The principle of relative locality

Abstract

We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature.

12 pages, 3 figures; in version 2 one reference added and some minor modifications in sects. II and III made

References in corpus (9)

• Prospects for constraining quantum gravity dispersion with near term observations
• Bounds on an energy-dependent and observer-independent speed of light from violations of locality
• Probing a Possible Vacuum Refractive Index with Gamma-Ray Telescopes
• Anatomy of a deformed symmetry: field quantization on curved momentum space
• Effective particle kinematics from Quantum Gravity
• Quantum Gravity, Dynamical Energy-Momentum Space and Vacuum Energy
• Kinematics of a relativistic particle with de Sitter momentum space
• Snyder Space-Time: K-Loop and Lie Triple System
• Comment on 'Large-scale non-locality in "doubly special relativity" with an energy-dependent speed of light'

Cited by in corpus (263)

• Minimal Length Scale Scenarios for Quantum Gravity
• The Spin Foam Approach to Quantum Gravity
• Probing Planck-scale physics with quantum optics
• Tests of Lorentz invariance: a 2013 update
• Gravitational Decoherence
• Fundamental quantum optics experiments conceivable with satellites -- reaching relativistic distances and velocities
• Born Reciprocity in String Theory and the Nature of Spacetime
• Hamilton geometry: Phase space geometry from modified dispersion relations
• Quantum Gravity, Dynamical Phase Space and String Theory
• Realization of DSR-relativistic symmetries in Finsler geometries
• The Universe as a Process of Unique Events
• Relative-locality distant observers and the phenomenology of momentum-space geometry
• 30 years in: Quo vadis generalized uncertainty principle?
• Planck-scale-modified dispersion relations in FRW spacetime
• OPERA-reassessing data on the energy dependence of the speed of neutrinos
• Diffusion on $\kappa$-Minkowski space
• Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime
• Challenge to Macroscopic Probes of Quantum Spacetime Based on Noncommutative Geometry
• Energetic Causal Sets
• Quantum Spaces are Modular
• Generalized uncertainty principles and quantum field theory
• Relative locality and the soccer ball problem
• Fractional and noncommutative spacetimes
• Relativistic deformed kinematics from momentum space geometry
• Local effects of the quantum vacuum in Lorentz-violating electrodynamics
• A Unique Connection for Born Geometry
• On the fate of Lorentz symmetry in relative-locality momentum spaces
• Spacetime-noncommutativity regime of Loop Quantum Gravity
• Relativistic kinematics beyond Special Relativity
• Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case
• Lorentz Invariance Violation and Chemical Composition of Ultra High Energy Cosmic Rays
• MOND as a regime of quantum gravity
• Rainbow metric from quantum gravity
• Generalized uncertainty principle or curved momentum space?
• Living in Curved Momentum Space
• Compact phase space, cosmological constant, discrete time
• Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
• High temperature dimensional reduction in Snyder space
• On the initial singularity problem in rainbow cosmology
• Particle Dynamics on Snyder space
• Spectral dimension in causal set quantum gravity
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Generalized Uncertainty Principle Removes The Chandrasekhar Limit
• Phenomenological consequences of a geometry in the cotangent bundle
• Planck-scale dimensional reduction without a preferred frame
• Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
• Deformed relativistic kinematics on curved spacetime -- a geometric approach
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• The kappa-(A)dS quantum algebra in (3+1) dimensions
• Gamma ray burst delay times probe the geometry of momentum space
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• The Theory of Metaparticles
• The Soccer-Ball Problem
• Lifting General Relativity to Observer Space
• Observables and Dispersion Relations in k-Minkowski Spacetime
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Observer-dependent locality of quantum events
• Planck-scale phenomenology with anti-de Sitter momentum space
• Unified description for kappa-deformations of orthogonal groups
• Curved momentum spaces from quantum (Anti-)de Sitter groups in (3+1) dimensions
• The DSR-deformed relativistic symmetries and the relative locality of 3D quantum gravity
• Natural Cutoffs via Compact Symplectic Manifolds
• Towards the map of quantum gravity
• Relative locality in a quantum spacetime and the pregeometry of $\kappa$-Minkowski
• Theory and Phenomenology of Spacetime Defects
• Noncommutative fields and the short-scale structure of spacetime
• A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
• Special Relativity in a Discrete Quantum Universe
• Dual redshift on Planck-scale-curved momentum spaces
• On de Sitter Spacetime and String Theory
• Neutrino Oscillations and Lorentz Invariance Violation
• Inertial frames without the relativity principle
• Quantum theory of the Generalised Uncertainty Principle
• Quantum Walks, Weyl equation and the Lorentz group
• $Ad{S}_4$ dyonic black holes in gravity's rainbow
• Homogeneously Modified Special Relativity (HMSR) -- A new possible way to introduce an isotropic Lorentz Invariance Violation in particle Standard Model
• Kinematics of particles with quantum de Sitter symmetries
• Deformed discrete symmetries
• Quantum statistics and noncommutative black holes
• Doubly-Special Relativity from Quantum Cellular Automata
• Testing Generalised Uncertainty Principles through Quantum Noise
• A (2+1) non-commutative Drinfel'd double spacetime with cosmological constant
