Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

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Decoherence, einselection, and the quantum origins of the classical

The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

Foundations Of Statistics

Many Worlds: an Introduction 1. WHY MANY WORLDS? 1. Decoherence and Ontology 2. Quasiclassical Realms 3. Macroscopic Superpositions, Decoherent Histories, and the Emergence of Hydrodynamical Behaviour 2. PROBLEMS WITH ONTOLOGY 4. Can the world be only wavefunction? 5. A metaphysician looks at the Everett interpretation Commentary. Reply to Hawthorne: Physics Before Metaphysics Transcript 1: ontology 3. PROBABILITY IN THE EVERETT INTERPRETATION 6. Chance in the Everett interpretation 7. A Scandal of Probability Theory 8. How to prove the Born rule 9. Everett and Evidence 4. CRITICAL REPLIES 10. One World versus Many: the Inadequacy of Everettian Accounts of Evolution, Probability, and Scientific Confirmation 11. Probability in the Everett picture 12. Decisions, Decisions, Decisions: Can Savage Salvage Everettian Probability? Transcript 2: Probability 5. ALTERNATIVES TO MANY WORLDS 13. Decoherence, Einselection, Envariance, and Quantum Darwinism: From Relative States to the Existential Interpretation 14. Two dogmas about quantum mechanics Commentary: Rabid Dogma? Comments on Bub and Pitowsky 15. The Principal Principle and Probability in the Many-Worlds interpretation 16. Pilot-wave theory: many worlds in denial? Commentary: Reply to Valentini 6. NOT ONLY MANY WORLDS 17. Everett and Wheeler, the Untold Story 18. Apart from universes 19. Many Worlds in Context 20. Time Symmetry and the Many-Worlds Interpretation Transcript 3: Not (only) many worlds Bibliography

Many worlds? : Everett, quantum theory, and reality

Particle indistinguishability has always been considered a purely quantum mechanical concept. In parallel, indistinguishable particles have been thought to be entities that are not properly speaking objects at all. I argue, to the contrary, that the concept can equally be applied to classical particles, and that in either case particles may (with certain exceptions) be counted as objects even though they are indistinguishable. The exceptions are elementary bosons (for example photons).

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Are quantum particles objects

Leibniz’s principles made for an elegant and coherent philosophy. In part metaphysical, in part methodological, they addressed fundamental questions - in the treatment of symmetry, in the relationship of physics to mathematics, in logic that are if anything even more pressing today than they were in Leibniz’s time. As I shall read them, they also expressed a distinctive and uncompromising form of realism, a commitment to the adequacy of purely descriptive concepts. This doctrine has been called ‘semantic universalism’by van Fraassen (1991), and the ‘generalist picture’by O’Leary-Hawthorne and Cover (1996): it will become clearer in due course just what it entails. The principles that I shall consider are the Principle of Su¢ cient Reason (PSR) and the Principle of Identity of Indiscernibles (PII). In the …rst instance I shall take them both to be methodological principles. The former I shall read as requiring that the concepts of physics be entirely transparent. Analysis and explanation are to proceed without any limits. The perspective is impersonal: any epistemological limitation, to do with our human situation or perceptual apparatus, is to be viewed as a purely practical matter, re‡ecting no fundamental constraint. This puts in place a part of the generalist picture. The PSR clearly promotes the use of mathematical concepts in physics. The PII, in contrast, depends on a sharp distinction between purely mathematical concepts, and physical ones. Leibniz too made use of this distinction (between ‘real’and ‘notional’or ‘ideal’concepts), but in his hands the principle depended heavily, though often tacitly, on his metaphysical theory of substance (and, with quali…cations, on his philosophical logic). He was led to a restrictive formulation of it in consequence: There are never in nature two beings which are perfectly alike and �);

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Physics and Leibniz's Principles

UANTUM MECHANICS, TOGETHER WITH RELATIVITY, are the basis of most of what we know of the very large, the very small, and the very fast. And in all of these areas our knowledge is extensive. It would be hard to say how good these theories are; Q arithmetic, one might say, is good mathematics. For all that, there is a problem, a strange and amorphous difficulty: it is the problem of measurement. This problem has become much more interesting, and much more pressing, as a result of some recent developments. Hitherto the difficulty has been so peculiar, and so formless, that physicists have on the whole thought it a matter of philosophy. But that is not quite right (or that is what I shall argue). It is certainly philosophical, but it is also a matter of methodology, a question of what physics is to do; and now the matter has come to seem quite pressing. In this sense the measurement problem has become a problem for physics. But what is the problem of measurement? As a first stab, we can say this: on the basis of quantum mechanics, there is a difficulty in accounting for the

What is the Problem of Measurement

A variety of ideas arising in decoherence theory, and in the ongoing debate over Everett's relative-state theory, can be linked to issues in relativity theory and the philosophy of time, specifically the relational theory of tense and of identity over time. These have been systematically presented in companion papers (Saunders 1995; 1996a); in what follows we shall consider the same circle of ideas, but specifically in relation to the interpretation of probability, and its identification with relations in the Hilbert Space norm. The familiar objection that Everett's approach yields probabilities different from quantum mechanics is easily dealt with. The more fundamental question is how to interpret these probabilities consistent with the relational theory of change, and the relational theory of identity over time. I shall show that the relational theory needs nothing more than the physical, minimal criterion of identity as defined by Everett's theory, and that this can be transparently interpreted in terms of the ordinary notion of the chance occurrence of an event, as witnessed in the present. It is in this sense that the theory has empirical content.

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Simon Saunders

Papers

Many worlds? : Everett, quantum theory, and reality

Are quantum particles objects

Physics and Leibniz's Principles

What is the Problem of Measurement

Time, Quantum Mechanics, and Probability