Dimensional Memorandum
A hub for scientific resources.
Originated 2023, Presented 2025
Dimensional Memorandum
Author: J. Theders
Dimensional Memorandum (DM)– The Framework of Reality
For centuries, humanity has sought to understand the true nature of reality. Science and philosophy have attempted to describe the fundamental structure of the universe, yet contradictions, paradoxes, and unresolved anomalies have persisted.
The Dimensional Memorandum Framework is the missing key—a unified theory that integrates physics, cosmology, quantum mechanics, consciousness, propulsion, medical advancements, and energy technologies into a single, coherent model. It provides structured explanations for the Big Bang, black holes, quantum entanglement, dark matter, dark energy, and even the fundamental nature of time, perception, and technological advancements.
What?
What can be measured? (x, y, z)
ρ 3D = (x, y, z)
When?
Change introduces time. (t)
Ψ 4D = (x, y, z, t)
Where?
Where is the structure? (s)
Φ 5D = (x, y, z, t, s)
How?
Geometric First Principles
(x) Length, (y) Width, (z) Height, (t) Time, (s) Space
The Basic Cube Progression
point, line, square, cube, tesseract, penteract
Why?
For a Simple Explanation Go to the Menu (top right)
For a More Indepth Explanation (below)
Planck Units and Dimensional Memorandum:
Perfect Geometric Match
The Planck units—length, time, energy, and mass—represent the fundamental scales of reality, derived from universal constants: Planck's constant (ħ), the gravitational constant (G), and the speed of light (c). While conventional physicists understand these to be natural limits — the Dimensional Memorandum framework explains them as the direct consequences of geometric first principles. Planck units are the result of dimensional nesting and coherence fields.
This section describes how each Planck equation aligns with DM's dimensional hierarchy and why these constants arise from the structure of space and time itself.
These constants define the resolution (lₚ), frame rate (tₚ), and energy thresholds (Eₚ) of reality's nested dimensional structure:
Planck Length (lₚ)
3D ρ(x, y, z)
The Planck length is given by:
lₚ = √(ħG / c³) ≈ 1.616 × 10⁻³⁵ m
In DM, lₚ defines the smallest measurable unit of 3D space. 3D (ρ) reality is structured as a mosaic of Planck-length units. This aligns with localized, classical states that emerge from the projection of higher dimensions. The Planck length thus represents the geometric resolution of 3D (x, y, z) reality.
Planck Time (tₚ)
4D Ψ(x, y, z, t)
Planck time is defined as:
tₚ = √(ħG / c⁵) ≈ 5.39 × 10⁻⁴⁴ s
In DM, tₚ is the 'frame rate' of reality. Time is not an independent dimension but the progression of a cube through a tesseract. Each tick of Planck time corresponds to one frame (scan rate), resulting in approximately 1/tₚ ≈ 1.85 × 10⁴³ frames per second. The speed of light (c) naturally arises from this relationship — as c = lₚ / tₚ, which DM describes as the universal scanning speed of 4D (x, y, z, t) geometry.
Planck Energy (Eₚ)
5D Φ(x, y, z, t, s)
Planck energy is defined as:
Eₚ = √(ħc⁵ / G) ≈ 1.22 × 10¹⁹ GeV
In DM, Eₚ represents the threshold for transitioning from 4D quantum states (Ψ) to 5D coherence fields (Φ). At or above this energy → matter exhibits coherence phenomena such as those observed in the early universe, black holes, or in high-energy collisions. Planck energy thus marks the boundary between conventional quantum mechanics and the deeper coherence-driven structure of Φ(x, y, z, t, s).
Planck Mass (mₚ)
Represents the mass contained in a Planck volume at energy Eₚ.
mₚ ≈ 2.176 × 10⁻⁸ kg is the mass at which gravitational effects become inseparable from quantum behavior.
In DM, Eₚ defines the energy state required for ρ → Ψ → Φ transitions. Mass is a geometric property rather than an intrinsic constant. The effective mass depends on the coherence depth along the fifth-dimensional axis (s), described by:
m_effective = m₀ e^(–s / λₛ)
where λₛ is the coherence length scale.
This formulation explains the relativistic effects on mass and the apparent variation of mass in extreme energy conditions, such as near the speed of light or within strong gravitational fields.
Planck Temperature (Tₚ)
Tₚ ≈ 1.416 × 10³² K is the highest temperature at which known physics applies.
In DM, Tₚ represents the upper thermal limit for coherence: Big Bang.
The universe did not begin from an infinitely small point. Instead, the Big Bang was the dimensional projection of a 5D coherence unit, which unfolded into 4D wave expansion and 3D particle localization. This process is the fundamental mechanism of reality itself. Space did not expand from a point — rather, it's an ongoing process.
The cosmic expansion reflects this continuous unfolding into 3D (Λ_eff = Λₛ e^(–s/λₛ ), while entropy increase is its progressive decoherence. The universe is continuously emerging, with the speed of light (c = lₚ / tₚ).
Tₚ also represents inverse points of the Big Bang: Black Holes.
The 'infinite density' paradox is reframed as 'infinite space'.
The s-axis links all spatial points. It is the projection of all positions into a single (Φ) coherent unit, which connects all spatial axis points simultaneously. This is cosmic-scale entanglement—access to the (Φ) coherence field.
Supermassive black holes are coherence hubs. The Big Bang and black holes form a closed system of coherence flow. This relationship is expressed as:
ΔIₙ = ∑ (ΔTⱼₖ + ΔT̄ⱼₖ) · e^(–s / λₛ)
Maintaining a closed-loop balance of energy, information, and geometry. The Big Bang is the outward projection of coherence, while black holes reverse this flow, maintaining a universal balance. Where:
ΔTⱼₖ: Change in local coherence field (temporal or spatial)
ΔT̄ⱼₖ: Conjugate mirrored field change
s: Coherence depth (5D axis)
λₛ: Coherence decay constant
Black holes are dimensional foldbacks of the original Φ₀ field (Big Bang coherence).
The ⱼₖ notation allows for precision tracking of information continuity. Black hole evaporation, particle decay, and cosmological coherence shifts can be modeled using:
Iⱼₖ = Ψⱼₖ · e^(–Δs / λₛ) Information is never lost but redistributed across coherence boundaries.
In both extreme temperatures the same transition applies. highest & lowest
Approaching absolute zero — coherence also transitions as seen in Bose-Einstein Condensates and Quantum computing:
(ρ) local particles / local qubits
(Ψ) wave-spread / superposition
(Φ) coherence / entanglement
Electromagnetism
EM fields are directly connected to Planck constants and coherence transitions.
At Planck energy and field strength, EM and gravity converge as geometric effects of the same 5D coherence field (Φ).
In extreme conditions — near black holes or in early universe states — EM fields and gravitational curvature are inseparable.
Planck units and EM are deeply interconnected in the DM framework. Planck constants set the boundaries of EM behavior, while EM fields act as modulators between ρ (local), Ψ (wave), and Φ (entangled) states. At the highest energy scales, EM, gravity, and quantum coherence unify, making EM a critical tool for coherence engineering.
