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In 1921 Einstein gave a series of lectures at Princeton on his then newly minted theory of gravity, which we know today as the General Theory of Relativity. Towards the end of his life, in circa 1950, he added the following lines: "One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system with finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accordance with continuum theory and must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory."
This book is an algebraic theory for the description of reality which Einstein dreamed of in his prophetic words. It is based on the development of algebras of quantum operators on Hilbert space by John von Neumann which started during the early 1950s. The development of a successful theory of quantum gravity in the context of the early universe is the key next step in theoretical physics. This book takes that step by describing a coherent mathematical framework for both the evolution of discrete space-time and the quantum graviton in the Planck regime. In doing so it successfully blends developments in both loop quantum gravity and superstring theory with data from the Large Hadron Collider. The result is a coherent mathematical framework that encapsulates new developments in black hole entropy. On this basis, we are able to demonstrate that when this"quantum ergodic theory" is sufficiently close to the classical case to allow the application of a Carnot cycle to the entropy of the surface area of a black hole, then we have, embedded in our theory as an approximation, Einstein's field equations for gravity. The book also discusses a number of developments of the theory for mathematics and physics including possible insights into the Clay Mathematics Institute Millennial question concerning Yang-Mills quantum theory and the mass gap.
This book is an algebraic theory for the description of reality which Einstein dreamed of in his prophetic words. It is based on the development of algebras of quantum operators on Hilbert space by John von Neumann which started during the early 1950s. The development of a successful theory of quantum gravity in the context of the early universe is the key next step in theoretical physics. This book takes that step by describing a coherent mathematical framework for both the evolution of discrete space-time and the quantum graviton in the Planck regime. In doing so it successfully blends developments in both loop quantum gravity and superstring theory with data from the Large Hadron Collider. The result is a coherent mathematical framework that encapsulates new developments in black hole entropy. On this basis, we are able to demonstrate that when this"quantum ergodic theory" is sufficiently close to the classical case to allow the application of a Carnot cycle to the entropy of the surface area of a black hole, then we have, embedded in our theory as an approximation, Einstein's field equations for gravity. The book also discusses a number of developments of the theory for mathematics and physics including possible insights into the Clay Mathematics Institute Millennial question concerning Yang-Mills quantum theory and the mass gap.
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