Auyang (1995), Sunny Y., How is Quantum Field Theory Possible?, Oxford University Press 1995 Jacket: 'Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena and particle interactions are encompassed in a unified framework.' 
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Cantor (1897, 1955), Georg, Contributions to the Founding of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain), Dover 1895, 1897, 1955 Jacket: 'One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc, as well as the entire field of modern logic.' 
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Darwin (1875, 1998), Charles, and Harriet Ritvo (Introduction), The Variation of Animals and Plants Under Domestication (Foundations of Natural History), Johns Hopkins University Press 1875, 1998 ' "The Variation, with its thousands of hard-won observations of the facts of variation in domesticated species, is a frustrating, but worthwhile read, for it reveals the Darwin we rarely see -- the embattled Darwin, struggling to keep his project on the road. Sometimes he seems on the verge of being overwhelmed by the problems he is dealing with, but then a curious fact of natural history will engage him (the webbing between water gun-dogs' toes, the absurdly short beak of the pouter pigeon) and his determination to make sense of it rekindles. As he disarmingly declares, 'the whole subject of inheritance is wonderful.'. 
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Dauben (1990), Joseph Warren, Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press 1990 Jacket: 'One of the greatest revolutions in mathematics occurred when Georg Cantor (1843-1918) promulgated his theory of transfinite sets. . . . Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradox in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.' 
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Everett III (1973), Hugh, and Bryce S Dewitt, Neill Graham (editors), The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press 1973 Jacket: 'A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book has developed. The volume contains Dr Everett's short paper from 1957, "'Relative State' formulation of quantum mechanics" and a far longer exposition of his interpretation entitled "The Theory of the Universal Wave Function" never before published. In addition other papers by Wheeler, DeWitt, Graham, Cooper and van Vechten provide further discussion of the same theme. Together they constitute virtually the entire world output of scholarly commentary on the Everett interpretation.' 
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Farmelo (2009), Graham, The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom, Basic Books 2009 Jacket: 'Paul Dirac was among the greatest scientific geniuses of the modern age. One of the discoverers of quantum mechanics, the most revolutionary theory of the last century, his contributions had a unique insight, eloquence, clarity and mathematical power. His prediction of antimatter was one of the greatest triumphs in the history of physics. One of Einstein's most admired colleagues, Dirac was in 1933 the youngest theoretician ever to win a Nobel Prize in physics. . . . Based on previously undiscovered archives, The Strangest Man reveals the many facets of Dirac's brilliantly original mind. The Strangest Man also depicts a spectacularly exciting era in scientific discovery.' 
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Fortun (1998), Mike, and Herbert J Bernstein, Muddling Through: Pursuing Science and Truths in the Twenty-First Century, Counterpoint 1998 Jacket: ' Messy. Clumsy. Volatile. Exciting. These words are not often associated with the science, which for most people still connote exactitude, elegance, reliability and a rather plodding certainty. But the real story is something quite different. The sciences are less about the ability to know and to control than they are about the unleashing of new forces, new capacities for changing the world. The sciences as practised exist not in some pristine world of "objectivity," but in what Mike Fortnum and Herbert Bernstein call "the Muddled Middle". This book explores the way science makes sense of the world and how the world makes sense of science. It is also about politics and culture—how these forces shape the sciences and are shaped by them in return.' 
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Galilei (1610, 1957), Galileo, and Stillman Drake (translator), Discoveries and Opinions of Galileo: Including the Starry Messenger (1610 Letter to the Grand Duchess Christina), Doubleday Anchor 1957 Amazon: 'Although the introductory sections are a bit dated, this book contains some of the best translations available of Galileo's works in English. It includes a broad range of his theories (both those we recognize as "correct" and those in which he was "in error"). Both types indicate his creativity. The reproductions of his sketches of the moons of Jupiter (in "The Starry Messenger") are accurate enough to match to modern computer programs which show the positions of the moons for any date in history. The appendix with a chronological summary of Galileo's life is very useful in placing the readings in context.' A Reader. 
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Goddard (1998), Peter , and Stephen Hawking, Abraham Pais, Maurice Jacob, David Olive, and Michael Atiyah, Paul Dirac, The Man and His Work, Cambridge University Press 1998 Jacket: Paul Adrien Maurice Dirac was one of the founders of quantum theory and the aithor of many of its most important subsequent developments. He is numbered alongside Newton, Maxwell, Einstein and Rutherford as one of the greatest physicists of all time. This volume contains four lectures celebrating Dirac's life and work and the text of an address given by Stephen Hawking, which were given on 13 November 1995 on the occasion of the dedication of a plaque to him in Westminster Abbey. In the first lecture, Abraham Pais describes from personal knowledge Dirac's character and his approach to his work. In the second lecture, Maurice Jacob explains not only how and why Dirac was led to introduce the concept of antimatter, but also its central role in modern particle physics and cosmology. In the third lecture, David Olive gives an account of Dirac's work on magnetic monopoles and shows how it has had a profound influence in the development of fundamental physics down to the present day. In the fourth lecture, Sir Michael Atiyah explains the widespread significance of the Dirac equation in mathematics, its roots in algebra and its implications for geometry and topology.' 
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Hopkins (2001), Keith, A World Full of Gods: The Strange Triumph of Christianity, Penguin Random House 2001 ' In this provocative, irresistibly entertaining book, Keith Hopkins takes readers back in time to explore the roots of Christianity in ancient Rome. Combining exacting scholarship with dazzling invention, Hopkins challenges our perceptions about religion, the historical Jesus, and the way history is written. He puts us in touch with what he calls “empathetic wonder”—imagining what Romans, pagans, Jews, and Christians thought, felt, experienced, and believed-by employing a series of engaging literary devices. These include a TV drama about the Dead Sea Scrolls; the first-person testimony of a pair of time-travelers to Pompeii; a meditation on Jesus’ apocryphal twin brother; and an unusual letter on God, demons, and angels.' 
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Howard (2000), Don, and John Steichel (editor), Einstein: The Formative Years, 1879-1909 (Einstein Studies volume 8), Birkhauser 2000 ' "What was Einstein like for the first thirty years of his life? Who were the personalities who guided him? What did he read? This book, which hopes to shed light on these questions, is a sequence of academic articles written by Einstein specialists for the Birkhäuser Einstein Studies series. . . .The [book] is remarkably readable and informative. . . .Indispensable for Einstein disciples, the book is also accessible to the general reader. The presentation is excellent and the editing conducted to a high standard. . . .Extensive references are given after each essay and an index of names is provided." ' --The Mathematical Gazette 
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Nielsen (2016), Michael A., and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2016 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002. 
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Popper (1972), Karl Raimund, Conjectures and Refutations: The Growth of Scientific Knowledge, Routledge and Kegan Paul 1972 Preface: 'The way in which knowledge progresses, and expecially our scientific knowledge, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism; that is, by attempted refutations, which include severely critical tests.' [p viii]  
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Streater (2000), Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2000 Amazon product description: 'PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.' 
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Wilczek (2008), Frank, The Lightness of Being: Mass, Ether, and the Unification of Forces, Basic Books 2008 ' In this excursion to the outer limits of particle physics, Wilczek explores what quarks and gluons, which compose protons and neutrons, reveal about the manifestation of mass and gravity. A corecipient of the 2004 Nobel Prize in Physics, Wilczek knows what he’s writing about; the question is, will general science readers? Happily, they know what the strong interaction is (the forces that bind the nucleus), and in Wilczek, they have a jovial guide who adheres to trade publishing’s belief that a successful physics title will not include too many equations. Despite this injunction (against which he lightly protests), Wilczek delivers an approachable verbal picture of what quarks and gluons are doing inside a proton that gives rise to mass and, hence, gravity. Casting the light-speed lives of quarks against “the Grid,” Wilczek’s term for the vacuum that theoretically seethes with quantum activity, Wilczek exudes a contagious excitement for discovery. A near-obligatory acquisition for circulating physics collections.' --Gilbert Taylor  
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Zee (2010), Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2010 ' Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading.' 
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Aether (classical element) - Wikipedia, Aether (classical element) - Wikipedia, the free encyclopedia, 'According to ancient and medieval science aether (Greek αἰθήρ aithēr), also spelled æther or ether, is the material that fills the region of the universe above the terrestrial sphere.' back

