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Integration and Refinement of Digital Physics,
Unifying Quantum and Classical with a Calculation:
A Formal Approach to Subparticles and Discrete
Universe Frames
Jesse Daniel Brown, PhD1and Anton Fedotov, B.A.2
1Armstrong Atlantic State University, Email: plasmatoid@gmail.com,
ORCID: 0009-0006-3889-534X
2Harbin Institute of Technology, Email: anvifedotov.biz@gmail.com,
ORCID: 0009-0004-2313-6530
December 11, 2024
Abstract
This paper expands upon and refines a model that introduces innovative con-
cepts such as metatags, temporal crystals, quantum tunneling, and quantum scar-
ring. These ideas offer a profound framework for understanding the discrete nature
of the universe and its evolution. We formalize these concepts and integrate them
with a frame-based model of a discrete universe, providing mathematical precision
and theoretical coherence. Additionally, we incorporate relevant techniques and
references from existing literature to support and contextualize our framework.
Contents
1 Introduction 2
1.1 Objective ................................... 2
1.2 KeyQuestions................................. 3
1.3 Context of Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 The Concept of a Discrete Universe Structure 3
2.1 Definition of the Frame-Based Model . . . . . . . . . . . . . . . . . . . . 3
2.2 Integration of Metatags into Frames . . . . . . . . . . . . . . . . . . . . . 4
2.3 Representation of Spacetime Pixels . . . . . . . . . . . . . . . . . . . . . 4
2.4 Advantages of the Discrete Model . . . . . . . . . . . . . . . . . . . . . . 4
2.5 Key Mathematical Formalism . . . . . . . . . . . . . . . . . . . . . . . . 5
1
3 Metatags as a Mechanism of Evolution 5
3.1 Formalization of Metatags . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Integration of Metatags into Frames . . . . . . . . . . . . . . . . . . . . . 6
3.3 Oscillatory Stability and Quantum Scarring . . . . . . . . . . . . . . . . 6
3.4 Linking Metatags to Macroscopic Processes . . . . . . . . . . . . . . . . . 6
4 Mechanisms of Subparticle Interaction 6
4.1 Interaction via Connection Function . . . . . . . . . . . . . . . . . . . . . 6
4.2 QuantumEntanglement ........................... 6
4.3 QuantumTunneling ............................. 7
5 Macroscopic Processes and the Big Bounce 7
5.1 Collapse and Density Gradients . . . . . . . . . . . . . . . . . . . . . . . 7
5.2 Temporal Crystals as Structured Elements of Spacetime . . . . . . . . . . 7
5.2.1 Explosion of Temporal Crystals . . . . . . . . . . . . . . . . . . . 7
5.3 TheBigBounce................................ 7
6 Experimental Validation and Simulations 7
6.1 Simulations of the Frame-Based Model . . . . . . . . . . . . . . . . . . . 7
6.2 Experiments on Entanglement and Tunneling . . . . . . . . . . . . . . . 8
6.3 Analysis of Cosmological Data . . . . . . . . . . . . . . . . . . . . . . . . 8
7 Conclusion 8
Supplementary Materials 8
*Acknowledgments 9
References 9
1 Introduction
The aim of this paper is to expand upon and refine a model that proposes the universe
operates as a discrete, frame-based system where subparticles are assigned metatags en-
coding their properties and states. Concepts such as temporal crystals, quantum tunnel-
ing, and quantum scarring are integral to this framework, offering insights into quantum
phenomena and cosmological processes.
1.1 Objective
Our contribution lies in:
1. Establishing a formal integration of metatags into the frame-based representation
of discrete spacetime.
2. Exploring how mechanisms like quantum scarring enrich the evolution of frames
within the model.
3. Proposing experimental and computational approaches to test the validity of the
refined concepts.
2
1.2 Key Questions
This work seeks to address the following critical questions:
•How can the concept of metatags, describing the properties and states of subparti-
cles, be systematically integrated into the frame-based model?
