Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness

Abstract

Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a phenomenological model of massive particles propagating in a Minkowski spacetime which arises from an underlying causal set. The particles undergo a Lorentz invariant diffusion in phase space, and we speculate on whether this could have any bearing on the origin of high energy cosmic rays.

13 pages. Replaced version with corrected fundamental solution, missing m's (mass) and c's (speed of light) added and reference on diffusion on the three sphere changed. Note with additional references added and addresses updated, as in published version

References in corpus (4)

• Forks in the Road, on the Way to Quantum Gravity
• Extremely High Energy Neutrinos, Neutrino Hot Dark Matter, and the Highest Energy Cosmic Rays
• Ultrahigh Energy Cosmic Rays: The state of the art before the Auger Observatory
• Quantum-Gravity Phenomenology: Status and Prospects

Cited by in corpus (75)

• Modern tests of Lorentz invariance
• Quantum Spacetime Phenomenology
• Tests of Lorentz invariance: a 2013 update
• Lorentz violation at high energy: concepts, phenomena and astrophysical constraints
• Lorentz invariance and quantum gravity: an additional fine-tuning problem?
• Phenomenological Implications of the Generalized Uncertainty Principle
• Dark energy as the weight of violating energy conservation
• The causal set approach to quantum gravity
• Black Holes in Loop Quantum Gravity
• Network geometry with flavor: from complexity to quantum geometry
• Interdisciplinary and physics challenges of Network Theory
• Discreteness without symmetry breaking: a theorem
• Particle propagators on discrete spacetime
• CPT Violating Decoherence and LSND: a possible window to Planck scale Physics
• Energy-momentum diffusion from spacetime discreteness
• Causal structures and causal boundaries
• Synchrotron Radiation in Lorentz-violating Electrodynamics: the Myers-Pospelov model
• Astrophysical constraints on Planck scale dissipative phenomena
• Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
• The Attractor and the Quantum States
• The structure of causal sets
• Spectral dimension in causal set quantum gravity
• About Locality and the Relativity Principle Beyond Special Relativity
• Spectral Line Broadening and Angular Blurring due to Spacetime Geometry Fluctuations
• Evidence for an entropy bound from fundamentally discrete gravity
• Statistical Mechanics of Graphity Models
• Relativistic collapse dynamics and black hole information loss
• Diffusion in unimodular gravity: Analytical solutions, late-time acceleration, and cosmological constraints
• Causal Sets: Quantum gravity from a fundamentally discrete spacetime
• Theory and Phenomenology of Spacetime Defects
• Light, Links and Causal Sets
• The Area Quantum and Snyder Space
• Phenomenology of Space-time Imperfection II: Local Defects
• Surface Tension and the Cosmological Constant
• Discreteness and the transmission of light from distant sources
• The Random Discrete Action for 2-Dimensional Spacetime
• Echoes of Asymptotic Silence in Causal Set Quantum Gravity
• Phenomenology of Space-time Imperfection I: Nonlocal Defects
• Low energy bounds on Poincare violation in causal set theory
• Compact objects in unimodular gravity
• Quantum Gravity Phenomenology without Lorentz Invariance Violation: a detailed proposal
• Unambiguous Quantum Gravity Phenomenology Respecting Lorentz Symmetry
• Inflation and the cosmological (not-so) constant in unimodular gravity
• Causal sets and conservation laws in tests of Lorentz symmetry
• Lorentz violation naturalness revisited
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Polarization Diffusion from Spacetime Uncertainty
• Constructing an interval of Minkowski space from a causal set
• Constraints from cosmic rays on non-systematic Lorentz violation
• Corrections to flat-space particle dynamics arising from space granularity
• Inflationary expansion of the universe with variable timescale
• Particle simulations in causal set theory
• Spectral dimension on spatial hypersurfaces in causal set quantum gravity
• A simple model of pointlike spacetime defects and implications for photon propagation
• Quantum Histories and Quantum Gravity
• The Universe in a Soap Film
• Extracting Geometry from Quantum Spacetime: Obstacles down the road
• Single particle energy diffusion from relativistic spontaneous localization
• Mass generation by a Lorentz-invariant gas of spacetime defects
• Probes for String-Inspired Foam, Lorentz, and CPT Violations in Astrophysics
• Symmetry-breaking and zero-one laws
• Causal Cones, Cone Preserving Transformations and Causal Structure in Special and General Theory of Relativity
• Stochastic dark matter: Covariant Brownian motion from Planckian discreteness
• Spacetime Entanglement Entropy: Covariance and Discreteness
• Lorentz violating electrodynamics
• Emergent quantum mechanics and the origin of quantum non-local correlations
• Particle propagation on spacetime manifolds with static defects
• Are There Testable Discrete Poincaré Invariant Physical Theories?
• Pilot-wave quantum theory in discrete space and time and the principle of least action
• Velocity-dependent deformations of the energy spectrum of a quantum cavity from Lorentz symmetry violations
• Numerical Evaluation of the Causal Set Propagator in 2D Anti-de Sitter Spacetime
• Benincasa-Dowker-Glaser causal set actions by quantum counting
• Curvature of an Arbitrary Surface for Discrete Gravity and for $d=2$ Pure Simplicial Complexes
• Phenomenological description of quantum gravity inspired modified classical electrodynamics
• Null Geodesics from Ladder Molecules