Albert Einstein (1905c), On a heuristic point of view concerning the production and transformation of light, ' The wave theory of light, which operates with continuous spatial functions, has proved itself splendidly in describing purely optical phenomena and will probably never be replaced by another theory. One should keep in mind, however, that optical observations apply to time averages and not to momentary values, and it is conceivable that despite the complete confirmation of the theories of diffraction, reflection, refraction, dispersion, etc., by experiment, the theory of light, which operates with continuous spatial functions, may lead to contradictions with experience when it is applied to the phenomena of production and transformation of light. Indeed, it seems to me that the observations regarding "black-body" light, and other groups of phenomena associated with the production or conversion of light can be understood better if one assumes that the energy of light is discontinuously distributed in space.' back

Albert Einstein (1905c), On a heuristic point of view concerning the production and transformation of light, ' In particular, black body radiation, photoluminescence, generation of cathode rays from ultraviolet light and other phenomena associated with the generation and transformation of light seem better modeled by assuming that the energy of light is distributed discontinuously in space. According to this picture, the energy of a light wave emitted from a point source is not spread continuously over ever larger volumes, but consists of a finite number of energy quanta that are spatially localized at points of space, move without dividing and are absorbed or generated only as a whole. Subsequently, I wish to explain the reasoning and supporting evidence that led me to this picture of light, in the hope that some researchers may find it useful for their experiments.' back

Albert Einstein (1915), The Field Equations of Gravitation, ' In two recently published papers I have shown how to obtain field equations of gravitation that comply with the postulate of general relativity, i.e., which in their general formulation are covariant under arbitrary substitutions of space-time variables. . . . With this, we have finally completed the general theory of relativity as a logical structure. The postulate of relativity in its most general formulation (which makes space-time coordinates into physically meaningless parameters) leads with compelling necessity to a very specific theory of gravitation that also explains the movement of the perihelion of Mercury. However, the postulate of general relativity cannot reveal to us anything new and different about the essence of the various processes in nature than what the special theory of relativity taught us already.' back

