Originally written: September 2026
Theory of Spheres' ('Quantum Gravity')'
or
'E'Empty Spheres in Dimensionless Space' – The 'Fundamental Force Behind Everything
(.Q('Quantum – Gravitational Force', 'Dark Matter' / 'Dark Energy', etc.)
Paper IX: MlD0 – The 0-D Light-Mass as the Oscillator Engine: Quantum/Macroscopic Coupling Between Universes
Eran Shimony (ORCID number – 0009-0003-5610-6736)
Physicist (B.Sc.), MBA, and Certified Real Estate Appraiser
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Download the complete research papers in PDF format for offline reading and citation:
[Download Article I: The Framework (PDF)]
[Download Article II: The Spheres Classical components (PDF)]
[ Download Article III: The Quantum–Gravitational Force as Derived from the Spheres (PDF)]
[Paper III(a) – Updated version: The Quantum–Gravitational Force as Derived from the Spheres (PDF)]
[Download Article Ⅳ: The Planck's constant – ℏ (PDF)]
[Download Article VII: Introduction to the New Quantum Geometry Formalism (PDF))]
[Download Article IX: Introduction to the New Quantum Geometry Formalim (PDF))]
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Publication History & Context: This article was published on September 29, 2026 (DOI: 10.17605/OSF.IO/8E24V).
It builds upon the foundational theory established in the previous work: 'Theory of Spheres – Part I', published on December 29, 2025 (DOI: 10.5281/zenodo.18081185)
and upon the 'Theory of Spheres – Part II' published on February 01, 2026 (DOI: 10.5281/zenodo.18446035) …..
ABSTRACT
This paper reveals the direct mathematical and structural link between the total oscillator mass (4 × baryonic mass of our universe) and the zero-dimensional (0-D) cosmic light-mass – MlD0. Instead of summing discrete resonant particles, we integrate the entire continuous frequency spectrum of the 0-D oscillator engine. Correcting the SI unit dimensions demonstrates that the fundamental oscillator integral yields a continuous dynamic action flow rate: (MAFD0 = π × ℏuniverse ≈ 2.51 × 1088kg/s) rather than a static inertial mass. Integrating this flow rate over the complete cosmic cycle (Tfull-cycle ≈ 1.44 trillion years; see paper Ⅴ chapter 1) produces the total accumulated 0-D isotropic quadratic action ((MlD0)2 ≈ 1.14 × 10108kg2).
To project this localized potential into our macroscopic 3-Dimensional spatial environment (X, Y, Z), we apply a dual geometric transformation: square root extraction to recover linear mass (kg), combined with 3D spatial equipartition (√(1/3)). This rigorously yields an observable cosmic mass of Mobs-total-oscillator ≈ 6.16 × 1053kg.
Furthermore, operating within a symmetric (4∙π) topology split into an entangled quartet of cosmic quarters, our observable baryonic universe constitutes precisely one quarter (25%, 1.54 × 1053kg). This exact result lands directly within the observed cosmological range mass of (1053-1054kg), with exact SI unit compliance without requiring dark energy (for the derivation of the intertwined quartet topology, see Paper I, Chapter 39, and throughout the series).
Part A: Introduction
In Paper VII, we began building a new quantum framework. Our original plan for Paper IX was to sum up discrete particles (leptons, quarks, and bosons) to find the engine's mass. However, we realized that particles are only secondary resonances – like notes on a guitar string – and not a part of the engine itself.
To find the true cosmic engine mass itself – MlD0, we changed our approach: we replaced the sum of separate particles with a continuous integral over the whole 0-D oscillator spectrum.
As derived in Chapter 1, this single shift accomplishes three major theoretical breakthroughs:
- It resolves dimensional inconsistencies by revealing that the 0-D engine operates as a continuous mass-energy action flow rate (MAFD0 in kg/s) rather than a static inertial mass. Accumulating this flow over a cosmic cycle yields the 0-D isotropic quadratic action potential ((MlD0)2 in kg2).
- It establishes that physical observable mass represents a 3-Dimensional geometric projection of the 0-D potential, where square root phase extraction recovers linear mass (kg) alongside a 3D spatial equipartition factor √(1/3).
- It establishes a symmetric (4∙π) topology split into an entangled quartet, where our observable universe constitutes precisely a single quarter (25% baryonic mass) without requiring dark energy.
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Through this framework, we provide a simple geometric link between universe Planck's constant (huniverse), the 0-D cosmic light-mass MlD0, and the total mass of the universe.
