Quantum Time and the Time-Dilation induced Interaction Transfer mechanism
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909399422861312 |
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| author | Cafasso, Dario Pranzini, Nicola Malo, Jorge Yago Giovannetti, Vittorio Chiofalo, Marilù |
| author_facet | Cafasso, Dario Pranzini, Nicola Malo, Jorge Yago Giovannetti, Vittorio Chiofalo, Marilù |
| contents | Given a bipartite quantum system in an energy eigenstate, the dynamical description for one component can be derived via entanglement using the other component as a clock. This is the essence of the Page and Wootters mechanism. Moreover, if the clock is subject to a gravitational-like interaction, relative time evolution is then described by a Time-Dilated Schrödinger equation, in which the so-called Redshift Operator describes a purely quantum effect, analogue to gravitational time-dilation. Here we adopt a non-perturbative approach and present a finite-dimensional generalisation of this mechanism, expressing the quantum time-dilation effect as an effective interaction involving previously non-interacting system components. We name this a Time-Dilation induced Interaction Transfer (TiDIT) mechanism and discuss an example using two coupled spins as a quantum clock model. Our approach is suitable for implementations in current quantum technology and provides a new tool for exploring gravity at the intersection with quantum physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00161 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Time and the Time-Dilation induced Interaction Transfer mechanism Cafasso, Dario Pranzini, Nicola Malo, Jorge Yago Giovannetti, Vittorio Chiofalo, Marilù Quantum Physics General Relativity and Quantum Cosmology Given a bipartite quantum system in an energy eigenstate, the dynamical description for one component can be derived via entanglement using the other component as a clock. This is the essence of the Page and Wootters mechanism. Moreover, if the clock is subject to a gravitational-like interaction, relative time evolution is then described by a Time-Dilated Schrödinger equation, in which the so-called Redshift Operator describes a purely quantum effect, analogue to gravitational time-dilation. Here we adopt a non-perturbative approach and present a finite-dimensional generalisation of this mechanism, expressing the quantum time-dilation effect as an effective interaction involving previously non-interacting system components. We name this a Time-Dilation induced Interaction Transfer (TiDIT) mechanism and discuss an example using two coupled spins as a quantum clock model. Our approach is suitable for implementations in current quantum technology and provides a new tool for exploring gravity at the intersection with quantum physics. |
| title | Quantum Time and the Time-Dilation induced Interaction Transfer mechanism |
| topic | Quantum Physics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2407.00161 |