The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example - but is spacetime really continuous? Throughout the history of science, many have felt that the continuum model is an unphysical idealization, and that spacetime should be thought of as 'quantized' at the smallest of scales. Combining novel conceptual analysis, a fresh historical perspective, and concrete physical examples, this unique book tells the story of the search for the fundamental unit of length in modern physics, from early classical electrodynamics to current approaches to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics research, are presented and defended in an accessible format that avoids complex mathematics. Blending history, philosophy, and theoretical physics, this refreshing outlook on the nature of spacetime sheds light on one of the most thought-provoking topics in modern physics.

This work is a detailed study of both the theoretical and phenomenological consequences of a massive graviton, within the ghost-free theory of massive gravity, the de Rham-Gabadadze-Tolley (dRGT) theory. Its aim is to test the physical viability of the theory. It begins by putting constraints on the parameters of the theory in the decoupling limit based on purely theoretical grounds, like classical stability in the cosmological evolution of self-accelerating and degravitating solutions. The author then constructs a proxy theory to massive gravity from the decoupling limit resulting in non-minimally coupled scalar-tensor interactions as an example of a subclass of Horndeski theories. Lastly, she addresses the natural question of whether the parameters introduced in the dRGT theory are subject to strong renormalization by quantum loops and shows how the non-renormalization theorem protects the graviton mass from quantum corrections. Beyond the decoupling limit the quantum corrections are found to be proportional to the graviton mass, proving its technical naturalness.

Tjonnie Li's thesis covers two applications of Gravitational Wave astronomy: tests of General Relativity in the strong-field regime and cosmological measurements. The first part of the thesis focuses on the so-called TIGER, i.e. Test Infrastructure for General Relativity, an innovative Bayesian framework for performing hypothesis tests of modified gravity using ground-based GW data. After developing the framework, Li simulates a variety of General Relativity deviations and demonstrates the ability of the aforementioned TIGER to measure them. The advantages of the method are nicely shown and compared to other, less generic methods. Given the extraordinary implications that would result from any measured deviation from General Relativity, it is extremely important that a rigorous statistical approach for supporting these results would be in place before the first Gravitational Wave detections begin. In developing TIGER, Tjonnie Li shows a large amount of creativity and originality, and his contribution is an important step in the direction of a possible discovery of a deviation (if any) from General Relativity. In another section, Li's thesis deals with cosmology, describing an exploratory study where the possibility of cosmological parameters measurement through gravitational wave compact binary coalescence signals associated with electromagnetic counterparts is evaluated. In particular, the study explores the capabilities of the future Einstein Telescope observatory. Although of very long term-only applicability, this is again a thorough investigation, nicely put in the context of the current and the future observational cosmology.

Originally published in 1921, this book presents a concise study of time and space relations by the renowned British physicist Alfred Robb (1873-1936). The text is one of a series of works on the topic of special relativity written by Robb from 1911 onwards. An appendix section is included. This book will be of value to anyone with an interest in special relativity, the development of physics and the history of science.

In early April 1911 Albert Einstein arrived in Prague to become full professor of theoretical physics at the German part of Charles University. It was there, for the first time, that he concentrated primarily on the problem of gravitation. Before he left Prague in July 1912 he had submitted the paper "Relativitat und Gravitation: Erwiderung auf eine Bemerkung von M. Abraham" in which he remarkably anticipated what a future theory of gravity should look like. At the occasion of the Einstein-in-Prague centenary an international meeting was organized under a title inspired by Einstein's last paper from the Prague period: "Relativity and Gravitation, 100 Years after Einstein in Prague". The main topics of the conference included: classical relativity, numerical relativity, relativistic astrophysics and cosmology, quantum gravity, experimental aspects of gravitation and conceptual and historical issues. The conference attracted over 200 scientists from 31 countries, among them a number of leading experts in the field of general relativity and its applications. This volume includes abstracts of the plenary talks and full texts of contributed talks and articles based on the posters presented at the conference. These describe primarily original results of the authors. Full texts of the plenary talks are included in the volume "General Relativity, Cosmology and Astrophysics--Perspectives 100 Years after Einstein in Prague", eds. J. Bicak and T. Ledvinka, published also by Springer Verlag.

Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also understand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic properties of particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N. Yang and R. Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry. The treatment of symmetries in this monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity.