Chapter 1: Mathematical & Physical Derivation
To determine the total cosmic output, we transition from discrete particle summations to a single continuous integral over the 0D oscillator spectrum.
The Continuous Action Integral and Dynamic Flow Rate
Using Planck's relation (E = h × f), we define the continuous action across the frequency spectrum of the 0D oscillator from zero to its maximum limit Cmax:
where (f) represents the continuous oscillation frequency. Applying mass-energy equivalence (E = MAFD0 × C2max), we equate both representations:
Dividing by Cmax isolates the fundamental dynamic mass flow rate MAFD0, and using: ћ ≈ 8 × 1087kg∙m2/sec (paper IV chapter 2, eq 4-5), spatially normalizing across the cosmic unit cross-section (L2ref = 1∙ m2) under zero-dimensional unit-circle projection yields the continuous mass-action flow rate in standard SI units:
This confirms that MAFD0 is a continuous mass-energy flow rate in kg/s.
Cosmic Time Integration & 0-D to 3-D Geometric Projection
To calculate the total 0-D cosmic light-mass potential (MlD0)2 we integrate MAFD0 over the entire cosmic cycle duration (Tfull-cycle = 1.44 ×1012years ≈ 4.54 ×1019second): (MlD0)2 = MAFD0 × Tfull-cycle × 1kg = 2.51 × 1088kg/s × 4.54 × 1019s × 1kg ≈ 1.14 ×10108kg2
The accumulated potential (MlD0)2 represents the isotropic spatial diagonal squared of the 0-D oscillator field (vector 3-D view). To extract the observable linear scalar mass quantity (Mobs-total-oscillator) projected into our macroscopic 3-Dimensional space (X, Y, Z), we apply phase amplitude extraction combined with 3D spatial equipartition (√(1/3) factor):
Mobs-total-oscillator = √((MlD0)2/3) = √(1.14 × 10108kg2) / √3 = (1.0677 × 1054kg) / √3 = (1.0677 × 1054kg) / 1.732 ≈ 6.16 × 1053kg
The Four-Quarter Cosmic Structure (Baryonic Component)
In our framework, the cosmos consists of four symmetric entangled quarters (4∙π) topology, where our observable universe constitutes a single quarter (25%-baryonic matter):
Mbaryonic = Mobs-total-oscillator / 4 = (6.16 × 1053) / 4 = 1.54 × 1053kg
This exact result matches astronomical observations of the total baryonic matter in the observable universe (1053 – 1054kg), validating the 0D oscillator engine
CONCLUSION
Paper IX completes a critical transition in our cosmological framework:
- Dimensional Clarification: Correcting SI unit interpretation reveals that the 0-D oscillator engine operates as a dynamic mass-energy action flow rate (MAFD0 = 2.51 × 1088kg/s), accumulating over the cosmic cycle into an isotropic quadratic action potential ((MlD0)2 ≈ 1.14 × 10108kg2).
- Geometric 0-D to 3-D Scaling: The observable universe (1.54 × 1053kg for a single baryonic quarter) is derived via 3D spatial equipartition (√(1/3)) combined with square root phase extraction from the underlying 0-D potential ((MlD0)2.
- Instantaneous Multi-Universe Coupling: Driven by (4∙π) phase interference across four entangled spatial quarters, mass-energy balance is maintained instantaneously via the zero-dimensional origin, requiring no physical travel across spatial coordinates.
- Remote Spectral Analysis & Parallel Cosmology: The theoretical framework allows determining the total mass of any additional closed, completely independent cosmic 0-D harmonic oscillator, and deriving its maximum speed of light, quantum energy levels, particle spectra, masses, and complete physical-chemical laws – all without requiring physical access. This is succinctly captured by the general cosmic projection relation:
Where n is the number of spatial coordinate dimensions of the observer ((n = 3) for our universe).
Numerically only, this translates directly to the linear extracted form:
By unifying Planck-scale action with cosmic-scale mass distribution, this short paper provides a direct, elegant foundation for unified quantum cosmology – forming the underlying 'physics beneath physics'.
Eran Shimony, 2026 ©
English translation based on the original Hebrew version of the 'Theory of Spheres' (ToS) (2017).
All rights reserved by the author.
To the beginning of the article
Related Papers in the Theory of Spheres Series:
'Theory of Spheres – experiment-proposal'
'Theory of Spheres – Part III'
'Theory of Spheres – Part III(a)'