Three-space as a quantum hyper-layer in 1+3 dimensions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908377008832512 |
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| author | Czachor, Marek |
| author_facet | Czachor, Marek |
| contents | We discuss a formalism where a universe is identified with the support of a wave function propagating through space-time. As opposed to classical cosmology, the resulting universe is not a spacelike section of some space-time, but a hyper-layer of a finite timelike width, a set which is not a three-dimensional submanifold of space-time. We test the formalism on the example of a universe that contains a single harmonic oscillator (a generalization of the curvature-dependent Cariñena-Rañada-Santander (CRS) model). As opposed to the original CRS formulation, here the curvature is not a parameter but a quantum observable, a function of the world-position operator. It is shown that asymptotically, for large values of the invariant evolution parameter $τ$, one reconstructs the standard quantum results, with one modifiication: The effective (renormalized) mass of the oscillator decreases with $τ$. The effect does not seem to be a peculiarity of harmonic oscillators, so one may speculate that masses of distant elementary quantum systems are greater from their values known from our quantum mechanical measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09487 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three-space as a quantum hyper-layer in 1+3 dimensions Czachor, Marek General Relativity and Quantum Cosmology We discuss a formalism where a universe is identified with the support of a wave function propagating through space-time. As opposed to classical cosmology, the resulting universe is not a spacelike section of some space-time, but a hyper-layer of a finite timelike width, a set which is not a three-dimensional submanifold of space-time. We test the formalism on the example of a universe that contains a single harmonic oscillator (a generalization of the curvature-dependent Cariñena-Rañada-Santander (CRS) model). As opposed to the original CRS formulation, here the curvature is not a parameter but a quantum observable, a function of the world-position operator. It is shown that asymptotically, for large values of the invariant evolution parameter $τ$, one reconstructs the standard quantum results, with one modifiication: The effective (renormalized) mass of the oscillator decreases with $τ$. The effect does not seem to be a peculiarity of harmonic oscillators, so one may speculate that masses of distant elementary quantum systems are greater from their values known from our quantum mechanical measurements. |
| title | Three-space as a quantum hyper-layer in 1+3 dimensions |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2406.09487 |