arXiv subjects

Joseph Balsells

Publications and source records attributed to Joseph Balsells.

4 recordsLinked to original sources

arXiv2025

Relativistic implications of entropy and purity

A quantum object is extended by virtue of uncertainty. When subjected to gravity, different parts of its wave function experience distinct local relativistic effects, leading to tidal and interference phenomena absent in the classical limit. These effects can be incorporated into a geometric extension of classical spacetime. For states quantum correlated in at least two directions, a complete description of motion requires a non-Riemannian geometry whose form is controlled by the state's entropy and purity and affects a broad range of phenomena from lab measurements to Hawking radiation. A specific implication of this framework is the appearance of quantum parameters in the time-dilation law in addition to the usual dependence on velocity and gravitational potential. The quantum-corrected time-dilation law is universal: the corrections depend solely on the external degrees of freedom and are independent of internal details of the clock mechanism.

quant-ph↗

arXiv2025

Quantum proper time: A Finsler space from entropy and purity

A quantum clock cannot be modeled as a point mass moving along a single geodesic if it is in a state with nonzero position fluctuations. Instead, it is an extended object subject to tidal forces and a superposition of time dilations at different altitudes. Here, a geometrical formulation of quantum mechanics is used to show that additional quantum properties representing correlations between different directions imply a non-Riemannian geometrical structure experienced by a quantum clock. A specific version of Finsler geometry parameterized by entropy and purity of the state provides a novel setting for a combination of quantum and gravitational effects. A crucial ingredient is given by a new parameterization of quantum-information properties related to second-order moments of a state and may also be useful in other applications.

quant-ph↗

arXiv2024

Geometry and proper time of a relativistic quantum clock

Classical clocks measure proper time along their worldline, and Riemannian geometry provides tools for predicting the time shown by clocks in both flat and curved spacetimes. Common approaches to time in quantum systems, based for instance on wave functions or density matrices, tend to obscure this geometric property at the quantum level. Here, a new framework is demonstrated for perturbing the classical path-length functional to include quantum degrees of freedom within a modified Riemannian geometry. In this framework, a quantum clock travels on geodesics of a family of spacetimes deformed by parameters specifying the clock's quantum state. Detailed derivations provide potentially testable corrections to gravitational time-dilation in Schwarzschild spacetime that scale with the ratio of the clock's Compton wavelength to its wave packet's spatial extent.

gr-qc↗

arXiv2023

Adherence and violation of the equivalence principle from classical to quantum mechanics

Investigation into the applicability of the equivalence principle in quantum mechanics has taken many forms, with varying conclusions. Here, a dynamical semi-classical description of a wave packet in terms of its center of mass and higher quantum fluctuations is applied to the case of a quantum particle in gravitational free fall. The analysis provides an intuitive account of the origin of mass-dependence in quantum-gravitational dynamics through an effective potential that enforces the uncertainty principle. This potential has two implications: (i) The lowest order quantum fluctuations encoding the width and spreading of the wave packet obey an uncertainty relation whose observance is mass-dependent. (ii) In an inhomogeneous gravitational field tidal effects couple the center of mass motion to the quantum fluctuations. The combined effect results in a clear demonstration of how some conceptions of the weak equivalence principle, based on mass dependence, are violated. The size of this violation is within sensitivities of current Eotvos and clock-based return time experiments.

quant-ph↗