• Geometric interpretation of Planck-scale-deformed co-products
• Beyond Special Relativity at second order
• Time Discretization From Noncommutativity
• Quantum mechanics and the principle of maximal variety
• Noncommutative spaces of worldlines
• New action for simplicial gravity in four dimensions
• Violations of Lorentz invariance in the neutrino sector: an improved analysis of anomalous threshold constraints
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Loop-deformed Poincaré algebra
• Generally covariant formulation of Relative Locality in curved spacetime
• Exploring Special Relative Locality with deSitter momentum-space
• The dynamics of difference
• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
• Gravity's rainbow: a bridge between LQC and DSR
• Deformed symmetries in noncommutative and multifractional spacetimes
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Constraints on the deformation scale of a geometry in the cotangent bundle
• Curved momentum spaces from quantum groups with cosmological constant
• Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space
• Different realizations of kappa-momentum space and relative-locality effect
• Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations
• Does a deformation of special relativity imply energy dependent photon time delays?
• Deformed Carroll particle from 2+1 gravity
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• An Introduction to Noncommutative Physics
• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• Effects of Planck-scale-modified dispersion relations on the thermodynamics of charged black holes
• Quantum kappa-deformed differential geometry and field theory
• Relativistic Extended Uncertainty Principle from Spacetime Curvature
• Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics
• Phenomenological Effects of CPT and Lorentz Invariance Violation in Particle and Astroparticle Physics
• Quantum-gravity-induced dual lensing and IceCube neutrinos
• Relativistic compatibility of the interacting $\kappa$-Poincaré model and implications for the relative locality framework
• Localization and observers in $\varrho$-Minkowski spacetime
• Relative-locality effects in Snyder spacetime
• Snyder Momentum Space in Relative Locality
• Observers and their notion of spacetime beyond special relativity
• Interaction Vertex for Classical Spinning Particles
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• OPERA neutrinos and relativity
• Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
• Hermitian realizations of kappa-Minkowski spacetime
• Casimir effect in Snyder Space
• Predictions of Ultra-High Energy Cosmic Ray Propagation in the Context of Homogeneously Modified Special Relativity
• Double Quantization
• Spacetime from locality of interactions in deformations of special relativity: the example of $\kappa$-Poincaré Hopf algebra
• The Nonlinear Field Space Theory
• Detecting the effects of quantum gravity with exceptional points in optomechanical sensors
• Bounds on Relativistic Deformed Kinematics from the Physics of the Universe Transparency
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Quantum theory of electromagnetic fields in a cosmological quantum spacetime
• Non-commutative Fourier transform for the Lorentz group via the Duflo map
• Reversing the irreversible: from limit cycles to emergent time symmetry
• Lorentz violation naturalness revisited
• Causality and momentum conservation from relative locality
• Intrinsic measurement errors for the speed of light in vacuum
• Relative-locality phenomenology on Snyder spacetime
• The black hole information paradox and relative locality
• Relativistic deformed kinematics from locality conditions in a generalized spacetime
• A short introduction to $\kappa$-deformation
• Time delays, choice of energy-momentum variables and relative locality in doubly special relativity
• Multi-particle systems in $\kappa$-Poincaré inspired by 2+1D gravity
• Misleading inferences from discretization of empty spacetime: Snyder-noncommutativity case study
• On the Physics of the Minimal Length: The Question of Gauge Invariance
• A model of quantum gravity with emergent spacetime
• The thermodynamics of quantum spacetime histories
• Noisy soccer balls
• Modified particle lifetimes as a signature of deformed relativity
• Classical electrodynamics on Snyder space
• Scalar Field Theory in Curved Momentum Space
• Relative Locality in Curved Space-time
• Noncommutative spaces and covariant formulation of statistical mechanics
• Metastring Theory and Modular Space-time
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• Lorentz breaking Effective Field Theory and observational tests
• Dimensional flow in the kappa-deformed space-time
• A new perspective on Doubly Special Relativity
• Space-time thermodynamics in momentum dependent geometries
• Non-universal relativistic kinematics
• The Quantum Gravity Disk: Discrete Current Algebra
• Squeezing the Parameter Space for Lorentz Violation in the Neutrino Sector by Additional Decay Channels
• Relativistic deformed kinematics: from flat to curved spacetimes
• Generalized relativistic kinematics in Poincaré-invariant models
• Quantum instability of gauge theories on $\kappa$-Minkowski space
• Between quantum and classical gravity: Is there a mesoscopic spacetime?
• Mixing coproducts for theories with particle-dependent relativistic properties
• Minisuperspace model of compact phase space gravity
• Quantization of fluctuations in DSR: the two-point function and beyond
• Field theories on $\rho$-deformed Minkowski space-time
• Entropy bound for the photon gas in noncommutative spacetime
• Weakness of accelerator bounds on electron superluminality without a preferred frame
