The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects.

The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.

This volume is dedicated to the one hundredth anniversary of the publication of Hermann Minkowski's paper "Raum und Zeit" in 1909 [1]. The paper presents the textofthetalkMinkowskigaveatthe80thMeetingoftheGermanNaturalScientists and Physicians in Cologne on September 21, 1908. Minkowski's work on the spacetime representation of special relativity had a huge impact on the twentieth century physics, which can be best expressed by merely stating what is undeniable - that modern physics would be impossible wi- out the notion of spacetime. It is suf cient to mention as an example only the fact that general relativity would be impossible without this notion; Einstein succeeded to identifygravitywith the curvatureofspacetime onlywhen he overcamehis initial hostile reactionto Minkowski'sfour-dimensionalrepresentationof special relativity and adopted spacetime as the correct relativistic picture of the world. While there exists an unanimous consensus on the mathematical signi cance of spacetime for theoretical physics, for a hundred years there has been no consensus on the nature of spacetime itself. The rst sign of this continuing controversy was Sommerfeld's remark in his notes on Minkowski's article [2]: "What will be the epistemologicalattitudetowardsMinkowski'sconceptionofthetime-spaceproblem is another question, but, as it seems to me, a question which does not essentially touch his physics".

Puts the emphasis on conceptual questions: Why is there no such thing as absolute motion? What is the physical meaning of relativity of simultaneity? But, the most important question that is addressed in this book is "what is the nature of spacetime?" or, equivalently, "what is the dimensionality of the world at the macroscopic level?"

Develops answers to these questions via a thorough analysis of relativistic effects and explicitly asking whether the objects involved in those effects are three-dimensional or four-dimensional.

Discusses the implication of the result (this analysis clearly shows that if the world and the physical objects were three-dimensional, none of the kinematic relativistic effects and the experimental evidence supporting them would be possible) for physics, philosophy, and our entire world view are discussed.

All physicists would agree that one of the most fundamental problems of the 21st century physics is the dimensionality of the world. In the four-dimensional world of Minkowski (or Minkowski spacetime) the most challenging problem is the nature of the temporal dimension. In Minkowski spacetime it is merely one of the four dimensions, which means that it is entirely given like the other three spacial dimensions. If the temporal dimension were not given in its entirety and only one constantly changing moment of it existed, Minkowski spacetime would be reduced to the ordinary three-dimensional space.

But if the physical world, represented by Minkowski spacetime, is indeed four-dimensional with time being the fourth dimension, then such a world is drastically different from its image based on our perceptions. Minkowski four-dimensional world is a block Universe, a frozen world in which nothing happens since all moments of time are given at once', which means that physical bodies are four-dimensional worldtubes containing the whole histories in time of the three-dimensional bodies of our everyday experience. The implications of a real Minkowski world for physics itself and especially for our world view are enormous.

The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension? It contains fourteen invited papers which either directly address the main question of the nature of spacetime or explore issues related to it."

In 1908 Hermann Minkowski gave the four-dimensional(spacetime) formulationof special relativity 1]. In fact, HenriPoincare 2] rst noticedin1906that the Lorentz transformations had a geometric interpretation as rotations in a four-dimensional space with time as the fourth dimension. However it was Minkowski, who succe- fully decoded the profound message about the dimensionality of the world hidden in the relativity postulate, which re ects the experimental fact that natural laws are the same in all inertial reference frames. Unlike Poincare, Minkowski did not regardspacetime - the uni cation of space and time - as a convenientmathematical space, but insisted that this absolute four-dimensional world, as Minkowski called it, represents physical phenomena and the world more adequately than the relativity postulate: "the word relativity-postulate. . . seems to me very feeble. Since the pos- late comes to mean that only the four-dimensional world in space and time is given by the phenomena. . . I prefer to call it the postulate of the absolute world" 3]. The impact of Minkowski's ideas on the twentieth century physics has been so immense that one cannot imagine modern physics without the notion of spacetime. It would hardly be an exaggeration to say that spacetime has been the greatest discoveryinphysicsofall times. Theonlyotherdiscoverythatcomesclosetospa- time is Einstein's general relativity, which revealed that gravity is a manifestation of the curvature of spacetime. But it was the discovery of spacetime, which paved the way for this deep understanding of what gravity really is. Einstein saw the link betweenthegeometryofspacetimeandgravitationonlyafterheovercamehis initial hostile attitude toward the notion of spacetime."

