Aristotle (1980), and (translated by P H Wickstead and F M Cornford), [Physics Books I-IV, Harvard University Press, William Heinemann 1980 Introduction: 'The title "Physics" is misleading. .. "Lectures on Nature" the alternative title found in editions of the Greek text, is more enlightening. ... The realm of Nature, for Aristotle, includes all things that move and change ... . Thus the ultimate "matter" which, according to Aristotle, underlies all the elementary substances must be studied, in its changes at least, by the Natural Philosopher. And so must the eternal heavenly spheres of the Aristotelean philosophy, insofar as they themselves move of are the cause of motion in the sublunary world.' 
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Carlson (2006), James, and Arthur Jaffe & Andrew Wiles, The Millennium Prize Problems, ClayMathematics Institute and American Mathematical Society 2006
1: The BirJaffe & Wilesaaffeaach and Swinnerton-Dyer Conjecture: Andrew Wiles
2: The Hodge Conjecture: Pierre Deligne
3: The Existence and Smoothness of the Navier-Stokes Equation: Charles L Fefferman
4: The Poincare Conjecture: John Milnor
5: The P versus NP Problem: Stephen Cook
6: The Riemann Hypothesis: Enrico Bombieri
7: Quantum Yang-Mills Theory: Arthur Jaffe and Edward Whitten 
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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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Hodges (1983), Andrew, Alan Turing: The Enigma, Burnett 1983 Author's note: '. . . modern papers often employ the usage turing machine. Sinking without a capital letter into the collective mathematical consciousness (as with the abelian group, or the riemannian manifold) is probably the best that science can offer in the way of canonisation.' (530) 
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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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Weinberg (1995), Steven, The Quantum Theory of Fields Volume I: Foundations, Cambridge University Press 1995 Jacket: 'After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and then the properties of particles that follow from these principles. Quantum field theory then emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. The account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum elelctrodynamics to elementary partricle physics and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. ' 
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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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, Luminiferous aether - Wikipedia, the free encyclopdia, ' Luminiferous aether or ether (luminiferous meaning 'light-bearing') is the formerly postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), something that waves should not be able to do. The assumption of a spatial plenum (space completely filled with matter) of luminiferous aether, rather than a spatial vacuum, provided the theoretical medium that was required by wave theories of light. [. . .]
The negative outcome of the Michelson–Morley experiment (1887) suggested that the aether did not exist, a finding that was confirmed in subsequent experiments through the 1920s. This led to considerable theoretical work to explain the propagation of light without an aether. A major breakthrough was the special theory of relativity, which could explain why the experiment failed to see aether, but was more broadly interpreted to suggest that it was not needed. The Michelson–Morley experiment, along with the blackbody radiator and photoelectric effect, was a key experiment in the development of modern physics, which includes both relativity and quantum theory, the latter of which explains the particle-like nature of light.' back

A. Einstein, B. Podolsky and N. Rosen (1935_03_25), Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, ' In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete. back

Albert Einstein (1905), On the Electrodynamics of Moving Bodiesx, 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 (1915), The Field Equations of Gravitation, '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. My opinion regarding this issue, recently expressed at this place, was erroneous. Any physical theory equivalent to the special theory of relativity, can be included in the general theory of relativity by means of the absolute differential calculus, without that the latter gives any criterion for the admissibility of that theory. f back

Albert Einstein (1933), Herbert Spencer Lecture 1933: On the Method of Theoretical Physics , ' It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience. back

Andrea Reichenberger (2019_01), From Solvability to Formal Decidability: Revisiting Hilbert’s “Non-Ignorabimus” , Abstract The topic of this article is Hilbert’s axiom of solvability, that is, his conviction of the solvability of every mathematical problem by means of a finite number of operations. The question of solvability is commonly identified with the decisionproblem. Given this identification, there is not the slightest doubt that Hilbert’s conviction was falsified by Gödel’s proof and by the negative results for the de- cision problem. On the other hand, Gödel’s theorems do offer a solution, albeit a negative one, in the form of an impossibility proof. In this sense, Hilbert’s optimism may still be justified. Here I argue that Gödel’s theorems opened the door to proof theory and to the emarkably successful development of generalized as well as relativized realizations of Hilbert’s programs. Thus, the fall of absolute certainty came hand in hand with the rise of partially secure and reliable foundations of mathematical knowledge. Not all was lost and much was gained.' back

