The Classical-Quantum Duality of Nature. New Variables for Quantum Gravity

Abstract

The classical-quantum duality at the basis of quantum theory is here extended to the Planck scale domain. The classical/semiclassical gravity (G) domain is dual (in the precise sense of the classical-quantum duality) to the quantum (Q) elementary particle domain through the Planck scale. This duality is universal. From the gravity and quantum variables (G, Q), we define new (QG) quantum gravity variables QG = (1/2) (G + Q) which include all (classical, semiclassical and quantum gravity) domains and the elementary particle domain passing by the Planck scale. Two values of G or Q variables are necessary for each variable QG. The complete analytic extension of the QG variables is performed. This allows us to reveal the classical-quantum duality of the Schwarzschild-Kruskal space-time: The exterior regions are classical/semiclassical while the interior is totally quantum, its boundaries being the Planck scale. Exterior and interior lose their difference near the horizon which turns to be quantum dressed, " l'horizon habille' ". QG variables are naturally invariant under G --> Q and conversely. Space-time reflections, antipodal symmetry and PT or CPT symmetry are contained in the QG symmetry, which also shed insight into the global properties of the Kruskal manifold and its present renewed interest...(Abridged)

22 pages, 3 figures, New original material

References in corpus (2)

• Black hole unitarity and antipodal entanglement
• Microcanonical model for a gaz of evaporating black holes and strings, scattering amplitudes and mass spectrum

Cited by in corpus (12)

• Soft graviton exchange and the information paradox
• Quantum Space-Time Symmetries: A Principle of Minimum Group Representation
• Quantum Discrete Levels of the Universe from the Early Trans-Planckian Vacuum to the Late Dark Energy
• New Quantum Phase of the Universe before Inflation and its Cosmological and Dark Energy Implications
• Classical Tools for Antipodal Identification in Reissner-Nordström Spacetime
• Quantum Trans-Planckian Physics inside Black Holes and its Spectrum
• Coherent states of quantum spacetimes for black holes and de Sitter spacetime
• Towards a unitary formulation of quantum field theory in curved space-time: the case of Schwarzschild black hole
• Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity
• New Quantum Structure of the Space-Time
• Classical (ontological) dual states in quantum theory and the minimal group representation Hilbert space
• Predictive Physics of Inflation and Grand Unification for and from the CMB observations