•In what ways do mechanisms like quantum scarring complement and enhance the
understanding of frame evolution?
•What experimental methods and simulations can be employed to validate these
theoretical advancements?
1.3 Context of Contribution
While the initial model provides a robust conceptual foundation, certain aspects, such
as the formal role of metatags, the dynamics of temporal crystals, and the interaction of
subparticles, require further exploration. By embedding these concepts within a mathe-
matically rigorous framework, we aim to:
1. Clarify the relationship between subparticles and the discrete frames of the universe.
2. Establish predictive mathematical tools to describe transitions between frames.
3. Provide pathways for empirical validation, bridging theory with observable phe-
nomena.
This paper thus seeks to complement the original insights and advance their applica-
bility through detailed mathematical formulations and experimental strategies.
2 The Concept of a Discrete Universe Structure
In this section, we define the discrete nature of the universe through a frame-based model.
This model conceptualizes spacetime as a series of discrete states, or frames Fn, each
capturing the entirety of the universe at a specific moment. We enhance this model by
incorporating the concept of metatags to describe the properties of subparticles, providing
a deeper understanding of their role in the discrete spacetime structure.
2.1 Definition of the Frame-Based Model
The universe is modeled as a sequence of frames:
Fn={Pn
i,j,k |i, j, k ∈Z},
where:
•Fnrepresents the discrete state of the universe at the n-th moment.
•Pn
i,j,k denotes the smallest units of spacetime (spacetime ”pixels”) within the n-th
frame, indexed by spatial coordinates i, j, k.
3
The evolution of the universe is described by the frame transition:
Fn+1 =T(Fn),
where Tis the transition operator responsible for updating the state of the universe from
frame Fnto Fn+1.
2.2 Integration of Metatags into Frames
Each spacetime pixel Pn
i,j,k is augmented with a metatag Mn
i,j,k that encodes the properties
and states of the subparticles within the pixel:
Mn
i,j,k ={x, y, z, e, p, S},
where:
•x, y, z: Spatial coordinates of the subparticle.
•e: Energy of the subparticle.
•p: Momentum of the subparticle.
•S: Quantum state or entanglement state of the subparticle.
The augmented frame is thus represented as:
Fn={Mn
i,j,k |i, j, k ∈Z}.
2.3 Representation of Spacetime Pixels
Subparticles are modeled as elements of discrete spacetime, forming a grid of spacetime
pixels:
S=[
i,j,k
SPi,j,k ,
where:
•S: The discrete spacetime structure.
•SPi,j,k : The subparticle associated with the pixel indexed by i, j, k.
The granularity of spacetime is defined by fundamental units ∆x(spatial resolution)
and ∆t(temporal resolution). These discrete units replace the continuous variables of
classical spacetime, providing a framework that avoids singularities and infinities.
2.4 Advantages of the Discrete Model
The frame-based model with metatags offers several advantages:
1. Elimination of Singularities: By discretizing spacetime, the model avoids singu-
larities where physical laws break down due to infinite densities or curvatures [8,16].
2. Resolution of Infinite Regress: The discrete nature imposes finite limits on
spacetime, ensuring that computations and physical processes are well-defined.
4
3. Enhanced Description of Subparticles: Metatags provide a detailed descrip-
tion of subparticle properties, enabling a comprehensive understanding of quantum
phenomena such as tunneling and entanglement [1, 18].
4. Compatibility with Simulations: The discrete model is naturally suited for
computational simulations, allowing numerical verification and experimental design
[2, 9].
Notably, our approach to representing subparticles and metatags was partly inspired
by ideas from 3D graphics and rendering techniques. Just as Kim et al. (2012) demon-
strated automated collection of detailed 3D avatar images [11], we analogously consider
each subparticle as a discrete entity that can be “rendered” in the frame-based model.
This analogy informed our conceptualization of particle-level rendering, where each sub-
particle’s state is encoded in a metatag and presented discretely within the simulation
framework.