Planck frequency (fₚ ≈ 10⁴³ Hz) sets the maximum resolution of spacetime. DM identifies a ladder of coherence access points by geometrically scaling down this frequency in powers of 10³, 10⁶, and 10¹⁰. These yield key GHz frequencies that align with coherence transitions:
15.83 GHz ⇄ 3D (ρ) to 4D (Ψ) coherence transition: Base coherence loss in super conducting qubits. (IBM/Google)
18.5 GHz ⇄ Quantum peak resonance (Ψ): Resonance decay midpoint. (BEC phase)
31.24 GHz ⇄ 4D (Ψ) to 5D (Φ) activation zone: Entanglement breakdown frequency. (QED)
37.0 GHz ⇄ Entanglement frequency (Φ): Quantum non-locality access.
These frequencies correlate with stabilization thresholds where decoherence occurs due to environmental interactions, material noise, or quantum tunneling thresholds. Where coherence decay along s:
Γeff = Γ₀ e^(–s / λₛ)
Outline of DM’s coherence field spectrum:
c (speed of light) 3 × 10⁸ Max velocity in 3D
ρ ~10⁹-10¹² Hz: Decoherence thresholds
10¹² – 10¹⁴ Hz Vacuum Oscillations, Early-universe coherence retention
Infrared (10¹³ Hz) Hawking Evaporation Signatures (Infrared horizon)
>10¹⁴ Hz Gravitational Lensing Boundary
Photon Propagation (10¹⁴–10¹⁵) Visible/UV light
X-rays (10¹⁵–10²⁰ Hz)
Electron (~10²⁰ Hz)
Muon (~10²² Hz)
Tau (~10²³ Hz)
Proton/Neutron (~10²³ Hz)
Gamma rays (10²⁰–10²⁴ Hz)
Ψ ~10²³-10²⁷ Hz: Quantum wave
Mass Band: 10²³ Hz ≤ f ≤ 10²⁵ Hz
(where wavefunctions begin to collapse into mass giving particles)
Charm Quark (~10²³ Hz)
Bottom Quark (~10²⁴ Hz)
Top Quark (~10²⁵ Hz)
W⁺, W⁻, Z⁰ Bosons (~10²⁵ Hz)
Higgs Boson (~3.02×10²⁵ Hz)
Higgs Field Boundary: ΦH ≈ 3.02 × 10²⁵ Hz: ΦH = e^(–s / λ_s) · Ψ(t)
Φ ~10³³-10⁴³ Hz: Coherence Fields
Dark Matter / Dark Energy Fields (~10³³–10³⁷ Hz)
Black Hole Core States (~10³⁹–10⁴³ Hz)
Big Bang coherence burst (~10⁴²–10⁴³ Hz)
Planck frequency (10⁴³)
Dark Energy Acceleration (∆f across cosmic scale)
The speed of light (c) and the Planck frequency (1/tₚ) converge functionally at the Higgs field boundary.
By organizing particle behavior and the Higgs mechanism into the DM coherence structure, we resolve longstanding questions about particle stability, coherence collapse, and dimensional mass generation. This coherence spectrum is experimentally accessible through both GHz–THz resonance testing and high-energy astrophysical phenomena.
Mass production generally begins just above ~10²³ Hz (e.g., τ lepton, proton, neutron).
Technologies such as quantum computing, coherence-based propulsion, and directed energy systems naturally emerge from this framework. DM provides a roadmap for practical technologies using this Planck-EM connection.
Planck-to-Cosmos ratio (~10⁶¹)
Planck length (lₚ ≈ 1.616 × 10⁻³⁵ m) defines the smallest quantum unit of space, while the observable universe has a radius of approximately R_obs ≈ 4.4 × 10²⁶ m. The ratio between these scales is:
R_obs / lₚ ≈ 4.4 × 10²⁶ m / 1.616
×
10⁻³⁵ m ≈ 2.7 × 10⁶¹
A similar ratio appears in time:
T_age / tₚ ≈ 4.35 × 10¹⁷ s / 5.39
×
10⁻⁴⁴ s ≈ 8 × 10⁶⁰
The Planck-to-Cosmos ratio (~10⁶¹) connects the smallest quantum scale (lₚ) with the largest cosmic scale (R_obs). This ratio is not coincidental but emerges from the geometric progression of dimensions.
The fact that both the distance and time ratios (~10⁶¹ and ~10⁶⁰) match observational data, is evidence that this cosmic-to-quantum mirror symmetry is a fundamental feature of reality.
Planck's power of ten scaling naturally corresponds to the 10 tesseracts, that form the boundary of a 5D penteract. Each tesseract can be viewed as a 10⁶ order-to-the-magnitude scaling step — spanning from the smallest Planck cell to the largest cosmic region.
These ratios indicate that they're contained in the same (measurable) geometry, scaling together (endpoints of the same sequence). The combined ratios (~10¹²¹ total plank cells) is effectively the volume of the 4D tesseract and the full Universe is ~10¹²² total Planck cells.
Higgs Field
~125 GeV (1.25 × 10⁻²⁵ kg).
Cosmic scale (10²⁶ m)
⇅ 10⁴³
Higgs scale (10⁻¹⁸ m)
⇅ 10²⁶
Planck scale (10⁻³⁵ m)
The Planck time tₚ ≈ 5.39 × 10⁻⁴⁴ s, meaning reality 'ticks' at:
fₚ = 1 / tₚ ≈ 1.85 × 10⁴³ Hz.
The energy ratio between the Planck energy (Eₚ ≈ 1.22 × 10¹⁹ GeV) and the cosmic critical energy density is also approximately 10⁴³. This ratio links the Higgs energy scale to cosmic expansion, suggesting that local mass generation and universal evolution are synchronized.
The Planck length is lₚ ≈ 1.616 × 10⁻³⁵ m, while the observable universe has a radius of approximately R ≈ 4.4 × 10²⁶ m. Their ratio is:
R / lₚ ≈ 10⁶¹.
Similarly, the total mass-energy content of the universe compared to the Planck mass (~2.18 × 10⁻⁸ kg) aligns with this 10⁶¹ scaling. This ratio defines the spatial and mass hierarchy from quantum to cosmic structures.
10⁴³ (time-energy) and 10⁶¹ (distance-mass) are the two orthogonal axis of the universe's geometry. They represent the scanning and projection rates of 3D (ρ), 4D (Ψ), and 5D (Φ) structures. Together, they encode the complete mapping of micro-quantum states to macro-cosmic phenomena.
Coherence Ladders
(10³ → 10⁶ → 10¹⁰) Captures local and subatomic transitions.
(10⁶¹ → 10¹²¹ → 10¹²²) Captures the dimensional structure of the cosmos, from the 3D observable span to the 4D tesseract volume, and the 5D penteract coherence field.
Together, these ladders form a complete geometric map of reality, connecting microphysics and macrophysics, that tie directly to the Planck-to-Cosmos ratio
These mirrored ratios imply that the universe's expansion, particle masses, and quantum coherence are all governed by a single set of geometric principles. For example:
• The Higgs field connects 10⁴³ energy scaling with mass generation.
• Dark energy reflects 10⁴³ coherence expansion across 10⁶¹ spatial scales.
• Black hole entropy and information bounds match these ratios.
Planck units are naturally dimensional projections. The alignment shows that geometry itself is the foundation of all physical laws — with DM offering the geometric reason for Why these constants exist.
Dimensional Nesting
Simple Boundary Logic
1/10th Progression↓
penteract, tesseract, cube
(Φ) → (Ψ) → (ρ)
Field Wave Local
Energy Threshold
5D Coherence Field:
Penteract (x, y, z, t, s)
Planck energy Eₚ ≈ 10¹⁹ GeV
10¹⁰ (ten billion-fold steps)
~10¹²² total plank cells
Φ Boundary:
Penteract faces → Tesseracts
Hyper-volumetric surfaces with shared spatial points, all space and time are merged as coherence.