Albert Einstein (1920), Ether and the Theory of Relativity, ' How does it come about that alongside of the idea of ponderable matter, which is derived by abstraction from everyday life, the physicists set the idea of the existence of another kind of matter, the ether? The explanation is probably to be sought in those phenomena which have given rise to the theory of action at a distance, and in the properties of light which have led to the undulatory theory. Let us devote a little while to the consideration of these two subjects. . . . .. Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.' back

Aquinas, Summa, I, 22, 3, Does God have immediate providence over everything?, ' I answer that, Two things belong to providence—namely, the type of the order of things foreordained towards an end; and the execution of this order, which is called government. As regards the first of these, God has immediate providence over everything, because He has in His intellect the types of everything, even the smallest; and whatsoever causes He assigns to certain effects, He gives them the power to produce those effects. Whence it must be that He has beforehand the type of those effects in His mind. As to the second, there are certain intermediaries of God's providence; for He governs things inferior by superior, not on account of any defect in His power, but by reason of the abundance of His goodness; so that the dignity of causality is imparted even to creatures.' back

Augustus - Wikipedia, Augustus - Wikipedia, the free encyclopedia, ' Gaius Julius Caesar Augustus (born Gaius Octavius; 23 September 63 BC – 19 August AD 14), also known as Octavian (Latin: Octavianus), was the founder of the Roman Empire. He reigned as the first Roman emperor from 27 BC until his death in AD 14. The reign of Augustus initiated an imperial cult, as well as an era associated with imperial peace (the Pax Romana or ,Pax Augusta) in which the Roman world was largely free of armed conflict (aside from expansionary wars and the Year of the Four Emperors, the latter of which occurring after Augustus' reign).' back

Cantor's theorem - Wikipedia, Cantor's theorem - Wikipedia, the free encyclopedia, ' In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A , the set of all subsets of A, the power set of A, has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with n elements has a total of n ² subsets, and the theorem holds because n² > n for all non-negative integers. Much more significant is Cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for infinite sets also.' back

Cardinal number - Wikipedia, Cardinal number - Wikipedia, the free encyclopedia, 'In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite sets.' back

Cardinality of the continuum - Wikipedia, Cardinality of the continuum - Wikipedia, the free encyclopedia, 'In mathematics, the cardinality of the continuum (sometimes also called the power of the continuum) is the cardinal number of the set of real numbers R (sometimes called the continuum). This cardinal number is often denoted by c, so c = R.' back

Claude Shannon (1949), Communication in the Presence of Noise, 'A method is developed for representing any communication system geometrically. Messages and the corresponding signals are points in two “function spaces,” and the modulation process is a mapping of one space into the other. Using this representation, a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect. Formulas are found for the maximum rate of transmission of binary digits over a system when the signal is perturbed by various types of noise. Some of the properties of “ideal” systems which transmit at this maximum rate are discussed. The equivalent number of binary digits per second for certain information sources is calculated.' [C. E. Shannon , “Communication in the presence of noise,” Proc. IRE, vol. 37, pp. 10–21, Jan. 1949.] back

Constantine the Great and Christianity - Wikipedia, Constantine the Great and Christianity - Wikipedia, the free encyclopedia, ' During the reign of the Roman Emperor Constantine the Great (AD 306–337), Christianity began to transition to the dominant religion of the Roman Empire. Historians remain uncertain about Constantine's reasons for favoring Christianity, and theologians and historians have often argued about which form of early Christianity he subscribed to. . . . Constantine's decision to cease the persecution of Christians in the Roman Empire was a turning point for early Christianity, sometimes referred to as the Triumph of the Church, the Peace of the Church or the Constantinian shift. In 313, Constantine and Licinius issued the Edict of Milan decriminalizing Christian worship. The emperor became a great patron of the Church and set a precedent for the position of the Christian emperor within the Church and raised the notions of orthodoxy, Christendom, ecumenical councils, and the state church of the Roman Empire declared by edict in 380. He is revered as a saint and is apostolos in the Eastern Orthodox Church, Oriental Orthodox Church, and various Eastern Catholic Churches for his example as a "Christian monarch”.' back

Cosmological constant - Wikipedia, Cosmological constant - Wikipedia, the free encyclopedia, 'In physical cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. Einstein abandoned the concept after the observation of the Hubble redshift indicated that the universe might not be stationary, as he had based his theory off the idea that the universe is unchanging. However, the discovery of cosmic acceleration in the 1990s has renewed interest in a cosmological constant.' back

Cosmological constant problem - Wikipedia, Cosmological constant problem - Wikipedia, the free encyclopedia, ' In cosmology, the cosmological constant problem or vacuum catastrophe is the disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and theoretical large value of zero-point energy suggested by quantum field theory. Depending on the Planck energy cutoff and other factors, the discrepancy is as high as 120 orders of magnitude, a state of affairs described by physicists as "the largest discrepancy between theory and experiment in all of science" and "the worst theoretical prediction in the history of physics".' back

