and testable predictions make it a promising avenue for future research.

\bibliographystyle{plainnat}
\begin{thebibliography}{9}
\bibitem{Bell1987}
Bell, J. S. (1987). \emph{Speakable and Unspeakable in Quantum Mechanics}. Cambridge University Press.

\bibitem{Bohm1952}
Bohm, D. (1952). A Suggested Interpretation of the Quantum Theory in Terms of ``Hidden'' Variables. \emph{Physical Review}, 85(2), 166--193.

\bibitem{Heisenberg1927}
Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. \emph{Zeitschrift für Physik}, 43, 172--198.

\bibitem{Everett1957}
Everett, H. (1957). ``Relative State'' Formulation of Quantum Mechanics. \emph{Reviews of Modern Physics}, 29(3), 454--462.

\bibitem{Bell1964}
Bell, J. S. (1964). On the Einstein Podolsky Rosen Paradox. \emph{Physics}, 1(3), 195--200.

\bibitem{Verlinde2011}
Verlinde, E. (2011). On the Origin of Gravity and the Laws of Newton. \emph{Journal of High Energy Physics}, 2011(4), 29.

\bibitem{Maldacena1998}
Maldacena, J. (1998). The Large N Limit of Superconformal Field Theories and Supergravity. \emph{Advances in Theoretical and Mathematical Physics}, 2, 231--252.

\bibitem{Marletto2017}
Marletto, C., \& Vedral, V. (2017). Gravitationally Induced Entanglement between Two Massive Particles is Sufficient Evidence of Quantum Effects in Gravity. \emph{Physical Review Letters}, 119(24), 240402.
\end{thebibliography}

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