Gravitational Quantum Limit for Length Measurements

最小长度对开普勒散射和引力透镜效应的影响

Minimal Length Effects on Keplerian Scattering and Gravitational Lensing

本文研究最小长度对开普勒问题中无界轨迹的影响，通过哈密顿矢量进动分析轨道扰动，推导出最小长度效应的轨迹修正，发现量子引力修正使散射角减小，特别是对光子等无质量粒子，空间量子化减弱引力透镜效应。

Minimal Length in quantum gravity and gravitational measurements

The existence of a minimal length is a common prediction of various theories of quantum gravity. This minimal length leads to a modification of the Heisenberg uncertainty principle to a Generalized Uncertainty Principle (GUP). Various studies showed that a GUP modifies the Hawking radiation of black holes. In this paper, we propose a modification of the Schwarzschild metric based on the modified Hawking temperature derived from the GUP. Based on this modified metric, we calculate corrections to the deflection of light, time delay of light, perihelion precession, and gravitational redshift. We …

Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale

Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy quantum spacetime with a fluctuating minimal length coinciding on average with the Planck scale. Considering deformed canonical commutation relations with a fluctuating deformation parameter, we derive a Lindblad master equation that yields localization in energy space and decoherence times consistent with the currently available observational evidence. Compared t…

Quantum gravitational decoherence of matter waves

One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of the Brownian motion whose correlation length is given by the Planck length up to a scaling fact…

Extra-symmetric Born--Infeld theory of electroweak and gravitational fields

This paper suggests a generalization of the Born--Infeld action (1932) for the case of electroweak and gravitational fields. Basic notions one deals with are Dirac matrices, $γ_{a}$, and dimensionless covariant derivatives, $π_{a} = - i\ell \nabla_{a}$, given in spinorial and scalar representations. The action contains a characteristic length $\ell$ (which is of order of magnitude of Planck's length), as a parameter and possesses an extra symmetry with respect to transformations of the Lorentz group imposed on pairs ($γ_{a}$, $π_{a}$). It's shown that parameter of the Lorentz group is associat…

引力量子力学的一种代数方法

An algebraic approach to gravitational quantum mechanics

本研究基于形变海森堡代数的位置表象，探究引力量子力学模型，分析了高斯波包自由演化与两类势阱中粒子的谱特性，为含普朗克尺度最小长度的量子引力研究提供了代数路径的新结果。