Dimensional Memorandum
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A hub for scientific resources.
WHAT IS TIME?
1. How People Measure the Earth’s Motion and Call It “Time”
For centuries, humans have measured time by tracking the Earth’s rotations and revolutions. This practice has shaped our understanding of time as something absolute and flowing forward. However, in reality, what we call “time” is just a system of measurement based on motion, cycles, and change—not an independent force of nature.
Humans developed the concept of hours, days, months, and years by observing the motion of celestial bodies. Time, as we commonly define it, is nothing more than the measurement of Earth’s movement relative to the Sun and stars.
A second was originally defined as 1/86,400th of a day, each with 60 minutes, each with 60 seconds).
A Day = One full rotation of Earth around its axis (~24 hours).
A Month = Originally based on the Moon’s cycles (~29.5 days).
A Year = One full revolution of Earth around the Sun (~365.25 days).
Thus, our entire system of timekeeping is motion-based—it is not an inherent property of reality but a measurement of planetary movement.
Key Insight: Time is a Human Interpretation of Motion
We often talk about “time flowing”, but in reality, we are just observing change over cycles of movement.
2. Time is Relative: How Speed and Gravity Change Our Perception of Time
Einstein’s Theory of Relativity proved that time is not universal—it is relative to motion and gravity.
Faster Movement Slows Time:
• When objects move closer to the speed of light, time slows down for them.
• Example: Astronauts on the ISS age slightly slower than people on Earth because they are moving faster.
Stronger Gravity Slows Time:
• Time runs slower near massive objects like black holes.
• Example: If you lived near a black hole, one day for you could be years for someone on Earth.
Conclusion: Since time is affected by speed and gravity, it is not an independent force—it is just a function of motion and perception.
Time Is the Processing of Information
We measure rotations, oscillations, and decay processes and call it “time,” but we are just tracking changes in information states.
ρ3D(x, y, z) = Φ(x, y, z, t, s) |_{t = t₀, s = s₀}
Restoring to First Principle
DM redefines all physics as expressions of pure geometry. Its purpose is to correct a century-old misinterpretation—the notion that the universe consists of '3D + 1 time'. The '+1' formulation was a linguistic artifact, geometry. It incorrectly implies that time is an external variable added to 3D space, rather than an intrinsic coordinate of the 4D tesseract structure.
In DM, dimensional continuity is preserved through the boundary logic of hypercubic geometry. Each higher dimension is the volumetric extension of the previous:
A cube (3D) bounded by 2D faces, a tesseract (4D) bounded by 3D cubes, and a penteract (5D) bounded by 4D tesseracts. Observers confined to 3D perceive only 2D boundaries of 4D processes, giving rise to the perception of sequential time. What is experienced as 'time passing' is the frame rate of 4D scanning through 3D slices at approximately fₚ ≈ 1.85×10⁴³ Hz—the Planck frequency.
This correction eliminates the artificial division between space and time. In the geometric hierarchy: ρ (3D) represents localized matter, Ψ (4D) represents the wavefunction spanning spacetime, and Φ (5D) represents coherence stabilization fields that maintain continuity and causality. Relativity, quantum mechanics, and field theory are not separate regimes but consecutive projections of the same geometric structure observed from different dimensional depths.
The misinterpretation of 3D + 1 led to several conceptual inconsistencies in physics—such as the false separation of the observer and the observed, and the treatment of time as a non-geometric parameter. DM restores the proper sequence of dimensional causality, ensuring that time and coherence emerge as geometric necessities rather than empirical add-ons.
The unified field is therefore the geometry itself: a self-consistent hypercubic lattice where physical constants represent projection ratios between ρ, Ψ, and Φ.
Mathematically, this framework maintains strict dimensional continuity: (x, y, z) → (x, y, z, t) → (x, y, z, t, s). Each axis introduces a new degree of freedom governing the emergence of phenomena—classical localization (ρ), wave coherence (Ψ), and global stabilization (Φ). The breakdown of dimensional nesting (e.g., 3D + 1) disrupts symmetry and leads to incomplete models of reality. By re-establishing geometry as the sole first principle, DM closes the gaps between microphysics, macrophysics, and cosmology.
