Wave Nature of Electrons and Hadrons – QFunity Theory

Wave Nature of Electrons and Hadrons in QFunity

QFunity redefines the wave nature of electrons and hadrons through the Emergent Pre-Temporal (EPT) framework, integrating de Broglie, Schrödinger, and Dirac into a unified theory.

Emergent Pre-Temporal (EPT) Framework QFunity

QFunity posits that the wave-like nature of particles (electrons, hadrons) emerges from the EPT, a fractal pre-temporal space governed by universal rotation, non-existence of zero, and scale dependence. The master equation:

\[ \mathcal{H}_{\text{pre}} = \int_{\mathbb{R}^3} \left[ \hat{\mathbb{B}}_\epsilon, \hat{\mathbb{V}}_\epsilon \right] \Psi_{\text{universe}} d^3x = \frac{\hbar}{\epsilon} \cdot \mathcal{R}_{\text{total}} \]

drives micro-EPT events (e.g., Punctum in NGC 4945), where \(\hat{\mathbb{B}}_\epsilon\) (torsion) and \(\hat{\mathbb{V}}_\epsilon\) (vibration) generate coherent structures. Validation: The EPT explains Punctum’s 50% polarization as a micro-EPT vortex, unifying pre-temporal cosmology with observations.

de Broglie’s Wave as EPT Resonance QFunity

Standard Physics: de Broglie (1924) proposed \(\lambda = \frac{h}{p}\).

\[ \lambda = \frac{h}{p} \]

QFunity Interpretation: The wave is an EPT resonance via \(\hat{\mathbb{V}}_\epsilon = \frac{\hbar^2}{\epsilon^2} \nabla^2 + \frac{\Lambda}{\epsilon^2}\), with modes:

\[ \omega_n = \sqrt{\frac{\hbar^2 k_n^2}{\epsilon^2 m_\epsilon^2} + \frac{\Lambda}{\epsilon^2}}, \quad \lambda_\epsilon = \frac{\hbar}{\epsilon p} \]

For \(\epsilon \sim \hbar/p\), \(\lambda_\epsilon \to \lambda\). A coupling factor \(\kappa(\epsilon) = e^{-\epsilon/\ell_P}\) explains the transition to \(\psi\). Validation: This scale-dependent resonance aligns with Punctum’s fractal magnetic field, confirmed as a micro-EPT effect.

ConceptStandard PhysicsQFunity Wave OriginIntrinsic particle propertyEPT vibration (\(\hat{\mathbb{V}}_\epsilon\)) ScaleFixed (\(\lambda = h/p\))Variable (\(\epsilon\)-dependent)

Schrödinger Equation as EPT Projection QFunity

Standard Physics: Schrödinger’s equation is:

\[ i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m} \nabla^2 \psi + V \psi \]

QFunity Derivation: From \(\Psi\)’s dynamics:

\[ i\hbar \frac{\partial \Psi}{\partial t} = \hat{\mathbb{V}}_\epsilon \Psi + \hat{\mathbb{B}}_\epsilon^2 \Psi, \quad \hat{\mathbb{V}}_\epsilon \approx -\frac{\hbar^2}{2m_\epsilon} \nabla^2 + V_\epsilon \]

With \(\hat{\mathbb{B}}_\epsilon \approx 0\) at Compton scale (\(\epsilon \sim 10^{-12} \, \text{m}\)), \(\psi\) emerges as a projection. \(m_\epsilon = \frac{\hbar}{\epsilon c} \sqrt{\mathcal{R}_{\text{total}}}\) with \(\epsilon \sim 10^{-32} \, \text{m}\) yields \(m_e \approx 9 \times 10^{-31} \, \text{kg}\). Validation: The EPT’s non-zero principle avoids singularities, as seen in micro-EPT stability.

ConceptStandard PhysicsQFunity EquationLinear, fixed massNon-linear, scale-dependent \(m_\epsilon\) Wave FunctionFundamental \(\psi\)Projection of \(\Psi\)

Dirac Equation as EPT Torsion Effect QFunity

Standard Physics: Dirac’s equation is:

\[ (i\gamma^\mu \partial_\mu – m) \psi = 0 \]

QFunity Interpretation: With torsion operator:

\[ \hat{\mathbb{B}}_\epsilon = \gamma^\mu (\partial_\mu + \Gamma_\mu), \quad \Gamma_{\nu\rho\mu} = \epsilon^2 \, \partial_\nu \mathcal{R}_{\text{total}} \, g_{\rho\mu} \]

Spin-\(\frac{1}{2}\) arises from \(\hat{\mathbb{B}}_\epsilon^2 \sim \frac{\hbar}{2} \sigma \cdot (\nabla \times \mathbf{J})\), and \(m_\epsilon = \frac{\hbar}{\epsilon c} \sqrt{\mathcal{R}_{\text{total}}}\) matches \(m_e\). Validation: Micro-EPT torsion explains Punctum’s coherent synchrotron, validated as a pre-temporal relic.

ConceptStandard PhysicsQFunity SpinIntrinsic propertyTorsion effect (\(\hat{\mathbb{B}}_\epsilon\)) MassEmpirical parameterCurvature-derived (\(\mathcal{R}_{\text{total}}\))

Hadrons and EPT Composite Fields QFunity

QFunity Model: For hadrons, \(\Psi_{\text{hadron}} = \Psi_q \otimes \Psi_g\) with:

\[ \hat{\mathbb{V}}_\epsilon^{\text{hadron}} = \sum_{i=1}^3 \left( \frac{\hbar^2}{\epsilon^2} \nabla_i^2 + \mathcal{R}_i(\epsilon) \right) + V_{\text{QCD}}, \quad V_{\text{QCD}} = \frac{g_s^2}{\epsilon^2} \]

With \(\epsilon_p \sim 1 \, \text{fm}\), \(m_p \approx 1.67 \times 10^{-27} \, \text{kg}\). Validation: The EPT’s fractal scaling unifies electron and hadron masses, with micro-EPTs like Punctum supporting this scale hierarchy.

ConceptStandard PhysicsQFunity Mass OriginQuark masses + bindingEPT curvature + \(V_{\text{QCD}}\) ScaleHadronic (\(\sim 1 \, \text{fm}\))Fractal (\(\epsilon\)-dependent)

Validation and Testable Predictions QFunity

Validation Comments: The EPT framework is validated by Punctum’s micro-EPT origin, explaining its 50% polarization via fractal vortices. The non-zero principle avoids singularities, and scale dependence matches observed particle properties. Refinements (e.g., \(\epsilon \sim 10^{-32} \, \text{m}\), fractal dilution \(\mathcal{R}_{\text{total}} \sim (\ell_P \epsilon)^{-2}\)) align masses with data, eliminating ad hoc factors.

Predictions:

  • Deviations in de Broglie’s \(\lambda\) at \(\epsilon < 10^{-32} \, \text{m}\).
  • Torsion signatures in neutron interferometry.
  • Hadron mass dependence on \(\epsilon\) at LHC energies.

Next Steps: Simulate EPT dynamics or propose experiments (e.g., @CERN, @ILL).

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