Deformed Spacetime
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Deformed Spacetime

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Fabio Cardone
157, Fundamental Theories of Physics
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"This volume provides a detailed discussion of the mathematical aspects and the physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy. Such a formalism (Deformed Special Relativity, DSR) allows one to account for breakdown of local Lorentz invariance in the usual, special-relativistic meaning (however, Lorentz invariance is recovered in a generalized sense); to provide an effective geometrical description of the four fundamental interactions (electromagnetic, weak, strong and gravitational). Moreover, the four-dimensional energy-dependent space-time is just a manifestation of a larger, five-dimensional space in which energy plays the role of a fifth (non-compactified) dimension. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism. TOC:From the contents
Physics Of Deformed Space-Time.- The Principle of Solidarity: Geometrical Descriptions of Interactions.- Description of Interactions by Energy-Dependent Metrics.- Deformed Special Relativity.- Metric Description of Interactions.- Mathematics Of Deformed Space-Time.- Generalized Minkowski Spaces and Killing Symmetries.- Infinitesimal Structure of Generalized Space-Time Rotation Groups.- Finite Structure of Deformed Chronotopical Groups.- Deformed Space-Time Translations in Four Dimensions.- Deformed Minkowski Space as Generalized Lagrange Space.- Experiments On Deformed Space-Time.- Lorentz and CPT Symmetries in DSR.- Lorentz Invariance Breakdown: A Brief Survey.- Superluminal Propagation of Electromagnetic Waves.- The Shadow of Light: Lorentzian Violation of Electrodynamics in Photon Systems.- The Coil Experiment.- The Speed of Gravity.- Piezonuclear Reactions in Cavitated Water.- Piezonuclear Reactions in Cavitated Solutions.- Deformed Space-Time In Five Dimensions: Geometry.- Multidimensional Space-Time.- Embedding Deformed Minkowski Space in a 5D Riemann Space.- Einstein's Field Equations in R5 and Their Solutions.- Killing Equations in the Space R5.- Killing Symmetries for the 5D Metrics of Fundamental Interactions.- Deformed Space-Time In Five Dimensions: Dynamics.- Dynamics in DR5.- Solution of the Geodesic Equations in the Power Ansatz.- Complete Solutions of Geodesic Equations.- Conclusions and Perspectives.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . human kind Cannot bear very much reality. (T. S. Eliot: Four Quartets Burnt Norton) Exegi monumentum aere perennius . . . . . . . . Non omnis moriar. (Quintus Horatius Flaccus: Carmina III, 30) The possible solution to the fundamental issue concerning the structure of the physical world an old-debated problem, starting from presocratic philosophers greatly bene?ted in the twentieth century from the ?nal merging of the separate streams of geometry and physics in a broad river of synthesis and progress. Actually, it can be traced back to Pythagoras h- selftheawarenessoftheintimatelink(andthereciprocalfeedback)between the physical measurements of times, spaces and distances and their ma- ematical representation in terms of relations among abstract geometrical entities. Thisleadsforinstancetoattachaphysicalmeaning,withinEucl- ean geometry, to the mere spatial relations between objects. However, only the basic work by Lorentz, Poincar´ e, Minkowski, and Einstein permitted to state that spacetime is something more than the simple union of space and time. Indeed, the Special and General theories of Relativity allowed xiv Preface physicists and mathematicians to recognize the arena where physical p- nomena take place as a 4D manifold, endowed with a global, Riemannian geometrical structure of Lorentzian signature, which links together space and time in an indissoluble bond. Whats more, it was possible for the ?rst timenotonlytousethemathematicallanguageinordertoexpressphysical laws (in accordance with the fundamental teaching by Galilei), but even to identify a physical interaction gravity with a geometric property of spacetime itself CauchyRiemann curvature namely to geometrize physics.