Crombie (1959, 1995), Alistsair Cameron, The History of Science from Augustine to Galileo, Dover 1995 Jacket: 'The Origins of modern science date back at least to the thirteenth century, but it was not until the end of the sixteenth century that the Scientific Revolution began to gather breathtaking speed. Since then, man's view of himself and his world has changed so profoundly that the Scientific Revolution has been compared in the history of civilization to the rise of the Ancient Greek philosophy in the sixth and fifth centuries B. C., and to the spread of Christianity throughout the Roman Empire to the third and fourth centuries AD. . ... Beginning with a brief account of ideas about the natural world in Western Christendom, from the Dark Ages to the twelfth century, the author goes on to show how the system of scientific thought accepted in the thirteenth century was introduced from Greek and Arabic sources. He also offers thought provoking insights into such topics as the relationship of technical activity to science throughout the medieval period, the criticism of Aristotle in the later Middle Ages and the Scientific Revolution itself.' 
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Einstein (1916, 2005), Albert, and Robert W Lawson (translator) Roger Penrose (Introduction), Robert Geroch (Commentary), David C Cassidy (Historical Essay), Relativity: The Special and General Theory, Pi Press 1916, 2005 Preface: 'The present book is intended, as far as possible, to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. ... The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated.' page 3  
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Feynman (2002), Richard, Feynman Lectures on Gravitation, Westview Press 2002 ' The Feynman Lectures on Gravitation are based on notes prepared during a course on gravitational physics that Richard Feynman taught at Caltech during the 1962-63 academic year. For several years prior to these lectures, Feynman thought long and hard about the fundamental problems in gravitational physics, yet he published very little. These lectures represent a useful record of his viewpoints and some of his insights into gravity and its application to cosmology, superstars, wormholes, and gravitational waves at that particular time. The lectures also contain a number of fascinating digressions and asides on the foundations of physics and other issues. ' 
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Hawking (1975), Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.' 
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Jammer (1957, 1999), Max, Concepts of Force: A Study in the Foundations of Dynamics, Dover 2011 'Both historical treatment and critical analysis, this work by a noted physicist takes a fascinating look at a fundamental of physics, tracing its development from ancient to modern times. Kepler's initiation of scientific conceptualization, Newton's definition, post-Newtonian reinterpretation — contrasting concepts of Leibniz, Boscovich, Kant with those of Mach, Kirchhoff, Hertz. In-depth analysis of contemporary trend toward eliminating force from conceptual scheme of physics. "An excellent presentation." — Science. 1962 edition.' 
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Kaku (1998), Michio, Introduction to Superstrings and M-Theory (Graduate Texts in Contemporary Physics), Springer 1998 ' Called by some "the theory of everything," superstrings may solve a problem which has eluded physicists for the past 50 years -- the final unification of the two great theories of the twentieth century, general relativity and quantum field theory. This is a course-tested comprehensive introductory graduate text on superstrings which stresses the most current areas of interest, not covered in other presentation, including: string field theory, multi loops, Teichmueller spaces, conformal field theory, and four-dimensional strings. The book begins with a simple discussion of point particle theory, and uses the Feynman path integral technique to unify the presentation of superstrings. Prerequisites are an acquaintance with quantum mechanics and relativity. This second edition has been revised and updated throughout.' 
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Newton (1729, 1962), Isaac, Principia volume II: The System of the World, University of California Press 1962 ' In the preceding books I have laid down the principle of philosophy; principles not philosophical but mathematical such: namely, as we may build our reasonings upon in philosophical inquiries. These principles are the laws and conditions of certain motions, and powers or forces, which chiefly have respect to philosophy; . . . It remains that, from the same principles, I now demonstrate the frame of the System of the World.' 
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Newton (1729, 1966), Isaac, Mathematical Principles of Natural Philosophy: volume I: The Motion of Bodies, University of California Press 1966 Jacket: '. . . one of the most important contributions to human knowledge. First translated from the Latin by Andrew Motte' 
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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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Streater, 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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Albert Einstein, Happiest thought, 'I was sitting in a chair in the patent office at Bern when all of sudden a thought occurred to me: If a person falls freely he will not feel his own weight. I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.' back

