Charis Anastopoulos

Proposed quantum experiments in deep space will be able to explore quantum information issues in regimes where relativistic effects are important. In this essay, we argue that a proper extension of quantum information theory into the relativistic domain requires the expression of all informational notions in terms of quantum field theoretic (QFT) concepts. This task requires a working and practicable theory of QFT measurements. We present the foundational problems in constructing such a theory, especially in relation to longstanding causality and locality issues in the foundations of QFT. Finally, we present the ongoing Quantum Temporal Probabilities program for constructing a measurement theory that (i) works, in principle, for any QFT, (ii) allows for a first- principles investigation of all relevant issues of causality and locality, and (iii) it can be directly applied to experiments of current interest.

Gravitational decoherence (GD) refers to the effects of gravity in actuating the classical appearance of a quantum system. Because the underlying processes involve issues in general relativity (GR), quantum field theory (QFT), and quantum information, GD has fundamental theoretical significance. There is a great variety of GD models, many of them involving physics that diverge from GR and/or QFT. This overview has two specific goals along with one central theme:(i) present theories of GD based on GR and QFT and explore their experimental predictions;(ii) place other theories of GD under the scrutiny of GR and QFT, and point out their theoretical differences. We also describe how GD experiments in space in the coming decades can provide evidence at two levels:(a) discriminate alternative quantum theories and non-GR theories;(b) discern whether gravity is a fundamental or an effective theory.

The probability ‘measure’ for measurements at two consecutive mo- ments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We demonstrate that there are only two ways to resolve this problem. The first solution places emphasis on the precise use of the concept of conditional probability for successive mea- surements. The physically correct conditional probabilities define additive probabilities for two-time measurements. These probabilities depend ex- plicitly on the resolution of the physical device and do not, therefore, correspond to a function of the associated projection operators. It follows that quantum theory distinguishes between physical events and proposi- tions about events, the latter are not represented by projection operators and that the outcomes of two-time experiments cannot be described by quantum logic. The alternative explanation is rather radical: it is conceivable that the relative frequencies for two-time measurements do not converge, unless a particular consistency condition is satisfied. If this is true, a strong revision of the quantum mechanical formalism may prove necessary. We stress that it is possible to perform experiments that will distinguish the two alternatives.

This is a textbook on quantum mechanics. It is addressed to graduates and advanced undergraduates. The book presents quantum theory as a logically coherent system, placing stronger emphasis on the theory' s probabilistic structure and on the role of symmetries. It makes students aware of foundational problems from the very beginning, but at the same time, it urges them to adopt a pragmatic attitude towards the quantum formalism. The book consists of five parts. Part I is a review of classical physics, including probability theory, and a historical introduction to quantum theory. Part II presents quantum theory in terms of six fundamental principles. The principles are presented together with the necessary mathematical background and with applications to simple systems. Part III analyses the properties of quantum particles. It starts with the description of symmetries, continues to non-relativistic particles, the introduction of spin, and particle statistics. It concludes with a symmetries-based introduction to relativistic quantum systems and with the first steps towards relativistic quantum field theory. Part IV presents techniques adapted to specific problems: the structure and spectra of composite systems, decays and transitions, particle scattering, and open quantum systems. Finally, Part V revisits quantum foundations: quantum measurement theory, the major interpretations of quantum theory, and the frontiers of quantum theory in contemporary research.

The idea that mind and body are distinct entities that interact is often claimed to be incompatible with physics. The aim of this paper is to disprove this claim. To this end, we construct a broad mathematical framework that describes theories with mind–body interaction (MBI) as an extension of current physical theories. We employ histories theory, i.e., a formulation of physical theories in which a physical system is described in terms of (i) a set of propositions about possible evolutions of the system and (ii) a probability assignment to such propositions. The notion of dynamics is incorporated into the probability rule. As this formulation emphasises logical and probabilistic concepts, it is ontologically neutral. It can be used to describe mental ‘degrees of freedom’ in addition to physical ones. This results into a mathematical framework for psycho-physical interaction (ΨΦ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi \Phi$$\end{document}I formalism). Interestingly, a class of ΨΦ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi \Phi$$\end{document}I theories turns out to be compatible with energy conservation.

The idea that mind and body are distinct entities that interact is often claimed to be incompatible with physics. The aim of this paper is to disprove this claim. To this end, we construct a broad mathematical framework that describes theories with mind-body interaction (MBI) as an extension of current physical theories. We employ histories theory, i.e., a formulation of physical theories in which a physical system is described in terms of (i) a set of propositions about possible evolutions of the system and (ii) a probability assignment to such propositions. The notion of dynamics is incorporated into the probability rule. As this formulation emphasises logical and probabilistic concepts, it is ontologically neutral. It can be used to describe mental `degrees of freedom' in addition to physical ones. This results into a mathematical framework for psycho-physical interaction (ΨΦI formalism). Interestingly, a class of ΨΦI theories turns out to be compatible with energy conservation.

Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence functional, introduced by the consistent histories approach to quantum theory. The acceptance of relative phases as a primitive ingredient of any quantum theory, liberates us from the need to use a Hilbert space and non-commutative observables. It is shown, that quantum phenomena are adequately described by a theory of relative phases and non-additive probabilities on the classical phase space. The only difference lies on the type of observables that correspond to sharp measurements. This class of theories does not suffer from the consequences of Bell's theorem (it is not a theory of Kolmogorov probabilities) and Kochen–Specker's theorem (it has distributive “logic”). We discuss its predictability properties, the meaning of the classical limit and attempt to see if it can be experimentally distinguished from standard quantum theory. Our construction is operational and statistical, in the spirit of Copenhagen, but makes plausible the existence of a realist, geometric theory for individual quantum systems

We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if we consider a quantum mechanical measurement device or the presence of an environment. We then examine the same issues in alternative interpretations of quantum theory. We first show that multi-time probabilities cannot be naturally defined in terms of a frequency operator. We next prove that local hidden variable theories cannot reproduce the predictions of quantum theory for sequential measurements, even when the degrees of freedom of the measuring apparatus are taken into account. Bohmian mechanics, however, does not fall in this category. We finally examine an alternative proposal that sequential measurements can be modeled by a process that does not satisfy the Kolmogorov axioms of probability. This removes contextuality without introducing non-locality, but implies that the empirical probabilities cannot be always defined (the event frequencies do not converge). We argue that the predictions of this hypothesis are not ruled out by existing experimental results (examining in particular the “which way” experiments); they are, however, distinguishable in principle