The effective theory of quantum gravity coupled to models of particle physics is being probed by cutting edge experiments in both high energy physics (searches for extra dimensions) and cosmology (testing models of inflation). This thesis derives new bounds that may be placed on these models both theoretically and experimentally. In models of extra dimensions, the internal consistency of the theories at high energies are investigated via perturbative unitarity bounds. Similarly it is shown that recent models of Higgs inflation suffer from a breakdown of perturbative unitarity during the inflationary period. In addition, the thesis uses the latest LHC data to derive the first ever experimental bound on the size of the Higgs boson's non-minimal coupling to gravity.

The search for gravitational radiation with optical interferometers is gaining momentum worldwide. Beside the VIRGO and GEO gravitational wave observatories in Europe and the two LIGOs in the United States, which have operated successfully during the past decade, further observatories are being completed (KAGRA in Japan) or planned (ILIGO in India). The sensitivity of the current observatories, although spectacular, has not allowed direct discovery of gravitational waves. The advanced detectors (Advanced LIGO and Advanced Virgo) at present in the development phase will improve sensitivity by a factor of 10, probing the universe up to 200 Mpc for signal from inspiraling binary compact stars. This book covers all experimental aspects of the search for gravitational radiation with optical interferometers. Every facet of the technological development underlying the evolution of advanced interferometers is thoroughly described, from configuration to optics and coatings and from thermal compensation to suspensions and controls. All key ingredients of an advanced detector are covered, including the solutions implemented in first-generation detectors, their limitations, and how to overcome them. Each issue is addressed with special reference to the solution adopted for Advanced VIRGO but constant attention is also paid to other strategies, in particular those chosen for Advanced LIGO.

This thesis explores the idea that the Higgs boson of the Standard Model and the cosmological inflation are just two manifestations of one and the same scalar field - the Higgs-inflation. By this unification two energy scales that are separated by many orders of magnitude are connected, thereby building a bridge between particle physics and cosmology. An essential ingredient for making this model consistent with observational data is a strong non-minimal coupling to gravity. Predictions for the value of the Higgs mass as well as for cosmological parameters are derived, and can be tested by future experiments. The results become especially exciting in the light of the recently announced discovery of the Higgs boson. The model of non-minimal Higgs inflation is also used in a quantum cosmological context to predict initial conditions for inflation. These results can in turn be tested by the detection of primordial gravitational waves. The presentation includes all introductory material about cosmology and the Standard Model that is essential for the further understanding. It also provides an introduction to the mathematical methods used to calculate the effective action by heat kernel methods.

This thesis presents theoretical and numerical studies on phenomenological description of the quark–gluon plasma (QGP), a many-body system of elementary particles. The author formulates a causal theory of hydrodynamics for systems with net charges from the law of increasing entropy and a momentum expansion method. The derived equation results can be applied not only to collider physics, but also to the early universe and ultra-cold atoms. The author also develops novel off-equilibrium hydrodynamic models for the longitudinal expansion of the QGP on the basis of these equations. Numerical estimations show that convection and entropy production during the hydrodynamic evolution are key to explaining excessive charged particle production, recently observed at the Large Hadron Collider. Furthermore, the analyses at finite baryon density indicate that the energy available for QGP production is larger than the amount conventionally assumed.

Several of the very foundations of the cosmological standard model — the baryon asymmetry of the universe, dark matter, and the origin of the hot big bang itself — still call for an explanation from the perspective of fundamental physics. This work advocates one intriguing possibility for a consistent cosmology that fills in the theoretical gaps while being fully in accordance with the observational data. At very high energies, the universe might have been in a false vacuum state that preserved B-L, the difference between the baryon number B and the lepton number L as a local symmetry. In this state, the universe experienced a stage of hybrid inflation that only ended when the false vacuum became unstable and decayed, in the course of a waterfall transition, into a phase with spontaneously broken B-L symmetry. This B-L Phase Transition was accompanied by tachyonic preheating that transferred almost the entire energy of the false vacuum into a gas of B-L Higgs bosons, which in turn decayed into heavy Majorana neutrinos. Eventually, these neutrinos decayed into massless radiation, thereby producing the entropy of the hot big bang, generating the baryon asymmetry of the universe via the leptogenesis mechanism and setting the stage for the production of dark matter. Next to a variety of conceptual novelties and phenomenological predictions, the main achievement of the thesis is hence the fascinating notion that the leading role in the first act of our universe might have actually been played by neutrinos.

