Restoring a Missing Meta-Symmetry of Quantum Mechanics
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911564044435456 |
|---|---|
| author | Ran, Sheng |
| author_facet | Ran, Sheng |
| contents | In conventional quantum mechanics, all unitary evolution takes place within the space-time Hilbert space $\mathcal H_{xt}=L^2(\mathcal M_{xt})$, with time as the sole evolution parameter. The momentum-energy representation $ϕ(k,E)$ is treated merely as a Fourier re-expression of the same state-kinematically equivalent but dynamically inert. Here we restore the fundamental symmetry between the conjugate pairs $(x,t)$ and $(k,E)$ by extending the quantum theory to an enlarged Hilbert space $\mathcal H_{\text{total}} = \mathcal H_{xt} \oplus \mathcal H_{kE}$, within which the momentum-energy sector $\mathcal H_{kE}=L^2(\mathcal M_{kE})$ carries its own autonomous unitary evolution generated by a self-adjoint operator $\hat{\mathcal T}$. The resulting structure establishes a meta-symmetry: a symmetry between two conjugate dynamical projections of a single global quantum state. It produces a dual-manifold geometry in which each domain is locally complete yet globally open, with divergent limits in one mapping onto extended regions in the other. Remarkably, the dual-manifold symmetry alone reproduces both the uniform dark-energy background and the exponential boundary mapping near black-hole horizons that underlies Hawking radiation. This framework thus opens a quantum-theoretic route to cosmological phenomena that are ordinarily treated within general relativity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Restoring a Missing Meta-Symmetry of Quantum Mechanics Ran, Sheng Quantum Physics Statistical Mechanics General Relativity and Quantum Cosmology In conventional quantum mechanics, all unitary evolution takes place within the space-time Hilbert space $\mathcal H_{xt}=L^2(\mathcal M_{xt})$, with time as the sole evolution parameter. The momentum-energy representation $ϕ(k,E)$ is treated merely as a Fourier re-expression of the same state-kinematically equivalent but dynamically inert. Here we restore the fundamental symmetry between the conjugate pairs $(x,t)$ and $(k,E)$ by extending the quantum theory to an enlarged Hilbert space $\mathcal H_{\text{total}} = \mathcal H_{xt} \oplus \mathcal H_{kE}$, within which the momentum-energy sector $\mathcal H_{kE}=L^2(\mathcal M_{kE})$ carries its own autonomous unitary evolution generated by a self-adjoint operator $\hat{\mathcal T}$. The resulting structure establishes a meta-symmetry: a symmetry between two conjugate dynamical projections of a single global quantum state. It produces a dual-manifold geometry in which each domain is locally complete yet globally open, with divergent limits in one mapping onto extended regions in the other. Remarkably, the dual-manifold symmetry alone reproduces both the uniform dark-energy background and the exponential boundary mapping near black-hole horizons that underlies Hawking radiation. This framework thus opens a quantum-theoretic route to cosmological phenomena that are ordinarily treated within general relativity. |
| title | Restoring a Missing Meta-Symmetry of Quantum Mechanics |
| topic | Quantum Physics Statistical Mechanics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2511.20907 |