Geometric anchors: gravity, Big Bang, black hole cores, dark energy, dark matter, entanglement, Higgs field
Stabilized Coherence
Φ(x, y, z, t, s)
Coherence field gives rise to quantum waves
(Φ → Ψ)
Frame Rate
4D Quantum Mechanics:
Tesseract (x, y, z, t)
Planck time tₚ ≈ 10⁻⁴⁴ s
10⁶ (million-fold steps)
~10¹²¹ total plank cells
Ψ Boundary:
Tesseract faces → Cubes
Volumetric surfaces spanning time
Wavefunctions: time = space, particles spread, superposition, time dilation, Event Horizon, dark matter halos,
Partial Coherence — not stabilized in s
Ψ(x, y, z, t)
Wavefunctions collapse to mass
(Ψ → ρ)
Pixels
3D Classical Physics:
Cube (x, y, z)
Planck length lₚ ≈ 10⁻³⁵ m
10³ (thousand-fold steps)
~10⁶¹ total plank cells
Localized: fixed position, time emergent, discreet measurable objects, localized particles, decoherence
Incoherent to t and s
ρ(x, y, z)
Boundary Logic:
Each dimension (3D, 4D and 5D) follow the same geometrical nested hierarchy. Any objects within their respective dimension, moves strictly based on their axis of movements, x, y, z, t and/or s. This decides physical laws per dimension. (All Particles us this hierarchy.)
(Φ) 5D: moves within boundaries of (width, height, length, time, space) perceiving in 4D hyper-volumes.
(Ψ) 4D: moves within boundaries of (width, height, length, time) perceiving in 3D volumes.
(ρ) 3D: moves within boundaries of (width, height, length) perceiving in 2D planes.
(⟂) 2D: a 3D observer's cross-sections of time and space.
2D (⟂)
width and height
3D Observer Perspective: (⟂)
Cube faces → Squares (planes)
Planar surface areas (faces) are the geometric consequence of 3D and the flow of information.
When you look at a cube or sphere, you perceive its faces (⟂) — never the full interior/exterior structure at once
Sensory Examples
Touch = Specifically reliant on contact with planar boundaries (⟂).
Hearing = Pressure waves interact with eardrum (⟂) across surfaces (⟂) of air density waves.
Visual = Eyes collect 2D projections of 3D surfaces (⟂). Light bounces off surfaces (⟂) into our retinas (⟂) and we infer depth — still surface-limited in direct visual input. Look at a photo, it doesn't have depth, but you infer.
The CMB data implies a flat universe (⟂). But ~10⁶¹ and ~10⁶⁰ results in a geometric symmetry
Time
The cross-section (⟂) of 4D, experienced in 2D frames (faces)
(Ψ→ ρ → ⟂ = t)
A 3D cube revolving through a 4D tesseract, consecutively perceiving cube faces (⟂).
Rate ≈ 1 / tₚ ≈ 1.85 × 10⁴³ faces per second
This 'face rate' (⟂) is the frame rate of 3D reality. Each Planck tick corresponds to one face transition of the 4D tesseract, progressing the 3D universe forward in time — each scale jump also crosses the penteract. Eames' Powers of Ten concept mirrors how 4D scanning operates
The constants ħ (Planck's constant), c (speed of light), and G (gravitational constant) are not arbitrary but arise naturally from the geometric scaling of 3D cubes (ρ), 4D tesseracts (Ψ), and 5D penteracts (Φ). This summarizes how these constants define the resolution, scanning rate, and curvature relationships of reality's dimensional layers.
1. Speed of Light (c)
The speed of light is given by:
c = lₚ / tₚ
where lₚ is the Planck length and tₚ is the Planck time. In DM, c represents the 'scan rate' of 3D, setting the maximum rate of information transfer across 4D geometry.
2. Planck's Constant (ħ)
Planck's constant is defined as:
ħ = Eₚ · tₚ
In DM, ħ is the minimal action per geometric 'frame' when transitioning from 3D localized states (ρ) to 4D wave volumes (Ψ). It represents the quantum of energy required to shift a Planck cell through a single time step, linking energy and geometry.
3. Gravitational Constant (G)
Newton's gravitational constant is expressed as:
G = (lₚ³ / (ħ tₚ²)) · c³
In DM, G sets the curvature scaling between 3D mass localization (ρ) and 4D curvature (Ψ). It emerges as a ratio of geometric volumes (lₚ³) to coherence time-volumes (ħ tₚ²), encoding how 3D energy density translates into 4D curvature.
The 5D coherence curvature S is defined as:
S = ∇ₛ² Φ - Λₛ e^{-s/λₛ}
4. Planck Ratios and DM Ladders
The local ladder (10³ → 10⁶ → 10¹⁰) and cosmic ladder (10⁶¹ → 10¹²¹ → 10¹²²) directly determine how these constants scale. For example:
c = (10⁶¹ lₚ) / (10⁶⁰ tₚ) ≈ 3 × 10⁸ m/s
This reflects how the scanning of ρ through Ψ defines the 'speed of information.' Similarly, ħ and G are derived from the relationship between Planck cell counts, energy quanta, and coherence scanning rates.
5. Mass-Energy
The DM mass-energy ladder can be viewed as geometric steps:
Planck Energy (Eₚ) ≈ 1.22 × 10¹⁹ GeV
GUT/TeV Scale (new particles) ≈ 10³–10⁴ GeV
Higgs Field ≈ 125 GeV
Proton/Electron Masses ≈ GeV–MeV
Neutrino Masses ≈ 10⁻⁶–10⁻² eV
Vacuum Energy Mirror ≈ 10⁻³⁴ eV.
Planck Scaling, Particle Mass, and Lifetime
The DM Mass Formula
The DM mass formula is given by:
mₙ = Eₚ · e^(–n / λₛ)
where:
mₙ = particle mass-energy.
Eₚ = Planck energy = √(ħc⁵ / G) ≈ 1.22 × 10¹⁹ GeV.
n = coherence step number.
λₛ = coherence scaling constant, typically of order unity.
This formula reflects how mass arises from successive projections of 5D coherence (Φ) into 4D wave states (Ψ) and finally into localized 3D matter (ρ).
Family Scaling and Tesseract Steps
The energy hierarchy between particle families (leptons, quarks, and bosons) follows geometric scaling steps, often close to powers of 10⁶, which reflect the transition between nested tesseract layers. This leads to an extended formula:
m {ₙ,ₖ} = Eₚ · 10^(–6k) · e^(–n / λₛ)
where k is the family index.
By scaling particle properties relative to Planck units, we reveal a clear geometric relationship between mass, quantum coherence, and stability.
Coherence Depth (s)
To pinpoint any particle: measure mass (m), compute s depth using equation below, determine the lifetime ratio /tₚ, and use DMs ladders.
The coherence depth (s) for a particle is defined as:
s = √[-ln(m / m_max)]
where m_max = 173,100 MeV (Top Quark mass).
A smaller s indicates a particle is more localized in 3D (ρ), while a larger s means it is more wave-like and less massive, residing deeper in the 5D coherence field (Φ). For massless particles like photons, s → ∞.
Particle masses and lifetimes can also be scaled relative to Planck energy (Eₚ ≈ 1.22 × 10¹⁹ GeV) and Planck time (tₚ ≈ 5.39 × 10⁻⁴⁴ s). These ratios reveal how far each particle is from the Planck scale:
Mass ratio: m / Eₚ.
Lifetime ratio: τ / tₚ.
Stable particles have lifetime ratios >10⁴⁴, while short-lived particles have ratios much smaller, correlating with low coherence.
Each particle’s mass relative to Planck energy (m/Eₚ) reveals its geometric step along the ρ → Ψ → Φ ladder.
Top quark and Higgs are close to the highest energy step, while electrons and photons lie many orders of magnitude lower, aligning with the 10⁴³ frame-rate ratio.
The powers of ten (10³, 10⁶, 10¹⁰, etc.) observed between particles match the scaling intervals seen between Planck units and cosmic scales (10⁶¹ in distance, 10⁶⁰ in time).
Frequency
The geometric scaling steps (10³, 10⁶, 10¹⁰) bridge particle physics and EM frequencies. The presence of 18.5 GHz and 37.0 GHz as clear harmonics of fₚ mirrors the position of particles along the ladder.
