Rendered Frame Theory: A Dissipative Field Theory of Observer‑Dependent Quantum Measurement V2
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2026
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| author | Grinstead, Liam.S |
| author_facet | Grinstead, Liam.S |
| contents | <p><strong>Rendered Frame Theory (RFT) </strong>is a fully reconstructed dissipative field theory of observer-dependent quantum measurement. This version replaces an earlier formulation that, upon detailed review, was found to contain structural inconsistencies in the dissipation law, the energy identity, and the canonical reduction. The theory has been rebuilt from first principles, with every equation re-derived and every assumption re-examined.</p> <p><strong>The updated formulation establishes:</strong></p> <p><strong>• a consistent Lagrangian and Euler–Lagrange structure,</strong></p> <p><strong> </strong><br><strong>• a corrected dissipative Hamiltonian system, </strong></p> <p><br><strong>• a strict energy decay law dE/dt = -gamma * ∫ Pi^2 dx, </strong></p> <p><br><strong>• a global attractor guaranteeing convergence to stationary states, </strong></p> <p><strong> </strong><br><strong>• and a rigorous ultraviolet (UV) reduction to the free Schrödinger equation.</strong></p> <p>Symbolic and numerical testing confirmed that the dissipation functional’s second derivative D''(Phi) is proportional to lambda_D, ensuring that all non-canonical terms vanish as lambda_D → 0. In this UV limit, the RFT Poisson bracket collapses to the standard symplectic form and the evolution equations reduce to:</p> <p><strong>i*hbar*∂_t psi = -(hbar^2 / 2m) * ∇^2 psi</strong></p> <p>recovering standard quantum mechanics exactly.</p> <p>The Operator Saturation Test remains the central experimental prediction: RFT forecasts a hard coherence bound |Phi| ≤ 2, in contrast to the unbounded behaviour predicted by standard quantum mechanics. This provides a concrete, falsifiable laboratory signature.</p> <p>This version represents the mathematically consistent, fully validated formulation of RFT.</p> <p><strong>contact: Liamgrinstead2@gmail.com</strong></p> <p><strong>rftsystems4ai@gmail.com</strong></p> <p><strong>https://symbolic-laws-of-computational-physics.pubpub.org</strong></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19600166 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Rendered Frame Theory: A Dissipative Field Theory of Observer‑Dependent Quantum Measurement V2 Grinstead, Liam.S Rendered Frame Theory, quantum measurement, collapse dynamics, dissipative field theory, coherence field, observer coupling, dissipation functional, reaction–diffusion equation, global attractor, renormalization group, UV fixed point, IR fixed point, Hamiltonian dissipation, phase‑space contraction, bounded coherence, trapped‑ion experiment, Operator Saturation Test, quantum foundations, nonlinear dynamics, variational principles <p><strong>Rendered Frame Theory (RFT) </strong>is a fully reconstructed dissipative field theory of observer-dependent quantum measurement. This version replaces an earlier formulation that, upon detailed review, was found to contain structural inconsistencies in the dissipation law, the energy identity, and the canonical reduction. The theory has been rebuilt from first principles, with every equation re-derived and every assumption re-examined.</p> <p><strong>The updated formulation establishes:</strong></p> <p><strong>• a consistent Lagrangian and Euler–Lagrange structure,</strong></p> <p><strong> </strong><br><strong>• a corrected dissipative Hamiltonian system, </strong></p> <p><br><strong>• a strict energy decay law dE/dt = -gamma * ∫ Pi^2 dx, </strong></p> <p><br><strong>• a global attractor guaranteeing convergence to stationary states, </strong></p> <p><strong> </strong><br><strong>• and a rigorous ultraviolet (UV) reduction to the free Schrödinger equation.</strong></p> <p>Symbolic and numerical testing confirmed that the dissipation functional’s second derivative D''(Phi) is proportional to lambda_D, ensuring that all non-canonical terms vanish as lambda_D → 0. In this UV limit, the RFT Poisson bracket collapses to the standard symplectic form and the evolution equations reduce to:</p> <p><strong>i*hbar*∂_t psi = -(hbar^2 / 2m) * ∇^2 psi</strong></p> <p>recovering standard quantum mechanics exactly.</p> <p>The Operator Saturation Test remains the central experimental prediction: RFT forecasts a hard coherence bound |Phi| ≤ 2, in contrast to the unbounded behaviour predicted by standard quantum mechanics. This provides a concrete, falsifiable laboratory signature.</p> <p>This version represents the mathematically consistent, fully validated formulation of RFT.</p> <p><strong>contact: Liamgrinstead2@gmail.com</strong></p> <p><strong>rftsystems4ai@gmail.com</strong></p> <p><strong>https://symbolic-laws-of-computational-physics.pubpub.org</strong></p> |
| title | Rendered Frame Theory: A Dissipative Field Theory of Observer‑Dependent Quantum Measurement V2 |
| topic | Rendered Frame Theory, quantum measurement, collapse dynamics, dissipative field theory, coherence field, observer coupling, dissipation functional, reaction–diffusion equation, global attractor, renormalization group, UV fixed point, IR fixed point, Hamiltonian dissipation, phase‑space contraction, bounded coherence, trapped‑ion experiment, Operator Saturation Test, quantum foundations, nonlinear dynamics, variational principles |
| url | https://doi.org/10.5281/zenodo.19600166 |