Aquinas, Summa I, 25, 3, Is God omnipotent?, '. . . God is called omnipotent because He can do all things that are possible absolutely; which is the second way of saying a thing is possible. For a thing is said to be possible or impossible absolutely, according to the relation in which the very terms stand to one another, possible if the predicate is not incompatible with the subject, as that Socrates sits; and absolutely impossible when the predicate is altogether incompatible with the subject, as, for instance, that a man is a donkey.' back

Aquinas, Summa, I, 8, 1, Is God in all things?, ' I answer that, God is in all things; not, indeed, as part of their essence, nor as an accident, but as an agent is present to that upon which it works. For an agent must be joined to that wherein it acts immediately and touch it by its power; hence it is proved in Phys. vii that the thing moved and the mover must be joined together. Now since God is very being by His own essence, created being must be His proper effect; . . .. Now God causes this effect in things not only when they first begin to be, but as long as they are preserved in being; . . .. Therefore as long as a thing has being, God must be present to it, according to its mode of being. back

Bell's theorem - Wikipedia, Bell's theorem - Wikipedia, the free encyclopdia, 'In theoretical physics, Bell's theorem (a.k.a. Bell's inequality) is a no-go theorem, loosely stating that:
No physical theory of local hidden variables can reproduce all of the predictions of quantum mechanics. [. . .]
Bell's theorem, derived in his seminal 1964 paper titled On the Einstein Podolsky Rosen paradox, has been called, on the assumption that the theory is correct, "the most profound in science". Perhaps of equal importance is Bell's deliberate effort to encourage and bring legitimacy to work on the completeness issues, which had fallen into disrepute. Later in his life, Bell expressed his hope that such work would "continue to inspire those who suspect that what is proved by the impossibility proofs is lack of imagination."' back

Boson - Wikipedia, Boson - Wikipedia, the free encyclopedia, 'In particle physics, bosons are particles with an integer spin, as opposed to fermions which have half-integer spin. From a behaviour point of view, fermions are particles that obey the Fermi-Dirac statistics while bosons are particles that obey the Bose-Einstein statistics. They may be either elementary, like the photon, or composite, as mesons. All force carrier particles are bosons. They are named after Satyendra Nath Bose. In contrast to fermions, several bosons can occupy the same quantum state. Thus, bosons with the same energy can occupy the same place in space.' back

Classical mechanics - Wikipedia, Classical mechanics - Wikipedia, the free encyclopedia, '' The earliest formulation of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on the 17th century foundational works of Sir Isaac Newton, and the mathematical methods invented by Newton, Gottfried Wilhelm Leibniz, Leonhard Euler and others to describe the motion of bodies under the influence of forces. Later, methods based on energy were developed by Euler, Joseph-Louis Lagrange, William Rowan Hamilton and others, leading to the development of analytical mechanics (which includes Lagrangian mechanics and Hamiltonian mechanics). These advances, made predominantly in the 18th and 19th centuries, extended beyond earlier works; they are, with some modification, used in all areas of modern physics' back

Claude E Shannon (1948), A Mathematical Theory of Communication, '' The recent development of various methods of modulation such as PCM and PPM which exchange T bandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication. A basis for such a theory is contained in the important papers of Nyquist1 and Hartley2 on this subject. In the present paper we will extend the theory to include a number of new factors, in particular the effect of noise in the channel, and the savings possible due to the statistical structure of the original message and due to the nature of the final destination of the information.
The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages. [. . .]
Actually, two signals can be reliably distinguished if they differ by only a small amount, provided this difference is sustained over a long period of time. Each sample of the received signal then gives a small amount of statistical information concerning the transmitted signal; in combination, these statistical indications result in near certainty. back