Albert Einstein (1905), On the Electrodynamics of Moving Bodies, An english translation of the paper that founded Special relativity. 'Examples of this sort, [in the contemporary application of Maxwell's electrodynamics to moving bodies] together with the unsuccessful attempts to discover any motion of the earth relatively to the ``light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.' back

Albert Einstein (1905b), Does the inertia of a body depend upon its energy-content?, ' If a body gives off the energy L in the form of radiation, its mass diminishes by L/c2. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 10^20, the energy being measured in ergs, and the mass in grammes. It is not impossible that with bodies whose energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test. If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies. ' 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 (1915, 2010), The Field Equations of Gravitation (Translation), ' By that, the general theory of relativity as a logical building is eventually finished. The relativity postulate in its general form that makes the space-time coordinates to physically meaningless parameters, is directed with stringent necessity to a very specific theory of gravitation that explains the perihelion motion of mercury. However, the general relativity postulate offers nothing new about the essence of the other natural processes, which wasn't already taught by the special theory of relativity.' back

Albert Einstein & Marcel Grossman (1913), Outline of a Generalized Theory of Relativity and of a Theory of Gravitation, ' The theory expounded in what follows derives from the conviction that the proportionality between the inertial and the gravitational mass of bodies is an exactly valid law of nature that must already find expression in the very foundation of theoretical physics. I already sought to give expression to this conviction in several earlier papers by seeking to reduce the gravitational mass to the inertial mass; this endeavor led me to the hypothesis that, from a physical point of view, an (infinitesimally extended, homogeneous) gravitational field can be completely replaced by a state of acceleration of the reference system. This hypothesis can be expressed pictorially in the following way: An observer enclosed in a box can in no way decide whether the box is at rest in a static gravitational field, or whether it is in accelerated motion, maintained by forces acting on the box, in a space that is free of gravitational fields (equivalence hypothesis).' back

Ansatz - Wikipedia, Ansatz - Wikipedia, the free encyclopedia, ' In physics and mathematics, an ansatz (German: initial placement of a tool at a work piece) is an educated guess that is verified later by its results.' back

Aquinas, Summa, I, 3, 4, Are essence and existence the same in God?, 'I answer that, God is not only His own essence, as shown in the preceding article, but also His own existence. This may be shown in several ways. First, whatever a thing has besides its essence must be caused either by the constituent principles of that essence (like a property that necessarily accompanies the species--as the faculty of laughing is proper to a man--and is caused by the constituent principles of the species), or by some exterior agent--as heat is caused in water by fire. Therefore, if the existence of a thing differs from its essence, this existence must be caused either by some exterior agent or by its essential principles. Now it is impossible for a thing's existence to be caused by its essential constituent principles, for nothing can be the sufficient cause of its own existence, if its existence is caused. Therefore that thing, whose existence differs from its essence, must have its existence caused by another. But this cannot be true of God; because we call God the first efficient cause. Therefore it is impossible that in God His existence should differ from His essence.' back

Aquinas, Summa I, 28, 3, Are the relations in God are really distinguished from each other?, ' I answer that, The attributing of anything to another involves the attribution likewise of whatever is contained in it. So when "man" is attributed to anyone, a rational nature is likewise attributed to him. The idea of relation, however, necessarily means regard of one to another, according as one is relatively opposed to another. So as in God there is a real relation (Article 1), there must also be a real opposition. The very nature of relative opposition includes distinction. Hence, there must be real distinction in God, not, indeed, according to that which is absolute—namely, essence, wherein there is supreme unity and simplicity—but according to that which is relative.' back

Aquinas, Summa: I, 2, 3, Does God exist?, 'I answer that, The existence of God can be proved in five ways. The first and more manifest way is the argument from motion. . . . ' back

Big Bang - Wikipedia, Big Bang - Wikipedia, the free encyclopedia, ' The Big Bang theory is the prevailing cosmological model explaining the existence of the observable universe from the earliest known periods through its subsequent large-scale evolution. The model describes how the universe expanded from an initial state of high density and temperature, and offers a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. ' back

Black hole thermodynamics - Wikipedia, Black hole thermodynamics - Wikipedia, the free encyclopedia, 'In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. Much as the study of the statistical mechanics of black body radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle.' back

Bohr model - Wikipedia, Bohr model - Wikipedia, the free encyclopedia, 'In atomic physics, the Rutherford–Bohr model or Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with attraction provided by electrostatic forces rather than gravity.' back

