Testable scenario for Relativity with minimum-length

Abstract

I propose a general class of space-times whose structure is governed by observer-independent scales of both velocity ($c$) and length (Planck length), and I observe that these space-times can naturally host a modification of FitzGerald-Lorentz contraction such that lengths which in their inertial rest frame are bigger than a "minimum length" are also bigger than the minimum length in all other inertial frames. With an analysis in leading order in the minimum length, I show that this is the case in a specific illustrative example of postulates for Relativity with velocity and length observer-independent scales.

10 pages, LaTex

References in corpus (1)

• Quantum theory's last challenge

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• Regularization of Kepler Problem in $\kappa$-spacetime
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• An Inflationary Scenario Taking into Account of Possible Dark Energy Effects in the Early Universe
• $\kappa$-Poincaré phase space: speed of massless particles and relativity of spacetime locality
• Lorentz-violating gaugeon formalism for rank-2 tensor theory
• Could LIV/noncommutativity alleviate the cosmological constant problem
• Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity
• Particle Dynamics and Lie-algebraic type of Non-commutativity of space-time
• Quantum Spacetime Pictures and Dynamics from a Relativity Perspective
• Seeking for the observational manifestation of de Sitter Relativity
• Conformal transformation route to gravity's rainbow
• The Quantum Vacuum of Spacetime with a Fundamental Length
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• Electroweak symmetries from the topology of deformed spacetime with minimal length scale
• Generalized uncertainty principles and black hole temperatures in rainbow gravity
• D-particles and the localization limit in quantum gravity
• Correction to the quantum relation of photons in the Doppler effect based on a special Lorentz violation model
• Thermodynamics of black holes in rainbow gravity
• Quantisation of $\kappa$-deformed Dirac equation
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime
• Velocity and Distribution of Primordial Neutrinos
• Towards a topological (dual of) quantum $\kappa$-Poincaré group
• Some considerations on duality concerning kappa-Minkowski spacetime theories
• Lie algebraic noncommuting structures from reparametrisation symmetry
• Gauge theory on kappa-Minkowski revisited: the twist approach
• Exact form of the generalized Lorentz force in Fock's nonlinear relativity
• Massive Gauge Fields and the Planck Scale
• Symplectic realization of generalized Snyder-Poisson algebra
• The analogy of the Lorentz-violating fermion-gravity and fermion photon couplings
• From quantum deformations of relativistic symmetries to modified kinematics and dynamics
• Quantum Gravity models - brief conceptual summary
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Supporting Abstract Relational Space-Time as Fundamental without Doctrinism against Emergence
• Noncommutative Extension of Minkowski Spacetime and Its Primary Application
• Velocity-dependent deformations of the energy spectrum of a quantum cavity from Lorentz symmetry violations
• DSR-relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation
• Probing modified gravitational-wave dispersion with bursts from eccentric black-hole binaries
• Algebraic structure of n-body systems
• Homogeneous Spaces of the Lorentz Group
• Maxwell's equations and Lorentz force in doubly special relativity
• Fuzzy worldlines with $\kappa$-Poincaré symmetries
• Phonons mimicking doubly special relativity kinematics
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• Equations for fields with additional fundamental physical constants
• Can Light Signals Travel Faster than c in Nontrivial Vacuua in Flat space-time? Relativistic Causality II
• On the invariance of the relative rest in doubly special relativity
• Kinetic gases in static spherically symmetric modified dispersion relations
• Primitively divergent diagrams in $\kappa$-deformed scalar field with quartic self-interaction
• Phenomenological description of quantum gravity inspired modified classical electrodynamics
• Note About String Theory with Deformed Dispersion Relations
• Discrete Spacetime Theories Can Explain the Muon Magnetic Moment Discrepancy
• Perturbative calculation of energy levels for the Dirac equation with generalised momenta
• Deriving Spin within a discrete-time theory
• Exact Solutions of the DKP Oscillator in 3D Spaces with Extended Uncertainty Principle
• Analysis of black hole thermodynamics under Generalized uncertainty principle from the doubly special relativity
• Super-Chandrasekhar limiting mass white dwarfs as emergent phenomena of noncommutative squashed fuzzy spheres
• A symplectic geometric origin of universal quartic modified dispersion relations
• Massive Neutron Stars and White Dwarfs as Noncommutative Fuzzy Spheres
• Effective Framework of kappa-Minkowski Spacetime and Its Application
• The covariant and on-shell statistics in kappa-deformed spacetime
• Algebraic structures in $\kappa$-Poincaré invariant gauge theories
• Deformed Special Relativity using a Generalized 't Hooft-Nobbenhuis Complex Transformation
• Quantum Physics in Space
• A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics
• Thermodynamics of Einstein-Gauss-Bonnet Black Holes under the Generalized Uncertainty Principle
• Braided Statistics from Abelian Twist in $\kappa$-Minkowski Spacetime
• Unruh effect using Doppler shift method in DSR framework
• A map between Galilean relativity and special relativity
• The universe is not a Lie, but actually an Hopf, algebra
• The Entropic Dynamics of Relativistic Quantum Fields in Curved Space-time
• Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space