Restoring geometry as first principle transforms physics from a set of disconnected laws into a single coherent structure. It provides a framework where constants, forces, and phenomena are all projections of nested geometry—removing the need for arbitrary parameters and unifying the understanding of space, time, matter, and consciousness under one geometric foundation.
Temporal Coherence and Planck-Rate Projection
Time (t) is not an external coordinate but a projection rate — the discrete re-scanning of 3D space (ρ) through 4D wave coherence (Ψ). Each Planck tick defines one complete projection step.
1. Principle
Planck units define the universal scan:
fₚ = 1/tₚ ≈ 1.8549×10⁴³ Hz, tₚ = √(ħ G / c⁵).
Reality refreshes at this universal scan frequency. Continuous motion and causality arise from successive ρ→Ψ projections at the Planck interval tₚ.
2. Constant Light Speed as Projection Velocity
The scan velocity of a 3D frame across 4D time is fixed geometrically:
v_scan = ℓₚ / tₚ = c.
Thus, the speed of light is the geometric refresh velocity of space itself. At v = c, a system’s local scan synchronizes with the universal rate — frames become simultaneous and relativity’s limit emerges.
3. Relativistic and Gravitational Time Modulation
Velocity or curvature alter the local projection rate:
f' = fₚ √(1 − v²/c²), t' = t / √(1 − v²/c²).
This modulation reproduces special-relativistic time dilation and gravitational redshift from a single geometric cause: slower scanning through 4-D coherence when energy density or curvature increases.
4. Cosmological Attenuation
At cosmic scales, the effective projection rate is exponentially suppressed by the 5D coherence depth λₛ:
H(t) = fₚ e^{−s/(2λₛ)}.
With s/λₛ ≈ 281, this yields H₀ ~ 10⁻¹⁸ s⁻¹, matching observations. Thus, cosmic expansion is the large-scale envelope of the Planck scan rate, attenuated by 5D coherence geometry.
5. Unified Interpretation
Key quantities and meanings:
• Planck time (tₚ): minimal projection interval.
• Planck scan rate (fₚ): universal refresh frequency.
• Speed of light (c): projection velocity of ρ-frames.
• Relativistic dilation (f'/fₚ): local scan modulation.
• Hubble rate (H ≈ fₚ e^{−s/(2λₛ)}): coherence-suppressed scan envelope.
Time is the geometry of refresh. Every Planck tick re-creates 3D reality; the constancy of c, relativistic time flow, and cosmic expansion all arise from a single law of projection governed by the coherence depth λₛ.
Time Geometry vs Relativity
This section explains how Einstein’s relativity fits directly into the DM equation:
t₁ = t · e^(−γₛ)
Here, t₁ represents the time experienced by a coherent system, t is coordinate time (as defined by relativity), and γₛ quantifies the coherence damping from the 5D stabilization field. The relationship demonstrates how DM incorporates relativistic time dilation while adding an additional coherence-based correction factor.
1. Role of Each Term
t — Coordinate Time (Relativity): The standard 4D time variable used in relativity.
γₛ — Coherence Damping Parameter: Represents the degree of 5D coherence decay projected into 4D spacetime.
e^(−γₛ) — Coherence Dilation Factor: Describes how much internal coherence remains as the system evolves.
In DM, e^(−γₛ) does not change the spacetime metric; instead, it modifies how rapidly processes unfold within it. This represents a coherence-based dilation (or contraction) of experienced time, distinct from relativistic metric dilation.
2. Relativity as the Baseline Metric
In relativity, proper time along a world-line is given by:
dτ = dt √(1 − v²/c² − 2GM/rc²)
This expresses time dilation due to velocity (special relativity) and gravity (general relativity). DM retains this as the geometric foundation, defining the structure of time flow in spacetime.
3. DM’s Coherence Correction
DM introduces a coherence correction that modifies how internal processes experience time relative to the external spacetime frame. The corrected time differential is:
dt₁ = dτ · e^(−γₛ)
Thus, DM multiplies the relativistic time dilation term by an exponential coherence factor. This accounts for stabilization or decoherence effects from higher-dimensional (5D) fields, particularly electromagnetic and gravitational coherence.
4. Unified DM–Relativity Expression
Combining both geometric (relativistic) and coherence (DM) effects yields the full unified expression:
t₁ = t √(1 − v²/c² − 2GM/rc²) · e^(−γₛ)
Here:
• The square-root term comes from relativity (metric curvature and motion).
