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Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Albert Einstein's geometric formulation rather than the treatment of gravity as a mysterious mechanism (force). As a theory, LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale on the order of a Planck length, approximately 10−35 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure.
Lee Smolin is an American theoretical physicist, a faculty member at the Perimeter Institute for Theoretical Physics, an adjunct professor of physics at the University of Waterloo, and a member of the graduate faculty of the philosophy department at the University of Toronto. Smolin's 2006 book The Trouble with Physics criticized string theory as a viable scientific theory. He has made contributions to quantum gravity theory, in particular the approach known as loop quantum gravity. He advocates that the two primary approaches to quantum gravity, loop quantum gravity and string theory, can be reconciled as different aspects of the same underlying theory. He also advocates an alternative view on space and time that he calls temporal naturalism. His research interests also include cosmology, elementary particle theory, the foundations of quantum mechanics, and theoretical biology.
Doubly special relativity (DSR) – also called deformed special relativity or, by some, extra-special relativity – is a modified theory of special relativity in which there is not only an observer-independent maximum velocity, but also an observer-independent maximum energy scale and/or a minimum length scale. This contrasts with other Lorentz-violating theories, such as the Standard-Model Extension, where Lorentz invariance is instead broken by the presence of a preferred frame. The main motivation for this theory is that the Planck energy should be the scale where as yet unknown quantum gravity effects become important and, due to invariance of physical laws, this scale should remain fixed in all inertial frames.
In physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description of quantum gravity. These structures are employed in loop quantum gravity as a version of quantum foam.
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The history of loop quantum gravity spans more than three decades of intense research.
In general relativity, Regge calculus is a formalism for producing simplicial approximations of spacetimes that are solutions to the Einstein field equation. The calculus was introduced by the Italian theoretician Tullio Regge in 1961.
Causal dynamical triangulation (CDT), theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, is an approach to quantum gravity that, like loop quantum gravity, is background independent.
In relativistic physics, Lorentz invariance states that the laws of physics should remain unchanged under Lorentz transformation. In quantum gravity, Lorentz invariance measures the universal features in the hypothetical loop quantum gravity universes; which is a hypothetical theory that explains the quantum theory of gravity based on a geometrical interpretation of the theory of relativity. The various hypothetical design models for the universe, multiverse, and loop quantum gravity could have various general covariant principle results.
Sundance Osland Bilson-Thompson is an Australian theoretical particle physicist. He has developed the idea that certain preon models may be represented topologically, rather than by treating preons as pointlike particles. His ideas have attracted interest in the field of loop quantum gravity, as they may represent a way of incorporating the Standard Model into loop quantum gravity. This would make loop quantum gravity a candidate theory of everything.
In mathematical physics, de Sitter invariant special relativity is the speculative idea that the fundamental symmetry group of spacetime is the indefinite orthogonal group SO(4,1), that of de Sitter space. In the standard theory of general relativity, de Sitter space is a highly symmetrical special vacuum solution, which requires a cosmological constant or the stress–energy of a constant scalar field to sustain.
Lorentz invariance follows from two independent postulates: the principle of relativity and the principle of constancy of the speed of light. Dropping the latter while keeping the former leads to a new invariance, known as Fock–Lorentz symmetry or the projective Lorentz transformation. The general study of such theories began with Fock, who was motivated by the search for the general symmetry group preserving relativity without assuming the constancy of c.
Group field theory (GFT) is a quantum field theory in which the base manifold is taken to be a Lie group. It is closely related to background independent quantum gravity approaches such as loop quantum gravity, the spin foam formalism and causal dynamical triangulation. Its perturbative expansion can be interpreted as spin foams and simplicial pseudo-manifolds (depending on the representation of the fields). Thus, its partition function defines a non-perturbative sum over all simplicial topologies and geometries, giving a path integral formulation of quantum spacetime.
Twisted geometries are discrete geometries that play a role in loop quantum gravity and spin foam models, where they appear in the semiclassical limit of spin networks. A twisted geometry can be visualized as collections of polyhedra dual to the nodes of the spin network's graph. Intrinsic and extrinsic curvatures are defined in a manner similar to Regge calculus, but with the generalisation of including a certain type of metric discontinuities: the face shared by two adjacent polyhedra has a unique area, but its shape can be different. This is a consequence of the quantum geometry of spin networks: ordinary Regge calculus is "too rigid" to account for all the geometric degrees of freedom described by the semiclassical limit of a spin network.
In theoretical physics, shape dynamics is a theory of gravity that implements Mach's principle, developed with the specific goal to obviate the problem of time and thereby open a new path toward the resolution of incompatibilities between general relativity and quantum mechanics.
Relative locality is a proposed physical phenomenon in which different observers would disagree on whether two space-time events are coincident. This is in contrast to special relativity and general relativity in which different observers may disagree on whether two distant events occur at the same time but if an observer infers that two events are at the same spacetime position then all observers will agree.
In physics, Born reciprocity, also called reciprocal relativity or Born–Green reciprocity, is a principle set up by theoretical physicist Max Born that calls for a duality-symmetry among space and momentum. Born and his co-workers expanded his principle to a framework that is also known as reciprocity theory.
In theoretical physics, the problem of time is a conceptual conflict between general relativity and quantum mechanics in that quantum mechanics regards the flow of time as universal and absolute, whereas general relativity regards the flow of time as malleable and relative. This problem raises the question of what time really is in a physical sense and whether it is truly a real, distinct phenomenon. It also involves the related question of why time seems to flow in a single direction, despite the fact that no known physical laws at the microscopic level seem to require a single direction.
References
- 1 2 Freidel, Laurent; Krasnov, Kirill (21 June 2008). "A new spin foam model for 4D gravity". Classical and Quantum Gravity. 25 (12): 125018. arXiv: 0708.1595 . Bibcode:2008CQGra..25l5018F. doi:10.1088/0264-9381/25/12/125018. S2CID 119138842.
- ↑ "Laurent Freidel's homepage at Perimeter Institute".
- ↑ Freidel, Laurent; Louapre, David (21 December 2004). "Ponzano–Regge model revisited: I. Gauge fixing, observables and interacting spinning particles". Classical and Quantum Gravity. 21 (24): 5685–5726. arXiv: hep-th/0401076 . Bibcode:2004CQGra..21.5685F. doi:10.1088/0264-9381/21/24/002. S2CID 42369187.
- ↑ Amelino-Camelia, Giovanni; Freidel, Laurent; Kowalski-Glikman, Jerzy; Smolin, Lee (October 2011). "Principle of relative locality". Physical Review D. 84 (8): 084010. arXiv: 1101.0931 . Bibcode:2011PhRvD..84h4010A. doi:10.1103/PhysRevD.84.084010. S2CID 49921081.
- ↑ Freidel, Laurent; Leigh, Robert; Minic, Djordje (2015). "Metastring Theory and Modular Space-time". Journal of High Energy Physics. 2015 (6): 6. arXiv: 1502.08005 . Bibcode:2015JHEP...06..006F. doi:10.1007/JHEP06(2015)006. S2CID 55570067.