This volume is dedicated to the one hundredth anniversary of the publication of Hermann Minkowski's paper "Raum und Zeit" in 1909 [1]. The paper presents the textofthetalkMinkowskigaveatthe80thMeetingoftheGermanNaturalScientists and Physicians in Cologne on September 21, 1908. Minkowski's work on the spacetime representation of special relativity had a huge impact on the twentieth century physics, which can be best expressed by merely stating what is undeniable - that modern physics would be impossible wi- out the notion of spacetime. It is suf cient to mention as an example only the fact that general relativity would be impossible without this notion; Einstein succeeded to identifygravitywith the curvatureofspacetime onlywhen he overcamehis initial hostile reactionto Minkowski'sfour-dimensionalrepresentationof special relativity and adopted spacetime as the correct relativistic picture of the world. While there exists an unanimous consensus on the mathematical signi cance of spacetime for theoretical physics, for a hundred years there has been no consensus on the nature of spacetime itself. The rst sign of this continuing controversy was Sommerfeld's remark in his notes on Minkowski's article [2]: "What will be the epistemologicalattitudetowardsMinkowski'sconceptionofthetime-spaceproblem is another question, but, as it seems to me, a question which does not essentially touch his physics".

Puts the emphasis on conceptual questions: Why is there no such thing as absolute motion? What is the physical meaning of relativity of simultaneity? But, the most important question that is addressed in this book is "what is the nature of spacetime?" or, equivalently, "what is the dimensionality of the world at the macroscopic level?"

Develops answers to these questions via a thorough analysis of relativistic effects and explicitly asking whether the objects involved in those effects are three-dimensional or four-dimensional.

Discusses the implication of the result (this analysis clearly shows that if the world and the physical objects were three-dimensional, none of the kinematic relativistic effects and the experimental evidence supporting them would be possible) for physics, philosophy, and our entire world view are discussed.

All physicists would agree that one of the most fundamental problems of the 21st century physics is the dimensionality of the world. In the four-dimensional world of Minkowski (or Minkowski spacetime) the most challenging problem is the nature of the temporal dimension. In Minkowski spacetime it is merely one of the four dimensions, which means that it is entirely given like the other three spacial dimensions. If the temporal dimension were not given in its entirety and only one constantly changing moment of it existed, Minkowski spacetime would be reduced to the ordinary three-dimensional space. But if the physical world, represented by Minkowski spacetime, is indeed four-dimensional with time being the fourth dimension, then such a world is drastically different from its image based on our perceptions.

In 1908 Hermann Minkowski gave the four-dimensional(spacetime) formulationof special relativity[1]. In fact,HenriPoincare[ ' 2] rst noticedin1906that the Lorentz transformations had a geometric interpretation as rotations in a four-dimensional space with time as the fourth dimension. However it was Minkowski, who succe- fully decoded the profound message about the dimensionality of the world hidden in the relativity postulate, which re ects the experimental fact that natural laws are the same in all inertial reference frames. Unlike Poincare, ' Minkowski did not regardspacetime - the uni cation of space and time - as a convenientmathematical space, but insisted that this absolute four-dimensional world, as Minkowski called it, represents physical phenomena and the world more adequately than the relativity postulate: "the word relativity-postulate...seems to me very feeble. Since the pos- late comes to mean that only the four-dimensional world in space and time is given by the phenomena...I prefer to call it the postulate of the absolute world"[3]. The impact of Minkowski's ideas on the twentieth century physics has been so immense that one cannot imagine modern physics without the notion of spacetime. It would hardly be an exaggeration to say that spacetime has been the greatest discoveryinphysicsofall times. Theonlyotherdiscoverythatcomesclosetospa- time is Einstein's general relativity, which revealed that gravity is a manifestation of the curvature of spacetime. But it was the discovery of spacetime, which paved the way for this deep understanding of what gravity really is. Einstein saw the link betweenthegeometryofspacetimeandgravitationonlyafterheovercamehis initial hostile attitude toward the notion of spacetime.

The greatest mystery in the world is its very existence. In our intellectual development, we all reach a turning point when we start asking the perennial existential questions: "What is the world?"; "What am I?"; "What is the meaning of the existence of the world and myself?." As the German philosopher Schopenhauer put it: "The lower a man stands in intellectual respects the less of a riddle does existence seem to him... but, the clearer his consciousness becomes the more the problem grasps him in its greatness." This book explores what fundamental physics tells us about the physical world and how the scientific picture of what exists often differs disturbingly from the "common sense" view based on the way our senses reflect the world. Centuries-old illusions are identified by showing that they contradict experimentally-confirmed results of modern physics, which clears the way toward deeper understanding of reality. The greatest illusion that the world exists only at the present moment of time has been realized by many great thinkers, but so far the human race has been unable to free itself from it, prompting Einstein to write this: "the distinction between past, present and future is only a stubbornly persistent illusion." Getting rid of such stubbornly persistent illusions by open-mindedly examining the implications of modern physics for the physical world can help us rise above the fog of everyday life and see Nature the way she herself is.

This is the first English translation of the book The World as Space and Time written by the great Russian physicist Alexander Friedmann who first showed in 1922 that Einstein's equations have solutions that describe a non-stationary Universe (later the experimental evidence did confirm that the Universe is expanding). The original Russian publication was in 1923. The book is one of the first introductions to the spacetime physics of the theory of relativity for a wider audience. Friedmann had succeeded in both making the book accessible to non-experts and providing rigorous explanations.