This work explores the interplay between gravity, information processing, and computational compl... more This work explores the interplay between gravity, information processing, and computational complexity across the universe. We present a framework integrating gravitational effects into computational complexity theory, revealing implications for computation in curved spacetime. By synthesizing principles from general relativity, quantum mechanics, and complexity theory, we introduce gravitationally modified complexity classes and derive constraints imposed by spacetime curvature on computational capacity. Our analysis uncovers phenomena such as gravitationally induced phase transitions in problem complexity and potential observer-dependent resolutions of issues like the P vs NP problem in extreme gravitational environments. We demonstrate that maximum computational capacity is linked to a system's energy content and local gravitational field, with quantum gravitational effects significant at smaller scales. The framework predicts novel phenomena, including gravitationally induced decoherence and potential enhancements to quantum computation in specific gravitational regimes. We explore cosmological implications, examining how the universe's expansion affects computational capacity and connecting the arrow of time to the growth of computational complexity. Grounded in rigorous theoretical and mathematical foundations, we propose experimental setups to test our predictions, ranging from Earth-based atomic clock experiments to satellite-based quantum computing tests and astronomical observations. This research suggests the universe may be inherently computational, with gravity shaping the informational landscape of reality. Our findings offer new perspectives on problems like the black hole information paradox and open technological possibilities, including gravity-assisted quantum algorithms and holographic quantum computation. By demonstrating how gravity shapes computation, this work provides a unified view of information processing in the universe and paves the way for a deeper understanding of the connections between spacetime structure, quantum mechanics, and computational complexity.
This work presents an extension to the Second Law of Thermodynamics by incorporating the concept ... more This work presents an extension to the Second Law of Thermodynamics by incorporating the concept of quantum complexity. The proposed modification suggests that the total entropy of an isolated system includes not only classical entropy changes but also contributions from quantum complexity and informational entropy. We provide a mathematical proof demonstrating that this extended law is consistent with both classical thermodynamics and quantum information theory. The implications of this extension are significant, offering potential advancements in understanding thermodynamic processes at the quantum scale, optimizing energy systems, and enhancing the theoretical framework of quantum thermodynamics. Our findings indicate that integrating quantum complexity into the Second Law provides new insights into the fundamental limits of thermodynamic systems, which could lead to improvements in energy efficiency and deeper understanding of quantum state dynamics. Future research directions include experimental verification and further theoretical development to explore the broader reach of this modification of the Second Law.
This paper proposes an extension to the Einstein Field Equations by integrating quantum informati... more This paper proposes an extension to the Einstein Field Equations by integrating quantum informational measures, specifically entanglement entropy and quantum complexity. These modified equations aim to bridge the gap between general relativity and quantum mechanics, offering a unified framework that incorporates the geometric properties of spacetime with fundamental aspects of quantum information theory. Our mathematical derivation demonstrates the consistency of the extended equations with both classical general relativity and quantum information theory. The theoretical implications include potential resolutions to the black hole information paradox and insights into the nature of dark energy. Additionally, the paper outlines future research directions focused on experimental verification, detailed mathematical analysis, and further theoretical development to explore specific solutions and their stability. This work represents a step towards a deeper understanding of the interplay between gravity and quantum information, inviting further investigation and interdisciplinary collaboration. Contents
This work introduces a modification to the Heisenberg Uncertainty Principle (HUP) by incorporatin... more This work introduces a modification to the Heisenberg Uncertainty Principle (HUP) by incorporating quantum complexity, including potential nonlinear effects. Our theoretical framework extends the traditional HUP to consider the complexity of quantum states, offering a more nuanced understanding of measurement precision. By adding a complexity term to the uncertainty relation, we explore nonlinear modifications such as polynomial, exponential, and logarithmic functions. Rigorous mathematical derivations demonstrate the consistency of the modified principle with classical quantum mechanics and quantum information theory. We investigate the implications of this modified HUP for various aspects of quantum mechanics, including quantum metrology, quantum algorithms, quantum error correction, and quantum chaos. Additionally, we propose experimental protocols to test the validity of the modified HUP, evaluating their feasibility with current and near-term quantum technologies. This work highlights the importance of quantum complexity in quantum mechanics and provides a refined perspective on the interplay between complexity, entanglement, and uncertainty in quantum systems. The modified HUP has the potential to stimulate interdisciplinary research at the intersection of quantum physics, information theory, and complexity theory, with significant implications for the development of quantum technologies and the understanding of the quantum-toclassical transition.
