SDKP: Scale–Density–Kinematic Principle - FatherTimeSDKP/CEN- GitHub Wiki

SDKP: Scale–Density–Kinematic Principle

Overview

The Scale–Density–Kinematic Principle (SDKP) is a unified physical framework that models mass, energy, and time as emergent properties governed by scale, density, and velocity factors. It introduces a novel scaling approach integrating particle topology (Shape and Number), spatial density, and cosmic orbital velocity to redefine mass and temporal flow across physical systems.

Mathematical Framework

1. Core Mass Function

The SDKP mass ( M ) is defined by the interaction of number ( N ), shape ( S ), and scaling coefficients ( \alpha, \beta, \gamma ):

[ \boxed{ M = \gamma \cdot (N \times S) + \beta \cdot S + \alpha \cdot N } ]

Where:

  • ( N \in \mathbb{R}^+ ) represents the number parameter from the SD&N framework (discrete or continuous particle counts).
  • ( S \in \mathbb{R}^+ ) encodes the shape or topological complexity of the particle/field.
  • ( \alpha, \beta, \gamma \in \mathbb{R} ) are empirical or derived scaling factors.

This formula generalizes traditional mass by incorporating topological and combinatorial complexity.

2. Density and Size Scaling

Mass depends on spatial density ( \rho ) and characteristic size ( d ), elevated by scaling exponents:

[ M \propto \rho^\alpha \cdot d^\beta \cdot v^\gamma ]

Where:

  • ( \rho = \frac{m}{V} ) is the density (mass per volume).
  • ( d ) is the characteristic linear dimension (scale).
  • ( v ) is the velocity factor relevant to the system (see EOS below).

This scaling replaces classical fixed-mass assumptions with dynamic scale-density relations.

3. Velocity Normalization: Earth Orbit Speed (EOS)

The EOS is introduced as a cosmic constant velocity, replacing or complementing the speed of light ( c ):

[ v = \text{EOS} = 29.78, \text{km/s} ]

This speed represents Earth’s orbital velocity around the Sun and anchors velocity scaling in SDKP:

[ M = f(\rho, d, v = \text{EOS}) ]

This approach embeds astrophysical orbital dynamics into the foundational physical constants, enabling a reinterpretation of relativistic effects under orbital kinematics.

4. Temporal Scaling and Kinematics

SDKP links spatial scale and velocity directly to effective time scales:

[ T_{\text{eff}} = \frac{d}{v} = \frac{d}{\text{EOS}} ]

This defines the flow of time as an emergent property of spatial extent and velocity, replacing classical absolute time:

  • Smaller scales or higher velocities shorten effective temporal intervals.
  • Larger spatial scales or slower velocities elongate time perception.

Integration with Existing Physics

A. Relation to Mass-Energy Equivalence

Classical physics defines mass-energy equivalence via:

[ E = mc^2 ]

SDKP modifies this by replacing ( c ) with EOS and embedding scale/density factors:

[ E = M \cdot v^2 = f(\rho^\alpha, d^\beta, v^\gamma) \cdot v^2 ]

Where ( v = \text{EOS} ), linking cosmic-scale velocity to local energy phenomena.

B. Quantum Scale and Topology

SDKP incorporates SD&N (Shape–Dimension–Number) topology parameters ( N, S ) as key quantum descriptors:

  • ( N ) captures particle multiplicity or quantum number analogs.
  • ( S ) encodes geometric or knot-theoretic topology (e.g., trefoil knots).

This extends quantum state space to include shape-topology degrees of freedom, aligning with knot theory and topological quantum field theory (TQFT).

C. Cosmological Implications

Embedding EOS aligns SDKP with cosmological orbital mechanics, providing:

  • A physical basis for linking local particle physics to cosmic orbital scales.
  • A dynamic reinterpretation of relativistic constants through orbital velocity normalization.

Summary

SDKP provides a mathematically rigorous and conceptually innovative framework for unifying particle mass, energy, time, and scale. By integrating density, size, velocity (via EOS), and topological shape-number complexity, it expands classical and quantum physics into a single coherent principle.

References & Further Reading

  • SDKP foundational papers and derivations (link)
  • SD&N topology and shape formalism (link)
  • EOS and astrophysical constants in SDKP (link)
  • Quantum Causal Compression (QCC) integration with SDKP (link)

Authored by Donald Paul Smith (FatherTime), Originator of SDKP, EOS, SD&N, QCC frameworks.
Timestamp: 2025-05-29