Compton scattering - Wikipedia, Compton scattering - Wikipedia, the free encyclopedia, ' Compton scattering is the inelastic scattering of a photon by a quasi-free charged particle, usually an electron. It results in a decrease in energy (increase in wavelength) of the photon (which may be an X-ray or gamma ray photon), called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering also exists, in which a charged particle transfers part of its energy to a photon.' back

Computable function - Wikipedia, Computable function - Wikipedia, the free encyclopedia, 'Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i.e. given an input of the function domain it can return the corresponding output. Computable functions are used to discuss computability without referring to any concrete model of computation such as Turing machines or register machines. Any definition, however, must make reference to some specific model of computation but all valid definitions yield the same class of functions. Particular models of computability that give rise to the set of computable functions are the Turing-computable functions and the general recursive functions.' back

Conservation of energy - Wikipedia, Conservation of energy - Wikipedia, the free encyclopedia, 'In physics, the law of conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither created nor destroyed, but can change form, for instance chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite. back

Cosmic microwave background - Wikipedia, Cosmic microwave background - Wikipedia, the free encyclopedia, 'The cosmic microwave background (CMB) is the thermal radiation left over from the time of recombination in Big Bang cosmology. . . . The CMB is a snapshot of the oldest light in our Universe, imprinted on the sky when the Universe was just 380,000 years old. It shows tiny temperature fluctuations that correspond to regions of slightly different densities, representing the seeds of all future structure: the stars and galaxies of today.' back

David E. Soper, Newton's reasoning for the orbit of the Moon , ' "I deduced that the forces which keep the Planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the Moon in her orb with the force of gravity at the surface of the earth, and found them to answer pretty nearly".' back

David Hume - Wikipedia, David Hume - Wikipedia, the free encyclopedia, ' David Hume (7 May 1711 – 25 August 1776) was a Scottish Enlightenment philosopher, historian, economist, and essayist, who is best known today for his highly influential system of philosophical empiricism, scepticism, and naturalism. Hume's empiricist approach to philosophy places him with John Locke, George Berkeley, Francis Bacon and Thomas Hobbes as a British Empiricist. ' back

Differentiable manifold - Wikipedia, Differentiable manifold - Wikipedia, the free encyclopedia, ' In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within the individual charts, since each chart lies within a vector space to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart. ' back

Equivalence principle - Wikipedia, Equivalence principle - Wikipedia, the free encyclopedia, ' In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.' back

Essence - Wikipedia, Essence - Wikipedia, the free encyclopedia, ' Essence (Latin: essentia) is a polysemic term, used in philosophy and theology as a designation for the property or set of properties that make an entity or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity. Essence is contrasted with accident: a property that the entity or substance has contingently, without which the substance can still retain its identity.' back

Eugene Wigner (1939), On Unitary Representations of the Inhomogeneous Lorentz Group, Annals of Mathematics Second Series vol 40 no 1 (jan, 1939) pp 149-204 ' It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold, in which a unitary scalar product is defined. The states are generally represented by wave functions in such a way that φ and constant multiples of φ represent the same physical state.' back

Evolution - Wikipedia, Evolution - Wikipedia, the free encyclopedia, '. . . Charles Darwin and Alfred Wallace were the first to formulate a scientific argument for the theory of evolution by means of natural selection. Evolution by natural selection is a process that is inferred from three facts about populations: 1) more offspring are produced than can possibly survive, 2) traits vary among individuals, leading to different rates of survival and reproduction, and 3) trait differences are heritable. . . . ' back

Feynman, Leighton & Sands FLP II:18, Chapter 18: Maxwell's Equations, 'In this chapter we come back to the complete set of the four Maxwell equations that we took as our starting point in Chapter 1. Until now, we have been studying Maxwell’s equations in bits and pieces; it is time to add one final piece, and to put them all together. We will then have the complete and correct story for electromagnetic fields that may be changing with time in any way. . . . Although we have been very careful to point out the restrictions whenever we wrote an equation, it is easy to forget all of the qualifications and to learn too well the wrong equations. Now we are ready to give the whole truth, with no qualifications (or almost none).' back

