"natural theology > notes > 2015 > Sunday 15 February "

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Carlyle, Thomas, and G B Tennyson (Editor), A Carlyle Reader, Copley Publishing Group 2000 Amazon Product Description 'A Carlyle Reader constitutes the most substantial one-volume presentation of representative writings of the great Victorian prose writer, historian, philosopher and social critic-Thomas Carlyle (1795-1881). It contains the full text of Carlyle's seminal work "Sartor Resartus" as well as the full text of five of his most influential essays. It also offers general selections from "The French Revolution", "Past and Present", "On Heroes and Hero Worship", and the celebrated Coleridge chapter from "The Life of John Sterling". In addition to offering a rich sampling of Carlyle in all his various literary manifestations, this volume enables the the reder to study Carlyle chronologically, the first entry being from 1823 and the last from 1876. The almost forty pages of introductory material provide a biographical overview of Carlyle's life, a presentation of his leading ideas and a discussion of his unique prose style. There is a bibliography of secondary writings and a chronology of Carlyle's life. Every section is preceded by an explanatory introduction by the editor.'
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Carlyle, Thomas, and G B Tennyson (Editor), A Carlyle Reader, Copley Publishing Group; 2nd edition (May 1, 2000) • Language: English • ISBN-10: 158390008X • ISBN-13: 978-1583900086 2000 Amazon Product Description 'A Carlyle Reader constitutes the most substantial one-volume presentation of representative writings of the great Victorian prose writer, historian, philosopher and social critic-Thomas Carlyle (1795-1881). It contains the full text of Carlyle's seminal work "Sartor Resartus" as well as the full text of five of his most influential essays. It also offers general selections from "The French Revolution", "Past and Present", "On Heroes and Hero Worship", and the celebrated Coleridge chapter from "The Life of John Sterling". In addition to offering a rich sampling of Carlyle in all his various literary manifestations, this volume enables the the reder to study Carlyle chronologically, the first entry being from 1823 and the last from 1876. The almost forty pages of introductory material provide a biographical overview of Carlyle's life, a presentation of his leading ideas and a discussion of his unique prose style. There is a bibliography of secondary writings and a chronology of Carlyle's life. Every section is preceded by an explanatory introduction by the editor.'
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Feynman, Richard P et al, The Feynman Lectures on Physics (volume 2) , Addison Wesley 1964
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Hobson, M P, and G. P. Efstathiou, A. N. Lasenby, General Relativity: An Introduction for Physicists, Cambridge University Press 2006 Amazon Editorial Reviews Book Description 'After reviewing the basic concept of general relativity, this introduction discusses its mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle.'
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Lonergan, Bernard J F, Insight : A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '. . . Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding'
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McLuhan, Marshall, and Quentin Fiore, The Medium is the Message, Random House 1967
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Pais, Abraham, Inward Bound: Of Matter and Forces in the Physical World, Clarendon Press, Oxford University Press 1986 Preface: 'I will attempt to describe what has been discovered and understood about the constituents of matter, the laws to which they are subject and the forces that act on them [in the period 1895-1983]. . . . I will attempt to convey that these have been times of progress and stagnation, of order and chaos, of belief and incredulity, of the conventional and the bizarre; also of revolutionaries and conservatives, of science by individuals and by consortia, of little gadgets and big machines, and of modest funds and big moneys.' AP
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't Hooft, Gerard, Under the Spell of the Gauge Principle , World Scientific Pub Co Inc 1994 Amazon Product Description 'This work features a collection of articles and review papers by the author on various subjects in quantum field theory, gauge field theory and quantum gravity. It covers: the mathematical aspects of the renormalization procedure needed to relate physically observable phenomena to the primary variables in these theories; a description of fundamental extended objects such as monopoles and instantons, aspects of quantum chromodynamics; and, finally, the author's approach to the problem of quantizing the gravitational force by considering black holes. All of these topics are important for the understanding of the elementary particles.'
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Veltman, Martinus, Diagrammatica: The Path to the Feynman Rules, Cambridge University Press 1994 Jacket: 'This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. ... The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. ...'
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Weyl, Hermann, and translated by H P Robertson, The Theory of Groups and Quantum Mechanics, Dover 1950 Jacket: 'This book is devoted to the consistent and systematic application of group theory to quantum mechanics. Beginning with a detailed introduction to the classical theory of groups, Dr Weyl continues with an account of the fundamental results of quantum physics. There follows a rigorous investigation of the relations holding between the mathematical and physical theories.'
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Wigner, Eugene Paul, The Collected Works of Eugene Paul Wigner: Part 1: Eugene Paul Wigner, A Biographical Sketch. Part 2: Applied Group Theory 1926-1935. Part 3: The Mathematical Papers , Springer 1993 Amazon Product Description 'Eugene Wigner is one of the few giants of 20th-century physics. His early work helped to shape quantum mechanics, he laid the foundations of nuclear physics and nuclear engineering, and he contributed significantly to solid-state physics. His philosophical and political writings are widely known. All his works will be reprinted in Eugene Paul Wigner's Collected Workstogether with descriptive annotations by outstanding scientists. The present volume begins with a short biographical sketch followed by Wigner's papers on group theory, an extremely powerful tool he created for theoretical quantum physics. They are presented in two parts. The first, annotated by B. Judd, covers applications to atomic and molecular spectra, term structure, time reversal and spin. In the second, G. Mackey introduces to the reader the mathematical papers, many of which are outstanding contributions to the theory of unitary representations of groups, including the famous paper on the Lorentz group.'
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Zee, Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2003 Amazon book description: 'An esteemed researcher and acclaimed popular author takes up the challenge of providing a clear, relatively brief, and fully up-to-date introduction to one of the most vital but notoriously difficult subjects in theoretical physics. A quantum field theory text for the twenty-first century, this book makes the essential tool of modern theoretical physics available to any student who has completed a course on quantum mechanics and is eager to go on. Quantum field theory was invented to deal simultaneously with special relativity and quantum mechanics, the two greatest discoveries of early twentieth-century physics, but it has become increasingly important to many areas of physics. These days, physicists turn to quantum field theory to describe a multitude of phenomena. Stressing critical ideas and insights, Zee uses numerous examples to lead students to a true conceptual understanding of quantum field theory--what it means and what it can do. He covers an unusually diverse range of topics, including various contemporary developments,while guiding readers through thoughtfully designed problems. In contrast to previous texts, Zee incorporates gravity from the outset and discusses the innovative use of quantum field theory in modern condensed matter theory. Without a solid understanding of quantum field theory, no student can claim to have mastered contemporary theoretical physics. Offering a remarkably accessible conceptual introduction, this text will be widely welcomed and used.
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Papers