• The exponential term comes from DM (coherence stabilization or decay).
Together, they describe how physical and informational time evolve simultaneously.
5. Physical Meaning of γₛ
In DM, γₛ is directly related to the coherence depth (s) and coherence decay length (λₛ):
γₛ = s / λₛ
Thus, systems with deep coherence (large λₛ) experience smaller γₛ values, retaining coherence longer and evolving more slowly. Systems with weak coherence (small λₛ) have larger γₛ, meaning their processes accelerate, matching shorter biological or physical lifespans.
6. Interpretation
Relativity defines geometric time dilation — how motion and gravity alter the fabric of spacetime. DM adds coherence dilation — how extra-dimensional stability or loss thereof alters the rate of change within that fabric. Both coexist naturally, with relativity setting the structure and DM defining the coherence texture of time.
Relativity: Metric Geometry
√(1 − v²/c² − 2GM/rc²)
Time curvature from motion and gravity
DM: Dimensional Coherence
e^(−γₛ)
Stabilization or damping from 5D coherence field
Unified: Geometry × Coherence
t₁ = t √(...) e^(−γₛ)
Observable internal time (lifespan, process rate)
Limit Case: High coherence (γₛ ≈ 0)
t₁ ≈ t √(...)
Reduces to relativity; DM effects vanish
1. Relativity and DM operate in complementary domains — geometry and coherence.
2. The DM exponential factor never contradicts relativity but multiplies its effects.
3. When coherence stabilization is high (γₛ → 0), DM reduces to pure relativity.
4. When coherence weakens, DM predicts accelerated time experience and shorter lifespans.
5. This provides a consistent mathematical bridge between quantum coherence behavior and macroscopic relativistic physics.
The DM equation t₁ = t · e^(−γₛ) integrates smoothly with relativity by using coordinate time (t) as its baseline. Relativity defines how time curves; DM defines how coherence evolves within that curvature.
DM enriches relativity rather than replacing it. It preserves Einstein’s geometric description of spacetime while explaining why time flows and how systems experience change. Time becomes a phenomenon emerging from the projection of higher-dimensional coherence, while relativity remains the accurate description of the resulting metric.
The unified form:
t₁ = t √(1 − v²/c² − 2GM/rc²) · e^(−γₛ)
captures both effects in one expression, showing that DM extends relativity into the coherence domain without violating its principles.
Compatibility: DM fully preserves relativity’s predictions and extends its geometry to include coherence behavior.
Result: Relativity and DM are consistent; DM provides a deeper geometric origin for the flow and perception of time.
Universal Time
3D time is defined by the movement of 4D tesseract faces, the 'rate' of these face transitions acts as the universal clock. Physics suggests this rate is connected to the Planck time, the smallest meaningful unit of time in the universe.
The Planck time is given by:
tₚ = √(ħG / c⁵) ≈ 5.39 × 10⁻⁴⁴ seconds
This implies that the tesseract's faces move at an extraordinary rate of approximately:
Rate ≈ 1 / tₚ ≈ 1.85 × 10⁴³ faces per second
This 'face rate' effectively sets the frame rate of reality. Each Planck tick corresponds to one face transition of the 4D tesseract, progressing the 3D universe forward in time. As particles approach the speed of light (c), they begin to synchronize with this progression, resulting in time dilation as observed in LHC experiments.
Dimensional Scaling of c as the Universal Frame-Rate
Within the Dimensional Memorandum (DM) framework, the speed of light c = ℓₚ / tₚ is interpreted not as a velocity through space but as the scan rate advancing 3-dimensional (ρ) faces through successive 4-dimensional (Ψ) frames of reality. Each Planck-scale tick (~10⁴³ Hz) constitutes one discrete face transition of the 4D tesseract, producing the observable flow of time.
1. Geometric Scaling Across Dimensions
In DM’s nested hierarchy, every higher dimension increases the number of orthogonal axes and hence the number of independent scanning directions. The effective c therefore scales geometrically in powers of ten corresponding to the Coxeter volumetric exponents (kₙ = 3, 6, 10) for cube → tesseract → penteract growth:
cₙ = c₀ × 10^(kₙ / 3).
