A freely falling frame at the interface of gravitational and quantum realms

Abstract

I briefly argue for logical necessity to incorporate, besides c, hbar, two fundamental length scales in the symmetries associated with the interface of gravitational and quantum realms. Next, in order to clear the proverbial bush, I discuss the CPT and indistinguishability issue related to recent non-linear deformations of special relativity and suggest why algebraically well-defined extensions of special relativity do not require non-linear deformations. That done, I suggest why the stable Snyder-Yang-Mendes Lie algebra should be considered as a serious candidate for the symmetries underlying freely falling frames at the interface of gravitational and quantum realms; thus echoing, and complementing, arguments recently put forward by Chryssomalakos and Okon. In the process I obtain concrete form of uncertainty relations which involve above-indicated length scales and a new dimensionless constant. I draw attention to the fact that because superconducting quantum interference devices can carry roughly 10^{23} Cooper pairs in a single quantum state, Planck-mass quantum systems already exist in the laboratory. These may be used for possible exploration of the interface of the gravitational and quantum realms.

19 pages (Significantly enlarged and revised since its initial informal circulation before arXiving.)

References in corpus (10)

• Triply Special Relativity
• General Relativistic Effects of Gravity in Quantum Mechanics -- A Case of Ultra-Relativistic, Spin 1/2 Particles --
• Generalized Quantum Relativistic Kinematics: a Stability Point of View
• Interpreting doubly special relativity as a modified theory of measurement
• Linear Form of 3-scale Relativity Algebra and the Relevance of Stability
• Some consequences of a noncommutative space-time structure
• Unphysical Predictions of Some Doubly Special Relativity Theories
• Operational indistinguishabilty of doubly special relativities from special relativity
• Current Status of the MiniBooNE Experiment
• Fermions, bosons, and locality in special relativity with two invariant scales

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• Modified Dirac equation with Lorentz invariance violation and its solutions for particles in an external magnetic field
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• Non-relativistic limit of quantum field theory in inertial and non-inertial frames and the Principle of Equivalence
• Beyond Special Relativity at second order
• Reflections of the observer and the observed in quantum gravity
• Minimal spatio-temporal extent of events, neutrinos, and the cosmological constant problem
• The Stabilized Poincare-Heisenberg algebra: a Clifford algebra viewpoint
• (Anti)de Sitter/Poincare symmetries and representations from Poincare/Galilei through a classical deformation approach
• Generalized commutation relations and Non linear momenta theories, a close relationship
• Contractions, deformations and curvature
• Space Noncommutativity Corrections to the Cardy-Verlinde Formula
• The deformation-stability fundamental length and deviations from c
• Space-time: Commutative or noncommutative ?
• Carroll spinors
• Exotic Statistics for Ordinary Particles in Quantum Gravity
• A Field Theory Model With a New Lorentz-Invariant Energy Scale
• Possible polarisation and spin dependent aspects of quantum gravity
• An extended Dirac equation in noncommutative space-time
• Electroweak symmetries from the topology of deformed spacetime with minimal length scale
• Deformations of spacetime and internal symmetries
• The Neutron as an Alternative Explanation for the Trans GZK Cosmic Rays
• Soft singularity and the fundamental length