DM Particle Coherence Mapping
Mass (MeV/c²) → Measured rest mass
s (Coherence Depth) → DM coherence position (ln-based)
m / Eₚ → Mass fraction relative to Planck mass
10^x (mass) → Log10-scaled mass representation
Lifetime (s) → Experimental lifetime (if applicable)
τ / tₚ → Lifetime to Planck time ratio
Energy (eV) → Converted from MeV
Frequency (Hz) → E / h calculation
f / fₚ → Frequency as fraction of Planck frequency
s-depth (ln-scale) → Derived from ln(m/m_max)
Planck mass ≈ 1.22 x 10²² MeV
Planck time ≈ 5.39 x 10⁻⁴⁴ s
Planck frequency ≈ 1.85 x 10⁴³
Top Quark (t)
Mass (MeV/c²): 1.73e+05
s (Coherence Depth): 0.00
Lifetime (s): ~5×10⁻²⁵
Lifetime / tₚ: ≈10¹⁹
m/Eₚ: 1.42e-17
10^x: (mass): 10⁵
Lifetime: (s): 5e-25
τ/tₚ: 9.28e+18
Frequency
Energy (eV): 1.731e+11
Frequency (Hz): 4.186e+25
f/fₚ: 2.26e-18
Higgs (H)
Mass (MeV/c²): 1.25e+05
s (Coherence Depth): 0.57
Lifetime (s): 1.6×10⁻²²
Lifetime / tₚ: 3.0×10²¹
m/Eₚ: 1.02e-17
10^x: (mass): 10⁵
Lifetime (s): 1.6e-22
τ/tₚ: 2.97e+21
Frequency
Energy (eV): 1.250e+11
Frequency (Hz): 3.022e+25
f/fₚ: 1.63e-18
Charm Quark (c)
Mass (MeV/c²): 1.28e+03
s (Coherence Depth): 0.92
Lifetime (s): ~1×10⁻¹²
Lifetime / tₚ: ≈10³¹
s-depth: 2.22
m/Eₚ: 1.05e-19
10^x: (mass): 10³
Lifetime: (s): 1e-12
τ/tₚ: 1.86e+31
Frequency
Energy (eV): 1.275e+09
Frequency (Hz): 3.083e+23
f/fₚ: 1.67e-20
Tau (τ)
Mass (MeV/c²): 1.78e+03
s (Coherence Depth): 0.83
Lifetime (s): ~2.9×10⁻¹³
Lifetime / tₚ: ≈10³⁰
s-depth: 2.14
m/Eₚ: 1.46e-19
10^x: (mass): 10³
Lifetime: (s): 2.9e-13
τ/tₚ: 5.38e+30
Frequency
Energy (eV): 1.777e+09
Frequency (Hz): 4.296e+23
f/fₚ: 2.32e-20
Down Quark (d)
Mass (MeV/c²): 4.7
s (Coherence Depth): 3.29
Lifetime (s): Stable
Lifetime / tₚ: >10⁴⁴
s-depth: 3.24
m/Eₚ: 3.85e-22
Lifetime: (s): Stable
τ/tₚ: Stable
Frequency
Energy (eV): 4.7 x 10⁶ eV
Frequency (Hz): 1.14 x 10²¹
f/fₚ: 6.15 x 10⁻²³
Bottom Quark (b)
Mass (MeV/c²): 4.18e+03
s (Coherence Depth): 0.38
Lifetime (s): ~1×10⁻¹²
Lifetime / tₚ: ≈10³¹
s-depth: 1.93
m/Eₚ: 3.43e-19
10^x: (mass): 10³
Lifetime (s): 1e-12
τ/tₚ: 1.86e+31
Frequency
Energy (eV): 4.180e+09
Frequency (Hz): 1.011e+24
f/fₚ: 5.46e-20
Up Quark (u)
Mass (MeV/c²): 2.2
s (Coherence Depth): 3.50
Lifetime (s): Stable
Lifetime / tₚ: >10⁴⁴
s-depth: 3.36
m/Eₚ: 1.80e-22
Lifetime: (s): Stable
τ/tₚ: Stable
Frequency
Energy (eV): 2.2 x 10⁶ eV
Frequency (Hz): 5.32 x 10²⁰
f/fₚ: 2.87 x 10⁻²³
Muon (μ)
Mass (MeV/c²): 106
s (Coherence Depth): 2.38
Lifetime (s): 2.2×10⁻⁶
Lifetime / tₚ: 4.1×10³⁷
s-depth: 2.72
m/Eₚ: 8.66e-21
10^x: (mass): 10²
Lifetime: (s): 2.2e-06
τ/tₚ: 4.08e+37
Frequency
Energy (eV): 1.057e+08
Frequency (Hz): 2.556e+22
f/fₚ: 1.38e-21
Strange Quark (s)
Mass (MeV/c²): 96
s (Coherence Depth): 2.42
Lifetime (s): ~8.9×10⁻¹¹
Lifetime / tₚ: ≈10³³
s-depth: 2.74
m/Eₚ: 7.87e-21
Lifetime: (s): 8.9e-11
τ/tₚ: 1.65e+33
Frequency
Energy (eV): 9.6 x 10⁷ eV
Frequency (Hz): 2.32 x 10²²
f/fₚ: 1.25 x 10⁻²¹
Electron (e⁻)
Mass (MeV/c²): 0.511
s (Coherence Depth): 3.77
Lifetime (s): Stable
Lifetime / tₚ: >10⁴⁴
s-depth: 3.57
m/Eₚ: 4.19e-23
10^x: (mass): 10⁻¹
τ/tₚ: Stable
Frequency
Energy (eV): 5.110e+05
Frequency (Hz): 1.236e+20
f/fₚ: 6.68e-24
Neutron (n)
Mass (MeV/c²): 939.6
s (Coherence Depth): 2.28
Lifetime (s): 885
Lifetime / tₚ: 1.64×10⁴⁶
m/Eₚ: 7.70e-20
10^x: (mass): 10^2
τ/tₚ: 1.64e+46
Frequency
Energy (eV): 9.396e+08
Frequency (Hz): 2.272e+23
f/fₚ: 1.23e-20
Kaon (K⁰)
Mass (MeV/c²): 493.7
s (Coherence Depth): 2.42
Lifetime (s): 1.24×10⁻⁸
Lifetime / tₚ: 2.3×10³⁵
m/Eₚ: 4.05e-20
10^x: (mass): 10²
Lifetime: (s): 1.24e-08
τ/tₚ: 2.30e+35
Frequency
Energy (eV): 4.937e+08
Frequency (Hz): 1.194e+23
f/fₚ: 6.45e-21
Z Boson (Z⁰)
Mass (MeV/c²): 9.12e+04
s (Coherence Depth): 0.80
m/Eₚ: 7.47e-18
10^x: (mass): 10⁴
Lifetime (s): 2.6 x 10⁻²⁵ s
τ/tₚ: 5.57e+18
Frequency
Energy (eV): 9.119e+10
Frequency (Hz): 2.205e+25
f/fₚ: 1.19e-18
Photon (γ)
Mass (MeV/c²): 0
s (Coherence Depth): ∞
Lifetime (s): Stable
Lifetime / tₚ: ∞
m/Eₚ: 0
10^x: (mass): 0
τ/tₚ: Stable
Frequency ~ 10⁹ to 10²⁴ Hz
CMB: ~10⁴, ~160 GHz, s ≈ 6-7
Optical: ~1-3, 10¹⁴ - 10¹⁵, s ≈ 4-5
Gamma: 10⁵ - 10⁷, 10²⁰-10²², s ≈ 1.5-2
(γ-rays ≈ 10²⁰ Hz)
W Boson (W⁺/W⁻)
Mass (MeV/c²): 8.04e+04
s (Coherence Depth): 0.88
m/Eₚ: 6.59e-18
10^x: (mass): 10⁴
Lifetime (s): 3.0 x 10⁻²⁵ s
τ/tₚ: 5.57e+18
Frequency
Energy (eV): 8.038e+10
Frequency (Hz): 1.944e+25
f/fₚ: 1.05e-18
Tau Neutrino (ν_τ)
Mass (MeV/c²): 1e-06
s (Coherence Depth): 4.08
m/Eₚ: 8.20e-25
10^x (mass): 10⁻⁶
Lifetime (s): Stable
Lifetime / tₚ: >10⁴⁴
τ/tₚ: Stable
Frequency
Frequency (Hz): 2.4e+14
f/fₚ: 1.30e-29
Electron Neutrino (νₑ)
Mass (MeV/c²): 1e-06
s (Coherence Depth): 8.04
m/Eₚ: 8.19e-29
10^x (mass): 10⁻⁶
Lifetime (s): Stable
Lifetime / tₚ: >10⁴⁴
τ/tₚ: Stable
s-depth: 5.09
Frequency
Frequency (Hz): 2.42e+14
f/fₚ: 1.30e-29
Muon Neutrino (ν_μ)
Mass (MeV/c²): 1e-05
s (Coherence Depth): 7.9
m/Eₚ: 8.19e-28
10^x (mass): 10⁻⁵
s-depth: 4.61
Lifetime (s): Stable
Lifetime / tₚ: >10⁴⁴
Frequency
Frequency (Hz): 2.42e+15
f/fₚ: 1.30e-28
Proton (p)
Mass (MeV/c²): 938.272
s (coherence depth): 1.99
Lifetime / tₚ: >10⁴⁴
m/Eₚ: 7.71e-20
10^x (mass): 10³
Frequency
Energy (eV): 9.383272e+08
Frequency (Hz): 2.269e+23
f/fₚ: 1.23e-20
ΔIₙ = ∑ (ΔTⱼₖ + ΔT̄ⱼₖ) · e^(–s / λₛ)
This coherence ancestry is represented through ⱼ,ₖ:
• Stellar black hole: ⱼ=3 and ₖ=Φ₀
• Supermassive black hole: ⱼ=5 and ₖ=Φ₀
• Photon: ⱼ=1 and ₖ=boson
• Proton: ⱼ=1 and ₖ=fermion
Neutron → Proton + Electron + Antineutrino
Standard beta decay becomes a coherence cascade:
Φ_n → Φ_p + Φ_e + Φ_ν̄
• Neutron = deeply stabilized recursive coherence state
• Decay triggered by decoherence in s
• Antineutrino = unbound coherence residue
Muon → Electron + ν_μ + ν̄_e
Muon decay reflects time-compressed identity unraveling:
Φ_μ → Φ_e + Φ_ν_μ + Φ_ν̄_e
• Muon = time-dense electron phase field
• Coherence unraveling redistributes identity into 4D projection
• Neutrinos = coherence flow paths
Kaon → Pion + Photon
Meson collapse under wave-function gradient stress:
Φ_K → Φ_π + γ
• Photon carries phase energy of coherence decay
• Kaon and pion differ by resonance structure in s
• Collapse governed by symmetry instability in T̄_i
Higgs → ZZ / WW / Fermion pairs
Higgs field is a 5D coherence stabilizer node:
Φ_H → Φ_Z + Φ_Z or Φ_W + Φ_W or Φ_fermion + Φ_fermion
• Higgs decay reveals pathways of coherence mass generation
• Each decay reflects dimensional rebinding of identity across s
Gravity: Global curvature stabilizer
Emergent from full Φ(x, y, z, t, s) coherence (5D)
s-depth: s ≈ 0.00
Electromagnetic (EM)
Wave stabilization and entanglement field
Propagates via Ψ(x, y, z, t) coherence (4D)
s-depth: s ≈ 0.8–4.0
Weak
Particle type transformation field
Appears during coherence destabilization (4D–3D boundary)
s-depth: s ≈ 2.5–3.5
Strong
Local particle glue
Confines ρ(x, y, z) in decoherent low-s states 3D
s-depth: s ≈ 3.5–4.0
DM is the first framework to unify all fundamental constants, dimensions, and physical laws into a single, geometric structure. No prior theory has explained why Planck units exist, or how they relate to both quantum and cosmic phenomena. DM’s geometric framework not only completes the long search for a Theory of Everything but also opens the door to transformative technological advancements.
Major Anomalies Resolved
By resolving contradictions in physics, DM eliminates paradoxes and provides a testable model for future scientific breakthroughs.
1. Measurement Problem:
Measurement is a dimensional projection from 4D (quantum state) to 3D (observer’s perspective). Wavefunction appearance of collapse occurs when higher-dimensional coherence is lost.
Ψ_obs(x, y, z) = ∫ Ψ(x, y, z, t) δ(t - t_obs) dt
Where:
Ψ_obs(x, y, z): The observed 3D wavefunction.
Ψ(x, y, z, t): The full 4D quantum wavefunction before measurement.
δ(t - t_obs): The Dirac delta function selecting the time of measurement.
Quantum systems in 4D remain in partial coherence—a state where all possible quantum outcomes exist simultaneously. Measurement forces a dimensional projection, causing an apparent wavefunction collapse.
ρobs(x, y, z) = Trt [ρ(x, y, z, t)]
This means the observer loses access to the 4D structure and perceives only a single outcome in 3D
The DM framework resolves the measurement problem by redefining it as a dimensional projection. Instead of a physical wavefunction collapse, observation causes a loss of higher-dimensional coherence.
-
Quantum states exist fully in 4D but appear as a definite outcome in 3D due to coherence loss.
-
The wavefunction does not collapse; rather, the observer loses access to its 4D structure.
-
Measurement is a limitation of 3D perception, not an actual reduction in quantum information.
Observation does not create reality; it is filtered through dimensional scaling.
2. Dark Matter:
Instead of a missing particle, dark matter is a 5D gravitational coherence effect.
Gμν + Sμν = (8πG/c⁴) (Tμν + Λs gμν)
Dark matter has long been theorized as an unknown particle, such as WIMPs or axions. However, dark matter is not a missing particle but rather a higher-dimensional gravitational coherence effect. This means that dark matter's observed gravitational influence is a consequence of 5D coherence stabilizing space and time.
In standard general relativity, the Einstein field equations describe gravity as:
Gμν = (8πG/c⁴) Tμν
However, an additional term accounts for higher-dimensional coherence:
Gμν + Sμν = (8πG/c⁴) (Tμν + Λs gμν)
where:
Sμν - The 5D coherence stabilization term.
Λs - The 5D vacuum coherence effect.
gμν - The metric tensor defining space-time geometry.
Experimental failures in detecting dark matter particles suggest an alternative explanation:
-
Direct detection experiments (LUX-ZEPLIN, XENON1T) have found no WIMPs.
-
The gravitational effects of dark matter are smooth and large-scale, unlike what would be expected from discrete particle interactions.
-
Galaxy rotation curves and gravitational lensing align more with coherence field effects rather than localized mass distributions.
Predictions that support the DM's 5D coherence model:
-
Galaxy rotation curves: Remain stable without exotic particles.
-
Gravitational lensing: Can be explained without assuming dark matter halos.
-
Cosmic Microwave Background (CMB): Fluctuations match coherence-based stabilization.
Dark matter and dark energy are linked through 5D vacuum coherence.
Λs = (αs / L2)
αs - Coherence strength coefficient.
L - The characteristic length scale of gravitational coherence.