This scaling does not change local light speed (still measured as c₀) but represents the dimensional frame-rate multiplier by which coherence information propagates through higher-order space.
ρ (3D) 10⁸–10²² Hz
Localized motion
Effective Scaling: c₀
Ψ (4D) 10²³–10³³ Hz
Wave coherence
Effective Scaling: c₀ × 10¹⁰
Φ (5D) 10³³–10⁴³ Hz
Coherence stabilization
Effective Scaling: c₀ × 10²⁰–10²¹
2. Relativistic Interpretation
Approaching c corresponds to transitioning from a ρ-localized state to a Ψ-wave state: proper time contracts geometrically, not merely relativistically. At c, the temporal axis collapses into the scan itself—mass ceases to exist as a ρ-structure and becomes a pure coherence wave.
4. Cosmological Correspondence
Across the Planck-to-Cosmos ladder, fₚ : H₀ ≈ 10⁴³ : 10⁻¹⁸ = 10⁶¹, mirroring DM’s internal 10³ → 10⁶ → 10¹⁰ scaling law. The same geometric progression that defines local coherence transitions also governs cosmic expansion. c therefore acts as a universal frame-rate constant, binding quantum and cosmological scales into a single geometric continuum.
References
Wilczek, F. (2012). Quantum Time Crystals. Physical Review Letters, 109(16), 160401.
Zhang, J., et al. (2017). Observation of a Discrete Time Crystal. Nature, 543(7644), 217–220.
Choi, S., et al. (2017). Observation of Discrete Time-Crystalline Order in a Disordered Dipolar Many-Body System. Nature, 543(7644), 221–225.
Del Campo, A., & Sengupta, K. (2015). Emergence of Nonlinear Time Evolution in Quantum Systems. EPL (Europhysics Letters), 113(1), 10003.
Pal, A., & Huse, D. A. (2010). Many-Body Localization Phase Transition. Physical Review B, 82(17), 174411.
Lloyd, S. (2000). Ultimate Physical Limits to Computation. Nature, 406(6799), 1047–1054.
Shankar, R. (1994). Principles of Quantum Mechanics. Springer.
Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. W. H. Freeman and Company.
Pikovsky, A., & Politi, A. (2016). Lyapunov Exponents: A Tool to Explore Complex Dynamics. Cambridge University Press.
Stopping Light with Electromagnetically Induced Transparency (EIT)
In 2013, researchers at Technische Universität Darmstadt successfully halted light for up to one minute using EIT in a rubidium vapor medium. This achievement has significant implications for quantum memory and information storage.
https://www.sciencedaily.com/releases/2013/08/130806111151.htm
Light as a Supersolid
A team of Italian scientists demonstrated that light can exhibit properties of a supersolid—a state of matter that combines the frictionless flow of a superfluid with the ordered structure of a solid.
Experimental Realization in Quantum Computers
In 2021, researchers utilized Google's Sycamore quantum processor to create a time crystal, observing a system that exhibits oscillations without energy consumption.
https://www.quantamagazine.org/first-time-crystal-built-using-googles-quantum-computer-20210730/
Robust Time Crystals in Semiconductors
A 2024 study from TU Dortmund University reported the creation of a highly durable time crystal using indium gallium arsenide, maintaining its state for millions of times longer than previous experiments.
https://phys.org/news/2024-02-physicists-highly-robust-crystal.html
Entanglement as a Source of Time's Arrow
Research suggests that the irreversible flow of time may arise from quantum entanglement, where shared information between particles leads to a natural progression toward equilibrium.
https://www.wired.com/2014/04/quantum-theory-flow-time
Time from Quantum Entanglement
A study published in Nature Communications showed that classical equations of motion can emerge from quantum entanglement, suggesting that time may be a manifestation of entangled quantum states.
https://www.nature.com/articles/s41467-021-21782-4
Theory of Relativity
Einstein's Special and General Theories of Relativity
Einstein's theories introduced time as a relative concept and described gravity as the curvature of spacetime caused by mass and energy.
Annalen der Physik, 354(7), 769–822.