Chayut, Michael, "From the Periphery: the genesis of Eugene P. Wigner's application of group theory to quantum mechanics", Foundations of Chemistry, 3, 1, January 2001, page 55-78. Abstract: 'is paper traces the origins of Eugene Wigner's pioneering application of group theory to quantum physics to his early work in chemistry and crystallography. In the early 1920s, crystallography was the only discipline in which symmetry groups were routinely used. Wigner's early training in chemistry, and his work in crystallography with Herman Mark and Karl Weissenberg at the Kaiser Wilhelm institute for fiber research in Berlin exposed him to conceptual tools which were absent from the pedagogy available to physicists for many years to come. This both enabled and pushed him to apply the group theoretic approach to quantum physics. It took many years for the approach first introduced by Wigner in the 1920s – and whose reception by the physicists was initially problematical – to assume the pivotal place it now holds in physical theory and education. This is but one example that attests to the historic contribution made by the periphery in initiating new types of thought-perspectives and scientific careers.'. back

Gross, David J, Frank Wilczek, "Ultraviolet Behaviour of Non-Abelian Gauge Theories", Physics Review Letters, 30, 26, 1973, page 1343 - 1346. 'It is shown that a wide class of non-Abelian gauge theories have, up to calculable logarithmic corrections, free-field-theory asymptotic behavior. It is suggested that Bjorken scaling may be obtained from strong-interaction dynamics based on non-Abelian gauge symmetry.'. back

't Hooft, Gerard, "The making of the standard model", Nature, 448, 7151, 19 July 2007, page 271 - 273. 'The standard model of particle physics is more than a model. It is a detailed thoery that encompasses nearly all that is known about the subatomic particles and forces in a concise set of principles and equations.. back

Zurek, Wojciech Hubert, "Decoherence, einselection, and the quantum origins of the classical", Review of Modern Physics, 75, , 2003, page 715-775. The manner in which states of some quantum systems become effectively classical is of great significance for the foundations of quantum physics, as well as for problems of practical interest such 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 “Schrödinger-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.. back