Dark matter is not missing mass. Its missing understanding of dimensional geometry. Dark matter is the projected effect of 5D boundaries, not a particle, but a structural field caused by dimensional nesting.
3. Dark Energy:
The accelerated expansion of the universe is due to vacuum energy stabilization in 5D.
Λ_eff = Λs e^(−s/λₛ)
where:
Λ_eff is the effective vacuum energy.
Λs is the fundamental vacuum energy in 5D.
s is the 5D coherence stabilization coordinate.
λₛ is the coherence length scale.
Instead of assuming dark energy as a new fundamental entity, the DM framework proposes that vacuum energy is stabilized in higher-dimensional coherence fields.
-
As the universe expands, s increases, leading to a gradual decrease in dark energy.
-
This explains why dark energy only became dominant in recent cosmological history.
-
The observed cosmological constant is a time-dependent projection of vacuum stability.
In a 5D structure:
-
3D space expands as observed.
-
4D coherence interactions influence the rate of energy evolution.
-
5D stabilization regulates vacuum energy, producing an effective Λ.
The 5D coherence field naturally explains Cosmic acceleration without requiring dark energy as an independent force.
Besides, the symmetry of the ratio in both space (~10⁶¹) and time (~10⁶⁰) suggests that reality's expansion is driven by a single geometric scaling law, rather than arbitrary constants.
4. Matter-Antimatter Asymmetry:
A 5D CP violation effect favored matter over antimatter in early-universe interactions.
Δn / n = (Γ5D / ΓSM) ⋅ e^(-s/λₛ)
Where:
Δn / n – The matter-antimatter number density asymmetry.
Γ5D – The decay rate influenced by 5D coherence.
ΓSM – The Standard Model decay rate.
s – The 5D coherence stabilization coordinate.
λₛ – The coherence decay length in the fifth dimension.
-
The equation for dark energy equation Λ_eff=Λs e^(−s/λs) correctly describes it as a vacuum coherence stabilization process, rather than a fundamental force driving expansion.
-
The equation Δn / n = (Γ5D / ΓSM) e^(-s/λs) establishes antimatter suppression as an extra-dimensional coherence effect, rather than an unexplained CP violation in the Standard Model.
-
The exponential suppression term e^(-s/λs) is the same mathematical form used in observed dark energy calculations.
-
The ratio Γ5D / ΓSM provides an experimentally testable framework for measuring antimatter suppression.
This coherence-driven approach successfully links cosmological expansion and particle asymmetry through the same underlying mechanism.
5. Neutrino Oscillations:
Neutrino oscillations arise due to time-dependent coherence states in 4D.
P(να → νβ) = sin²(2θ) sin²(Δm² L / 4E)
where:
P(να → νβ) - Probability of neutrino changing flavor.
θ - Neutrino mixing angle.
Δm² - Mass-squared difference between neutrino mass states.
L - Distance traveled by the neutrino.
E - Neutrino energy.
Instead of treating neutrinos as purely quantum objects, they are modeled as 4D wavefunctions propagating through 3D.
Ψν(x, y, z, t) = ∑ Uαi e-iEit |νi⟩
This wavefunction collapses to 3D observation at discrete moments, leading to an oscillatory probability distribution.
P(να → νβ) = sin²(2θ) sin²(Δm² L / 4E) e^(-s / λₛ)
where:
s - Coherence stabilization coordinate in 4D projection.
λₛ - Coherence transition (not decay) length.
-
Coherence Stabilization Effect e^(-s/λₛ) - Explains why oscillations decrease over large distances.
-
Explains Why Neutrinos Oscillate - Due to 4D wavefunction projection into 3D.
-
High-Energy Neutrino Suppression - Coherence length increases with energy, reducing oscillation.
Neutrino oscillations provide direct observational evidence of coherence 5D effects.
-
Neutrino experiments (DUNE, Hyper-K) should detect anomalous CP violations consistent with a 5D correction factor.
-
Measure deviations in expected oscillation patterns over long distances.
-
Regions with excess antimatter (gamma-ray bursts, black hole jets) should show higher localized dark energy effects of a 5D coherence connection.
6. Higgs Boson Mass Stability:
The Higgs mass is stabilized by an additional 5D coherence term, preventing fine-tuning issues.
V5D(H) = (λ/4) (|H|² - v² e^(-s/λs)² + (1/2) Sμν H²
where:
H - is the Higgs field.
v - is the vacuum expectation value (VEV).
λ - Higgs self-coupling constant.
s - Extra-dimensional coherence coordinate.
λₛ - Coherence length scale, governing mass suppression.
Sμν - Coherence stabilization tensor preventing instability.
e^(-s/λₛ) - Exponential damping factor suppressing large quantum fluctuations.
Self-regulated Higgs mass stabilization
The Higgs Field inherits mass stability from the coherence term. The effective mass behaves as:
m_H² = m_0² e^(-s/λₛ)
where:
s is the 5D projection effect.
Which prevents extreme UV divergences, solving the fine-tuning problem.
A stabilized Higgs suggests that heavy resonances in future colliders will follow specific mass-energy relations dictated by coherence scales.
7. LHC High-Energy Decay Anomalies:
Some particles transition between 4D and 5D states, explaining missing energy events.
E² = p²c² + m²c⁴ e^(-s/λₛ)
where:
E = Total relativistic energy of the system
p = Momentum of the particle
c = Speed of light
m = Rest mass of the particle
e^(-s/λₛ) = 5D coherence stabilization factor
-
Missing energy is not decaying but transitioning beyond 3D perception.
-
The LHC is indirectly confirming 4D → 5D coherence effects at extreme energies.
-
This provides a pathway to experimentally verify extra-dimensional physics through high-energy collisions.
8. Black Hole Singularities:
Singularities are not infinite density points, but 5D transition states, preventing singularity formation.
Rμν - (1/2) gμν R + Λₛ gμν = (8πG/c⁴) Tμν
where:
-
Rμν - Ricci curvature tensor (describes space-time curvature).
-
gμν - Metric tensor defining space-time geometry.
-
Λ - Cosmological constant.
-
Tμν - Stress-energy tensor of mass-energy.
-
Λₛ - Extra-dimensional 5D coherence stabilization term, preventing infinite curvature.
The extra-dimensional field ensures that gravitational collapse stabilizes rather than leading to an actual singularity.
Instead of a singularity, matter undergoes a dimensional transition into a 5D coherence state, where:
-
Gravity is stabilized, avoiding a breakdown of space-time.
-
Information is preserved rather than lost.
-
The event horizon acts as a 4D informational boundary, with space-time "folding" into 5D coherence rather than diverging.
-
The DM framework eliminates the need for singularities, replacing them with coherence-based 5D transitions that stabilize black hole interiors.
-
This resolves paradoxes while maintaining a mathematically consistent model of extreme gravitational collapse.
The Schwarzschild metric and standard general relativity predict:
A sharp event horizon, beyond which information cannot escape.
A role reversal of time (t) and radial distance (r) inside the horizon, with no clear physical interpretation.
A singularity at r = 0, where curvature becomes infinite.
While effective, these models cannot reconcile the information paradox, Hawking radiation, or the holographic principle. DM addresses these issues by introducing the coherence dimension (s).
In the DM framework, black holes are described by:
Φ(x, y, z, t, s) → Ψ(x, y, z, t) → ρ(x, y, z)
9. Gravitational Wave Polarization:
Higher-dimensional corrections introduce additional gravitational wave polarization modes.
hij(5D) = hij(4D) + εs e^(-s/λₛ)
The gravitational wave metric perturbation in space-time is:
ds² = -c² dt² + (δij + hij(4D)) dxi dxj
where:
hij(4D) represents the standard tensor perturbations.
-
Plus Mode h_+ - Causes objects to stretch and squeeze in perpendicular directions.
