The classical limit of quantum mechanics through coarse-grained measurements
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915964776349696 |
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| author | Bibak, Fatemeh Cepollaro, Carlo Sánchez, Nicolás Medina Dakić, Borivoje Brukner, Časlav |
| author_facet | Bibak, Fatemeh Cepollaro, Carlo Sánchez, Nicolás Medina Dakić, Borivoje Brukner, Časlav |
| contents | Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs. When the resolved phase-space area is large compared with Planck's constant, the accessible statistics of any quantum state admit an effective classical description: coarse-grained observables become approximately jointly measurable and the induced probability density is positive. We derive the exact evolution equation for this density and show that, in the strong coarse-graining regime, its non-Liouville corrections are suppressed up to an Ehrenfest time, resulting in classical Hamiltonian flow generated by a Hamiltonian smoothed over the measurement cell. When the Hamiltonian varies negligibly across such a cell, the smoothed Hamiltonian reduces to the classical Hamiltonian whose quantization produced the quantum dynamics, thereby closing the quantization--classical-limit loop. Repeated finite-resolution measurements then generate stochastic records confined, with high probability, to tubes around classical trajectories. Our results provide a unified operational framework for the quantum-to-classical transition in microscopic and macroscopic systems, and establish the consistency of the quantization--classical-limit cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The classical limit of quantum mechanics through coarse-grained measurements Bibak, Fatemeh Cepollaro, Carlo Sánchez, Nicolás Medina Dakić, Borivoje Brukner, Časlav Quantum Physics Classical Physics Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs. When the resolved phase-space area is large compared with Planck's constant, the accessible statistics of any quantum state admit an effective classical description: coarse-grained observables become approximately jointly measurable and the induced probability density is positive. We derive the exact evolution equation for this density and show that, in the strong coarse-graining regime, its non-Liouville corrections are suppressed up to an Ehrenfest time, resulting in classical Hamiltonian flow generated by a Hamiltonian smoothed over the measurement cell. When the Hamiltonian varies negligibly across such a cell, the smoothed Hamiltonian reduces to the classical Hamiltonian whose quantization produced the quantum dynamics, thereby closing the quantization--classical-limit loop. Repeated finite-resolution measurements then generate stochastic records confined, with high probability, to tubes around classical trajectories. Our results provide a unified operational framework for the quantum-to-classical transition in microscopic and macroscopic systems, and establish the consistency of the quantization--classical-limit cycle. |
| title | The classical limit of quantum mechanics through coarse-grained measurements |
| topic | Quantum Physics Classical Physics |
| url | https://arxiv.org/abs/2503.15642 |