David Hilbert (1900), Mathmtical Problms: Lecture delivered before the Interntional Congress of Mathematicians, Paris 1900, back

David Hilbert (1925), On the Infinite, ' We encounter a completely different and quite unique conception of the notion of infinity in the important and fruitful method of ideal elements. The method of ideal elements is used even in elementary plane geometry. The points and straight lines of the plane originally are real, actually existent objects. One of the axioms that hold for them is the axiom of connection: one and only one straight line passes through two points. It follows from this axiom that two straight lines intersect at most at one point. There is no theorem that two straight lines always intersect at some point, however, for the two straight lines might well be parallel. Still we know that by introducing ideal elements, viz., infinitely long lines and points at infinity, we can make the theorem that two straight lines always intersect at one and only one point come out universally true. These ideal "infinite" elements have the advantage of making the system of connection laws as simple and perspicuous as possible. Another example of the use of ideal elements are the familiar complex-imaginary magnitudes of algebra which serve to simplify theorems about the existence and number of the roots of an equation.' back

David J Gross (1996_05_11), The Role of Symmetry in Fundamwental Physics, ' Until the 20th century principles of symmetry played little conscious role in theoretical physics. The Greeks and others were fascinated by the symmetries of objects and believed that these would be mirrored in the structure of nature. Even Kepler attempted to impose his notions of symmetry on the motion of the planets. Newton’s laws of mechanics embodied symmetry principles, notably the principle of equivalence of inertial frames, or Galilean invariance. These symmetries implied conservation laws. Although these conservation laws, especially those of momentum and energy, were regarded to be of fundamental importance, these were regarded as consequences of the dynamical laws of nature rather than as consequences of the symmetries that underlay these laws. Maxwell’s equations, formulated in 1865, embodied both Lorentz invariance and gauge invariance. But these symmetries of electrodynamics were not fully appreciated for over 40 years or more' back

Dirac equation - Wikipedia, Dirac equation - Wikipedia, the free encyclopedia, 'In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1⁄2 massive particles such as electrons and quarks, for which parity is a symmetry, and is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It accounted for the fine details of the hydrogen spectrum in a completely rigorous way.' back

Elementary particle - Wikipedia, Elementary particle - Wikipedia, the free encyclopedia, ' In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include the fundamental fermions (quarks, leptons, antiquarks, and antileptons), which generally are "matter particles" and "antimatter particles", as well as the fundamental bosons (gauge bosons and the Higgs boson), which generally are "force particles" that mediate interactions among fermions. A particle containing two or more elementary particles is a composite particle.' back

Fermion - Wikipedia, Fermion - Wikipedia, the free encyclopedia, 'In particle physics, fermions are particles with a half-integer spin, such as protons and electrons. They obey the Fermi-Dirac statistics and are named after Enrico Fermi. In the Standard Model there are two types of elementary fermions: quarks and leptons. . . . In contrast to bosons, only one fermion can occupy a quantum state at a given time (they obey the Pauli Exclusion Principle). Thus, if more than one fermion occupies the same place in space, the properties of each fermion (e.g. its spin) must be different from the rest. Therefore fermions are usually related with matter while bosons are related with radiation, though the separation between the two is not clear in quantum physics. back

Formalism (philosophy of mathematics) - Wikipedia, Formalism (philosophy of mathematics) - Wikipedia, the free encyclopedia, 'In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess."
A major figure of formalism was David Hilbert, whose program was intended to be a complete and consistent axiomatization of all of mathematics.[9] Hilbert aimed to show the consistency of mathematical systems from the assumption that the "finitary arithmetic" (a subsystem of the usual arithmetic of the positive integers, chosen to be philosophically uncontroversial) was consistent (i.e. no contradictions can be derived from the system). back