-
Cross Mode h_× - Causes diagonal stretching and squeezing.
But gravitational waves gain extra polarization states due to higher-dimensional coherence effects:
hij(5D) = hij(4D) + εs e^(-s/λₛ)
where:
εs - Is the amplitude correction induced by 5D coherence.
s - Is the extra-dimensional coordinate modifying space-time.
λₛ - Is the coherence decay length, regulating the effects.
This leads to new gravitational wave polarization states, beyond the standard + and × modes.
-
Scalar-Longitudinal Mode (h_L): Longitudinal stretching along the wave's propagation axis.
-
Vector-x & Vector-y Modes (h_V^x, h_V^y): Shearing distortions that shift matter transversely.
-
Scalar-Breathing Mode (h_B): Isotropic expansion and contraction. resembling a "breathing effect"
Connected to 5D coherence induced expansion, linking gravitational waves to dark energy effects.
The full 5D gravitational wave polarization matrix is:
hij(5D) = | h_+ + h_B h_× + h_V^x h_L | | h_× + h_V^x -h_+ + h_B h_V^y | | h_L h_V^y 0 | e-s/λₛ
10. Quantum Entanglement:
Entanglement is a 5D wavefunction coherence link rather than a purely 4D effect.
Ψentangled(x, y, z, t) = ∫ Φ(x, y, z, t, s) ds
where:
Φ(x,y,z,t,s) is the 5D wavefunction extending into the coherence dimension.
s represents the hidden coherence dimension, stabilizing entanglement links.
The integral over s accounts for higher-dimensional wavefunction overlap.
-
In 3D, wavefunctions are localized.
-
In 4D, they evolve in time.
-
In 5D, coherence fields stabilize quantum correlations.
Entanglement is a coherence link in 5D space, where entangled particles remain connected via a higher-dimensional coherence structure.
A quantum state propagating through 5D space can be written as:
Φ(x,y,z,t,s)=Φ0e^(−s2λ2ₛ)
where:
Φ0 is the initial wavefunction amplitude.
s is the extra coherence dimension.
λₛ is the coherence length scale.
In the 5D coherence model:
-
Measurement is a projection from 4D to 3D.
-
Collapse occurs due to decoherence, not true information loss.
This equation describes how a 3D observer perceives only a slice of the full 4D wavefunction.
Ψobs(x,y,z)=∫Ψentangled(x,y,z,t)δ(t−tobs)dt
The presence of higher-dimensional coherence fields naturally explains entanglement persistence without violating relativity.
11. Big Bang Singularity:
The Big Bang was a 5D-to-3D dimensional transition rather than a singularity.
a(t)∼e^(s/λₛ) ,for t→0
Instead of a singularity, the early universe was a 5D coherence field that transitioned into a 4D evolving universe.
The scale factor follows a coherence-stabilized expansion:
Λ_eff = Λse^(-s/λₛ)
Dimensional Transition: 5D → 4D → 3D
3D Local (incoherent)
-
Objects exist with fixed spatial properties.
-
No concept of intrinsic time evolution, or what time is in general.
4D (wavefunction evolution)
-
Time (t) enables causality and motion.
-
Wavefunction evolution governs particle states.
5D (coherence stabilization and dimensional projection)
-
The universe originated as a 5D structure.
DM's 5D framework eliminates the infinite-density issue:
-
The Big Bang was not a singularity but a dimensional transition from 5D to 4D to 3D.
-
3D space did not "appear"—it was already embedded in 5D and unfolded naturally.
-
Dark energy is a leftover effect of 5D vacuum stabilization.
-
This framework provides a singularity-free, mathematically consistent explanation for the origin of the universe.
The paradox of 'infinite density' is reframed as "infinite space", because it is the projection of all positions along the s-axis into a single coherent unit Φ(x, y, z, t, s), which connects all spatial points simultaneously (the projection of all positions along the s-axis into a single coherent unit).
12. General Relativity Extended to 5D
Gμν + Sμν = 8πG\c⁴ Tμν
where:
-
Gμν - Einstein curvature term (standard GR).
-
Sμν - Higher-dimensional coherence stabilization (prevents singularities, stabilizes Higgs, explains dark matter).
-
Tμν - Energy-momentum tensor (includes matter, radiation, and quantum fields).
The unification of gravity, quantum mechanics, dark matter, dark energy, Higgs stabilization, and coherence-based transitions:
Gμν + Sμν = 8πG\c⁴ (Tμν + Λs e^(−s/λs) gμν) + ∂\∂s(∫Φ(x,y,z,t,s)ds)
Conclusion
The Dimensional Memorandum framework successfully resolves all major anomalies in physics by adhering to dimensional geometry and mathematical consistency. By applying higher-dimensional coherence effects, DM provides an explanation for wavefunction collapse, dark matter, dark energy, neutrino oscillations, high-energy physics anomalies, and cosmological expansion. This presents a structured resolution of long-standing physics problems while remaining fully aligned with experimental data and known physical laws.
The Big Bang: Birth of Incoherence
1. Introduction
Traditional cosmology describes the Big Bang as the beginning of space and time. However, within the Dimensional Memorandum (DM) framework, a deeper reality is revealed: the Big Bang represents not the true beginning of existence, but the beginning of incoherent, entropic time. Prior to the Big Bang, reality existed as a stabilized coherence field across a five-dimensional projection Φ(x, y, z, t, s). The Big Bang was a coherence rupture event, triggering the collapse of dimensional stability and the emergence of what we perceive as time.
2. Time Perception and Coherence Factor
The observed passage of time for an internal observer is not fundamental but depends on coherence field stability. The experienced time (t₁) relative to the absolute structure (t) is governed by:
t₁ = t · e^(−γₛ)
where:
- t₁: Experienced (sequential) time
- t: Absolute 4D time
- γₛ: Dimensional coherence stabilization factor
High coherence (large γₛ) results in near-simultaneous perception—no sequential time. Loss of coherence initiates the perception of directional, entropic time flow.
3. Coherence Stability Across Dimensional Transitions
The degradation of coherence across dimensional transitions is mathematically governed by:
C_n = e^(−ΔE / ħω) C_(n−1)
where:
- C_n: Coherence stability at the current dimensional layer
- C_(n−1): Coherence stability at the prior dimensional layer
- ΔE: Energy fluctuation disrupting coherence
- ħω: Quantum resonance energy stabilizing coherence
As ΔE rises during the dimensional collapse (e.g., the Big Bang), coherence stability exponentially decays, leading to spatial fragmentation.
4. Big Bang as Coherence Collapse
Prior to the Big Bang:
- γₛ → ∞
- C_n ≈ 1
- t₁ → 0
Reality existed as a fully stabilized Φ(x, y, z, t, s) coherence field.
During the Big Bang:
Sudden energy fluctuation (ΔE ↑)
Coherence collapse (C_n ↓)
Observer-experienced time (t₁) unfolds sequentially.
Thus, entropy and decoherence were born from the rupture of stabilized dimensional coherence.
5. Implications for Modern Physics
-
The arrow of perceived time is tied directly to the decay rate of C_n.
-
Mass-energy fields, gravitational curvature, and quantum decoherence are natural projections of fractured coherence structures.
-
Dark energy (Λ) is the remnant stabilization effect of the original coherence field attempting to rebalance dimensional tension.
The equations:
t₁ = t e^(−γₛ) and C_n = e^(−ΔE/ħω) C_(n−1) form the foundation of understanding how time, entropy, and structure emerged from a stabilized coherence field collapse. The Big Bang is thereby reinterpreted as the beginning of incoherent dimensional projection, not the beginning of existence. The Dimensional Memorandum completes the mathematical, and physical understanding of cosmological origin.
