The study of the quantum–classical correspondence has been focused on the quantum measurement problem. However, most of the discussion in the preceding chapters is motivated by a broader question: Why do we perceive our quantum Universe as classical? Therefore, emergence of the classical phase space and Newtonian dynamics from the quantum Hilbert space must be addressed. Chapter 6 starts by re-deriving decoherence rate for non-local superpositions using the Wigner representation of quantum states. We then discuss the circumstances that, in some situations, make classical points a useful idealization of the quantum states of many-body systems. This classical structure of phase space emerges along with the (at least approximately reversible) Newtonian equations of motion. Approximate reversibility is a non-trivial desideratum given that the quantum evolution of the corresponding open system is typically irreversible. We show when such approximately reversible evolution is possible. We also discuss quantum counterparts of classically chaotic systems and show that, as a consequence of decoherence, their evolution tends to be fundamentally irreversible: They produce entropy at the rate determined by the Lyapunov exponents that characterize classical chaos. Thus, quantum decoherence provides a rigorous rationale for the approximations that led to Boltzmann’s H-theorem.

Chapter 5 explores the consequences of decoherence. We live in a Universe that is fundamentally quantum. Yet, our everyday world appears to be resolutely classical. The aim of Chapter 5 is to discuss how preferred classical states, and, more generally, classical physics, arise, as an excellent approximation, on a macroscopic level of a quantum Universe. We show why quantum theory results in the familiar “classical reality” in open quantum systems, that is, systems interacting with their environments. We shall see how and why, and to what extent, quantum theory accounts for our classical perceptions. We shall not complete this task here—a more detailed analysis of how the information is acquired by observers is needed for that, and this task will be taken up in Part III of the book. Moreover, Chapter 5 shows that not just Newtonian physics but also equilibrium thermodynamics follows from the same symmetries of entanglement that led to Born’s rule (in Chapter 3).

Quantum Darwinism demonstrates not only that preferred states are selected for their stability but also that information about them is broadcast by the same environment that causes decoherence and einselection. That environment acts both as a censor and as an advertising agent that disseminates information about pointer states while suppressing complementary information. Chapter 8 explores the implications and limitations of quantum Darwinism using models inspired by the structure of the Universe we inhabit. We perceive our Universe using light and other means of information transmission. We explore models that have a well-defined relation with our everyday reality, and where one can also selectively relax some of the idealized assumptions and investigate the consequences. Light is the communication channel through which we obtain most of our information. Fortunately, it is an ideal channel in the sense of quantum Darwinism, and simple but realistic cases are exactly solvable. The solution presented herein demonstrates the inevitability of the consensus between observers who rely on scattered photons: The emergence of classical objective reality (classical because pointer states are einselected, and objective because redundancy imposes consensus) is inevitable. This is how the classical world we perceive emerges from within the quantum Universe we inhabit.

The aim in Chapter 7 is to take into account the role of the means of information transmission on the nature of the states that can be perceived. Our point of departure is the recognition that the information we obtain is acquired by observers who monitor fragments of the same environment that decohered the system, einselecting preferred pointer states in the process. Moreover, we only intercept a fraction of the environment. The only information about the system that can be transmitted by its fraction must have been reproduced in many copies in that environment. This process of amplification limits what can be found out to the states einselected by decoherence. Quantum Darwinism provides a simple and natural explanation of this restriction, and, hence, of the objective existence—the essence of classicality—for the einselected states. This chapter introduces and develops information-theoretic tools and concepts (including, e.g., redundancy) that allow one to explore and characterize correlations and information flows between systems, environments, and observers, and illustrates them on an exactly solvable yet non-trivial model.