Galaxy - Wikipedia, Galaxy - Wikipedia, the free encyclopedia, ' A galaxy is a system of stars, stellar remnants, interstellar gas, dust, and dark matter bound together by gravity. The word is derived from the Greek galaxias (γαλαξίας), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. Galaxies, averaging an estimated 100 billion stars, range in size from dwarfs with less than a hundred million stars, to the largest galaxies known – supergiants with one hundred trillion stars, each orbiting its galaxy's center of mass. Most of the mass in a typical galaxy is in the form of dark matter, with only a few percent of that mass visible in the form of stars and nebulae. Supermassive black holes are a common feature at the centres of galaxies.' back

Galilean invariance - Wikipedia, Galilean invariance - Wikipedia, the free encyclopedia, ' Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames. Galileo Galilei first described this principle in 1632 in his Dialogue Concerning the Two Chief World Systems using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer below the deck would not be able to tell whether the ship was moving or stationary.' back

Gaussian curvature - Wikipedia, Gaussian curvature - Wikipedia, the free encyclopedia, ' In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ1 and κ2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how distances are measured on the surface, not on the way it is isometrically embedded in space. This result is the content of Gauss's Theorema egregium.' back

Genesis I:1-4, Genesis, from the Holy Bible, King James Version, ' 1: In the beginning God created the heaven and the earth. 2: And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. 3: And God said, Let there be light: and there was light. 4: And God saw the light, that it was good: and God divided the light from the darkness. ' back

Geodesics in general relativity - Wikipedia, Geodesics in general relativity - Wikipedia, the free encyclopedia, ' In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational force, is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.' back

George Smoot, Precession of the perihelion of Mercury, ' As seen from Earth the precession of Mercury's orbit is measured to be 5600 seconds of arc per century (one second of arc = 1/3600 degrees). Newton's equations, taking into account all the effects from the other planets (as well as a very slight deformation of the Sun due to its rotation) and the fact that the Earth is not an inertial frame of reference, predicts a precession of 5557 seconds of arc per century. There is a discrepancy of 43 seconds of arc per century. This discrepancy cannot be accounted for using Newton's formalism. . . . . In contrast, Einstein was able to predict, without any adjustments whatsoever, that the orbit of Mercury should precess by an extra 43 seconds of arc per century should the General Theory of Relativity be correct.' 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

Gospel, John 1, And the Word was made flesh , ' 14: And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth. back

Gravitational constant - Wikipedia, Gravitational constant - Wikipedia, the free encyclopedia, 'The gravitational constant denoted by letter G, is an empirical physical constant involved in the calculation(s) of gravitational force between two bodies.' back

Gravitational-wave observatory - Wikipedia, Gravitational-wave observatory - Wikipedia, the free encyclopedia, 'A gravitational-wave detector (used in a gravitational-wave observatory) is any device designed to measure tiny distortions of spacetime called gravitational waves. Since the 1960s, various kinds of gravitational-wave detectors have been built and constantly improved. The present-day generation of laser interferometers has reached the necessary sensitivity to detect gravitational waves from astronomical sources, thus forming the primary tool of gravitational-wave astronomy.' back

Gregory J. Chaitin (1982), Gödel's Theorem and Information, 'Abstract: Gödel's theorem may be demonstrated using arguments having an information-theoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread rather than pathological and unusual.'
International Journal of Theoretical Physics 21 (1982), pp. 941-954 back

Harmonic Oscillator - Wikipedia, Harmonic Oscillator - Wikipedia, the free encyclopedia, ' In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: F = kx, where k is a positive constant. If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).' back

Hawking radiation - Wikipedia, Black hole - Wikipedia, the free encyclopedia, ' Hawking radiation is dependent on the Unruh effect and the equivalence principle applied to black-hole horizons. Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing Hawking radiation.' back

Heinrich Hertz - Wikipedia, Heinrich Hertz - Wikipedia, the free encyclopedia, ' Heinrich Rudolf Hertz (22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's equations of electromagnetism. The unit of frequency, cycle per second, was named the "hertz" in his honor.' back