Links

Asymptotic freedom - Wikipedia, Asymptotic freedom - Wikipedia, the free encyclopedia, 'In physics, asymptotic freedom is the property of some gauge theories in which the interaction between the particles, such as quarks, becomes arbitrarily weak at ever shorter distances, i.e. length scales that asymptotically converge to zero (or, equivalently, energy scales that become arbitrarily large). Asymptotic freedom implies that in high-energy scattering the quarks move within nucleons, such as the neutron and proton, mostly as free non-interacting particles. It allows physicists to calculate the cross sections of various events in particle physics reliably using parton techniques.' back

Bolzano-Weierstrass theorem - Wikipedia, Bolzano-Weierstrass theorem - Wikipedia, the free encyclopedia, In real analysis, the Bolzano–Weierstrass theorem is a fundamental result about convergence in a finite-dimensional Euclidean space . The theorem states that each bounded sequence in Rⁿ has a convergent subsequence. An equivalent formulation is that a subset of Rⁿ is sequentially compact if and only if it is closed and bounded. back

E Paul J de Haas - Historic Papers, Physis Project, Historic papers of Max Abraham Albert Einstein Niels Bohr J. Frenkel Hermann Minkowski Erwin Schrödinger Max Born S. Goudsmit Wolfgang Pauli Arnold Sommerfeld Louis de Broglie Max von Laue Henri Poincaré L.H. Thomas Paul Dirac Gustav Mie E. Rutherford G. E. Uhlenbeck back

Eric W Weisstein, Coulomb Gauge - from Eric Weisstein's World of Physics, 'The gauge defined by del . A = 0 where A is the magnetic vector potential. back

Gauge fixing - Wikipedia, Gauge fixing - Wikipedia, the free encyclopedia, 'In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom.' back

Gauge theory - Wikipedia, Gauge theory - Wikipedia, the free encyclopedia, 'In physics, gauge theory is a quantum field theory where the Lagrangian is invariant under certain transformations. The transformations (called local gauge transformations) form a Lie group which is referred to as the symmetry group or the gauge group of the theory. For each group parameter there is a corresponding vector field called gauge field which helps to make the Lagrangian gauge invariant. The quanta of the gauge field are called gauge bosons. If the symmetry group is non-commutative, the gauge theory is referred to as non-abelian or Yang-Mills theory.' back

Gerard 't Hooft, Gerard 't Hooft - Home page, Professor of Theoretical Physics, Spinza Institute, back

Gilad Lotan, Israel, Gaza, War and Data, 'Media Constructs Reality As I’m writing this post, details of an Israeli Air Force missile attack near the entrance of a United Nations school in Rafah are emerging. The attack killed at least 10, injuring many more. The IDF claims it had targeted three members of the Islamic Jihad riding a motorcycle near the school, not the school itself.' back

Intel 4004 - Wikipedia, Intel 4004 - Wikipedia, the free encyclopedia, 'The Intel 4004 was a 4-bit central processing unit (CPU) released by Intel Corporation in 1971. It was the first complete CPU on one chip, and also the first commercially available microprocessor. Such a feat of integration was made possible by the use of then new silicon gate technology allowing a higher number of transistors and a faster speed than was possible before.' back

J C Oxtoby et al, John Von Neumann 1903 - 1957 - Google Book Search, Key words and phrases 'von Neumann algebra, Hilbert space, ergodic theory, quantum mechanics, bounded operators, Minimax Theorem, modular lattice, self-adjoint operators, payoff matrix, measure space, unitary operator, mixed strategy, measure theory, game theory, measure-preserving transformations, Euclidean space, quantum theory, lattice theory, John von Neumann, Lebesgue measure' back

Marhsall McLuhan - Wikipedia, Marhsall McLuhan - Wikipedia, the free encyclopedia, 'Herbert Marshall McLuhan, CC (July 21, 1911 – December 31, 1980) was a Canadian educator, philosopher, and scholar — a professor of English literature, a literary critic, a rhetorician, and a communications theorist. McLuhan's work is viewed as one of the cornerstones of the study of media theory. McLuhan is known for the expressions "the medium is the message" and "global village". McLuhan was a fixture in media discourse from the late 1960s to his death and he continues to be an influential and controversial figure. More than ten years after his death he was named the "patron saint" of Wired magazine.' back