Pulsar timing is a promising method for detecting gravitational waves in the nano-Hertz band. In his prize winning Ph.D. thesis Rutger van Haasteren deals with how one takes thousands of seemingly random timing residuals which are measured by pulsar observers, and extracts information about the presence and character of the gravitational waves in the nano-Hertz band that are washing over our Galaxy. The author presents a sophisticated mathematical algorithm that deals with this issue. His algorithm is probably the most well-developed of those that are currently in use in the Pulsar Timing Array community. In chapter 3, the gravitational-wave memory effect is described. This is one of the first descriptions of this interesting effect in relation with pulsar timing, which may become observable in future Pulsar Timing Array projects. The last part of the work is dedicated to an effort to combine the European pulsar timing data sets in order to search for gravitational waves. This study has placed the most stringent limit to date on the intensity of gravitational waves that are produced by pairs of supermassive black holes dancing around each other in distant galaxies, as well as those that may be produced by vibrating cosmic strings. Rutger van Haasteren has won the 2011 GWIC Thesis Prize of the Gravitational Wave International Community for his innovative work in various directions of the search for gravitational waves by pulsar timing. The work is presented in this Ph.D. thesis.

Proceedings from the 2012 Fourth International Meeting on Gravitation and Cosmology, focusing on accelerated cosmic expansion This volume provides both an update and a review of the state of alternative theories of gravity in connection with the accelerated expansion of the universe issue. Different theoretical proposals exist to explain the acceleration in the cosmic expansion, generating the dark energy issue and opening the possibility to theories of gravity alternative to general relativity. Related issues such as the dark matter problem are also surveyed in order to give the readers profound insight on the subject from different points of view. Comprised of short talks and plenary lectures given by leading experts in the field, some of them with brilliant and historic contributions, the book allows the reader to find readable and referenced surveys in topics like f(R) theories, the dark matter and dark energy issues, Modified Newtonian Dynamics (MOND) scenarios, f(T) theories, scalar-tensor theories derived from non-Riemannian geometries, emergent universes, the cosmological constant and other topics of current interest for younger and senior physicists and graduate students. These proceedings are from the Fourth International Meeting on Gravitation and Cosmology, held in Guadalajara, Jalisco, México, from 20 - 25 May, 2012, was sponsored by ICTP- Trieste, Italy and COECyTJAL-Universidad de Guadalajara, México. This event is a series of scientific meetings started in 2004 in Cuba, focusing on current and selected topics in the fields of gravitation and cosmology.

This book contains contributions from the Spanish Relativity Meeting, ERE 2012, held in Guimaraes, Portugal, September 2012. It features more than 70 papers on a range of topics in general relativity and gravitation, from mathematical cosmology, numerical relativity and black holes to string theory and quantum gravity. Under the title "Progress in Mathematical Relativity, Gravitation and Cosmology," ERE 2012 was attended by an exceptional international list of over a hundred participants from the five continents and over forty countries. ERE is organized every year by one of the Spanish or Portuguese groups working in this area and is supported by the Spanish Society of Gravitation and Relativity (SEGRE). This book will be of interest to researchers in mathematics and physics.

In this thesis the author discusses the phenomenology of supersymmetric models by means of experimental data set analysis of the electric dipole moment. There is an evaluation of the elementary processes contributing to the electric dipole moments within R-parity-violating supersymmetry, which call for higher-order perturbative computations. A new method based on linear programming is developed and for the first time the non-trivial parameter space of R-parity violation respecting the constraints from existing experimental data of the electric dipole moment is revealed. As well, the impressive efficiency of the new method in scanning the parameter space of the R-parity-violating sector is effectively demonstrated. This new method makes it possible to extract from the experimental data a more reliable constraint on the R-parity violation.

With his Ph.D. thesis, presented here in the format of a "Springer Theses", Paul Fulda won the 2012 GWIC thesis prize awarded by the Gravitational Wave International Committee. The impact of thermal noise on future gravitational wave detectors depends on the size and shape of the interrogating laser beam. It had been known since 2006 that, in theory, higher-order Laguerre-Gauss modes could reduce thermal noise. Paul Fulda's research brings Laguerre-Gauss modes an enormous step forward. His work includes analytical, numerical and experimental work on table-top setups as well as experiments at the Glasgow 10m prototype interferometer. Using numerical simulations the LG33 mode was selected as the optical mode to be tested. Further research by Paul and his colleagues since then concentrated on this mode. Paul has developed and demonstrated simple and effective methods to create this mode with diffractive optics and successfully demonstrated its compatibility with the essential building blocks of gravitational wave detectors, namely, optical cavities, Michelson interferometers and opto-electronic sensing and control systems. Through this work, Laguerre-Gauss modes for interferometers have been transformed from an essentially unknown entity to a well understood option with an experimental basis.