Coherence Transition Conditions
Modern physics assumes that three-dimensional spacetime constitutes the “default” reality. However, the evidence from BECs, quantum computing, high-energy physics and cosmological research confirms that coherence defines reality.
3D- Incoherent to (t) and (s)
Localized mass (x, y, z) = Observer perspective (info received in 2D plains)
4D- Coherence of x, y, z and (t)
Wavefunction of Time (x, y, z, t) = Superposition, Time dilation (info received in 3D volumes)
5D- Full Coherence of all axis
Field of Time and Space (x, y, z, t, s) = Entanglement (info received in 4D hypervolumes)
3D space is inherently incoherent to the full structure of reality. Stabilized reality requires coherence fields extending into 5D.
Quantum Computing Example: Superconducting qubits and ion traps only maintain coherence by isolating themselves from the ambient 3D environment. The moment quantum states interact with our 3D environment, decoherence occurs. This decoherence isn’t a defect of the qubits; it is the property of 3D itself.
The environmental "noise" is simply 3D’s natural state of incoherence to (t) and (s).
Because 3D is Localized and deterministic, governed by classical causality.
While, a 4D Superposition reflects partial coherence—multiple possibilities coexist for a single system, but without stable phase-locking between systems. Because 5D Entanglement is the effect where systems are connected through shared coherence fields, stabilizing a unified phase identity.
Without this higher-dimensional coherence stabilization, the effects in quantum computing remain partial and fragile.
Example: Bose-Einstein Condensate's- 3D local, 4D wave, 5D unit phase transitions.
Near 0 Kelvin - Decoherence minimized: wavefunction spreads, stabilizing superposition 3D → 4D
0 Kelvin - Full coherence sustained; entanglement/unity phase achieved 4D → 5D
15.83 GHz - Entry into wavefunction spread (superposition zone); coherence extends into time 3D → 4D
31.24 GHz - Full coherence stabilization; entanglement and phase unity 4D → 5D
v → near c - Time dilation; wavefunction spreads along t axis 3D → 4D
v → c - Coherence freeze; full stabilization, entanglement achieved 4D → 5D
These are measurable 3D → 4D → 5D boundary conditions.
This structure of information perception, physical interaction, and the coherence stability across 3D, 4D, and 5D are derived from geometric first principles and experimental data.
0D→ 1D x→ 2D x, y→ 3D x, y, z→ 4D x, y, z, t→ 5D x, y, z, t, s
(x) Length, (y) Width, (z) Height, (t) Time, (s) Space
Coherence Field
Φ(x, y, z, t, s) = Φ₀ e^{-s² / λₛ²}
Observable Wavefunction
Ψ(x, y, z, t) = ∫ Φ(x, y, z, t, s) e^{-s / λₛ} ds
Unified Governing Equation
G_{μν} + S_{μν} = 8πG/c⁴(T_{μν} + Λₛ e^{-s/λₛ} g_{μν}) + ∂/∂s(∫ Φ(x, y, z, t, s) ds)
Mass arises from coherence field stabilization:
m = m₀ e^{-s/λₛ}
Entangled Identity:
𝓘ₙ = ∑(Tᵢ + T̄ᵢ) · e^(–s / λₛ)
This is where physics is stuck today and why.
Time is Not One Dimensional
Misconception:
3D (x, y, z) plus a 1D line of time (t), and they call that 4D.
(Missing the structure of the 4D Ψ(x, y, z, t) wavefunction.)
Classical Physics Error
Tries to cover 3D and 4D, while mistaking 4D as a 1D line.
Quantum Mechanics Error
Tries to cover (Ψ) wave behavior, but they've completely misinterpreted 4D by this point, and don't understand what the wavefunction is or where it comes from.
Therefore, 5D is ignored, and that leaves no understanding for the (Φ) field architecture to explain gravity, blackholes, dark matter, or how entangled systems stay unified (this is the state of physics today).
The Dimensional Memorandum framework is a necessary reconfiguration in resolving the contradictions in physics.
Reality:
5D Φ(x, y, z, t, s) → 4D Ψ(x, y, z, t) → 3D ρ(x, y, z) → 2D ⟂(x, y) → 1D (x) → 0D
ρ 3D (x, y, z)
3D observer perspective arena:
x = Length
y = Width
z = Height
A cube in 3D is a localized object. Here, mass is a frozen waveform — a structure collapsed into three spatial dimensions, with no access to the time axis. It appears static and solid because it is a cross-section of a higher-dimensional dynamic process.
Subjective Mass = Localized wave without time.
Ψ 4D (x, y, z, t)
In 4D, each spatial dimension expands with time. This transforms static geometry into dynamic wave behavior:
x(t): Length evolving over time
y(t): Width evolving over time
z(t): Height evolving over time
This forms a tesseract: a 4D hypercube representing the evolution of a 3D object over time. The structure Ψ(x, y, z, t) captures superposition, interference, and coherence across time, producing quantum behavior. Each axis becomes a dynamic path through time. Instead of observing just position, one now observes a volume of wave behavior.
Orientation = Distributed wave across time.
Φ 5D: (x, y, z, t, s)
The final extension introduces the coherence-space axis (s) — the fifth dimension. Here, the wavefunction becomes:
Φ(x, y, z, t, s)
Now each axis is no longer just evolving — it becomes phase-locked across both time and coherence-space, enabling full entanglement and stabilization.
Wavefunction extended across coherence field:
x(t) · s: Length's time-spread extended across coherence field
y(t) · s: Width's time-spread extended across coherence field
z(t) · s: Height's time-spread extended across coherence field
Forming a penteract. A 5D hypercube containing the entire history, future, and spatial structure of an object simultaneously.
Objective Identity = Stabilized coherence across time and space
ħ = Eₚ · tₚ
Minimum action per frame; energy-geometry link.
c = lₚ / tₚ
Scan rate of 3D cubes (ρ) through 4D tesseract (Ψ).
G = (lₚ³ / (ħ tₚ²)) · c³
Curvature scaling between 3D mass and 4D geometry.
"Face Value" Perspective
3D: Face of Cube = Point → Line → Square
Perspective is planar = All objects have planar surfaces = ρ Local, Classical
10⁶¹ (3D Observable Span): The ratio of the cosmic radius (10²⁶ m) to the Planck length (10⁻³⁵ m) represents the number of spatial Planck units filling the observable universe.
4D: Face of Tesseract = Line → Square → Cube
Perspective is a volume = All objects have volumetric surfaces = Ψ Quantum Wave
10¹²¹ (4D Tesseract Volume): Combining (10⁶¹) and (10⁶⁰) Planck ratios result in ~10¹²¹ Planck cells, defining the 4D tesseract volume.
5D: Face of Penteract = Square → Cube → Tesseract
Perspective is a hyper-volume = All objects have hyper-volumetric surfaces = Φ Coherence Field
10¹²² (5D Penteract Coherence): The jump from 10¹²¹ to 10¹²² represents the transition from 4D wave to 5D coherence, encompassing the full penteract structure.
The Simplest Langrangian
𝓛DM = (c⁴ / 16πG)(R + S) + 𝓛ρ + 𝓛Ψ + 𝓛Φ
Where:
R = Ricci scalar curvature of 4D tesseract volumes (Ψ).
S = Coherence curvature along the 5D s-axis, stabilizing Φ.
𝓛ρ = 3D localized energy on cube faces.
𝓛Ψ = 4D wavefunction propagation across tesseract volumes.
𝓛Φ = 5D coherence stability and dimensional projection.
The 5D coherence curvature S is defined as:
S = ∇ₛ² Φ - Λₛ e^{-s/λₛ}
This term governs the stabilization of 5D coherence surfaces, preventing singularities and ensuring smooth projection into 4D and 3D states. Λₛ represents the intrinsic curvature of the 5D penteract, while λₛ is the coherence length scale along s.
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