Localising relational degrees of freedom in quantum mechanics PDF Download

Author: Hugo Vaughan Cable
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Caslav Brukner
Publisher: Frontiers Media SA
ISBN: 2889744329
Category : Science
Languages : en
Pages : 126

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Author: Michael Epperson
Publisher: Lexington Books
ISBN: 0739180339
Category : Philosophy
Languages : en
Pages : 441

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If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond.

Author: Craig Callender
Publisher: Cambridge University Press
ISBN: 9780521664455
Category : Science
Languages : en
Pages : 380

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Was the first book to examine the exciting area of overlap between philosophy and quantum mechanics with chapters by leading experts from around the world.

Author: Márk Koppany Mezei
Publisher:
ISBN:
Category :
Languages : en
Pages : 208

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We devote this thesis to the exploration of how to define the number of degrees of freedom in quantum field theory. Intuitively, the number of degrees of freedom should decrease along the renormalization group (RG) flow, and should be independent of the RG scale at a conformal fixed point. We argue that a refinement of entanglement entropy is a promising candidate for such measure. Indeed, in two and three spacetime dimensions the number of degrees of freedom defined this way can be proven to monotonically decrease under RG flows. Firstly, we define renormalized entanglement entropy (REE) and show that it is finite in the continuum limit in a renormalizable field theory. We argue that it is most sensitive to degrees of freedom at a scale determined by the size of the entangling region, and interpolates between the ultraviolet and infrared RG fixed point vales. We discuss how it can be used to count the degrees of freedom at a given scale. Secondly, we test whether REE is monotonic along the RG flow. In two dimensions it was known to be monotonic before our study. In higher dimensions, we study REE in free theory examples and in the framework of holography. Holography is tailormade for the study of RG flows, and allows an efficient determination of entanglement entropy. We make use of its power and flexibility to conjecture that in three spacetime dimensions REE is monotonic, while in four dimensions it is neither monotonic nor positive. Subsequent work has proven the conjecture. Thirdly, we count the degrees of freedom in three-dimensional superconformal field theories that are the infrared limit of supersymrnetric gauge theories with matter. Supersymmetric localization reduces the computation of entanglement entropy to a matrix integral. We solve this matrix model in the large N number of colors limit using two different methods; in a saddle point approximation we obtain the next-to-leading order expression in 1/N, while mapping the matrix model to a non-interacting Fermi gas enables us to determine the result to all orders in 1/N. We match the leading piece with N3/ 2 scaling - a strong coupling phenomenon in the field theory - with the holographic duals of these theories. Establishing a measure for the number of degrees of freedom provides nonperturbative understanding of RG fixed points and flows. Our hope is that the constraints coming from RG monotonicity can be efficiently used to constrain the long-distance physics of certain systems of interest. The first applications are only starting to emerge.

Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 332

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Author: Matti Pitkanen
Publisher: Luniver Press
ISBN: 0955117089
Category : Mathematics
Languages : en
Pages : 822

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Topological GeometroDynamics is a modification of general relativity inspired by the conceptual problems related to the definitions of inertial and gravitational energy in general relativity. Topological geometrodynamics can be also seen as a generalization of super string models. Physical space-times are seen as four-dimensional surfaces in certain eight-dimensional space. The choice of this space is fixed by symmetries of the standard model so that geometrization of known classical fields and elementary particle quantum numbers results. The notion of many-sheeted space-time allows re-interpretation of the structures of perceived world in terms of macroscopic space-time topology. The generalization of the number concept based on fusion of real numbers and p-adic number fields implies a further generalization of the space-time concept allowing to identify space-time correlates of cognition and intentionality. Quantum measurement theory extended to a quantum theory of consciousness becomes an organic part of theory. A highly non-trivial prediction is the existence of a fractal hierarchy of copies of standard model physics with dark matter identified in terms of macroscopic quantum phases characterized by dynamical and quantized Planck constant. The book is a comprehensive overview and analysis of topological geometrodynamics as a mathematical and physical theory.

Author: Dean Rickles
Publisher: Oxford University Press
ISBN: 0199269696
Category : Mathematics
Languages : en
Pages : 283

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Book Description
What is spacetime? General relativity and quantum field theory answer this question in different ways. This collection of essays looks at the problem of uniting these two fundamental theories of our world, focusing on the nature of space and time within this quantum framework.

Author: Steffen Gielen
Publisher: MDPI
ISBN: 3039361783
Category : Mathematics
Languages : en
Pages : 338

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Book Description
Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research.

Author: Khalil Chamcham
Publisher: Cambridge University Press
ISBN: 1107145392
Category : Science
Languages : en
Pages : 527

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Book Description
This book addresses foundational questions raised by observational and theoretical progress in modern cosmology. As the foundational volume of an emerging academic discipline, experts from relevant fields lay out the fundamental problems of contemporary cosmology and explore the routes toward finding possible solutions, for a broad academic audience.