The presentations at this NASA-hosted Symposium in honor of Mino Freund will touch upon the fields, to which his prolific mind has made significant contributions. These include low temperature physics, cosmology, and nanotechnology with its wide-ranging applicability to material science, neuroscience, Earth sciences and satellite technology. To learn more about Mino’s career you can download the "Tribute" http://multimedia.seti.org/mino/Tribute.pdf which outlines his journey from (i) low-temperature physics and superconductivity at the ETH Zürich to (ii) building one remarkable milliKelvin refrigerator for the US-Japan IRTS mission at UC Berkeley and ISAS in Japan to (iii) a decade in cosmology, to (iv) being on the micro-bolometer team at NASA Goddard for the HAWC instrument on SOFIA, to (v) developing at AFRL the nanotechnology portfolio for the entire Air Force. This was followed by six years at the NASA Ames Research Center, where Mino formulated his far-ahead ideas about swarms of capable nanosats circling the Earth, which have since started to become a reality. He engaged in a broad range of nanotechnology projects, including novel applications in neuroscience well before he himself was struck by the deadly brain tumor.

This course-tested textbook conveys the fundamentals of magnetic fields and relativistic plasma in diffuse cosmic media, with a primary focus on phenomena that have been observed at different wavelengths. Theoretical concepts are addressed wherever necessary, with derivations presented in sufficient detail to be generally accessible. In the first few chapters the authors present an introduction to various astrophysical phenomena related to cosmic magnetism, with scales ranging from molecular clouds in star-forming regions and supernova remnants in the Milky Way, to clusters of galaxies. Later chapters address the role of magnetic fields in the evolution of the interstellar medium, galaxies and galaxy clusters. The book is intended for advanced undergraduate and postgraduate students in astronomy and physics and will serve as an entry point for those starting their first research projects in the field.

This book provides a chronological introduction to the sciences of astronomy and cosmology based on the reading and analysis of significant selections from classic texts, such as Ptolemy's The Almagest, Kepler's Epitome of Copernican Astronomy, Shapley's Galaxies and Lemaitre's The Primeval Atom. Each chapter begins with a short introduction followed by a reading selection. Carefully crafted study questions draw out key points in the text and focus the reader's attention on the author's methods, analysis, and conclusions. Numerical and observational exercises at the end of each chapter test the reader's ability to understand and apply key concepts from the text. The Heavens and the Earth is the first of four volumes in A Student's Guide Through the Great Physics Texts. This book grew out of a four-semester undergraduate physics curriculum designed to encourage a critical and circumspect approach to natural science, while at the same time preparing students for advanced coursework in physics. This book is particularly suitable as a college-level textbook for students of the natural sciences, history or philosophy. It also serves as a textbook for advanced high-school students, or as a thematically-organized source-book for scholars and motivated lay-readers. In studying the classic scientific texts included herein, the reader will be drawn toward a lifetime of contemplation.

This book is a small but practical summary of how one can and should learn science. The author argues that science cannot be taught but has to be learnt. Based on historical examples he shows that practicing science means putting one's intellect into the understanding of simple questions like what, why, how and when events around you happen. The reader understands that the search for the cause and effect relationship of so called normal happenings is a very provocative experience and learning science leads one to it. This is underpinned by looking at everyday experiences and how they can help any lay-person learn science. The author also explains the methodology of science and discusses an integrated approach to science communication. Finally he elaborates on the influence and role of science in society. The book addresses interested general readers, teachers and science communicators.

This book provides a chronological introduction to the science of motion and rest based on the reading and analysis of significant portions of Galileo's Dialogues Concerning Two New Sciences, Pascal's Treatise on the Equilibrium of Fluids and the Weight of the Mass of Air, Newton's Mathematical Principles of Natural Philosophy, and Einstein's Relativity. Each chapter begins with a short introduction followed by a reading selection. Carefully crafted study questions draw out key points in the text and focus the reader's attention on the author's methods, analysis, and conclusions. Numerical and laboratory exercises at the end of each chapter test the reader's ability to understand and apply key concepts from the text. Space, Time and Motion is the second of four volumes in A Student's Guide through the Great Physics Texts. This book grew out of a four-semester undergraduate physics curriculum designed to encourage a critical and circumspect approach to natural science, while at the same time preparing students for advanced coursework in physics. This book is particularly suitable as a college-level textbook for students of the natural sciences, history or philosophy. It also serves as a textbook for advanced high-school students, or as a thematically-organized source-book for scholars and motivated lay-readers. In studying the classic scientific texts included herein, the reader will be drawn toward a lifetime of contemplation.