Isaac Newton (1713), The General Scholium to the Principia Mathematica, 'Published for the first time as an appendix to the 2nd (1713) edition of the Principia, the General Scholium reappeared in the 3rd (1726) edition with some amendments and additions. As well as countering the natural philosophy of Leibniz and the Cartesians, the General Scholium contains an excursion into natural theology and theology proper. In this short text, Newton articulates the design argument (which he fervently believed was furthered by the contents of his Principia), but also includes an oblique argument for a unitarian conception of God and an implicit attack on the doctrine of the Trinity, which Newton saw as a post-biblical corruption. The English translation here is that of Andrew Motte (1729). Italics and orthography as in original.' back

John D. Norton (2022), The world's quickest derivation of E = mc^2, ' Consider a body that moves at very close to the speed of light. A uniform force acts on it and, as a result, the force pumps energy and momentum into the body. That force cannot appreciably change the speed of the body because it is going just about as fast as it can. So all the increase of momentum = mass x velocity of the body is manifest as an increase of mass. We want to show that in unit time the energy E gained by the body due to the action of the force is equal to mc^2, where m is the mass gained by the body.' back

John Palmer (Stanford Encyclopedia of Philosophy), Parmenides, ' Immediately after welcoming Parmenides to her abode, the goddess describes as follows the content of the revelation he is about to receive:
You must needs learn all things,/ both the unshaken heart of well-rounded reality/ and the notions of mortals, in which there is no genuine trustworthiness./ Nonetheless these things too will you learn, how what they resolved/ had actually to be, all through all pervading. (Fr. 1.28b-32) ' back

Karl Marx - Wikipedia, Karl Marx - Wikipedia, the free encyclopedia, 'Karl Heinrich Marx (Berlin 5 May 1818 – 14 March 1883) was a German philosopher, economist, sociologist, historian, journalist, and revolutionary socialist. His ideas played a significant role in the establishment of the social sciences and the development of the socialist movement. He is also considered one of the greatest economists in history. He published numerous books during his lifetime, the most notable being The Communist Manifesto (1848) and Capital (1867 –1894). He often worked closely with his friend and fellow revolutionary socialist, Friedrich Engels.' back

Lagrangian - Wikipedia, Lagrangian - Wikipedia, the free encyclopedia, ' The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as Lagrangian mechanics. In classical mechanics, the Lagrangian is defined as the kinetic energy, T, of the system minus its potential energy, V. In symbols, L = T - V. ' back

Lagrangian mechanics - Wikipedia, Lagrangian mechanics - Wikipedia, the free encyclopedia, ' Introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788, Lagrangian mechanics is a formulation of classical mechanics and is founded on the stationary action principle. Given a system of point masses and a pair, t₁ and t₂ Lagrangian mechanics postulates that the system's trajectory (describing evolution of the system over time) . . . must be a stationary point of the action functional S = ∫ L dt. By convention, L = T − V, where T and V are the kinetic and potential energy of the system, respectively.' back

Lorentz transformation - Wikipedia, Lorentz transformation - Wikipedia, the free encyclopedia, 'In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik Lorentz. It reflects the surprising fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events.' back

Louis de Broglie (1929), Nobel Lecture: The Wave Nature of the Electron, ' Nevertheless, it was still necessary to adopt the wave theory to account for interference and diffraction phenomena and no way whatsoever of reconciling the wave theory with the existence of light corpuscles could be visualized. The necessity of assuming for light two contradictory theories-that of waves and that of corpuscles - and the inability to understand why, among the infinity of motions which an electron ought to be able to have in the atom according to classical concepts, only certain ones were possible: such were the enigmas confronting physicists at the time I resumed my studies of theoretical physics.Now a purely corpuscular theory does not contain any element permitting the definition of frequency. This also renders it necessary in the case of light to introduce simultaneously the corpuscle concept and the concept of periodicity. On the other hand the determination of the stable motions of the electrons in the atom involves whole numbers, and so far the only phenomena in which whole numbers were involved in physics were those of interference and of eigenvibrations. That suggested the idea to me that electrons themselves could not be represented as simple corpuscles either, but that a periodicity had also to be assigned to them too. In other words the existence of corpuscles accompanied by waves has to be assumed in all cases. However, since corpuscles and waves cannot be independent because, according to Bohr's expression, it must be possible to establish a certain parallelism between the motion of a corpuscle and the propagation of the associated wave. . . .. They showed clearly that it was possible to establish a correspondence between waves and corpuscles such that the laws of mechanics correspond to the laws of geometrical optics. . . .. This prompted the thought that classical mechanics is also only an approximation relative to a vaster wave mechanics. I stated as much almost at the outset of my studies, i.e. "A new mechanics must be developed which is to classical mechanics what wave optics is to geometrical optics". This new mechanics has since been developed, thanks mainly to the fine work done by Schrödinger. . . .. I cannot attempt even briefly to sum up here the development of the new mechanics. I merely wish to say that on examination it proved to be identical with a mechanics independently developed, first by Heisenberg, then by Born, Jordan, Pauli, Dirac, etc quantum mechanics. The two mechanics, wave and quantum, are equivalent from the mathematical point of view. . . .. Since the wavelength of the electron waves is of the order of that of X-rays, it must be expected that crystals can cause diffraction of these waves completely analogous to the Laue phenomenon. . . . Thus to describe the properties of matter as well as those of light, waves and corpuscles have to be referred to at one and the same time. The electron can no longer be conceived as a single, small granule of electricity; it must be associated with a wave and this wave is no myth; its wavelength can be measured and its interferences predicted. It has thus been possible to predict a whole group of phenomena without their actually having been discovered. And it is on this concept of the duality of waves and corpuscles in Nature, expressed in a more or less abstract form, that the whole recent development of theoretical physics has been founded and that all future development of this science will apparently have to be founded.' back