Gamma matrices - Wikipedia, Gamma matrices - Wikipedia, the free encyclopedia, 'In mathematical physics, the gamma matrices, {γ⁰, γ¹, γ²,γ³}, also known as the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cl_1,3(R). When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of space time acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate space-time computations in general, and in particular are fundamental to the Dirac equation for relativistic spin-1/2 particles.' back

Hamiltonian mechanics - Wikipedia, Hamiltonian mechanics - Wikipedia, the free encyclopedia, ' Hamiltonian mechanics is a mathematically sophisticated formulation of classical mechanics. Historically, it contributed to the formulation of statistical mechanics and quantum mechanics. Hamiltonian mechanics was first formulated by William Rowan Hamilton in 1833, starting from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788. Like Lagrangian mechanics, Hamiltonian mechanics is equivalent to Newton's laws of motion in the framework of classical mechanics.' 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

Hermann Minkowski - Wikipedia, Hermann Minkowski - 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 ds² = x² + y² + z² + (ict)². back

Hermann Minkowski (1908), Space and Time – lecture given at the 80th Meeting of the Natural Scientists in Cologne on September 21, 1908., ' Gentlemen! The views of space and time which I want to present to you arose from the domain of experimental physics, and therein lies their strength. Their tendency is radical. From now onwards space by itself and time by itself will recede completely to become mere shadows and only a type of union of the two will still stand independently on its own.' back

International Organization for Standardization - Wikipedia, International Organization for Standardization - Wikipedia, th free ncyclopedia, ' The International Organization for Standardization (ISO) [. . .] is an independent, non-governmental, international standard development organization composed of representatives from the national standards organizations of member countries. [. . .]
ISO was founded on 23 February 1947, and it has published over 25,000 international standards as of July 2024, covering almost all aspects of technology and manufacturing. It has over 800 technical committees (TCs) and subcommittees (SCs) to take care of standards development.' back

J. Clerk Maxwell (1865), A Dynamical Theory of the Electromagnetic Field, '(3) The theory I propose may therefore be called a theory of the Elecromagnetic Field, because it has to do with the space in the neighbourhood of electric or magnetic bodies, and it may be called a Dynamical Theory because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced.' back

Jacquard machine - Wikipedia, Jacquard machine - Wikipedia, the free encyclopedia, ' The Jacquard machine is a device fitted to a loom that simplifies the process of manufacturing textiles with such complex patterns as brocade, damask and matelassé. The resulting ensemble of the loom and Jacquard machine is then called a Jacquard loom. The machine was patented by Joseph Marie Jacquard in 1804, based on earlier inventions by the Frenchmen Basile Bouchon (1725), Jean Baptiste Falcon (1728), and Jacques Vaucanson (1740). The machine was controlled by a "chain of cards"; a number of punched cards laced together into a continuous sequence. Multiple rows of holes were punched on each card, with one complete card corresponding to one row of the design. [. . .]
The term "Jacquard" is not specific or limited to any particular loom, but rather refers to the added control mechanism that automates the patterning. The process can also be used for patterned knitwear and machine-knitted textiles such as jerseys.
This use of replaceable punched cards to control a sequence of operations is considered an important step in the history of computing hardware, having inspired Charles Babbage's Analytical Engine. ' back

Juan Yin et al (2013_03_04), Lower Bound on the Speed of Nonlocal Correlations without Locality and Measurement Choice Loopholes , ' In their well-known paper, Einstein, Podolsky, and Rosen called the nonlocal correlation in quantum entanglement a “spooky action at a distance.” If the spooky action does exist, what is its speed? All previous experiments along this direction have locality and freedom-of-choice loopholes. Here, we strictly closed the loopholes by observing a 12 h continuous violation of the Bell inequality and concluded that the lower bound speed of spooky action was 4 orders of magnitude of the speed of light if Earth’s speed in any inertial reference frame was less than 10^-3 time the speed of light. ' back

