arXiv subjects

Tommaso Favalli

Publications and source records attributed to Tommaso Favalli.

9 recordsLinked to original sources

arXiv2026

Quantum spacetime from constraints: wave equations and fields

In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both quantum clocks and rods, and imposing global constraints on total energy and momentum, we constructed a fully relational model of quantum spacetime. Here we take a further step: working in 1+1 dimensions, we show that the standard wave equations governing quantum particles (the Schrödinger, Klein-Gordon and Dirac equations) emerge naturally from this framework. The solutions of the equations are derived directly from the constraints, without assuming any external spacetime structure. The second quantization formalism is also implemented and discussed. Our results provide further support for the idea that quantum dynamics in spacetime may emerge from entanglement and constraints.

gr-qc↗

arXiv2025

Insensitivity points and performance of open quantum interferometers under number-conserving & non-conserving Lindblad dynamics

We investigate the phase sensitivity of a linear two-mode atom interferometer subject to environmental noise, modeled within the framework of open quantum systems with both number-conserving and non-conserving Lindblad operators. Considering several input states, we first study the cases N=1,2 (N number of particles) and perform numerical simulations for N>2. The sensitivity as a function of the holding time can display divergence points where phase estimation becomes impossible, to which we refer as insensitivity points. We characterize their behavior as the input state, particle number, and noise operator are varied, and we find that their positions are independent of the noise intensity. Moreover, while our fixed measurement scheme may favor number-conserving noise at small N (i.e., having better sensitivity), the Cramér-Rao bound reveals that particle non-conserving noise yields strictly lower achievable sensitivity for all particle numbers.

quant-ph↗

arXiv2025

On the Emergence of Time and Space in Closed Quantum Systems

Time, space and entanglement are the main characters in this work. Their nature is still a great mystery in physics and we study here the possibility that these three phenomena are closely connected, showing how entanglement can be at the basis of the emergence of time and space within closed quantum systems. We revisit and extend the Page and Wootters theory that was originally introduced in order to describe the emergence of time through entanglement between subsystems in a globally static, quantum Universe. In the book, after providing a complete review of the salient aspects of the theory, we establish a connection with recent research on the foundations of statistical mechanics and we propose a new understanding of the thermalization process. Furthermore, we generalize the framework in order describe the spatial degree of freedom and we provide a model of 3+1 dimensional, quantum spacetime emerging from entanglement among different subsystems in a globally "timeless" and "positionless" Universe. Finally, via the Page and Wootters theory, the evolution of quantum clocks within a gravitational field is treated and a time dilation effect is obtained in agreement with the Schwarzschild solution.

quant-ph↗

arXiv2025

Effect of Energy Extensivity on the Performance of Open Quantum Interferometers

Studying the performance of a quantum interferometer coupled to an external environment is a problem of conceptual and practical importance. If we consider a quantum interferometer featuring Heisenberg-limited sensitivity, then a typical result is that introducing coupling with the environment degrades the sensitivity to the shot-noise limit. Here we argue that this result crucially depends on whether the interferometer-environment coupling term is subject (or not) to the so-called Kac rescaling that restores extensivity, i.e., whether the coupling Hamiltonian is extensive or not. We present results of the Lindblad equation in the presence and absence of Kac rescaling of the coupling constant. Our results show that for a linear coupling and a harmonic model of the environment, often used in modeling of a quantum interferometer coupled with an environment, the Heisenberg-limited sensitivity may be restored after the Kac rescaling. This result points out the need and the importance to characterize the (model of the) environment of the interferometer at hand.

quant-ph↗

arXiv2025

Relativistic limits on the discretization and temporal resolution of a quantum clock

We provide a brief discussion regarding relativistic limits on the discretization and temporal resolution of time values in a quantum clock. Our clock is characterized by a time observable chosen to be the complement of a bounded and discrete Hamiltonian which can have an equally-spaced or a generic spectrum. In the first case the time observable can be described by a Hermitian operator and we find a limit in the discretization for the time eigenvalues. Nevertheless, in both cases, the time observable can be described by a POVM and, by increasing the number of time states, we show how the bound on the minimum time quantum can be reduced and identify the conditions under which the clock values can be treated as continuous. Finally, we find a limit for temporal resolution of our time observable when the clock is used (together with light signals) in a relativistic framework for measuring spacetime distances.

quant-ph↗

arXiv2025

Time dilation of quantum clocks in a relativistic gravitational potential

We study the dynamical evolution of two quantum clocks interacting with a relativistic gravitational potential. We find a time dilation effect for the clocks in agreement with the gravitational time dilation as obtained from the Schwarzschild solution in General Relativity. We perform our investigation via the Page and Wootters quantum time formalism, exploring the dynamics of clocks assuming them in both a product state and a more general (entangled) state. The gravitational redshift, as emerging from our framework, is also proposed and discussed.

gr-qc↗

arXiv2022

A model of quantum spacetime

We consider a global quantum system (the "Universe") satisfying a double constraint, both on total energy and total momentum. Generalizing the Page and Wootters quantum clock formalism, we provide a model of 3+1 dimensional, non-relativistic, quantum spacetime emerging from entanglement among different subsystems in a globally "timeless" and "positionless" Universe.

quant-ph↗

arXiv2022

Peaceful coexistence of thermal equilibrium and the emergence of time

We consider a quantum Universe composed by a small system S and a large environment. It has been demonstrated that, for the vast majority of randomly chosen wave-functions of the Universe satisfying a total energy constraint, the reduced density matrix of the system S is given by the canonical statistical distribution. Here, through the Page and Wootters mechanism, we show that time and non-equilibrium dynamics can emerge as a consequence of the entanglement between the system and the environment present in the (randomly chosen) global wave-function of the Universe. The clock is provided by the environment, which ticks the temporal evolution of S. The paradox of the peaceful coexistence of statistical equilibrium and non-equilibrium dynamics is solved by identifying the trace over the environment degrees of freedom with the temporal trace over the entire history of the system S.

quant-ph↗

arXiv2022

Time Observables in a Timeless Universe

Time in quantum mechanics is peculiar: it is an observable that cannot be associated to an Hermitian operator. As a consequence it is impossible to explain dynamics in an isolated system without invoking an external classical clock, a fact that becomes particularly problematic in the context of quantum gravity. An unconventional solution was pioneered by Page and Wootters (PaW) in 1983. PaW showed that dynamics can be an emergent property of the entanglement between two subsystems of a static Universe. In this work we first investigate the possibility to introduce in this framework a Hermitian time operator complement of a clock Hamiltonian having an equally-spaced energy spectrum. An Hermitian operator complement of such Hamiltonian was introduced by Pegg in 1998, who named it "Age". We show here that Age, when introduced in the PaW context, can be interpreted as a proper Hermitian time operator conjugate to a "good" clock Hamiltonian. We therefore show that, still following Pegg's formalism, it is possible to introduce in the PaW framework bounded clock Hamiltonians with an unequally-spaced energy spectrum with rational energy ratios. In this case time is described by a POVM and we demonstrate that Pegg's POVM states provide a consistent dynamical evolution of the system even if they are not orthogonal, and therefore partially un-distinguishables.

quant-ph↗