It is usually believed that the problem of producing a classical theory of gravitation compatible with the requirement of general covariance was completely solved more than a century ago by the creation of the general theory of relativity. Since then, all efforts have thus been focused on trying to make this theory compatible with quantum theory, the other great pillar of fundamental theoretical physics. But despite the enormous progress which was achieved in this direction, those efforts have not been entirely successful. In face of the mounting difficulties encountered in the field of observational cosmology a growing number of researchers have come to believe that the problem may have to do with relativity theory itself. Through a critical review of some of our most basic assumptions concerning the physical concept of time direction a decisive shift in our understanding of gravitation has recently been achieved that is based on a reexamination of the problem of negative-energy states. It is by insisting on applying the principle of relativity to all physical quantities, including the sign of energy, that an improved classical theory of gravitation can emerge that preserves the basic mathematical structure of relativity, but that simplifies the theory in the presence of negative-energy matter and vacuum energy. This renewed perspective has already allowed to shed light on several long-standing puzzles in cosmology, such as the problem of the nature of dark matter and dark energy and that of the origin of the arrow of time. But it was also shown to be necessary to explain why it is that the strange world of quantum mechanics can give rise to the classical world of our daily experience. This book exposes in a rigorous, yet accessible manner the most significant aspects of those essential developments. CONTENTS 1 Introduction 2 Negative Energy and Gravitation 2.1 The negative-energy problem 2.2 The time-direction degree of freedom 2.3 Our current understanding 2.4 The negative-mass concept 2.5 The equivalence principle with negative mass 2.6 An effect of voids in the matter distribution 2.7 Six problems for negative-energy matter 2.8 The origin of repulsive gravitational forces 2.9 No energy out of nothing 2.10 The problem of vacuum decay 2.11 Energy and momentum conservation 2.12 Absolute inertial mass 2.13 A few other misconceptions 2.14 An axiomatic formulation 2.15 Generalized gravitational field equations 3 Time Reversal and Information 3.1 The problem of discrete symmetries 3.2 The constraint of relational definition 3.3 The concept of bidirectional time 3.4 Alternative definition of C, P, and T 3.5 The time-reversal operation 3.6 The charge-conjugation operation 3.7 Invariance under combined reversals 3.8 The significance of classical equations 3.9 Reversal of action 3.10 Black-hole entropy 3.11 Negative temperatures 4 Cosmology and Irreversibility 4.1 The outstanding problems of cosmology 4.2 The cosmological-constant problem 4.3 Missing mass and dark matter 4.4 Large-scale structure 4.5 The flatness problem and matter creation 4.6 The problem of time asymmetry 4.7 Gravitational entropy 4.8 The initial singularity 4.9 The horizon problem and irreversibility 4.10 A criticism of inflation theory 5 Quantum Theory and Causality 5.1 The problem of interpretation 5.2 A simple analogy 5.3 Time-symmetric causality 5.4 Closed causal chains and time travel 5.5 Advanced waves and time asymmetry 5.6 Early interpretations 5.7 The constraint of scientific realism 5.8 Time-symmetric quantum theory 5.9 Quantum entanglement and non-locality 5.10 The quantum measurement problem 5.11 The emergence of time in quantum cosmology 5.12 Universal causal chain and quasiclassicality 5.13 A possible role for gravitation 6 Conclusion