The weak field limit of quantum matter back-reacting on classical spacetime
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913447795490816 |
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| author | Layton, Isaac Oppenheim, Jonathan Russo, Andrea Weller-Davies, Zachary |
| author_facet | Layton, Isaac Oppenheim, Jonathan Russo, Andrea Weller-Davies, Zachary |
| contents | Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such classical-quantum (CQ) theories of gravity. Our results are obtained both via the gauge fixing of the recently proposed path integral theory of CQ general relativity and via the CQ master equation approach. In each case, we find the same weak field dynamics. We find that the Newtonian potential diffuses by an amount lower bounded by the decoherence rate into mass eigenstates. We also present our results as an unravelled system of stochastic differential equations for the trajectory of the hybrid classical-quantum state and provide a series of kernels for constructing figures of merit, which can be used to rule out part of the parameter space of classical-quantum theories of gravity by experimentally testing it via the decoherence-diffusion trade-off. We compare and contrast the weak field limit to previous models of classical Newtonian gravity coupled to quantum systems. Here, we find that the Newtonian potential and quantum state change in lock-step, with the flow of time being stochastic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_02557 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The weak field limit of quantum matter back-reacting on classical spacetime Layton, Isaac Oppenheim, Jonathan Russo, Andrea Weller-Davies, Zachary General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such classical-quantum (CQ) theories of gravity. Our results are obtained both via the gauge fixing of the recently proposed path integral theory of CQ general relativity and via the CQ master equation approach. In each case, we find the same weak field dynamics. We find that the Newtonian potential diffuses by an amount lower bounded by the decoherence rate into mass eigenstates. We also present our results as an unravelled system of stochastic differential equations for the trajectory of the hybrid classical-quantum state and provide a series of kernels for constructing figures of merit, which can be used to rule out part of the parameter space of classical-quantum theories of gravity by experimentally testing it via the decoherence-diffusion trade-off. We compare and contrast the weak field limit to previous models of classical Newtonian gravity coupled to quantum systems. Here, we find that the Newtonian potential and quantum state change in lock-step, with the flow of time being stochastic. |
| title | The weak field limit of quantum matter back-reacting on classical spacetime |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2307.02557 |