2.5 Key Mathematical Formalism
1. Discrete Frame Transition:
Fn+1 =T(Fn),
where Tdepends on local and global physical laws.
2. Augmentation of Pixels with Metatags:
Pn
i,j,k →Mn
i,j,k ={x, y, z, e, p, S}.
3. Discrete Spacetime Representation:
S=[
i,j,k
SPi,j,k .
4. Granularity of Spacetime:
∆x, ∆tdefine the minimal units of spacetime.
3 Metatags as a Mechanism of Evolution
We explore how metatags serve as a mechanism for the evolution of frames in the dis-
crete universe. We formalize the transition dynamics of metatags and frames, including
mechanisms such as quantum scarring and oscillatory stability [13].
3.1 Formalization of Metatags
Metatags Mi(t) encode the properties and states of subparticles. The evolution of a
metatag over time is governed by correction dynamics:
Mi(t+ ∆t) = Mi(t)−ϵ∆M,
where:
•∆Mrepresents deviations from the equilibrium state of the metatag.
•ϵis a correction coefficient that determines the rate at which the deviation is cor-
rected.
5
3.2 Integration of Metatags into Frames
The evolution of frames reflects changes in the aggregate state of metatags:
Fn+1 =Fn−ϵ∆F,
where:
∆F=X
i,j,k
∆Mi,j,k.
3.3 Oscillatory Stability and Quantum Scarring
Quantum scarring introduces a stabilizing mechanism that connects micro- and macro-
level dynamics:
∆M=−ϵSmemory,
where Smemory represents the memory effect driving the system toward equilibrium.
3.4 Linking Metatags to Macroscopic Processes
Changes in metatag energy eand momentum paggregate to form macroscopic density
gradients:
Fdensity =∇X
i,j,k
ei,j,k.
4 Mechanisms of Subparticle Interaction
We examine the fundamental mechanisms through which subparticles interact, including
interaction dynamics described by a connection function, quantum entanglement modeled
through metatag synchronization, and tunneling phenomena explained by metatag-based
transition probabilities [10, 17, 20].
4.1 Interaction via Connection Function
Subparticle interaction is described by:
Vi(t) = F(SPi, S Pj),
where Fis the interaction function.
4.2 Quantum Entanglement
Entanglement is modeled as synchronization of metatags:
Sk=Sm=⇒Mk=Mm.
The connection parameter is:
L(Ak, Am) = e−αd(Ak,Am),
where d(Ak, Am) is the spatial separation [12].
6
4.3 Quantum Tunneling
The probability of a subparticle transitioning through a barrier is:
P(x2, t) = Zx2
x1
e−B(x)dx,
where B(x) is the barrier potential.
5 Macroscopic Processes and the Big Bounce
We focus on the macroscopic processes that emerge from the interactions of subparticles
and their metatags, including the collapse of spacetime regions through density gradients,
the role of temporal crystals, and the cyclical nature of the universe [15, 21].
5.1 Collapse and Density Gradients
The density gradient responsible for collapse is:
Fcollapse =X
i,j
∇Mi,j .
5.2 Temporal Crystals as Structured Elements of Spacetime
Subparticles within a temporal crystal are described as:
SPi,j,k = crystal(t).
5.2.1 Explosion of Temporal Crystals
Energy release during phase transition is:
Erelease =Zt2
t1
crystal(t)dt.
5.3 The Big Bounce
The transition from collapse to expansion is characterized by:
Fexpansion =−Fcollapse,
suggesting a cyclical cosmological model without singularities [4, 5].
6 Experimental Validation and Simulations
We propose methods to validate the model through simulations, quantum experiments,
and cosmological data analysis.
6.1 Simulations of the Frame-Based Model
Use high-performance computing to simulate the evolution of metatags and frame tran-
sitions [9, 14].
7
6.2 Experiments on Entanglement and Tunneling
Conduct quantum optics experiments to test metatag synchronization and tunneling
probabilities.