Dark Ages (historiography) - Wikipedia, Dark Ages (historiography) - Wikipedia, the free encyclopedia, ' The Dark Ages is a term for the Early Middle Ages (c. 5th–10th centuries), or occasionally the entire Middle Ages (c. 5th–15th centuries), in Western Europe after the fall of the Western Roman Empire, which characterises it as marked by economic, intellectual, and cultural decline. The concept of a "Dark Age" as a historiographical periodization originated in the 1330s with the Italian scholar Petrarch, who regarded the post-Roman centuries as "dark" compared to the "light" of classical antiquity. . . . Others, however, have used the term to denote the relative scarcity of records regarding at least the early part of the Middle Ages.' back

David J. Gross (2004), Nobel lecture: The Discovery of Asymptotic Freedom and the Emergence of QCD, ' The emergence of QCD is a wonderful example of the evolution from farce to triumph. During a very short period, a transition occurred from experimental discovery and theoretical confusion to theoretical triumph and experimental confirmation. In this Nobel lecture I shall describe the turn of events that led to the discovery of asymptotic freedom, which in turn led to the formulation of QCD, the final element of the remarkably comprehensive theory of elementary particle physics – the Standard Model. I shall then briefly describe the experimental tests of the theory and the implications of asymptotic freedom.' back

Deep inelastic scattering - Wikipedia, Deep inelastic scattering - Wikipedia, the free encyclopedia, ' Deep inelastic scattering is the name given to a process used to probe the insides of hadrons (particularly the baryons, such as protons and neutrons), using electrons, muons and neutrinos. It provided the first convincing evidence of the reality of quarks, which up until that point had been considered by many to be a purely mathematical phenomenon. . . . Henry Way Kendall, Jerome Isaac Friedman and Richard E. Taylor were joint recipients of the Nobel Prize of 1990 "for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics".' back

Eigenvalues and eigenvectors - Wikipedia, Eigenvalues and eigenvectors - Wikipedia, the free encyclopedia, ' In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by λ, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated.' back

Electroweak interaction - Wikipedia, Electroweak interaction - Wikipedia, the free encyclopedia, ' In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV, they would merge into a single force.' back

Entropy (information theory) - Wikipedia, Entropy (information theory) - Wikipedia, the free encyclopedia, 'In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits. In this context, a 'message' means a specific realization of the random variable. Equivalently, the Shannon entropy is a measure of the average information content one is missing when one does not know the value of the random variable. The concept was introduced by Claude E. Shannon in his 1948 paper "A Mathematical Theory of Communication".' back

Feynman, Leighton and Sands FLP II_02, Chapter 2: Differential Calculus of Vector Fields, ' Ideas such as the field lines, capacitance, resistance, and inductance are, for such purposes, very useful. So we will spend much of our time analyzing them. In this way we will get a feel as to what should happen in different electromagnetic situations. On the other hand, none of the heuristic models, such as field lines, is really adequate and accurate for all situations. There is only one precise way of presenting the laws, and that is by means of differential equations. They have the advantage of being fundamental and, so far as we know, precise. If you have learned the differential equations you can always go back to them. There is nothing to unlearn.' back

Frank Wilczek (2004), Nobel lecture: Asymptotic Freedom: from Paradox to Paradigm, ' Frank Wilczek held his Nobel lecture December 8, 2004, at Aula Magna, Stockholm University. He was presented by Professor Sune Svanberg, Chairman of the Nobel Committee for Physics. Summary: The idea that Quarks that are born free are confined and can’t be pulled apart was once considered a paradox. The emerging theory for strong interactions, Quantum Chromo Dynamics (QCD) predicts the existence of gluons, which together with quarks can be seen indirectly as jets from hard scattering reactions between particles. Quantum Chromo Dynamics predicts that the forces between quarks are feeble for small separations but are powerful far away, which explains confinement. Many experiments have confirmed this property of the strong interaction. ' back

Function (mathematics) - Wikipedia, Function (mathematics) - Wikipedia, the free encyclopedia, ' The mathematical concept of a function expresses dependence between two quantities, one of which is given (the independent variable, argument of the function, or its "input") and the other produced (the dependent variable, value of the function, or "output"). A function associates a single output with every input element drawn from a fixed set, such as the real numbers.' back

Georg Cantor - Wikipedia, Georg Cantor - Wikipedia, the free encyclopedia, Georg Ferdinand Ludwig Philipp Cantor (March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician, born in Russia. He is best known as the creator of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware of.' back

Gluon - Wikipedia, Gluon - Wikipedia, the free encyclopedia, ' A gluon (/ˈɡluːɒn/) is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged particles.[6] In layman's terms, they "glue" quarks together, forming hadrons such as protons and neutrons. In technical terms, gluons are vector gauge bosons that mediate strong interactions of quarks in quantum chromodynamics (QCD). Gluons themselves carry the color charge of the strong interaction. This is unlike the photon, which mediates the electromagnetic interaction but lacks an electric charge. Gluons therefore participate in the strong interaction in addition to mediating it, making QCD significantly harder to analyze than quantum electrodynamics (QED). ' back

