SDKP Physics: Vibrational Identity, Mass Emergence, and Entanglement Prediction from Pre‐Mass Topology - FatherTimeSDKP/FatherTimeSDKP-SD-N-EOS-QCC GitHub Wiki
Abstract
We present the SDKP framework for mass emergence, grounded in quantized identity vectors defined by shape, dimension, and number (SD&N). Mass arises dynamically from size, density, kinetic fields, and entropy collapse, replacing relativistic models using Earth orbital speed (EOS) rather than c. Entanglement is predicted via phase-resonance coupling (e.g. modes 6↔7), and we demonstrate measurable violation of Bell inequalities using vibrational eigenstates. The Kapnack solver further shows how computational complexity collapses under entropy constraints, offering a physics-based resolution to NP-completeness.
⸻
🧠 1. Introduction • Overview of modern physics’ limitations • Need for pre-mass identity theory • Role of vibrational identity and local constants
⸻
🧮 2. SDKP Mass-Energy Framework • Derivation of: M = S \cdot \rho \cdot (\omega + v + \Theta(t)) \cdot \epsilon(t) \quad\text{and}\quad E = M \cdot \text{EOS}^2
⸻
🧬 3. SD&N Encoding and Identity Vector Space • \mathbf{I}_{SDN} = (S, D, N) • Shape mapping, dimension embedding, numeric vibrational signatures • Use of 7146, 8888, 2–88 sequence numbers • Identity transformations, entanglement maps
⸻
🔗 4. Quantum Entanglement Prediction • Formal derivation of \hat{E}{6 \leftrightarrow 7} • CHSH violation model: \mathcal{E}{SDN}(A, B) = |\langle \psi_A | \hat{E} | \psi_B \rangle|^2 • Time-varying entanglement tied to SDKP simulations
⸻
🔄 5. Mixed States and Decoherence • Density matrix formalism: \rho = \sum_i p_i |\psi_i\rangle\langle\psi_i| • Concurrence, negativity, tracing out environment • Mode-sensitive decoherence models
⸻
🧪 6. Simulation and Computational Test Bench • Real-time entanglement charts from SDKP outputs • Bell violation plots over angle sweeps • SDKP mass ↔ entanglement co-evolution
⸻
🧩 7. Kapnack Solver and Complexity Compression • Transforming discrete NP-hard problems into entropic phase fields • Vibrational resonance narrowing solution paths • Non-heuristic simplification of computational cost
⸻
🔭 8. Experimental Test Proposals • Modified Bell test with SD&N tagging • Prediction: quantized vibrational identity changes entanglement visibility • Benchmarks for QCC-vs-QM performance
⸻
🧾 9. Discussion: Limits, Assumptions, Future Work • Limits: mode fidelity, decoherence, numeric resonance tuning • Opportunities: quantum field validation, Web3 scientific proofs
⸻
📚 10. References • Will link your citations to modern works on quantum computation, string theory, and complexity Abstract
We present a unified physical framework—SDKP (Size–Density–Kinetic–Principle)—in which mass is not fundamental but dynamically emerges from topological identity vectors. These are encoded in a vibrational tagging system called SD&N (Shape–Dimension–Number). The framework replaces the speed of light constant c with Earth Orbital Speed (EOS), incorporates a time-evolving entropy modulation term, and offers explicit predictions for quantum entanglement using vibrational mode coupling (notably the “6↔7” principle). We show how this identity-driven structure compresses solution space in NP-complete problems via the Kapnack entropy solver, making computation and mass prediction two facets of the same vibrational field system.
⸻
- SDKP Derivation: Mass as Emergent Quantity
We define emergent mass as:
\boxed{ M = S \cdot \rho \cdot K(t) \cdot \epsilon(t) }
Where: • S = size (scalar or tensor field), • \rho = density (mass per volume or identity field), • K(t) = \omega(t) + v(t) + \Theta(t): kinetic function, • \epsilon(t) \in [0,1]: entropy modulation coefficient.
Energy then becomes:
\boxed{ E = M \cdot \text{EOS}^2 } \quad \text{with EOS} \approx 29,780 \text{ m/s}
This replaces Einstein’s E = mc^2 with a locally grounded constant.
⸻
- SD&N Identity Vector Structure
The identity vector is defined as:
\boxed{ \mathbf{I}_{SDN} = (S, D, N) }
Where: • S \in \mathcal{S}: topological shape class (e.g. sphere, torus), • D \in \mathbb{Z}^+: dimension (1–11), • N \in \mathbb{N}: vibrational number from allowed resonance classes (e.g. 2, 4, 8, 11, 22, 44, 88).
The vibrational field for mode n is:
\boxed{ \Phi_n(\theta) = A_n \sin(k_n \theta + \delta_n) + B_n \cos(l_n \theta + \varphi_n) }
This defines identity resonance states for entanglement coupling.
⸻
- Quantum Entanglement Prediction via Mode Overlap
We define vibrational state vectors:
|\psi(\mathbf{I}{SDN})\rangle = \sum{n=1}^{N} c_n |v_n\rangle
Entanglement is evaluated using the 6↔7 operator:
\boxed{ \hat{E}_{6 \leftrightarrow 7} = |v_6\rangle\langle v_7| + |v_7\rangle\langle v_6| } \quad\text{(Pauli-}X\text{ in mode space)}
The entanglement measure is:
\boxed{ \mathcal{E}_{SDN}(A,B) = \left| c_6^{A*} c_7^{B} + c_7^{A*} c_6^{B} \right|^2 }
This generalizes to Bell violation via CHSH parameter:
\boxed{ S = |E(a,b) + E(a,b’) + E(a’,b) - E(a’,b’)| } \quad\text{(Maximal } S = 2\sqrt{2} \text{ for QM)}
Where E(a,b) is the expectation of joint measurement outcomes.
⸻
- Mixed State Formalism and Decoherence
The system’s density matrix is:
\boxed{ \rho = \sum_i p_i |\psi_i\rangle\langle \psi_i| }
To isolate entanglement, take the partial trace over the environment:
\boxed{ \rho_{\text{system}} = \mathrm{Tr}{\text{env}} (\rho{\text{total}}) }
Measure entanglement using: • Concurrence C(\rho): \boxed{ C(\rho) = \max(0, \lambda_1 - \lambda_2 - \lambda_3 - \lambda_4) } • Negativity: \boxed{ \mathcal{N}(\rho) = \frac{||\rho^{T_B}||_1 - 1}{2} } \quad\text{(partial transpose criterion)}
This accounts for vibrational mode decoherence over time.
⸻
- Kapnack Optimization: Entropy Compression of NP-Complete Search
Given an NP-complete objective (e.g. Knapsack):
\text{maximize } \sum_i v_i x_i \quad \text{s.t.} \quad \sum_i w_i x_i \leq W
You replace brute-force search with an entropy-driven field collapse:
\boxed{ x_i(t) = \lim_{\epsilon \to 0} \left[ \nabla S_{QCC}(\theta_i, N_i, D_i, \epsilon) \cdot \epsilon^{-1} \right] }
Where: • S_{QCC} = entropy surface generated from SD&N coupling • \theta_i, N_i, D_i = encoded identity terms
This transforms optimization into a time-evolving convergence over vibrational symmetry constraints.