This book provides a rather self-contained survey of the construction of Hadamard states for scalar field theories in a large class of notable spacetimes, possessing a (conformal) light-like boundary. The first two sections focus on explaining a few introductory aspects of this topic and on providing the relevant geometric background material. The notions of asymptotically flat spacetimes and of expanding universes with a cosmological horizon are analysed in detail, devoting special attention to the characterization of asymptotic symmetries. In the central part of the book, the quantization of a real scalar field theory on such class of backgrounds is discussed within the framework of algebraic quantum field theory. Subsequently it is explained how it is possible to encode the information of the observables of the theory in a second, ancillary counterpart, which is built directly on the conformal (null) boundary. This procedure, dubbed bulk-to-boundary correspondence, has the net advantage of allowing the identification of a distinguished state for the theory on the boundary, which admits a counterpart in the bulk spacetime which is automatically of Hadamard form. In the last part of the book, some applications of these states are discussed, in particular the construction of the algebra of Wick polynomials. This book is aimed mainly, but not exclusively, at a readership with interest in the mathematical formulation of quantum field theory on curved backgrounds.

"What Bodanis does brilliantly is to give us a feel for Einstein as a person. I don't think I've ever read a book that does this as well . . . Whenever there's a chance for storytelling, Bodanis triumphs." --Popular Science "Fascinating." --Forbes Widely considered the greatest genius of all time, Albert Einstein revolutionized our understanding of the cosmos with his general theory of relativity and helped lead us into the atomic age. Yet in the final decades of his life, he was ignored by most working scientists, and his ideas were opposed by even his closest friends. How did this happen? Best-selling biographer David Bodanis traces the arc of Einstein's life--from the skeptical, erratic student to the world's most brilliant physicist to the fallen-from-grace celebrity. An intimate biography in which "theories of the universe morph into theories of life" (Times, London), Einstein's Greatest Mistake reveals what we owe Einstein today--and how much more he might have achieved if not for his all-too-human flaws.

Subtlety in Relativity is the only book that has been written after the author's discovery of a new way in which wave phenomena occur-the emission origin of waves. This drastically changes most issues of the old debate over the world being either deterministic or probabilistic. The emission origin of waves is not incompatible with the ideas of quantum theory; rather, this new and novel way in which waves can be generated justifies the use of mathematical and probabilistic methods of quantum theory. However, the emission origin of waves shows that quantum theory is statistically incomplete in, precisely, Einstein's sense. There exists, then, a certain, previously unexplored, conceptual framework underlying the ideas of quantum theory. Whether this is the theory that Einstein and others were looking for then, how this way of thinking is related to the ideas of relativity, and whether this is a relativistic theory in the usual sense of this word are questions this book answers. The book demonstrates how the Doppler effect with acceleration is essential to interpreting astronomical observations. It also offers a detailed and self-sufficient technical background of mathematical ideas of category theory. The book is divided into two parts. The first is less mathematical and more conceptual in its orientation. The second focuses on mathematical ideas needed to implement physical concepts. The book is a great reference for advanced undergraduate- and graduate-level students of physics and researchers in physics, astronomy, and cosmology, who will gain a deeper understanding of relativity from it.

When predictions of Einstein's theory of General Relativity are compared against observations of our Universe, a huge inconsistency is found. The most popular fix for this inconsistency is to "invent" around 94% of the content of the universe: dark matter and dark energy. The dark energy is some exotic substance responsible for the apparent observed acceleration of the Universe. Another fix is to modify the theory of gravity: it is entirely plausible that Einstein's theory of General Relativity breaks down on cosmological scales, just as Newton's theory of gravity breaks down in the extreme gravitational field of the Sun. There are many alternative theories of gravity, each with the aim of describing observations of our Universe where General Relativity fails. Whether it is dark energy or some modified theory of gravity, it is clear that there is some "dark sector" in the Universe. In this thesis the author constructs a unifying framework for understanding the observational impact of general classes of dark sector theories, by formulating equations of state for the dark sector perturbations.