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arXiv · 2407.00161

Quantum Time and the Time-Dilation induced Interaction Transfer mechanism

Dario Cafasso·Nicola Pranzini·Jorge Yago Malo·Vittorio Giovannetti·Marilù Chiofalo
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Abstract

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 Schr\"odinger 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.

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Dario Cafasso, Nicola Pranzini, Jorge Yago Malo, Vittorio Giovannetti, Marilù Chiofalo. 2024-06-28. Quantum Time and the Time-Dilation induced Interaction Transfer mechanism. https://doi.org/10.1103/physrevd.110.106014

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