6.3 Analysis of Cosmological Data
Analyze gravitational waves, redshift anomalies, and cosmic microwave background pat-
terns for signatures consistent with the model [6, 7, 19].
7 Conclusion
We have integrated and formalized concepts such as metatags, temporal crystals, and
quantum scarring within a discrete spacetime model. Our unified framework describes
micro- and macro-scale phenomena, in a way, justifying the separation of quantum me-
chanics and cosmology, while providing a unifying underlying foundational model in which
all justifications of the entire system can operate without violations, and simultaneously
explaining spooky effects.
Supplementary Materials
The following supplementary materials are provided to support the results and validations
discussed in this paper:
•EoS Validation Wr=0.5 Wt=0.7 R0=1 N=3.png: Available at: https://
drive.google.com/file/d/16lfRrs8YkDu6s7il_ebXjkGksKc3K4Kn/view?usp=sharing
This image displays the equation of state (EoS) validation results for the given pa-
rameters. It demonstrates that the energy conditions hold under these conditions.
•EoS Energy Density and Pressures.png: Available at: https://drive.google.
com/file/d/101UocenveXvvlSJDqgzW9_I3pdgSHYc1/view?usp=sharing This fig-
ure shows the radial distribution of energy density and pressures, confirming the
internal consistency of the model.
•Pressure Profiles and Anisotropy.png: Available at: https://drive.google.
com/file/d/1VQ7ryjb7MHEhuR5gpG3Ouojic2wb4AqZ/view?usp=sharing This im-
age illustrates the pressure profiles (radial and tangential) and the anisotropy factor,
highlighting how the pressures differ in radial and tangential directions.
•Energy Density Profile.png: Available at: https://drive.google.com/file/
d/1FRpn1pXqqDGh9DBLnvQU3XZ2AY3xVzdd/view?usp=sharing This figure shows how
the energy density changes with radius, ensuring it remains finite and well-behaved.
•Scalar Field and Potential.png: Available at: https://drive.google.com/
file/d/1QsPpe9Oe87p0LjSmRGcU24xQ7ztPtmGV/view?usp=sharing This plot com-
pares the scalar field ϕ(r) and its associated potential V(ϕ), confirming smoothness
and boundedness.
8
•Extended EoS Validation Results (Google Sheets): https://docs.google.
com/spreadsheets/d/17WTD1u1Ypovg7K8cVILr3XF6HIfVGQxcy7cUcKZqLvY/edit?
usp=sharing Contains extended numerical validation results for various parameter
sets.
•EoS Numerical Validation Results (Google Sheets): https://docs.google.
com/spreadsheets/d/1OZwJABKo24CmjjPU8Lafx83KeAxgI50bKSKxoDM1PY4/edit?
usp=sharing Provides the raw numerical data used to validate the energy condi-
tions. This dataset is associated with a published preprint.
•Formulas numerically (2).pdf: Available at: https://drive.google.com/file/
d/1b3FYbIm7alLYneIhgwukieSd3uhF05Zl/view?usp=sharing This PDF outlines
the validation process for the equations, showing smoothness and boundedness of
the scalar field and verifying energy conditions. Also available as a preprint: Vali-
dation of Equations for Finite-Density Black Hole Model, December 2024, DOI: 10.
13140/RG.2.2.23192.51201,https://www.researchgate.net/publication/386544679_
Validation_of_Equations_for_Finite-Density_Black_Hole_Model
Acknowledgments
We acknowledge contributions from researchers and existing literature that have informed
and supported this work. A special thanks to John Cumbers for his ever helpful hints,
ideas, and force of nature, Roman Yampolskiy for his encouragement, Raki Brown for
his confirmations and steady flow of informative articles, Andrew Lustig for influencing
the early years of Jesse Brown’s research, and Gary Goodman for his countless years of
Astronomy service and influence in Jesse Brown’s life.
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