Abstract
So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the preliminary results for a model of quantum universe, in which gravity is fundamentally and by construction quantic. The model is based on three well motivated assumptions with compelling observational and theoretical evidence: quantum mechanics is valid at all scales; quantum systems are described by their symmetries; universe has infinite independent degrees of freedom. The last assumption means that the Hilbert space of the Universe has SU(N→∞)≅areapreservingDiff.(S2) symmetry, which is parameterized by two angular variables. We show that, in the absence of a background spacetime, this Universe is trivial and static. Nonetheless, quantum fluctuations break the symmetry and divide the Universe to subsystems. When a subsystem is singled out as reference—observer—and another as clock, two more continuous parameters arise, which can be interpreted as distance and time. We identify the classical spacetime with parameter space of the Hilbert space of the Universe. Therefore, its quantization is meaningless. In this view, the Einstein equation presents the projection of quantum dynamics in the Hilbert space into its parameter space. Finite dimensional symmetries of elementary particles emerge as a consequence of symmetry breaking when the Universe is divided to subsystems/particles, without having any implication for the infinite dimensional symmetry and its associated interaction-percived as gravity. This explains why gravity is a universal force.
Highlights
Introduction and Summary of ResultsMore than a century after the discovery of general relativity and description of gravitational force as the modification of spacetime geometry by matter and energy, we still lack a convincing model for explaining these processes in the framework of quantum mechanics
In absence of a background spacetime, its dynamics is trivial and its Lagrangian is defined on the group manifold of SUp8q symmetry
Quantum fluctuations break the state symmetry and factorize the Hilbert space to blocks of tensor product of subspaces according to criteria studied in [24,25]
Summary
More than a century after the discovery of general relativity and description of gravitational force as the modification of spacetime geometry by matter and energy, we still lack a convincing model for explaining these processes in the framework of quantum mechanics. The similarity of the compact group of local Lorentz transformations to Yang–Mills gauge symmetry has encouraged quantum gravity models that are based on the first order formulation of general relativity. Any violation of Coleman–Madula theorem and Lorentz symmetry at high energies can be convoyed to low energies [10] and violate e.g., equivalence principle and other tested predictions of general relativity [11,12] For these reasons, modern approaches to the unification of gravity as a gauge field with other interactions consider the two sectors as separate gauge field models. There are other issues that a priori should be addressed by a QGR model, but are less discussed in the literature: Should spacetime be considered as a physical entity similar to quantum fields associated to particles, or rather it presents a configuration space ?. In this work we study a standalone quantum system, which is considered to be the Universe
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