Restoring a Missing Meta-Symmetry of Quantum Mechanics

• URL: http://arxiv.org/abs/2511.20907v1
• Date: Tue, 25 Nov 2025 22:49:32 GMT
• Title: Restoring a Missing Meta-Symmetry of Quantum Mechanics
• Authors: Sheng Ran,
• Abstract summary: In conventional quantum mechanics, all unitary evolution takes place within the space-time Hilbert space $mathcal H_xt=L2(mathcal M_xt)$.<n>We extend the quantum theory to an enlarged Hilbert space $mathcal H_xt oplus mathcal H_kE$.<n>The resulting structure establishes a meta-symmetry: a symmetry between two conjugate dynamical projections of a single global quantum state.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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