Marcelo Samuel Berman (2009), On the Zero-energy Universe, ' We consider the energy of the Universe, from the pseudo-tensor point of view (Berman,1981). We find zero values, when the calculations are well-done.The doubts concerning this subject are clarified, with the novel idea that the justification for the calculation lies in the association of the equivalence principle, with the nature of co-motional observers, as demanded in Cosmology. In Section 4, we give a novel calculation for the zero-total energy result.' back

Mass-energy equivalence - Wikipedia, Mass-energy equivalence - Wikipedia, the free encyclopedia, In physics, mass–energy equivalence is the concept that any mass has an associated energy and vice versa. In special relativity this relationship is expressed using the mass–energy equivalence formula E = mc² where E is the energy of a physical system m is the mass of the system, and c = the speed of light in a vacuum . . . ' back

Maxwell's equations - Wikipedia, Maxwell's equations - Wikipedia, the free encyclopedia, ' Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields.' back

Metaphysics - Wikipedia, Metaphysics - Wikipedia, the free encyclopedia, ' Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility.] It includes questions about the nature of consciousness and the relationship between mind and matter, between substance and attribute, and between potentiality and actuality.' back

Michelson and Morley (1887), On the relative motion of the earth and the lumeniferous ether, The classic paper, 1887. They conclude that "It appears, from all that precedes, reasonably certain that if there be any relative motion between the earth and the luminiferous ether, it must be small; . . . " back

Minkowski space - Wikipedia, Minkowski space - Wikipedia, the free encyclopedia, ' By 1908 Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein in 1905 and based on the previous work of Lorentz and Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which time and space are not separated entities but intermingled in a four-dimensional space–time, and in which the Lorentz geometry of special relativity can be effectively represented using the invariant interval x² + y² + z² − c² t².' back

Newton's law of universal gravitation - Wikipedia, Newton's law of universal gravitation - Wikipedia, the free encyclopedia, ' Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The publication of the theory has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.' back

Newton's Laws of motion - Wikipedia, Newton's Laws of motion - Wikipedia, the free encyclopedia, 'Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: Law 1. A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. Law 2. When a body is acted upon by a force, the time rate of change of its momentum equals the force. Law 3. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.' back

No-cloning theorem - Wikipedia, No-cloning theorem - Wikipedia, the free encyclopedia, ' In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computing among others. The theorem is an evolution of the 1970 no-go theorem authored by James Park, in which he demonstrates that a non-disturbing measurement scheme which is both simple and perfect cannot exist . . .. The aforementioned theorems do not preclude the state of one system becoming entangled with the state of another as cloning specifically refers to the creation of a separable state with identical factors.' back

Observable Universe - Wikipedia, Observable Universe - Wikipedia, the free encyclopedia, 'The observable universe is a spherical region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. There are at least 2 trillion galaxies in the observable universe.' back

Pendulum - Wikipedia, Pendulum - Wikipedia, the free encyclopedia, 'A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth.' back