Chapter 4 begins to discuss decoherence, and, thus, to address the overarching question: How does the classical world—classical states that are responsible for the objective reality of our everyday experience—emerge from within the Universe that is, as we know from compelling experimental evidence, made out of quantum stuff. The short answer to this question is that decoherence selects (from the vast number of superpositions that populate Hilbert space in the process of environment-induced superselection (also known as einselection) the few states that are—in contrast to all the other alternatives—stable in spite of their immersion in the environment. Decoherence is illustrated with a detailed discussion of two models. A spin decohered by an environment of spins as well as quantum Brownian motion have become paradigmatic models of decoherence for good reason: They are exactly solvable and yet they capture (albeit in an idealized manner) the emergence of the preferred classical states in settings that are relevant for quantum measurements and for Newtonian dynamics in effectively classical phase space.

Chapter 2 shows how the discreteness that sets the stage for discontinuous quantum jumps between a restricted set of states is a consequence of the symmetry breaking that resolves the tension between the unitarity of quantum evolutions, and repeatable information transfer (the essence of quantum Darwinism, the subject of Chapters 7 and 8). Chapter 2 shows that, while the quantum superposition principle declares that every superposition is an equally legal quantum state, repeatability restricts states that can be recorded (found out) multiple times to an orthogonal set determined by the unitary dynamics of the process responsible for the repeated information transfer (i.e., for amplification). Such states persist and can imprint the evidence of their continued presence in other systems, e.g., on the subsystems of the environment. They become the elements of objective reality—e.g., outcomes of the measurements we perceive. Moreover, Chapter 2 motivates the need for the derivation of the probabilities of measurements (to be carried out in Chapter 3).

Chapter 1 begins by re-examining the textbook quantum postulates. It concludes with the realization that some of them are inconsistent with quantum mathematics, but also that they may not have to be postulated. Indeed, in the following two chapters it is shown that their consequences follow from the other, consistent postulates. This simplification of the quantum foundations provides a consistent, convenient, and solid starting point. The emergence of the classical from the quantum substrate is based on this foundation of “core quantum postulates”—the “quantum credo”. Discussion of the postulates is accompanied by a brief summary of their implications for the interpretation of quantum theory. This discussion touches on questions of interpretation that are implicit throughout the book, but will be addressed more fully in Chapter 9. Chapter 1 ends with a “decoherence primer” that provides a quick introduction to decoherence (discussed in detail in Part II). Its aim is to provide the reader with an overview of the process that will play an important role throughout the book, and to motivate Chapters 2 and 3 that lay the foundations for the physics of decoherence (Part II) as well as for quantum Darwinism, the subject of Chapters 7 and 8.

Chapter 3 describes how quantum entanglement leads to probabilities based on a symmetry, but—in contrast to subjective equal likelihood based solely on ignorance—it is an objective symmetry of known quantum states. Entanglement-assisted invariance (or envariance for short) relies on quantum correlations: One can know the quantum state of the whole and use this to quantify the resulting ignorance of the states of parts. Thus, quantum probability is, in effect, an objective consequence of the Heisenberg-like indeterminacy between global and local observables. This derivation of Born’s rule is based on the consistent subset of quantum postulates. It justifies statistical interpretation of reduced density matrices, an indispensable tool of decoherence theory. Hence, it gives one the mandate to explore—in Part II of this book—the fundamental implications of decoherence and its consequences using reduced density matrices and other customary tools.

There are two widely known interpretations of quantum theory: Bohr’s Copenhagen interpretation and Everett’s interpretation. The focus of Chapter 9 is to assess, within the context they provide, the interpretation-independent advances discussed in this book. We want to see whether the advances that include decoherence and quantum Darwinism fit these two established and widely known points of view. In fact, it is surprising that (with minor but significant adjustments) decoherence and quantum Darwinism fit very naturally, addressing questions that were recognized as open and important. We then discuss the existential interpretation. It can be seen as a continuation of the Copenhagen interpretation, with the Universe consisting of quantum and classical realms, but with classicality that is emergent, rather than preordained. It is also compatible with Everett’s interpretation, since quantum states and evolutions are all that is needed. However, unlike the Many Worlds interpretation (which regards the quantum state of the Universe as objectively existing, akin to a classical point in phase space or a classical electromagnetic field), the existential interpretation recognizes that quantum states combine information and existence—they are epiontic. The mix of existence and information they represent fits the relative states reading of Everett’s approach.