P A M Dirac, The Quantum Theory of the Emission and Absorption of Radiation, Proceedings of the Royal Society, A114, 243 (1927). 'Introduction and Summary. The new quantum theory, based on the assumption that the dynamical variables do not obey the commutative law of multiplication, has by now been developed sufficiently to form a fairly complete theory of dynamics. One can treat mathematically the problem of any dynamical system composed of a number of particles with instantaneous forces acting between them, provided it is describable by a Hamiltonian function, and one can interpret the mathematics physically by a quite definite general method. On the other hand, hardly anything has been done up to the present on quantum electrodynamics. . . . ' back

P A M Dirac, NASA ADS: The Quantum Theory of Dispersion, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Volume 114, Issue 769, pp. 710-728 (May 1927) back

P. A. M. Dirac, On the Theory of Quantum Mechanics, Proc. Roy. Soc. A112 (1926) 661; Abstract 'The present theory is shown to account for the absorption and stimulated emission of radiation, and also shows that the elements of the matrices representing the total polarization determine the transition probabilities. One cannot take spontaneous emission into account without a more elaborate theory involving the positions of the various atoms and the interference of their individual emissions, as the effects will depend upon whether the atoms are distributed at random, or arranged in a crystal lattice, or all confined in a volume small compared with a wave-length. The last alternative mentioned, which is of no practical interest, appears to be the simplest theoretically. It should be observed that we get the simple Einstein results only because we have averaged over all initial phases of the atoms.' back

Product rule - Wikipedia, Product rule - Wikipedia, the free encyclopedia, 'In calculus, the product rule (also called Leibniz's law; see derivation) is a formula used to find the derivatives of products of functions. It may be stated thus: (f . g)' = f' . g + f . g'. back

Qubit - Wikipedia, Qubit - Wikipedia, the free encyclopedia, 'A quantum bit, or qubit . . . is a unit of quantum information. That information is described by a state vector in a two-level quantum mechanical system which is formally equivalent to a two-dimensional vector space over the complex numbers. Benjamin Schumacher discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in a state, and storing the information on a smaller number of states. This is now known as Schumacher compression. In the acknowledgments of his paper (Phys. Rev. A 51, 2738), Schumacher states that the term qubit was invented in jest, during his conversations with Bill Wootters.' back

Soliton - Wikipedia, Soliton - Wikipedia, the free encyclopedia, 'In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. "Dispersive effects" refer to dispersion relations between the frequency and the speed of the waves. Solitons arise as the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described by John Scott Russell (1808–1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation".' back

Tests of general relativity - Wikipedia, Tests of general relativity - Wikipedia, the free encyclopedia, 'At its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's law of universal gravitation with special relativity. That light appeared to bend in gravitational fields in line with the predictions of general relativity was found in 1919 but it was not until a program of precision tests was started in 1959 that the various predictions of general relativity were tested to any further degree of accuracy in the weak gravitational field limit, severely limiting possible deviations from the theory. Beginning in 1974, Hulse, Taylor and others have studied the behaviour of binary pulsars experiencing much stronger gravitational fields than found in our solar system. Both in the weak field limit (as in our solar system) and with the stronger fields present in systems of binary pulsars the predictions of general relativity have been extremely well tested locally.' back

Thomas Carlyle & G B Tennyson (Editor), A Carlyle Reader: Selections from . . . - Google Book Search , 'Our clock strikes when there is a change from hour to hour; but no hammer in the Horologe of Time peals through the universe when there is a change from Era to Era. Men understand not what is among their hands; as calmness is the characteristic of strength, so the weightiest causes may be the most silent.' page 59 back

Venn diagram - Wikipedia, Venn diagram - Wikipedia, the free encyclopedia, 'A Venn diagram or set diagram is a diagram that shows all possible logical relations between a finite collection of different sets. Venn diagrams were conceived around 1880 by John Venn. They are used to teach elementary set theory, as well as illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.' back

vol VII: Notes

2015

Notes

Sunday 15 February 2015

Monday 16 February 2015

Tuesday 17 February 2015

Wednesday 18 February 2015

Thursday 19 February 2015

Friday 20 February 2015

Saturday 21 February 2015

Further reading

Books

Papers

Links