Klein-Gordon equation - Wikipedia, Klein-Gordon equation - W ikipedia, th free encyclopedia, ' In particle physics, the Klein–Gordon equation is a relativistic wave equation for spinless particles. It was discovered in 1926 as the relativistic generalization of the Schrödinger equation, developed independently by numerous authors, among them Oskar Klein and Walter Gordon, after whom it is commonly named. Within relativistic quantum mechanics, it suffers from numerous conceptual problems that are only resolved in quantum field theory, where the equation describes the dynamics of spin-0 fields. Mathematically, it is a linear second-order hyperbolic partial differential equation that is manifestly Lorentz covariant and can be viewed as the wave equation form of the relativistic energy–momentum relation. It plays a fundamental role in many areas of modern physics, such as quantum field theory, particle physics, and cosmology.' back

Louis de Broglie (1929), Nobel Lecture: The Wave Nature of the Electron, ' 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. . . . 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 predicta 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

Luminiferous aether - Wikipedia, Luminiferous aether - Wikipedia, he free eencyclopedia, 'Luminiferous aether or ether (luminiferous meaning 'light-bearing') is the formerly postulated medium for the propagation of light.[2] It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), something that waves should not be able to do. The assumption of a spatial plenum (space completely filled with matter) of luminiferous aether, rather than a spatial vacuum, provided the theoretical medium that was required by wave theories of light. back

Mary Sirridge (1999), "Quam videndo intus dicimus": Seeing and Saying in De Trinitate XV, ' What is being asserted is that thought has the same form as seeing or speaking respectively, i.e., that it works essentially like seeing or speaking, that thought is a formal and functional isomorph of seeing or speaking.' back

Matrix mechanics - Wikipedia, Matrix mechanics - Wikipedia, the free encyclopedia, 'Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps occur. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, and is the basis of Dirac's bra-ket notation for the wave function. 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

Minkowski spacetime - Wikipedia, Minkowski spacetime - Wikipedia, the free encyclopedia, ' By1908 Minkowski recalized 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 Laws of Motion - Wikipedia, Newton's Laws of Motion - Wikipedia, the free encyclopedia, 'Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows:

A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force.
At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time.
If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

Philosophiae Naturalis Principia Mathematica - Wikipedia, Philosophiae Naturalis Principia Mathematica - Wikipedia, the free encyclopedia, 'The Philosophiæ Naturalis Principia Mathematica (Latin: "mathematical principles of natural philosophy" often Principia or Principia Mathematica for short) is a three-volume work by Isaac Newton published on 5 July 1687. It contains the statement of Newton's laws of motion forming the foundation of classical mechanics, as well as his law of universal gravitation and a derivation of Kepler's laws for the motion of the planets (which were first obtained empirically). The Principia is widely regarded as one of the most important scientific works ever written.' back

Planck constant - Wikipedia, Planck constant - Wikipedia, the free encyclopedia, ' Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to replacing the metal cylinder, called the International Prototype of the Kilogram (IPK), that had defined the kilogram since 1889. [. . .] For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.626 070 150 × 10-34 J⋅s exactly. ' back

Qian, Vamivakas & Eberly (2018_03_14), Bohr’s Complementarity Completed with Entanglement, In the Beginning Ninety years ago in 1927, at an international congress in Como, Italy, Niels Bohr gave an address which is recognized as the first instance in which the term “complementarity”, as a physical concept, was spoken publicly revealing Bohr’s own thinking about Louis de Broglie’s “duality”. Bohr had very slowly accepted duality as a principle of physics: close observation of any quantum object will reveal either wave-like or particle-like behavior, one or the other of two fundamental and complementary features. Little disagreement exists today about complementarity’smportance and broad applicability in quantum science. [. . .]
Confusion evident in Como following his talk was not eliminated by Bohr’s article, and complementarity has been subjected to nine decades of repeated examination ever since with no agreed resolution. Semi-popular treatments as well as expert examinations show that the topic cannot be avoided, and complementarity retains its central place in the interpretation of quantum mechanics. However, recent approaches by our group and others to the underlying notion of coherence now allow us to present a universal formulation of complementarity that may signal the end to the confusion. We demon- strate a new relationship that constrains the behavior of an electromagnetic field (quantum or classical) in the fundamental context of two-slit experiments. We show that entanglement is the ingredient needed to completeBohr’s formulation of complementarity, debated for decades because of its incompleteness.' back

