This volume provides a detailed discussion of the mathematical aspects and 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. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism.

This monograph provides an introduction to deformations of Poincaré symmetries focusing on models with a Lie group momentum space and associated non-commutative space-times. The emphasis is put on the emergence of such structures from quantum gravity, their mathematical features described in terms of Hopf algebras and applications to particle kinematics and field theory. Part I of this work focuses on the link between gravity and deformed symmetries in the case of 2+1 and 3+1 space-time dimensions. Part II is devoted to the description of classical particles with group valued momenta, their phase spaces and kinematics. The last part of these notes provides an introduction to the basic features of classical and quantum field theory on κ-Minkowski space-time, the prototypical example of non-commutative space-time exhibiting deformed Poincaré symmetry. The text, being the first providing a detailed overview of these topics, is primarily intended for researchers and graduate students interested in non-commutative field theories and quantum gravity phenomenology.

Unified Field Mechanics, the topic of the 9th international symposium honoring noted French mathematical physicist Jean-Pierre Vigier cannot be considered highly speculative as a myopic critic might surmise. The 8th Vigier Symposium proceedings 'The Physics of Reality' should in fact be touted as a companion volume because of its dramatic theoretical Field Mechanics in additional dimensionality. Many still consider the Planck-scale zero-point field stochastic quantum foam as the 'basement of reality'. This could only be considered true under the limitations of the Copenhagen interpretation of quantum theory. As we enter the next regime of Unified Field Mechanics we now know that the energy-dependent Einstein-Minkowski manifold called spacetime has a finite radius beyond which a large-scale multiverse beckons. So far a battery of 14 experiments has been designed to falsify the model. When the 1st is successfully performed, a revolution in Natural Science will occur! This volume strengthens and expands the theoretical and experimental basis for that immanent new age.

There are many approaches to noncommutative geometry and to its use in physics. This volume addresses the subject by combining the deformation quantization approach, based on the notion of star-product, and the deformed quantum symmetries methods, based on the theory of quantum groups. The aim of this work is to give an introduction to this topic and to prepare the reader to enter the research field quickly. The order of the chapters is "physics first": the mathematics follows from the physical motivations (e.g. gauge field theories) in order to strengthen the physical intuition. The new mathematical tools, in turn, are used to explore further physical insights. A last chapter has been added to briefly trace Julius Wess' (1934-2007) seminal work in the field.

There are very few concepts that fascinate equally a theoretical physicist studying black holes and a patient undergoing seriolls mental psychosis. Time, undoubtedly, can well be ranked among them. For the measure of time inside a black hole is no less bizarre than the perception of time by a schizophrenic, who may perceive it as completely "suspended," "standing still," or even "reversing its direction. " The nature of time is certainly shrouded in profound mystery. This, perhaps, since the concept entails multifarious, and occasionally incongruous, facets. No wonder the subject attracts the serious attention of scholars on the one hand, and of the lay public on the other. Our Advanced Research Workshop is an excellent il lustration of this point, as the reader will soon discover. It turned out to be a unique professional forum for an unusually lively, effective and fruitful exchange of ideas and beliefs among 48 participants from 20 countries worldwide, selected out of more than a hundred applicants. The present book is based on the select talks presented at the meeting, and aims to provide the interested layperson and specialist alike with a multidisciplinary sampling of the most up-to-date scholarly research on the nature of time. It represents a coherent, state-of-the-art volume showing that research relevant to this topic is necessarily interdisciplinary and does not ignore such delicate issues as "altered" states of consciousness, religion and metaphysics.

In Toward a Directionalist Theory of Space: On Going Nowhere, H. Scott Hestevold formulates a new relationalist theory of space by appealing to the view that the universe is directioned in the sense that there exist directional relations—a class of spatial relations that Leibniz overlooked. Extending the directionalist/relationalist theory of space to the problem of when it is that discrete objects compose a whole, Hestevold revisits his answer to the Special Composition Question. He also uses the directionalist/relationalist theory to formulate reductivist theories of boundaries and holes—theories that may allow one to resist the view that boundaries and holes are ontologically parasitic entities. Finally, he explores directionalism/relationalism vis-à-vis spacetime. After noting findings of modern physics that favor substantivalist spacetime and then developing metaphysical concerns that favor instead directionalist/relationalist spacetime, Hestevold notes the ontological benefit of endorsing spatiotemporal directional relations even if spacetime substantivalism is the winning theory.

The book presents seven fundamental concepts in spacetime physics mostly by following Hermann Minkowski’s revolutionary ideas summarized in his 1908 lecture "Space and Time." These concepts are: spacetime, inertial and accelerated motion in spacetime physics, the origin and nature of inertia in spacetime physics, relativistic mass, gravitation, gravitational waves, and black holes. They have been selected because they appear to be causing most misconceptions and confusion in spacetime physics. This second edition has been revised to include additional clarifications, more detailed elaboration of the arguments and also new material published in the interim.