This work explores the hypothesis that time is an emergent phenomenon arising from underlying qua... more This work explores the hypothesis that time is an emergent phenomenon arising from underlying quantum informational processes. By integrating principles from quantum mechanics, thermodynamics, and general relativity, we develop a comprehensive framework that elucidates the relationship between quantum complexity, entanglement, and the nature of time. We investigate the role of quantum complexity in the evolution of quantum states and demonstrate how the increase in entanglement entropy provides a microscopic basis for the arrow of time. Using the AdS/CFT correspondence and the holographic principle, we establish connections between spacetime geometry and quantum informational measures like entanglement entropy. We address the black hole information paradox within this context, arguing that information is preserved in a highly scrambled form. Additionally, we propose an experimental design using black hole analogues to empirically validate our theoretical predictions, focusing on fast scrambling and the growth of quantum complexity. Our findings suggest that quantum informational dynamics govern the emergence of time and spacetime geometry. This work bridges quantum mechanics, thermodynamics, information theory, and general relativity, offering potential applications in quantum technologies and new insights into the fundamental nature of reality.
This paper extends the classical Maxwell equations by incorporating quantum informational measure... more This paper extends the classical Maxwell equations by incorporating quantum informational measures, specifically entanglement entropy and quantum complexity. The goal is to unify classical electromagnetism with quantum information theory, creating a framework that captures both classical and quantum properties of electromagnetic fields. We derive these extended equations using a modified action principle and verify their consistency through dimensional analysis and stability checks. Our results indicate potential modifications to electromagnetic wave propagation, stress-energy distribution, and fieldparticle interactions, providing new insights into the quantum nature of fields. This framework has significant implications for quantum computing, communication systems, and fundamental physics. We propose specific experimental setups to validate the theoretical predictions and explore the potential technological advancements arising from this integration. The appendices construct rigorous mathematical derivations and detailed analyses to support the robustness of the proposed framework. This work aims to deepen our understanding of the relationship between electromagnetism and quantum information, fostering interdisciplinary collaboration and further exploration.
This thesis introduces an extension to the Einstein Field Equations by incorporating quantum info... more This thesis introduces an extension to the Einstein Field Equations by incorporating quantum informational measures, specifically entanglement entropy and quantum complexity, into the gravitational framework. This approach aims to bridge the gap between general relativity and quantum mechanics, offering a unified theory that integrates the geometric structure of spacetime with the principles of quantum information. The extended field equations derived in this work remain consistent with both classical general relativity and quantum information theory. This novel formulation provides potential solutions to the black hole information paradox and offers new insights into the nature of dark energy. Our investigation reveals unexpected findings, implying the role of quantum complexity in driving cosmic inflation and the emergence of classical spacetime from quantum entanglement patterns. Through perturbative and non-perturbative analyses, we explore quantum corrections to classical gravitational solutions, modified particle motion equations, and new perspectives on black hole thermodynamics and cosmological evolution. Notably, this study suggests that entanglement entropy may influence largescale structure formation and that quantum informational terms might naturally explain the universe's late-time acceleration. The thesis also proposes observable predictions, such as unique signatures in gravitational wave observations and cosmological data, to guide future experimental tests of this framework. By investigating how gravity and quantum information interact, this work sheds light on how spacetime might emerges from quantum properties, offering a comprehensive framework for exploring quantum gravity.
Shannon's Channel Capacity, a foundational concept in classical information theory, establishes t... more Shannon's Channel Capacity, a foundational concept in classical information theory, establishes the fundamental constraints on information transmission through classical channels. This paper extends Shannon's seminal work to cosmic scales, integrating quantum and gravitational effects to formulate a novel framework for "cosmic channel capacity." This framework addresses the unique challenges associated with information processing and transmission across vast cosmic distances and within extreme gravitational environments. Our principal contributions are: (1) a generalized formula for cosmic channel capacity that incorporates quantum entanglement and spacetime curvature; (2) modified limits on information transmission in the presence of black holes and the expanding universe; and (3) identification of potential observational signatures in gravitational waves and anisotropies in the cosmic microwave background. This comprehensive approach enhances our understanding of the fundamental limits of information processing and transmission in the universe, with significant implications for quantum gravity, cosmology, and the intrinsic nature of information.
This paper presents a novel reinterpretation of the Higgs mechanism through the lens of quantum i... more This paper presents a novel reinterpretation of the Higgs mechanism through the lens of quantum information theory and extended quantum gravity. We propose that the Higgs field emerges from the entanglement structure of quantum gravitational degrees of freedom, with spontaneous symmetry breaking arising as a complexity threshold phenomenon. Our framework introduces quantum informational measures directly into the gravitational field equations, leading to a novel understanding of spacetime as an emergent phenomenon rooted in quantum information. We develop a mathematical formalism that relates the Higgs potential and couplings to quantum entanglement entropy and complexity, predicting specific quantum gravitational corrections to Standard Model physics. Our approach offers potential resolutions to long-standing issues such as the hierarchy problem and the cosmological constant problem, while suggesting deep connections between particle physics and cosmology through a holographic perspective. The paper outlines experimental proposals to test our theory, including precision Higgs measurements at future colliders, cosmological observations, and quantum simulations. We also explore the philosophical implications of our framework, challenging traditional notions of physical law and the nature of reality itself.
