Why Quantum in RFT?
- RFT unifies quantum mechanics with gravity by showing both emerge from the same geometric structure—the scalaron-twistor resonance
- Instead of quantizing classical fields, RFT derives quantum behavior from the fundamental discreteness of twistor space
- The Standard Model gauge groups and particle spectrum arise naturally from the index-3 twistor bundle structure
Twistor Quantization & Standard-Model Emergence
Key Results:
- Penrose–Ward path-integral derivation in CP³ twistor space
- Automatic emergence of SU(3)×SU(2)×U(1) from index-3 bundle
- Three fermion families from topological winding numbers
- Higgs mechanism as twistor bundle reduction
Core twistor quantization:
$$\mathcal{Z} = \int_{\mathbb{CP}^3} \mathcal{D}\omega^{(0,2)} \exp\left[\frac{i}{\hbar}\int_{\mathbb{CP}^3} \omega \wedge H_{\text{tw}}\right]$$Gauge group emergence:
$$G_{\text{SM}} = \frac{\text{Aut}(\mathcal{E}_3)}{\text{Stab}(\phi_0)} \cong SU(3) \times SU(2) \times U(1)$$Matrix–Scalaron Quantum Gravity & Emergent Spacetime
Key Results:
- Spectral-triple → classical manifold emergence proof
- Einstein equations from scalaron condensate dynamics
- Resolution of cosmological constant problem via self-tuning
- Black hole microstates as matrix configurations
Matrix action:
$$S_{\text{matrix}} = \text{Tr}\left[\frac{1}{2}[D_\mu, \Phi][D^\mu, \Phi] + V(\Phi) + \Phi J_{\text{tw}}\right]$$Emergent metric:
$$g_{\mu\nu} = \lim_{N \to \infty} \frac{1}{N}\text{Tr}[\gamma_\mu, \Phi][\gamma_\nu, \Phi]$$