Gödel's incompleteness theorems - Wikipedia, Gödel's incompleteness theorems - Wikipedia, the free encyclopedia, ' Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (i.e., any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.' back

Hadron - Wikipedia, Hadron - Wikipedia, the free encyclopedia, In particle physics, a hadron is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the electric force. Most of the mass of ordinary matter comes from two hadrons: the proton and the neutron, while most of the mass of the protons and neutrons is in turn due to the binding energy of their constituent quarks, due to the strong force.' back

Hilbert's program - Wikipedia, Hilbert's program - Wikipedia, the free encyclopedia, ' In mathematics, Hilbert's program, formulated by German mathematician David Hilbert, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic.' back

Hugh Everett III (1957), "Relative State" Formulation of Quantum Mechanics, ' 1. Introduction 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 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.' back

John von Neumann (2014), Mathematical Foundations of Quantum Mechanics, ' Mathematical Foundations of Quantum Mechanics by John von Neumann translated from the German by Robert T. Beyer (New Edition) edited by Nicholas A. Wheeler. Princeton UP Princeton & Oxford. Preface: ' This book is the realization of my long-held intention to someday use the resources of TEX to produce a more easily read version of Robert T. Beyer’s authorized English translation (Princeton University Press, 1955) of John von Neumann’s classic Mathematische Grundlagen der Quantenmechanik (Springer, 1932).'This content downloaded from 129.127.145.240 on Sat, 30 May 2020 22:38:31 UTC back

Kashgarian, Lusuegro & Siddique (2024), The Warfare State: How Funding for Militarism Compromises Our Welfare, ' In FY 2023, out of a $1.8 trillion federal discretionary budget, $1.1 trillion— or 62% — was for militarized programs that use violence or the threat of violence or imprisonment, including war and weapons, law enforcemen and mass incarceration, and detention and deportation. . . .. The U.S. spent $16 on the military and war for every $1 that was spent on diplomacy and humanitarian foreign aid. The vast majority of militarized pending was for weapons, war and the Pentagon, at $920 billion. Only 56 billion was spent for international affairs, diplomacy, and humanitarian foreign aid. . . . . The U.S. federal budget allocated twice as much for federal law enforcement, which includes federal prisons, the FBI and other law enforcement agencies $31 billion), as for child care and early childhood education programs ($15 billion).' back

Kirchoff's law of thermal radiation - Wikipedia, Kirchoff's law of thermal radiation - Wikipedia, the free encyclopedia, 'Kirchhoff's law states that: For a body of any arbitrary material, emitting and absorbing thermal electromagnetic radiation at every wavelength in thermodynamic equilibrium, the ratio of its emissive power to its dimensionless coefficient of absorption is equal to a universal function only of radiative wavelength and temperature, the perfect black-body emissive power. back

Lamb shift - Wikipedia, Lamb shift - Wikipedia, the free encyclopedia, 'In physics, the Lamb shift, named after Willis Lamb (1913–2008), is a difference in energy between two energy levels ²S_½ and ²P_½ (in term symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy. Interaction between vacuum energy fluctuations and the hydrogen electron in these different orbitals is the cause of the Lamb Shift, as was shown subsequent to its discovery.' back

Light cone - Wikipedia, Light cone - Wikipedia, the free encyclopedia, 'A Light cone is the path that a flash of light, emanating from a single event E (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime. Imagine the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs—and when graphed the growing circle with the vertical axis of the graph representing time, the result is a cone, known as the future light cone (some animated diagrams depicting this concept can be seen here.) ' back

Map (mathematics) - Wikipedia, Map (mathematics) - Wikipedia, the free encyclopedia, ' n mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. In category theory, a map may refer to a morphism. The term transformation can be used interchangeably, but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory. ' back

Martinus J G Veltman, Nobel Lecture 1999: From weak interactions to gravitation, ' This lecture is about my contribution to the renormalizability of gauge theories. There is of course no perfectly clear separation between my contributions and those of my co-laureate 't Hooft, but I will limit mysef to some brief comments on those publications that carry only his name. An extensive review on the subject including detailed references to contemporary work can be found elsewhere. As is well known, the work on renormalizability of gauge theories caused a complete change in the landscape of particle physics.' back

Mathematical formulation of the standard model - Wikipedia, Mathematical formulation of the standard model - Wikipedia, the free encyclopedia, ' This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson. The Standard Model is renormalizable and mathematically self-consistent, however despite having huge and continued successes in providing experimental predictions it does leave some unexplained phenomena. In particular, although the physics of special relativity is incorporated, general relativity is not, and the Standard Model will fail at energies or distances where the graviton is expected to emerge. Therefore, in a modern field theory context, it is seen as an effective field theory.' back

