Modified Special Relativity on a fluctuating spacetime
arXiv:gr-qc/0607024 · doi:10.1103/PhysRevD.74.085017
Abstract
It was recently proposed that deformations of the relativistic symmetry, as those considered in Deformed Special Relativity (DSR), can be seen as the outcome of a measurement theory in the presence of non-negligible (albeit small) quantum gravitational fluctuations [1,2]. In this paper we explicitly consider the case of a spacetime described by a flat metric endowed with stochastic fluctuations and, for a free particle, we show that DSR-like nonlinear relations between the spaces of the measured and classical momenta, can result from the average of the stochastic fluctuations over a scale set be the de Broglie wavelength of the particle. As illustrative examples we consider explicitly the averaging procedure for some simple stochastic processes and discuss the physical implications of our results.
7 pages, no figures
References in corpus (12)
- Deformed Special Relativity as an effective flat limit of quantum gravity
- Interpretation of Quantum Field Theories with a Minimal Length Scale
- Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
- The Free Particle in Deformed Special Relativity
- Asymptotic Flatness in Rainbow Gravity
- Interpreting doubly special relativity as a modified theory of measurement
- Deformed Special Relativity as an effective theory of measurements on quantum gravitational backgrounds
- Doubly Special Relativity in Position Space Starting from the Conformal Group
- A note on DSR-like approach to space-time
- Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique
- Hamiltonian formalism and spacetime symmetries in generic DSR models
- Continuous distribution of frequencies and deformed dispersion relations
Cited by in corpus (15)
- Quantum reference frames and deformed symmetries
- Metric fluctuations and the Weak Equivalence Principle
- Lorentz Invariance Violation from String Theory
- Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
- Acceleration and propagation of ultra high energy cosmic rays
- Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
- Foundations of anisotropic relativistic mechanics
- Constraints on the deformation scale of a geometry in the cotangent bundle
- Selected Topics in Cosmic Ray Physics
- Causal sets and conservation laws in tests of Lorentz symmetry
- Intrinsic measurement errors for the speed of light in vacuum
- Damped Corrections to Inflationary Spectra from a Fluctuating Cutoff
- Bogoliubov space of a Bose--Einstein condensate and quantum spacetime fluctuations
- From Noncommutative Sphere to Nonrelativistic Spin
- The Theory of a Quantum Noncanonical Field in Curved Spacetimes