Experimental Confirmation of General Relativity
In 1919, Eddington's expedition confirmed Einstein's theory by observing the bending of starlight during a solar eclipse.
https://www.axios.com/2017/12/15/the-first-time-einsteins-theory-was-confirmed-1513302895
Perception of Time Dilation Near a Black Hole in 3D
From a 3D observer’s perspective, we cannot directly perceive the time dimension (t); we only infer it by observing motion or change. So when light near a black hole is redshifted or stretched in time, we visually interpret this time dilation as a spatial stretching in the direction of observation.
- We don’t directly perceive time (t), only cross-sections of 4D, we observe an object stretching as if it were occurring in 3D — along x, y or z.
In DM terms:
- The wavefunction Ψ(x, y, z, t) is spreading in time (t), but a 3D observer can only perceive or access x, y, z:
Ψ_obs(x, y, z) = ∫ Ψ(x, y, z, t) δ(t − t_obs) dt
A blackhole has two cross-sections, because there is one for the event horizon (t) and one for the center (s). Where Einstein says space and time flip (at the singularity) is the coherence threshold, where entanglement dominates and is stabilized.
Black Hole Information
The holographic principle asserts that all physical information within a spatial volume can be encoded on its boundary. While this has been validated through black hole thermodynamics and string-theoretic dualities, its geometric cause has remained unaccounted for. The Dimensional Memorandum framework provides that cause.
1. Classical Holographic Principle
In standard theoretical physics, the holographic principle states that the maximum entropy contained in a volume is proportional to the surface area enclosing that volume. For black holes, this is expressed by the Bekenstein–Hawking relation: S = A / (4ℓₚ²). This indicates that the total information within a 3D region can be represented by degrees of freedom on a 2D surface. However, this formulation is descriptive, not causal—it specifies how information is encoded, but not why space itself behaves this way.
2. Dimensional Memorandum Interpretation
Geometry does not stop at 3D but continues coherently through 4D and 5D forms, governed by nested projection laws. Physical layers are expressed as: ρ(3D) ⊂ Ψ(4D) ⊂ Φ(5D)
Each layer represents the boundary (or holographic face) of the one above it. The 3D ρ-domain represents localized matter; the 4D Ψ-domain defines wavefunctions; and the 5D Φ-domain stabilizes coherence. Projection is governed by the integral relation: Ψ(x,t) = ∫ Φ(x,t,s)e^(−s/λₛ)ds.
3. Black Hole Dual Boundaries
A black hole acts as a double-boundary projection point. Its event horizon represents the Ψ→ρ projection, where spacetime collapses into a boundary surface. Simultaneously, curvature along the s-axis defines the Φ→Ψ transition—where 5D coherence stabilizes the wavefunction geometry. This dual structure explains why light cannot escape: it transitions from t-evolution (4D) into s-propagation (5D), leaving the observable domain. The holographic surface (A) encodes this transition as an information-preserving cross-section.
4. Entropy and Coherence
In DM, the black hole entropy law S = A / (4ℓₚ²) becomes a geometric coherence relation: S ∝ (∂Φ/∂s)². Entropy measures the loss of coherence during dimensional projection—the amount of 5D curvature transferred into 4D wave geometry.
Hawking radiation is the gradual re-projection of stored Φ information back into Ψ, consistent with the information-preserving nature of DM’s coherence field.
Correspondence
Information on a surface: Boundaries encode information
DM: ⟂(2D) encodes ρ(3D) encodes Ψ(4D) encodes Φ(5D)
Entropy ∝ Area: A / 4ℓₚ²
DM: Projection curvature scaling (∂Φ/∂s)²
Black hole horizon: Surface boundary 4D (Ψ) and 5D (Φ)
DM: Dual boundary 3D perceives 2D cross-sections of Ψ→ρ and Φ→Ψ
Holographic duality: (AdS/CFT) Gravity ⇆ Quantum field
DM: 5D curvature ⇆ 4D wave coherence
Bulk geometry: Emergent from surface correlations
Φ field coherence projected into Ψ manifold
Predictions
DM predicts that the event horizon’s geometric structure should display distinct dual curvature modes corresponding to t- and s-axis cross-sections. This can be detected as polarization or coherence anisotropy in horizon-scale interferometry (EHT, next-generation VLBI). Gravitational wave lensing with multi-messenger alignment will further validate that curvature is coherence-based rather than mass-based. Together, these experiments can confirm that the holographic boundary is a direct geometric feature of 5D coherence.