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A Mathematical Framework for QPOs in Temporal Flow Segmentation

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Temporal Physics: A Mathematical Framework for QPOs in Temporal Flow Segmentation Abstract: This is a mathematical framework for understanding quasi-periodic oscillations (QPOs) in the context of temporal flow segmentation. By modeling temporal flows as superpositions of sinusoidal components and introducing discrete interactions at the Planck scale, we provide a deterministic yet complex approach to the behavior of these flows in extreme astrophysical environments. The model accounts for the finite bandwidth of temporal flows, interactions at the Planck scale, and the effects of spacetime curvature on flow behavior, offering a potential explanation for the periodic emissions observed in black holes and neutron stars. I derive mathematical relations for QPO frequencies and make predictions for future observational tests. 1. Introduction Background: The study of quasi-periodic oscillations (QPOs) in astrophysical systems, particularly in the vicinity of black holes and neutron stars, re...

Temporal Flows: A Definition and Mathematical Framework

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Temporal Flows: A Definition and Mathematical Framework Abstract: Concept of Temporal Flows Temporal flows describe the active, dynamic progression of time within a system, where time begins as a single-dimensional flow. As these flows accumulate and interact with each other, they create a multi-dimensional perspective of time. Unlike the traditional view of time as a passive backdrop, temporal flows are generative, shaping and being shaped by the distribution of energy, mass, and spatial curvature. These flows are the foundational mechanism behind the emergence of macroscopic phenomena, including gravity and quantum behaviors, with mass and energy themselves arising from the temporal dynamics. This model redefines time not as a constant, linear entity, but as an evolving participant that interacts with matter and energy, with its dimensionality increasing through the accumulation and interaction of flows. By treating time as a dynamic process influenced by its own structure, this appr...

Temporal Physics: Markovian or Non-Markovian?

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Temporal Physics: Markovian or Non-Markovian? Abstract This paper presents a novel model of temporal physics, where a system’s state inherently encodes its history. By analyzing the roles of momentum and energy, I examine how conserved quantities link past and present, demonstrating the enduring impact of historical interactions. This study investigates the duality between local and nonlocal descriptions, emphasizing their implications for Markovian and non-Markovian dynamics. The findings suggest that momentum and energy serve as bridges connecting time scales, offering insights into the entanglement of past, present, and future, with potential applications in quantum mechanics and cosmology. Introduction Temporal physics investigates how systems evolve, focusing on how past states influence the present. Traditional models often rely on Markovian assumptions, where predictions depend solely on current states, neglecting historical context. While these assumptions simplify modeling, th...

A Unified Theory of Temporal Flow and Gravity: From Quantum Fluctuations to Macroscopic Dynamics

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A Unified Theory of Temporal Flow and Gravity: From Quantum Fluctuations to Macroscopic Dynamics Abstract This paper proposes a unified framework for understanding gravity as an emergent phenomenon arising from temporal flow dynamics, bridging macroscopic non-linear dynamics with quantum fluctuations. We suggest a cubic relationship between temporal flow and spacetime curvature for large-scale phenomena and derive quantum gravitational effects using a path integral formulation of temporal flow. Temporal flows are viewed as the generative mechanism underlying gravitational phenomena, where the curvature of spacetime is not an intrinsic property but a result of the interactions and accumulation of temporal flows. This synthesis provides a comprehensive model that unifies quantum mechanics and general relativity, resolving conceptual inconsistencies and offering new insights into cosmological phenomena, gravitational waves, and the quantum nature of spacetime. 1. Introduction Time has tra...

Gödel's Incompleteness and Paradox Theory

Gödel's incompleteness theorem demonstrates that in any formal system (strong enough to include basic arithmetic), there are truths that cannot be proven within the system. This suggests that no formal system can be complete or fully consistent within itself. I look at this idea and apply it to the interaction of two systems. If two systems share a common invariant, or a constant foundation, then the question of whether the systems are "equal" or "paradoxical" arises, depending on how they differ or align within that foundation. Key Concepts of my Paradox Theory: Invariant/Foundation: This represents the shared, constant base between the two systems. It’s the part of the system that is untouched by the dynamics or the context-specific variations. Nominator (Contextual Difference): The nominator in this case is the contextual element that exists between the systems—the part that makes the two systems appear different or even paradoxical. These differences, or the...

Temporal Flows and Amplitudes

Temporal Physics: Temporal Flow and Dynamics Abstract In this paper, I present a new perspective on physical interactions, based on temporal flows . By treating time as a fundamental construct rather than space or matter, I propose a model where energy, mass, and fields emerge from interactions of time itself. This framework offers new insights into classical and quantum mechanics, black hole dynamics, and gravitational waves. I introduce a set of mathematical equations that describe these temporal flows , their interactions, and their implications for our understanding of the universe. 1. Introduction The Motivation The traditional models of physics—classical mechanics, quantum mechanics, and general relativity—have done an excellent job of describing physical phenomena. However, they often rely on an underlying assumption that space is more fundamental than time, with the understanding that matter and energy interact within this space. But I believe that time itself is the more funda...