In 1964, Yu. A. Gol'fand proposed an extension of quantum mechanics to discrete time, predicting intrinsic non-unitarity and entropy increase. While historically significant, this formalism predates the modern theory of open quantum systems. In this work, we rigorously recast Gol'fand's discrete evolution equation as a Completely Positive Trace-Preserving (CPTP) quantum channel and derive its continuous-time coarse-grained limit. We demonstrate that the dynamics converge to a specific Lindblad master equation characterized by a fundamental time scale $τ$ , which induces decoherence in both the energy basis and a fundamental operator basis $W$ . We analyze the thermodynamic implications using Spohn's entropy production formalism, proving that the discrete time step induces a strictly positive entropy production rate driven by the decay of quantum coherences, thereby providing a microscopic foundation for the arrow of time independent of environmental coupling. Furthermore, we quantify the loss of quantum coherence via fidelity decay and purity loss, establishing exact constraints for fault-tolerant quantum computing. We further investigate the impact of this intrinsic decoherence on Discrete Time Crystals (DTCs), showing that Gol'fand dynamics impose a fundamental lifetime limit on time-translation symmetry breaking phases. Finally, we utilize precision data from optical lattice clocks, matter-wave interferometry, and neutrino oscillations to place stringent upper bounds on $τ$ . Our results constrain the fundamental time discretization to $τ\lesssim 10^{-26}$ s, significantly tightening previous limits and offering a testable framework for quantum gravity phenomenology.In 1964, Yu. A. Gol'fand proposed an extension of quantum mechanics to discrete time, predicting intrinsic non-unitarity and entropy increase. While historically significant, this formalism predates the modern theory of open quantum systems. In this work, we rigorously recast Gol'fand's discrete evolution equation as a Completely Positive Trace-Preserving (CPTP) quantum channel and derive its continuous-time coarse-grained limit. We demonstrate that the dynamics converge to a specific Lindblad master equation characterized by a fundamental time scale $τ$, which induces decoherence in both the energy basis and a fundamental operator basis $W$. We analyze the thermodynamic implications using Spohn's entropy production formalism, proving that the discrete time step induces a strictly positive entropy production rate driven by the decay of quantum coherences, thereby providing a microscopic foundation for the arrow of time independent of environmental coupling. Furthermore, we quantify the loss of quantum coherence via fidelity decay and purity loss, establishing exact constraints for fault-tolerant quantum computing. We further investigate the impact of this intrinsic decoherence on Discrete Time Crystals (DTCs), showing that Gol'fand dynamics impose a fundamental lifetime limit on time-translation symmetry breaking phases. Finally, we utilize precision data from optical lattice clocks, matter-wave interferometry, and neutrino oscillations to place stringent upper bounds on $τ$. Our results constrain the fundamental time discretization to $τ\lesssim 10^{-26}$ s, significantly tightening previous limits and offering a testable framework for quantum gravity phenomenology.

quant-pharXiv:2606.22187Jun 23, 20260 citations

Strongly incoherent gravity

Daniel Carney, Jacob M. Taylor

While most fundamental interactions in nature are known to be mediated by quantized fields, the possibility has been raised that gravity may behave differently. Making this concept precise enough to test requires consistent models. Here we construct an explicit example of a theory where a non-entangling version of an arbitrary two-body potential $V(r)$ arises from local measurements and feedback forces. While a variety of such theories exist, our construction causes particularly strong decoherence compared to more subtle approaches. Regardless, expectation values of observables obey the usual classical dynamics, while the interaction generates no entanglement. Applied to the Newtonian potential, this produces a non-relativistic model of gravity with fundamental loss of unitarity. The model contains a pair of free parameters, a substantial range of which is not excluded by observations to date. As an alternative to testing entanglement properties, we show that the entire remaining parameter space can be tested by looking for loss of quantum coherence in small systems like atom interferometers coupled to oscillating source masses.While most fundamental interactions in nature are known to be mediated by quantized fields, the possibility has been raised that gravity may behave differently. Making this concept precise enough to test requires consistent models. Here we construct an explicit example of a theory where a non-entangling version of an arbitrary two-body potential $V(r)$ arises from local measurements and feedback forces. While a variety of such theories exist, our construction causes particularly strong decoherence compared to more subtle approaches. Regardless, expectation values of observables obey the usual classical dynamics, while the interaction generates no entanglement. Applied to the Newtonian potential, this produces a non-relativistic model of gravity with fundamental loss of unitarity. The model contains a pair of free parameters, a substantial range of which is not excluded by observations to date. As an alternative to testing entanglement properties, we show that the entire remaining parameter space can be tested by looking for loss of quantum coherence in small systems like atom interferometers coupled to oscillating source masses.

arXiv:2301.08378Jan 20, 20232 citations

Decoherence of Quantum Systems due to Gravitational Interaction

Martine Schut

Jul 25, 20190 citations

The Montevideo interpretation of quantum mechanics: frequently asked questions

Rodolfo Gambini, Jorge Pullin

In a series of recent papers we have introduced a new interpretation of quantum mechanics, which for brevity we will call the Montevideo interpretation. In it, the quantum to classical transition is achieved via a phenomenon called "undecidability" which stems from environmental decoherence supplemented with a fundamental mechanism of loss of coherence due to gravity. Due to the fact that the interpretation grew from several results that are dispersed in the literature, we put together this straightforward-to-read article addressing some of the main points that may confuse readers.In a series of recent papers we have introduced a new interpretation of quantum mechanics, which for brevity we will call the Montevideo interpretation. In it, the quantum to classical transition is achieved via a phenomenon called "undecidability" which stems from environmental decoherence supplemented with a fundamental mechanism of loss of coherence due to gravity. Due to the fact that the interpretation grew from several results that are dispersed in the literature, we put together this straightforward-to-read article addressing some of the main points that may confuse readers.

arXiv:0905.4402Journal of Physics Conference SeriesJun 1, 200912 citations

τ

, which induces decoherence in both the energy basis and a fundamental operator basis

W

. We analyze the thermodynamic implications using Spohn's entropy production formalism, proving that the discrete time step induces a strictly positive entropy production rate driven by the decay of quantum coherences, thereby providing a microscopic foundation for the arrow of time independent of environmental coupling. Furthermore, we quantify the loss of quantum coherence via fidelity decay and purity loss, establishing exact constraints for fault-tolerant quantum computing. We further investigate the impact of this intrinsic decoherence on Discrete Time Crystals (DTCs), showing that Gol'fand dynamics impose a fundamental lifetime limit on time-translation symmetry breaking phases. Finally, we utilize precision data from optical lattice clocks, matter-wave interferometry, and neutrino oscillations to place stringent upper bounds on

τ

. Our results constrain the fundamental time discretization to

τ\lesssim 10^{-26}

s, significantly tightening previous limits and offering a testable framework for quantum gravity phenomenology.

V(r)

arises from local measurements and feedback forces. While a variety of such theories exist, our construction causes particularly strong decoherence compared to more subtle approaches. Regardless, expectation values of observables obey the usual classical dynamics, while the interaction generates no entanglement. Applied to the Newtonian potential, this produces a non-relativistic model of gravity with fundamental loss of unitarity. The model contains a pair of free parameters, a substantial range of which is not excluded by observations to date. As an alternative to testing entanglement properties, we show that the entire remaining parameter space can be tested by looking for loss of quantum coherence in small systems like atom interferometers coupled to oscillating source masses.