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 (36)

• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Generalized Lorentz invariance with an invariant energy scale
• Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510
• Group Field Theory: An overview
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• Doubly-Special Relativity: First Results and Key Open Problems
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Prospects for constraining quantum gravity dispersion with near term observations
• Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
• De Sitter space as an arena for Doubly Special Relativity
• Doubly Special Relativity and de Sitter space
• 2+1 gravity and Doubly Special Relativity
• Taming nonlocality in theories with Planck-scale-deformed Lorentz symmetry
• Bounds on an energy-dependent and observer-independent speed of light from violations of locality
• Twisting of quantum differentials and the Planck scale Hopf algebra
• Modifications to Lorentz invariant dispersion in relatively boosted frames
• Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity
• Poisson structure and symmetry in the Chern-Simons formulation of (2+1)-dimensional gravity
• Probing a Possible Vacuum Refractive Index with Gamma-Ray Telescopes
• Momentum space metric, non-local operator, and topological insulators
• Topological field theory and the quantum double of SU(2)
• Large-scale non-locality in "doubly special relativity" with an energy-dependent speed of light
• Anatomy of a deformed symmetry: field quantization on curved momentum space
• Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity
• Physics of Deformed Special Relativity
• 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
• Meaning of Noncommutative Geometry and the Planck-Scale Quantum Group
• 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'
• Quantum Gravity Momentum Representation and Maximum Invariant Energy

Cited by in corpus (265)

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