Photon - Wikipedia, Photon - Wikipedia, the free encyclopedia, ' A photon (from Ancient Greek φῶς, φωτός (phôs, phōtós) 'light') is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always move at the speed of light in vacuum, 299792458 m/s . . .. The photon belongs to the class of bosons.' back

Potential gradient - Wikipedia, Potential gradient - Wikipedia, the free encyclopedia, ' In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux. back

Second law of thermodynamics - Wikipedia, Second law of thermodynamics - Wikipedia - The free encyclopedia, 'The second law of thermodynamics states that in a natural thermodynamic process, there is an increase in the sum of the entropies of the participating systems. The second law is an empirical finding that has been accepted as an axiom of thermodynamic theory. back

Special relativity - Wikipedia, Special relativity - Wikipedia, the free encyclopedia, ' Special relativity . . . is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity—that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)—from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.' back

Unmoved mover - Wikipedia, Unmoved mover - Wikipedia, the free encyclopedia, ' The unmoved mover (Ancient Greek: ὃ οὐ κινούμενον κινεῖ, lit. 'that which moves without being moved' or prime mover (Latin: primum movens) is a concept advanced by Aristotle as a primary cause (or first uncaused cause) or "mover" of all the motion in the universe. As is implicit in the name, the unmoved mover moves other things, but is not itself moved by any prior action. In Book 12 (Greek: Λ) of his Metaphysics, Aristotle describes the unmoved mover as being perfectly beautiful, indivisible, and contemplating only the perfect contemplation: self-contemplation. He equates this concept also with the active intellect. This Aristotelian concept had its roots in cosmological speculations of the earliest Greek pre-Socratic philosophers and became highly influential and widely drawn upon in medieval philosophy and theology. St. Thomas Aquinas, for example, elaborated on the unmoved mover in the Quinque viae. ' back

Vacuum permeability - Wikipedia, Vacuum permeability - Wikipedia, the free encyclopedia, ' The physical constant μ₀, (pronounced "mu nought" or "mu zero"), commonly called the vacuum permeability, permeability of free space, permeability of vacuum, or [preferred name] magnetic constant, is the magnetic permeability in a classical vacuum. Vacuum permeability is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field production in a vacuum. . . . ' back

Vacuum permittivity - Wikipedia, Vacuum permittivity - Wikipedia, the free encyclopedia, ' The physical constant ε_o (pronounced as "epsilon nought" or "epsilon zero"), commonly called the vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum, is an ideal, (baseline) physical constant, which is the value of the absolute dielectric permittivity of classical vacuum. . . . It is the capability of the vacuum to permit electric field lines. This constant relates the units for electric charge to mechanical quantities such as length and force.' back

Variety (cybernetics) - Wikipedia, Variety (cybernetics) - Wikipedia, the free encyclopedia, 'The term Variety was introduced by W. Ross Ashby to denote the count of the total number of states of a system. The condition for dynamic stability under perturbation (or input) was described by his Law of Requisite Variety. Ashby says: Thus, if the order of occurrence is ignored, the set {c, b, c, a, c, c, a, b, c, b, b, a} which contains twelve elements, contains only three distinct elements- a, b, c. Such a set will be said to have a variety of three elements. He adds The observer and his powers of discrimination may have to be specified if the variety is to be well defined. Variety can be stated as an integer, as above, or as the logarithm to the base 2 of the number i.e. in bits.' back

Wiliam E. Ritter (1932), Why Aristotle Invented the Word Entelecheia, ' The definition of entelecheia given by Ross and others, namely, "actuality, complete reality," appears to be true to the make-up of the word: enteles, complete, in full; echein, have, hold. ... Again with but little violence to truth we may say that the treatises on Logic, Rhetoric, and Poetry; and on Politics and Ethics are the Aristotelian effort to analyze the entelecheia of man on the spiritual side of his nature.' back

Zero-energy universe - Wikipedia, Zero-energy universe - Wikipedia, the free encyclopedia, 'The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly cancelled out by its negative energy in the form of gravity. . . . The zero-energy universe theory originated in 1973, when Edward Tryon proposed in the journal Nature that the universe emerged from a large-scale quantum fluctuation of vacuum energy, resulting in its positive mass-energy being exactly balanced by its negative gravitational potential energy.' back