This paper presents a novel hypothesis that the gauge group structure of the Standard Model, SU (... more This paper presents a novel hypothesis that the gauge group structure of the Standard Model, SU (3) × SU (2) × U (1), emerges from underlying quantum informational spacetime structure. By incorporating measures such as entanglement entropy and quantum complexity into the theoretical framework, we offer a new perspective on the unification of gauge symmetries within the Standard Model. Our approach provides a rigorous mathematical treatment of how specific entanglement patterns give rise to the SU (3) × SU (2) × U (1) symmetries and proposes that the 16-dimensional representation of the Standard Model is a consequence of quantum error correction principles operating at the Planck scale. We further explore the implications of this framework for particle physics, including the generation structure of fermions and the emergence of CKM and PMNS matrices, as well as potential experimental predictions and resolutions to existing problems in particle physics. This work builds on recent advancements in quantum information theory and extended gravitational theories, offering a path towards a more unified understanding of nature's fundamental forces.
The reconciliation of quantum mechanics and general relativity remains one of the most profound c... more The reconciliation of quantum mechanics and general relativity remains one of the most profound challenges in modern physics. This paper introduces and rigorously investigates a novel framework proposing that spacetime emerges from quantum entanglement in a lower-dimensional quantum system. We develop a precise mathematical mapping between entanglement structures and geometric properties of emergent spacetime, demonstrating how Einstein's field equations can be derived from fundamental quantum entanglement dynamics. Our approach provides a unified perspective on quantum mechanics and general relativity, offering potential resolutions to long-standing problems, including the black hole information paradox. We extend this framework to cosmological scenarios and discuss experimental predictions, representing a significant step towards a complete theory of quantum gravity. This work not only advances our understanding of the nature of space, time, and gravity as emergent phenomena but also suggests new avenues for empirical investigation of quantum gravitational effects.
The quest to reconcile quantum mechanics and general relativity under a single, unified theory is... more The quest to reconcile quantum mechanics and general relativity under a single, unified theory is one of the foremost challenges in scientific inquiry. This thesis introduces an innovative framework to that end, suggesting that gravity and spacetime geometry emerge from quantum informational processes. By blending the principles of quantum mechanics with general relativity, we uncover the profound roles of entanglement entropy, quantum complexity, and quantum error correction in shaping our universe. Utilizing key discoveries such as the Ryu-Takayanagi formula and the complexity-action duality, we demonstrate how these quantum phenomena underpin the creation of spacetime geometry and gravitational dynamics in the cosmos. Our findings propose that the macroscopic structure of spacetime and gravity are emergent properties arising from the collective behavior of more fundamental quantum particles. This represents a paradigm-shifting view that advances our understanding of the universe, offering potential breakthroughs in quantum technologies, resolution of longstanding paradoxes, and the unification of fundamental forces. This thesis challenges established paradigms to unify the principles of quantum mechanics and general relativity, heralding new frontiers in theoretical physics and deepening our understanding of the fabric of reality.
This paper investigates the fundamental limits imposed on computation by gravitational effects ac... more This paper investigates the fundamental limits imposed on computation by gravitational effects across all scales, from quantum to cosmic, through the lens of an extended quantum gravity framework that incorporates quantum informational measures into Einstein's field equations. This framework reveals intricate connections between spacetime geometry, quantum entanglement, and computational complexity, yielding novel bounds on information processing in curved spacetime with implications for quantum computing, black hole physics, and cosmology. Key findings include a generalized Margolus-Levitin theorem that accounts for gravitational time dilation, a modified holographic bound on information density incorporating quantum gravitational corrections, predictions for gravitationally induced decoherence rates in quantum systems, and an analysis of the total computational capacity of the observable universe. We derive scale-dependent computational limits and explore their consequences for specific quantum algorithms and error correction protocols. Additionally, we examine the philosophical implications of these gravitational constraints on computation, discussing their relevance to concepts such as determinism, free will, and the arrow of time, and propose experimental setups to test our theoretical predictions, ranging from table-top quantum experiments to astrophysical observations. Our results suggest that gravity plays a fundamental role in shaping the informational structure of the universe, potentially placing ultimate limits on knowledge acquisition, aiming to provide a unified perspective on the interplay between gravity, quantum mechanics, and information theory, offering new insights into the nature of space, time, and computation in our universe.
Uploads
Papers by Logan Nye