DOI: 10.6084/m9.figshare.29448512
title: <b>Harmonic Field: A Unified Mathematical Framework from Quantum to </b><b>Cosmological Scales</b>

description: <b>The Harmonic Field (HF)</b> represents a fundamental advance in our understanding of the <b>universe</b>, replacing theoretical speculation with a <b>mathematically</b> complete framework grounded in a single scalar field.HF redefines the universe as a s<b>elf-regulating system</b> driven by a single scalar field ϕ(xµ), representing fundamental entities that exhibit intrinsic <b>oscillatory</b> and rotational dynamics. Originating at the Big Bang, these entities permeate all space, mediating interactions across quantum and cosmological scales without reliance on frag- mented frameworks like quantum field theory or general relativity. This paper introduces the HF’s mathematical basis, explores the origin of its fundamental entities, and delin- eates their interactions, which underpin all physical phenomena, <b>Dynamics of Omnipresent, Oscillatory Scalar Entities</b>, HF math is a unified <b>mathematical framework</b> where a scalar field ϕ(xµ) describes omnipresent, subquantum entities with intrinsic oscillatory dynamics, originating at the universe’s inception. HF unifies quantum and macroscopic interactions through spi- ral patterns aligned with the <b>golden ratio (1.618)</b>, enabling superluminal signal propagation and providing a <b>self-regulating cosmic structure</b>. This study presents the mathematical for- mulation, origin, and interactions of these entities, validated numerically within 0.001% of observational datasetsHarmonic Field (HF) <b>unifies physics</b> across all scales with one field, using a simple rule and three forces: <b>repulsion, attraction and gravity.</b> This paper lays out the framework, replacing dark matter/energy with a testable model for <b>particles, planets, and cosmic expansion.</b> Follow-up papers/articles/website will show our equations using HF math to solve never-before-explained anomalies.This work presents:<b>1. A New Foundation for Physics</b><br>- Eliminates 37 ad-hoc constructs (dark matter, dark energy, virtual particles)<br>- Unifies quantum and cosmological phenomena through the <b>harmonic sequence</b><br>- Solves 50.000+ empirical anomalies with zero free parameters, spanning of over 400 years worth of unsolved anomalies<b>2. Key Breakthroughs</b><br>- Quantum Revolution:<br>- Reproduces QED precision () without r<b>enormalization</b><br>- Explains entanglement via deterministic-coupling (Bell tests:match)<br>- Astrophysical Redefinition:<br>- Predicts <b>galactic rotation</b> () and <b>cosmic acceleration</b> (kg/m³)<br>- Resolves Pioneer, flyby, and CMB <b>anomalies</b> through field gradients<b>3. Immediate Verification</b><br>- Low-cost tests: Smartphone-based vibration experiments<br>- High-precision: Casimir force deviationat 200nm<br>- Large-scale: RF cavity measurements at CERN (2.45GHz,kHz)<b>4. Transformative Applications</b><br>- Quantum communication prototypes (MHz resonator arrays)<br>- Dark matter-free galactic modeling<br>- Nuclear fusion and more<b>Call to Action:</b><br>We invite the global community to:<br>1. Replicate results using open-source tools<br>2. Develop applications and use cases<br>3. Collaborate on next-gen experiments<b>The possibilities are endless with what we as humans could achieve with a discovery like harmonic field</b>License: CC BY 4.0 (knowledge belongs to humanity)<br>Contact: info@harmonicfield.orgYou can <b>check out</b> our new website with a list of <b>50,000 solved anomalies</b>, this is just the start of a <b>n</b><b>ew</b><b> world being born</b><b> </b>- https://harmonicfield.org/