Meinard Kuhlmann (Stanford Encyclopedia of Philosophy), Quantum Field Theory, ' Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. In a rather informal sense QFT is the extension of quantum mechanics (QM), dealing with particles, over to fields, i.e. systems with an infinite number of degrees of freedom. (See the entry on quantum mechanics.) In the last few years QFT has become a more widely discussed topic in philosophy of science, with questions ranging from methodology and semantics to ontology. QFT taken seriously in its metaphysical implications seems to give a picture of the world which is at variance with central classical conceptions of particles and fields, and even with some features of QM.' back

Nuclear fission - Wikipedia, Nuclear fission - Wikipedia, the free encyclopedia, ' Nuclear fission of heavy elements was discovered on December 17, 1938 by German Otto Hahn and his assistant Fritz Strassmann at the suggestion of Austrian-Swedish physicist Lise Meitner who explained it theoretically in January 1939 along with her nephew Otto Robert Frisch. Frisch named the process by analogy with biological fission of living cells. For heavy nuclides, it is an exothermic reaction which can release large amounts of energy both as electromagnetic radiation and as kinetic energy of the fragments (heating the bulk material where fission takes place).' back

Ordinal number - Wikipedia, Ordinal number - Wikipedia, the free encyclopedia, 'Whereas the notion of cardinal number is associated with a set with no particular structure on it, the ordinals are intimately linked with the special kind of sets that are called well-ordered (so intimately linked, in fact, that some mathematicians make no distinction between the two concepts). A well-ordered set is a totally ordered set (given any two elements one defines a smaller and a larger one in a coherent way) in which there is no infinite decreasing sequence (however, there may be infinite increasing sequences); equivalently, every non-empty subset of the set has a least element. Ordinals may be used to label the elements of any given well-ordered set (the smallest element being labelled 0, the one after that 1, the next one 2, "and so on") and to measure the "length" of the whole set by the least ordinal that is not a label for an element of the set. This "length" is called the order type of the set.' back

Øystein Linnebo (Stanford Encyclopedia of Philosophy), Platonism in the Philosophy of Mathematics, ' Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented.' back

Paul Dirac - Wikipedia, Paul Dirac - Wikipedia, the free encyclopedia, ' Paul Adrien Maurice Dirac OM FRS (8 August 1902 – 20 October 1984) was an English mathematical and theoretical physicist who is considered to be one of the founders of quantum mechanics and quantum electrodynamics. He is credited with laying the foundations of quantum field theory. . . .. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics, coining the latter term. Among other discoveries, he formulated the Dirac equation in 1928, which describes the behaviour of fermions and predicted the existence of antimatter, and is considered one of the most important equations in physics, with it being considered by some to be the "real seed of modern physics". back

Photoelectric effect - Wikipedia, Photoelectric effect - Wikipedia, the free encyclopedia, 'The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. . . . The experimental results disagree with classical electromagnetism, which predicts that continuous light waves transfer energy to electrons, which would then be emitted when they accumulate enough energy. An alteration in the intensity of light would theoretically change the kinetic energy of the emitted electrons, with sufficiently dim light resulting in a delayed emission. The experimental results instead show that electrons are dislodged only when the light exceeds a certain frequency—regardless of the light's intensity or duration of exposure.' back

Planck's Law - Wikipedia, Planck's Law - Wikipedia, the free encyclopedia, ' In physics, Planck's law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at temperature T. As a function of frequency ν. back

Plant reproduction - Wikipedia, Plant reproduction - Wikipedia, the free encyclopedia, ' Plant reproduction is the production of new offspring in plants, which can be accomplished by sexual or asexual reproduction. Sexual reproduction produces offspring by the fusion of gametes, resulting in offspring genetically different from either parent. Asexual reproduction produces new individuals without the fusion of gametes, resulting in clonal plants that are genetically identical to the parent plant and each other, unless mutations occur.' back

Plant reproductive morphology - Wikipedia, Plant reproductive morphology - Wikipedia, the free encyclopedia, ' Flowering plants: Basic flower morphology: The flower is the characteristic structure concerned with sexual reproduction in flowering plants (angiosperms). Flowers vary enormously in their structure (morphology). A perfect flower, like that of Ranunculus glaberrimus shown in the figure, has a calyx of outer sepals and a corolla of inner petals and both male and female sex organs. The sepals and petals together form the perianth. Next inwards there are numerous stamens, which produce pollen grains, each containing a microscopic male gametophyte. Stamens may be called the "male" parts of a flower and collectively form the androecium. Finally in the middle there are carpels, which at maturity contain one or more ovules, and within each ovule is a tiny female gametophyte. Carpels may be called the "female" parts of a flower and collectively form the gynoecium.' back

Plato - Wikipedia, Plato - Wikipedia, the free encyclopedia, ' Plato (c. 427 – 348 BC) was an ancient Greek philosopher of the Classical period who is considered a top thinker in Philosophy. Plato founded the Academy, a philosophical school in Athens where Plato taught the doctrines that would later become known as Platonism. The philosopher was an innovator of the written dialogue and dialectic forms in philosophy. He was a system-builder. He also raised problems for what became all the major areas of both theoretical philosophy and practical philosophy.' back