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

Renormalization - Wikipedia, Renormalization - Wikipedia, the free encyclopedia, ' Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of quantities to compensate for effects of their self-interactions. But even if it were the case that no infinities arose in loop diagrams in quantum field theory, it could be shown that renormalization of mass and fields appearing in the original Lagrangian is necessary.' 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

Schrödinger equation - Wikipedia, Schrödinger equation - Wikipedia, the free encyclopedia, ' The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system.  Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger, an Austrian physicist, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.
Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterization of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave. The equation predicted bound states of the atom in agreement with experimental observations.' back

Sin-Itiro Tomonaga (1965), Nobel Lecture: Development of Quantum Electrodynamics: Personal recollections, ' (1) In 1932, when I started my research career as an assistant to Nishina, Dirac published a paper in the Proceedings of the Royal Society, London. In this paper, he discussed the formulation of relativistic quantum mechanics, especially that of electrons interacting with the electromagnetic field. At that time a comprehensive theory of this interaction had been formally completed by Heisenberg and Pauli, but Dirac was not satisfied with this theory and tried to construct a new theory from a different point of view. Heisenberg and Pauli regarded the (electromagnetic) field itself as a dynamical system amenable to the Hamiltonian treatment; its interaction with particles could be described by an interaction energy, so that the usual method of Hamiltonian quantum mechanics could be applied. On the other hand, Dirac thought that the field and the particles should play essentially different roles. That is to say, according to him, “the role of the field is to provide a means for making observations of a system of particles” and therefore “we cannot suppose the field to be a dynamical system on the same footing as the particles and thus be something to be observed in the same way as the particles”. [. . .]' 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

Theorema Egregium - Wikpedia, Theorema Egregium - Wikipedia, the free encyclopedia, 'Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a foundational result in differential geometry proved by Carl Friedrich Gauss that concerns the curvature of surfaces. The theorem says that the Gaussian curvature of a surface can be determined entirely by measuring angles, distances and their rates on the surface itself, without further reference to the particular way in which the surface is embedded in the ambient 3-dimensional Euclidean space. Thus the Gaussian curvature is an intrinsic invariant of a surface.' back

Thomas Aquinas, De Ente et Essentia, Latin text of one of Thomas Aquinas early works.
Textum a L. Baur Monasterii Westfalorum 1933 editum emendatum a J. Koch ac translatum in taenias magneticas a Roberto Busa SJ. denuo recognovit Enrique Alarcón atque instruxit<
[69871] De ente et essentia, pr.
Quia parvus error in principio magnus est in fine, secundum philosophum in I Caeli et Mundi, ens autem et essentia sunt quae primo intellectu concipiuntur, ut dicit Avicenna in principio suae metaphysicae, ideo ne ex eorum ignorantia errare contingat, ad horum difficultatem aperiendam dicendum est quid nomine essentiae et entis significetur et quomodo in diversis inveniatur et quomodo se habeat ad intentiones logicas, scilicet genus, speciem et differentiam. Quia vero ex compositis simplicium cognitionem accipere debemus et ex posterioribus in priora devenire, ut, a facilioribus incipientes, convenientior fiat disciplina, ideo ex significatione entis ad significationem essentiae procedendum est. back

Turing machine - Wikipedia, Turing machine - Wikipedia, the free encyclopedia, ' A Turing machine is a hypothetical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a computer. The "machine" was invented in 1936 by Alan Turingwho called it an "a-machine" (automatic machine). The Turing machine is not intended as practical computing technology, but rather as a hypothetical device representing a computing machine. Turing machines help computer scientists understand the limits of mechanical computation.' back