This chapter begins the final section of the book, which presents both review and new results of original research on decoherence and measurement theory. In this chapter, it is shown that normal quantum mechanics can lead to irreversible behavior in an open system, in contrast to the expectation of the Poincaré theorem that predicts repeating, cyclical behavior for all closed systems. The quantum Boltzmann equation, which implies the famous H-theorem that underlies all statistical mechanics, is derived.

This chapter gives a quantitative introduction to decoherence theory, including density matrix formalism in the context of quantum field theory, and a survey of the quantum trajectories method. Finally, the mathematical structure for a new proposal for spontaneous collapse, introduced nonmathematically in Chapter 6, is given.

This chapter surveys modern progress in physics on the topic of “decoherence,” the physical process by which irreversible behavior can occur in wave systems. A substantial part of the chapter discusses a proposal by the author of this book for a spontaneous collapse theory that is connected to decoherence.

This chapter surveys several different mathematical methods for time-dependent change of quantum states using quantum field theory. The Bloch sphere method is introduced, which can be used to show the physics discussed in Chapter 3, that electronic transitions, or “jumps,” are not instantaneous.

In Chapter 6, we discuss quantum jumps, or leaps, beginning with a historical discussion of quantum jumps, or leaps, and giving the motivating example of blinking atoms in trapped ions and quantum jumps in superconducting circuits. Despite the disruptive name, we discuss how jumps fit into the category of continuous measurement. In some cases, quantum jumps can be predicted, and even reversed. We build up the mathematical formalism by discussing the quantum Zeno effect, Lindblad-type master equations, leading to jump and no-jump dynamics - an inseparable combination of discrete and continuous dynamics. In fact, the discrete nature of the jump is illusory. We discuss the dynamics of a quantum jump and the transition from jumps to diffusion.

This first chapter gives an introduction to the book and guides the reader through much of the history of the field of quantum mechanics, focusing on what we view as the most important episodes in the field. We discuss the essential properties of quantum mechanics and how they have been reimagined in the decades that followed the era of the founders.

In this chapter we discuss the effects of losses on quantum optical systems. We discuss quantum jumps and master equations. We introduce the notion of using fictitious beam splitters to model losses. We introduce the decoherence of pure quantum mechanical states into a statistical mixture.

This chapter presents the theoretical framework that allows us to describe evolutions in the general case using Kraus operators as the main tool. It considers in detail the phenomenon of decoherence and gives examples of such maps. It shows that any evolution can be considered as unitary by going in a larger Hilbert space. The Lindblad equation for the evolution of the density matrix appears as a particular case of evolution in the short memory or Markov approximation. Up-jumps and down-jumps are also described within this framework using cavity damping, spontaneous emission, and the shelving technique as examples.

This chapter presents the theoretical framework, based on Gleason’s theorem, allowing to describegeneralized measurements, in addition to von Neumann measurements, in terms of POVMs, probability operators and post-measurement operators. It mentions the Naimark theorem according to which a generalized measurement is a von Neumann measurement if one describes it in a Hilbert space of higher dimension. Examples of generalized measurements are given: imperfect measurements, simultaneous measurements of noncommuting operators. It presents the Zurek model that accounts for the decoherence process occurring in a measurement and shows that the quantum measurement process, including state collapse, is not a physical evolution. Finally, it studies the case of successive measurements using Bayes statistics in which the state collapse appears as an updating of the information about a system, and the fundamental property of repeatability of quantum mechanics.

The Representation View provides a strategy for determining whether time itself has an arrow, but most purported arrows fail to establish this.

In this chapter, the relativistic transactional interpretation (RTI) is shown to completely nullify the Maudlin objection (a type of contingent absorber experiment) to the original, nonrelativistic TI. RTI is applied to some prominent quantum “paradoxes” such as the quantum eraser and the Frauchiger–Renner paradox and shown to resolve these. In addition, RTI derives standard decoherence results while also providing an account of concrete measurement outcomes that is missing in standard (unitary-only) decoherence theory.

This chapter serves as an elementary introduction to the basic quantum puzzles such as the measurement problem, indeterminacy, nonlocality, entanglement, and ambiguity surrounding the projection postulate. It briefly reviews the standard extant interpretations such as the Copenhagen interpretation, many-worlds interpretation, and hidden variables interpretation, and introduces the idea that quantum theory is about a new metaphysical category: physical possibility or res potentia.

This chapter discusses further types of multiverse hypotheses: the branching worlds of Everettian quantum theory, the totality of possible worlds according to David Lewis’s modal realism, and the totality of mathematical structures, which – according to Max Tegmark – are all physically realized. I argue that suggested solutions to the probability problem in Everettian quantum theory are unconvincing. A recent proposal by Sebens and Carroll to derive the Born rule in the Everettian framework using considerations about self-locating belief turns out to suffer from a circularity problem because the central principle on which the derivation is based has no independent motivation besides, possibly, appeal to the Born rule itself. I further argue that it is not possible to coherently, in full seriousness, believe David Lewis's modal realism. Nor is it possible to coherently believe Max Tegmark's thesis that there is a multiverse of all mathematical structures in which they are physically realized. Tegmark's claim that our universe is itself a mathematical universe hypothesis is found to be incoherent.