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In 1988, Rovelli, Lee Smolin and Abhay Ashtekar introduced a theory of quantum gravity called loop quantum gravity. In 1995, Rovelli and Smolin obtained a basis of states of quantum gravity, labelled by Penrose's spin networks, and using this basis they were able to show that the theory predicts that area and volume are quantized. This result ...
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 ...
(Later, loop quantum gravity inherited this geometric interpretation of gravity, and posits that a quantum theory of gravity is fundamentally a quantum theory of spacetime.) In the 1920s, the French mathematician Élie Cartan formulated Einstein's theory in the language of bundles and connections, [ 1 ] a generalization of Riemannian geometry ...
In the second part, The World without Time, Rovelli writes that events constitute the universe instead of particles, and introduces the concept of quanta of time in loop quantum gravity. The final section, The Sources of Time, proposes that the apparent flow of time is due to the inability to observe all the microscopic details of the world. [4]
The book's opening chapters trace the history and evolution of quantum gravity. Starting with pre-socratic philosopher Democritus through to the ideas of Sir Isaac Newton and, eventually, Albert Einstein, Rovelli puts forward a theory that quantum gravity brings great unity to the universe. Rovelli then states that space and time, waves and ...
In loop quantum gravity (LQG), a spin network represents a "quantum state" of the gravitational field on a 3-dimensional hypersurface. The set of all possible spin networks (or, more accurately, " s-knots " – that is, equivalence classes of spin networks under diffeomorphisms ) is countable ; it constitutes a basis of LQG Hilbert space .
The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of loop quantum gravity (LQG). In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in the Planck regime , overwhelming the classical gravitational ...
The loop representation also provides a natural solution of the spatial diffeomorphism constraint, making a connection between canonical quantum gravity and knot theory. Surprisingly there were a class of loop states that provided exact (if only formal) solutions to Ashtekar's original (ill-defined) Wheeler–DeWitt equation .