The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an alternative approach to quantum gravity starts with the postulate that inertial energy-momentum and gravitational energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the quantum gauge field theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The classical limit of this theory coupled to a quantized scalar field is derived for an on-shell particle where inertial energy-momentum and gravitational energy-momentum coincide. In that process the symmetry under volume-preserving diffeomorphisms disappears and a new symmetry group emerges: the group of coordinate transformations of four-dimensional spacetime and with it General Relativity coupled to a classical relativistic point particle.
Quantum Gravity, Quantum Gauge Theory of Volume-Preserving Diffeomorphism Group, GR Emerging as the Classical Limit of Above, Different Roles of Inertial and Gravitational Momentum, Observability of Spacetime at Microscopic Level
Wiesendanger, C. (2014) General Relativity as the Classical Limit of the Renormalizable Gauge Theory of Volume Preserving Diffeomorphisms. Journal of Modern Physics, 5, 948-958. doi: 10.4236/jmp.2014.510098.
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