Plutonium - Wikipedia, Plutonium - Wikipedia, the fee encyclopedia, ' Plutonium is a radioactive actinide metal whose isotope, plutonium-239, is one of the three primary fissile isotopes (uranium-233 and uranium-235 are the other two); plutonium-241 is also highly fissile. To be considered fissile, an isotope's atomic nucleus must be able to break apart or fission when struck by a slow moving neutron and to release enough additional neutrons to sustain the nuclear chain reaction by splitting further nuclei.' back

Principia Mathematica - Wikipedia, Principia Mathematica - Wikipedia, the free encyclopedia, 'The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by the mathematicians Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.PM, . . . PM, according to its introduction, had three aims: (1) to analyze to the greatest possible extent the ideas and methods of mathematical logic and to minimize the number of primitive notions and axioms, and inference rules; (2) to precisely express mathematical propositions in symbolic logic using the most convenient notation that precise expression allows; (3) to solve the paradoxes that plagued logic and set theory at the turn of the 20th century, like Russell's paradox.' back

Quantum chromodynamics - Wikipedia, Quantum chromodynamics - Wikipedia, the free encyclopedia, ' In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics.' back

Quark - Wikipedia, Quark - Wikipedia, the free encyclopedia, 'Quarks . . . are a type of elementary particle and major constituents of matter. They combine to form composite particles called hadrons, the most well-known of which are protons and neutrons. They are the only particles in the Standard Model to experience the strong force, and thereby the only particles to experience all four fundamental forces, which are also known as fundamental interactions.' back

Richard P. Feynman (1981), Simulating Physics with Computers, 'I want to talk about the possibiilty that there is to be an exact simulation, that the computer will do exactly the same as nature. If this is to be proved and the type of computer is as I've already explained, then it's going to be necessary that everything that happens in a finite volume of space and time would have to be exactly analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore if this proposition is right, physical law is wrong.' International Journal of Theoretical Physics, VoL 21, Nos. 6/7, 1982 back

Riemannian geometry - Wikipedia, Riemannian geometry - Wikipedia, the free encyclopedia, ' Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area, and volume. From those some other global quantities can be derived by integrating local contributions. . . . It enabled Einstein's general relativity theory, made profound impact on group theory and representation theory, as well as analysis, and spurred the development of algebraic and differential topology.' back

Rule of Saint Augustine - Wikipedia, Rule of Saint Augustine - Wikipedia, the free encyclopedia, ' The Rule of Saint Augustine, written in about the year 400, is a brief document divided into eight chapters and serves as an outline for religious life lived in community. It is the oldest monastic rule in the Western Church. The rule, developed by Augustine of Hippo (354–430), governs chastity, poverty, obedience, detachment from the world, the apportionment of labour, the inferiors, fraternal charity, prayer in common, fasting and abstinence proportionate to the strength of the individual, care of the sick, silence and reading during meals. . . .. At the Fourth Lateran Council (1215) it was accepted as one of the approved rules of the church. It was then adopted by the Order of Preachers in 1216 when their order received papal recognition. back

Shelter Island Conference - Wikipedia, Shelter Island Conference - Wikipedia, the free encyclopedia, ' The first Shelter Island Conference on the Foundations of Quantum Mechanics was held from June 2–4, 1947 at the Ram's Head Inn in Shelter Island, New York. Shelter Island was the first major opportunity since Pearl Harbor and the Manhattan Project for the leaders of the American physics community to gather after the war. As Julian Schwinger would later recall, "It was the first time that people who had all this physics pent up in them for five years could talk to each other without somebody peering over their shoulders and saying, 'Is this cleared?" ' back

Shelter Island Conference - Wikipedia, Shelter Island Conference - Wikipedia, the free encyclopedia, ' The first Shelter Island Conference on the Foundations of Quantum Mechanics was held from June 2–4, 1947 at the Ram's Head Inn in Shelter Island, New York. Shelter Island was the first major opportunity since Pearl Harbor and the Manhattan Project for the leaders of the American physics community to gather after the war. As Julian Schwinger would later recall, "It was the first time that people who had all this physics pent up in them for five years could talk to each other without somebody peering over their shoulders and saying, 'Is this cleared?" ' back

Space (mathematics) - Wikipedia, Space (mathematics) - Wikipedia, the free encyclopedia, ' n mathematics, a space is a set (sometimes called a universe) with some added structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. The nature of the points can vary widely: for example, the points can be elements of a set, functions on another space, or subspaces of another space. It is the relationships that define the nature of the space.' back

Standard model - Wikipedia, Standard model - Wikipedia, the free encyclopedia, 'The Standard Model of particle physics is a theory that describes three of the four known fundamental interactions between the elementary particles that make up all matter. It is a quantum field theory developed between 1970 and 1973 which is consistent with both quantum mechanics and special relativity. To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions. However, the Standard Model falls short of being a complete theory of fundamental interactions, primarily because of its lack of inclusion of gravity, the fourth known fundamental interaction, but also because of the large number of numerical parameters (such as masses and coupling constants) that must be put "by hand" into the theory (rather than being derived from first principles) . . . ' back

