Unification of Quantum and Gravity by Non Classical Information Entropy Space (original) (raw)
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Quantum gravity, from the entropy of geometries
Europhysics News, 2011
This article describes an attempt to reconcile the theory of general relativity with quantum theory from first principles. The universe is assembled from building blocks, and computer simulations reveal their collective behaviour. For small universes quantum fluctuations are large and dominant, but still some semiclassical concepts of geometry survive.
Entropy
We give a review, in the style of an essay, of the author's 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarsegraining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state-entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author's recent arguments based on this alternative description which suggest that the AdS/CFT correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory.
Quantum gravity as an emergent phenomenon
2019
There ought to exist a reformulation of quantum theory which does not depend on classical time. To achieve such a reformulation, we introduce the concept of an atom of space-time-matter (STM). An STM atom is a classical non-commutative geometry, based on an asymmetric metric, and sourced by a closed string. Different such atoms interact via entanglement. The statistical thermodynamics of a large number of such atoms gives rise, at equilibrium, to a theory of quantum gravity. Far from equilibrium, where statistical fluctuations are large, the emergent theory reduces to classical general relativity. In this theory, classical black holes are far-from-equilibrium low entropy states, and their Hawking evaporation represents an attempt to return to the (maximum entropy) equilibrium quantum gravitational state.
Proposal for a New Quantum Theory of Gravity
Zeitschrift für Naturforschung A, 2019
We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65, 599 (2002)]. We explain why this is a significant gravitational theory and in what sense classical general relativity is an approximation to it. We propose that a noncommutative generalisation of this theory (in the sense of Connes’ noncommutative geometry and Adler’s trace dynamics) is a “quantum theory of gravity.” The theory is in fact a classical matrix dynamics with only two fundamental constants – the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of noncommuting coordinates. The action for this noncommutative torsion gravity can be elegantly expressed as an invariant area integral and represents an atom of space–time–matter. The statistical thermodynamics of ...
From quantum foundations to quantum gravity: an overview of the new theory
arXiv: Quantum Physics, 2019
Spontaneous localisation is a falsifiable dynamical mechanism which modifies quantum mechanics, and explains the absence of position superpositions in the macroscopic world. However, this is an ad hoc phenomenological proposal. Adler's theory of trace dynamics, working on a flat Minkowski space-time, derives quantum (field) theory, and spontaneous localisation, as a thermodynamic approximation to an underlying classical matrix dynamics. We describe how to incorporate gravity into trace dynamics, by using ideas from Connes' non-commutative geometry programme. This leads us to a new quantum theory of gravity, from which we can predict spontaneous localisation, and give an estimate of the Bekenstein-Hawking entropy of a Schwarzschild black hole.
Spacetime and the Philosophical Challenge of Quantum Gravity
1999
We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction, we briefly review the conceptual problems of the ingredient theories and introduce the enterprise of quantum gravity We then describe how three main research programmes in quantum gravity treat four topics of particular importance: the scope of standard quantum theory; the nature of spacetime; spacetime diffeomorphisms, and the so-called problem of time. By and large, these programmes accept most of the ingredient theories' treatment of spacetime, albeit with a metric with some type of quantum nature; but they also suggest that the treatment has fundamental limitations. This prompts the idea of going further: either by quantizing structures other than t...
Gravity from quantum information
Journal of the Korean Physical Society, 2013
It is suggested that the Einstein equation can be derived from Landauer's principle applied to an information erasing process at a local Rindler horizon and Jacobson's idea linking the Einstein equation with thermodynamics. When matter crosses the horizon, the information of the matter disappears and the horizon entanglement entropy increases to compensate the entropy reduction. The Einstein equation describes an information-energy relation during this process, which implies that entropic gravity is related to the quantum entanglement of the vacuum and has a quantum information theoretic origin.
It is shown how a Noncommutative spacetime leads to an area, mass and entropy quantization condition which allows to derive the Schwarzschild black hole entropy A/4G , the logarithmic corrections, and further corrections, from the discrete mass transitions taken place among different mass states in D = 4. The higher dimensional generalization of the results in D = 4 follow. The discretization of the entropy-mass relation S = S(M) leads to an entropy quantization of the form S = S(M_n) = n, and such that one may always assign n "bits" to the discrete entropy, and in doing so, make contact with quantum information. The physical applications of mass quantization, like the counting of states contributing to the black hole entropy, black hole evaporation, and the direct connection to the black holes-string correspondence [23] via the asymptotic behavior of the number of partitions of integers, follows. To conclude, it is shown how the recent large N Matrix model (fuzzy sphere) of [20] leads to very similar results for the black hole entropy as the physical model described in this work and which based on the discrete mass transitions originating from the noncommutativity of the spacetime coordinates.
arXiv (Cornell University), 2019
We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein-Maxwell and Kaluza--Klein, KK, theories formulated in Lagrange-Hamilton and general covariant variables. There are considered nonholonomic deformations of Grigory Perelman's F- and W-functionals (originally postulated for Riemannian metrics) for describing relativistic geometric flows, gravity and matter field interactions, and associated statistical thermodynamic systems. We argue that the concept of Perelman W-entropy presents more general and alternative possibilities to characterize geometric flow evolution, GIF, and gravity models than the Bekenstein--Hawking and another area--holographic type entropies. The geometric and classical and quantum thermodynamics methods allow us to understand and describe important classical and quantum physical properties of more general classes of exact solutions in modified gravity and geometric flow theories. Formulating the theory of QGIFs, a set of fundamental geometric, probability and quantum concepts, and methods of computation, are reconsidered for curved spacetime and (relativistic) phase spaces. Such generalized metric-affine spaces are modelled as nonholonomic Lorentz manifolds, (co) tangent Lorentz bundles and associated vector bundles. Using geometric and entropic and thermodynamic values, we define QGIF versions of the von Neumann entropy, relative and conditional entropy, mutual information etc. There are analyzed certain important inequalities and possible applications of G. Perelman and related entanglement and Rényi entropies to theories of KK QGIFs and emergent gravitational and electromagnetic interactions.
Aspects of quantum gravity phenomenology
2015
Quantum gravity effects modify the Heisenberg's uncertainty principle to the generalized uncertainty principle (GUP). Earlier work showed that the GUP-induced corrections to the Schrödinger equation, when applied to a non-relativistic particle in a one-dimensional box, led to the quantization of length. Similarly, corrections to the Klein-Gordon and the Dirac equations, gave rise to length, area and volume quantizations. These results suggest a fundamental granular structure of space. This thesis investigates how spacetime curvature and gravity might influence this discreteness of space. In particular, by adding a weak background gravitational field to the above three quantum equations, it is shown that quantization of lengths, areas and volumes continue to hold. Although the nature of this new quantization is quite complex, under proper limits, it reduces to cases without gravity. These results indicate the universality of quantum gravity effects. I am thankful to my supervisor Dr. Saurya Das for his inspiring guidance, constructive criticism, friendly advice and academic as well as non-academic support throughout the research project. I would like to express my gratitude to my committee members Dr. Mark Walton and Dr. Kent Peacock for all the valuable suggestions and comments they provided. I would also like to thank my family and friends for their help and encouragement. v Contents List of Figures viii vi 3.6.1 Case 1 : Length quantization along x axis .