• Particle-antiparticle asymmetry in a relativistic deformed kinematics
• Naturalizing Gravity of the Quantum Fields, and the Hierarchy Problem
• On the space of generalized fluxes for loop quantum gravity
• Causal loop in the theory of relative locality
• Fine-tuning problems in quantum field theory and Lorentz invariance: A scalar-fermion model with a physical momentum cutoff
• Generalized uncertainty principle in quantum cosmology for the maximally symmetric space
• Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral
• Noncommutative momentum and torsional regularization
• Early universe thermostatistics in curved momentum spaces
• Deformed phase spaces with group valued momenta
• Relativistic Planck-scale polymer
• Observational Constraints on Local Lorentz Invariance
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Minkowski Spacetime and QED from Ontology of Time
• Multi-particle systems in quantum spacetime and a novel challenge for center-of-mass motion
• Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
• BMS algebras in 4 and 3 dimensions, their quantum deformations and duals
• $\kappa$-Galilean and $\kappa$-Carrollian noncommutative spaces of worldlines
• The general gravitational Lagrangian with deformed covariance
• Neutrinos as possible probes for quantum gravity
• Relative-locality geometry for the Snyder model
• Quasinormal modes of noncommutative geometry-inspired dirty black holes
• From Causal Dynamical Triangulations To Astronomical Observations
• Modified energy-momentum conservation laws and vacuum Cherenkov radiation
• Quantum superpositions of the speed of light
• Photon gas thermodynamics in dS and AdS momentum spaces
• Twisting loops and global momentum non-conservation in Relative Locality
• Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
• Symmetries of the Dirac quantum walk and emergence of the de Sitter group
• Relative localization of point particle interactions
• General-relativistic spin system
• Testing energy non-additivity in white dwarfs
• Longitudinal and transverse relativity of spacetime locality in Planck-scale-deformed phase spaces
• Squeezing of light from Planck-scale physics
• Exploring black hole mechanics in cotangent bundle geometries
• Cosmic Neutrinos as a Window to Departures from Special Relativity
• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
• Non-local quantum field theory from doubly special relativity
• Universal Horizons without Hypersurface Orthogonality
• Quantum fluctuations of the compact phase space cosmology
• Deformations of the Canonical Commutation Relations and Metric Structures
• Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity
• Noncommutative spacetime symmetries from covariant quantum mechanics
• Quantum gravity & BH-NS binaries
• Orientability of loop processes in relative locality
• The Quantum Vacuum of Spacetime with a Fundamental Length
• Towards quantum Mechanics on the curved cotangent bundle
• $\kappa$-Poincaré phase space: speed of massless particles and relativity of spacetime locality
• Views, variety and quantum mechanics
• Total momentum and other Noether charges for particles interacting in a quantum spacetime
• Clock-dependent spacetime
• Lorentz-covariant sampling theory for fields
• Twistor relative locality
• Born Reciprocity and Cosmic Accelerations
• Testing the universality of quantum gravity theories with cosmic messengers in the context of DSR theories
• DSR-relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation
• Path Integral in Modular Space
• Doubly Quantum Mechanics
• On the nature of quantum gravity
• The Lagrangian and Hamiltonian Aspects of the Electrodynamic Vacuum-Field Theory Models
• Quantum causality in $\kappa$-Minkowski and related constraints
• Gamma Ray Bursts, The Principle of Relative Locality and Connection Normal Coordinates
• On the Relative Distance of Entangled Systems in Emergent Spacetime Scenarios
• Gauge theory on kappa-Minkowski revisited: the twist approach
• Born's prophecy leaves no space for quantum gravity
• Fuzzy worldlines with $\kappa$-Poincaré symmetries
• Spacetime defects and group momentum space
• Star-products for Lie-algebraic noncommutative Minkowski space-times
• A democratic Cosmos?
• $\kappa$-General-Relativity II: An Astrophysical Observable from a 2-Body system
• Nonlocality in Quantum Gravity and the Breakdown of Effective Field Theory
• Quantum Physics in Space
• Beyond Noether: A Covariant Study of Poisson-Lie Symmetries in Low Dimensional Field Theory
• Discrete Spacetime Theories Can Explain the Muon Magnetic Moment Discrepancy
• On the invariance of the relative rest in doubly special relativity
• Coherence and Entanglement in a Non-commutative Spacetime
• A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics
• Quantum fields in curved space-time, semiclassical gravity, quantum gravity phenomenology, and analogue models: Report on session D4 at GR20
• Curved Momentum Space and Relative Locality
• Five dimensional formulation of a DSR
• Generalized relative locality and causal sets
• Relative locality and relative Co-locality as extensions of the Generalized Uncertainty Principle
• Time Delay in $\kappa$-Anti-de Sitter Spacetime
• Three-dimensional gravity and deformations of relativistic symmetries
• Unifying relativity and classical dynamics
• The universe is not a Lie, but actually an Hopf, algebra
• Spontaneous breaking of Lorentz symmetry for canonical gravity
• Photon Absorption in a Doubly Special Relativity Model with Undeformed Free Propagation and Total Momentum Conservation
• Constraining the deformed dispersion relation with the hydrogen atom 1S-2S transition
• A Cosmology of a Trans-Planckian Theory and Dark Energy