Tensor product - Wikipedia, Tensor product - Wikipedia, the free encyclopedia, ' In mathematics, the tensor product V ⊗ W of two vector spaces V and W (over the same field) is itself a vector space, endowed with the operation of bilinear composition, denoted by ⊗, from ordered pairs in the Cartesian product V × W to V ⊗ W in a way that generalizes the outer product. Essentially the difference between a tensor product of two vectors and an ordered pair of vectors is that if one vector is multiplied by a nonzero scalar and the other is multiplied by the reciprocal of that scalar, the result is a different ordered pair of vectors, but the same tensor product of two vectors. The tensor product of V and W is the vector space generated by the symbols v ⊗ w, with v ∈ V and w ∈ W, in which the relations of bilinearity are imposed for the product operation ⊗, and no other relations are assumed to hold. The tensor product space is thus the "freest" (or most general) such vector space, in the sense of having the fewest constraints.' back

The Principles of Quantum Mechanics - Wikipedia, The Principles of Quantum Mechanics - Wikipedia, the free encyclopedia, The Principles of Quantum Mechanics is an influential monograph on quantum mechanics written by Paul Dirac and first published by Oxford University Press in 1930. Dirac gives an account of quantum mechanics by "demonstrating how to construct a completely new theoretical framework from scratch"; "problems were tackled top-down, by working on the great principles, with the details left to look after themselves". It leaves classical physics behind after the first chapter, presenting the subject with a logical structure. Its 82 sections contain 785 equations with no diagrams.' back

Theodicy - Wikipedia, Theodicy - Wikipedia, the free encyclopedia, ' In the philosophy of religion, a theodicy (meaning 'vindication of God', from Ancient Greek θεός theos, "god" and δίκη dikē, "justice") is an argument that attempts to resolve the problem of evil that arises when omnipotence, omnibenevolence, and omniscience are all simultaneously ascribed to God. Unlike a defence, which merely tries to demonstrate that the coexistence of God and evil is logically possible, a theodicy additionally provides a framework wherein God's existence is considered plausible. The German philosopher and mathematician Gottfried Leibniz coined the term "theodicy" in 1710 in his work Théodicée, though numerous attempts to resolve the problem of evil had previously been proposed.' back

Three-body problem - Wikipedia, Three-body problem - Wikipedia, the free encyclopedia, ' In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation.[1] The three-body problem is a special case of the n-body problem. Unlike two-body problems, no general closed-form solution exists,[1] as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required. Historically, the first specific three-body problem to receive extended study was the one involving the Moon, Earth, and the Sun.[2] In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles.' back

Turing's Proof - Wikipedia, Turing's Proof - Wikipedia, the free encyclopedia, 'Turing's proof is a proof by Alan Turing, first published in January 1937 with the title "On Computable Numbers, with an Application to the Entscheidungsproblem." It was the second proof of the assertion (Alonzo Church's proof was first) that some decision problems are "undecidable": there is no single algorithm that infallibly gives a correct "yes" or "no" answer to each instance of the problem. In his own words: "...what I shall prove is quite different from the well-known results of Gödel ... I shall now show that there is no general method which tells whether a given formula U is provable in K [Principia Mathematica]..." '. back

Uranium-235 - Wikipedia, Uranium-235 - Wikipedia, the free encyclopedia, ' Uranium-235 (235U or U-235) is an isotope of uranium making up about 0.72% of natural uranium. Unlike the predominant isotope uranium-238, it is fissile, i.e., it can sustain a nuclear chain reaction. It is the only fissile isotope that exists in nature as a primordial nuclide. Uranium-235 has a half-life of 703.8 million years. It was discovered in 1935 by Arthur Jeffrey Dempster. Its fission cross section for slow thermal neutrons is about 584.3±1 barns. For fast neutrons it is on the order of 1 barn.' back

Vacuum polarization - Wikipedia, Vacuum polarization - Wikipedia, the free encyclopedia, ' In quantum field theory, and specifically quantum electrodyn amics, vacuum polarization describes a process in which a background electromagnetic field produces virtual electron–positron pairs that change the distribution of charges and currents that generated the original electromagnetic field. It is also sometimes referred to as the self-energy of the gauge boson (photon). After developments in radar equipment for World War II resulted in higher accuracy for measuring the energy levels of the hydrogen atom, I.I. Rabi made measurements of the Lamb shift and the anomalous magnetic dipole moment of the electron. These effects corresponded to the deviation from the value −2 for the spectroscopic electron g-factor that are predicted by the Dirac equation. Later, Hans Bethe theoretically calculated those shifts in the hydrogen energy levels due to vacuum polarization on his return train ride from the Shelter Island Conference to Cornell.' back

Xavier Waintal (2023_12_29), The Quantum House Of Cards, ' Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new artificial intelligence applications. Yet, to date, a simple task such as multiplying 3 by 5 is beyond existing quantum hardware. This article examines the difficulties that would need to be solved for quantum computers to live up to their promises. I discuss the whole stack of technologies that has been envisioned to build a quantum computer from the top layers (the actual algorithms and associated applications) down to the very bottom ones (the quantum hardware, its control electronics, cryogeny, etc.) while not forgetting the crucial intermediate layer of quantum error correction.' back