page 3: From Aristotle's energeia to Planck's quantum
3.1: A story from Ancient Greece
When Plato proposed eternal forms to guide the structure of the world he was following a suggestion by Parmenides (5th - 6th century bce). We have fragments of a didactic poem from Parmenides describing his education by a Goddess. In this poem he proposed a foundation for science, based on the proposition that permanently true knowledge is only possible if the subject of knowledge is immutable or invariant. John Palmer: Parmenides
The Goddess contrasted the unshaken heart of well-rounded reality with the notions of mortals, in which there is no genuine trustworthiness. (Fr. 1.28b-32)
She went on to describe true reality, what is:
First, it is ungenerated and deathless. Further it it is whole and uniform, motionless . . .
. . . it is perfected from every side, like the bulk of a well-rounded globe, from the middle equal every way: for that it be neither any greater nor any smaller in this place or in that is necessary; for neither is there non-being, which would stop it reaching to its like, nor is What Is such that it might be more than What Is here and less there. Since it is all inviolate, for it is equal to itself from every side, it extends uniformly in limits.
This suite of attributes have remained central to the description of what is, also known as God, for 2500 years. Parmenides' student Zeno supported Parmenides' position with a series of subtle arguments to show that motion is impossible. Zeno's paradoxes - Wikipedia
Plato guessed that Parmenides what is is a system of invisible, eternal forms which guide the structure of the world and our knowledge of it. Unlike Parmenides, Plato's student Aristotle considered motion to be an integral part of realty but he needed to preserve the stability of Plato's forms. He devised the theory of matter and form known as hylomorphism to explain changes in the world. Theory of Forms - Wikipedia, Hylomorphism - Wikipedia
We may see hylomorphism as a form of two factor authentication. In its abstract form, this theory explains that neither matter nor form can exist on their own, but together they make a real thing. Change is possible because in reality matters and forms could be swapped around to make different things. Thomas Ainsworth: Form vs. matter
Hylomorphism, in a more abstract form, is Aristotle's hypothesis of potency and act. Aristotle saw matter as potentially something and form as the element that made it actually something. The theory of potency and act is built around one axiom: no potential can actualize itself. This led him to postulate an unmoved mover as the source of all motion. Unmoved mover - Wikipedia
Aristotle saw motion as a transition from potential to actuality. It follows that nothing can move itself, everything is moved by something else. But there must be a source of motion, otherwise there would be no motion. This is the unmoved mover which is, by definition, pure actuality. In it and through it, all potentials are actualized.
Aristotle's works gradually entered the newly formed Christian universities of Europe when contact was established between the two halves of the old Roman empire, partly a consequence of the Christian Crusades to gain access to the Holy Land. Albert the Great and Thomas Aquinas used Aristotle's work to set up a new philosophical and scientific foundation for Christian theology. Aquinas developed a new Catholic model of God (which has since become standard) from Aristotle's theological treatment of the unmoved mover. Crusades - Wikipedia, Aristotle Metaphysics XII, vi, 2
3.2: Aristotle and the definition of God
Aristotle was among the first to study action. He coined two words for it, energeia (ενεργεια) and entelecheia (εντελεχεια). Energeia may be translated as being-at-work and entelecheia as completeness, the end of work. Both these terms are contrasted to potentiality dunamis (δυναμις), which can mean either active power or passivity. In Aristotle's theory the potential is passive. In modern physics, it is active, identical but opposite to kinetic energy, the two forms adding up to zero, like energy and anti-energy. Aristotle's axiom does not hold. The action of a pendulum transforms actual (kinetic) energy into potential and back again as it swings up and down. It may be that the total energy of the Universe is zero, the actual energy of matter being exactly balanced by the potential energy of gravitation. Zero-energy universe - Wikipedia
Aristotle thought that the unmoved mover was an integral part of the Cosmos and that the world is eternal so it had no need for a creator. Aquinas used Aristotle's argument to establish the existence of God but, faithful to his religion, placed this creator outside the Universe. The doctrine of the Summa has never been supeseded in the Church. It remains officially endorsed in Canon Law. Aquinas' definition of God as actus purus is, by papal fiat, standard. Aquinas's philosophy has been codified, reduced to 24 tutae normae directivae (safe directive norms), and so sterilized by the Church, but there is plenty of inspiration in his enormous body of writing. Aristotle, Metaphysics XII : God's happiness (1072b25-31), Aquinas Summa I, 2, 3: Does God exist?, Holy See: Code of Canon Law: Canon 252 § 3: The Formation of Clerics
Implicit in these ancient ideas are the dichotomies of God and the World, Heaven and Earth, Matter and Spirit. The leading idea is that matter is dead and inert. It cannot move itself. It cannot be the seat of understanding. It cannot be creative. Since the advent of modern physics, founded on energy, relativity and quantum theory, these ideas are exactly wrong. Physics based on quantum theory describes a Universe in perpetual motion as a gigantic network of communication (which is a form of computation) equivalent to a mind.
Medieval scholars, engineers, farmers and parents gradually learnt that ancient texts and pure reason could not fully explain the world. This attitude was strongly supported by astronomy, the first science based on instrumental observation. Galileo's telescope led to radical developments in astronomy, and some conflict with ancient religious beliefs. Galileo's opinion that mathematics is the language of the Universe reached a high point in Isaac Newton's description of gravitation. Newton showed that the Moon in the heavens and falling apples on Earth are guided by the same invisible structure. Wisely, he declined to speculate about what this structure might be and left it in the hands of the divinity, the traditional answer to all insoluble problems. Galileo affair - Wikipedia, Isaac Newton (1729, 1972): Philosophiae Naturalis Principia Mathematica, Isaac Newton (1726): General Scholium to Principia
3.3: From Newton to Lagrange
Newton's work sparked huge developments in mathematics and physics which still continue. On a more philosophical level, Maupertuis (1698-1759) speculated that a wise creator would have made the world as efficient as possible, and started a train of thought that lead to Hamilton's principle, the amalgamation of the calculus of variations with Langrangian mechanics. We might also imagine that the effectiveness of Hamilton's principle is the result of natural evolution selecting the most efficient mechanical processes to dominate the physical world.
Joseph-Louis Lagrange sought to express classical Newtonian mechanics in a form that would make it easier to study many body problems like the solar system. His work, Mecanique Analytique, placed mechanics on an algebraic rather than a geometric foundation. Joseph-Louis Lagrange (1811): Mécanique analytique: Volume 1
In the Lagrangian approach the action S associated with an event x that takes place between times t1 and t2 is expressed by the action functional
S(x) = ∫ L dt
The Lagrangian L = (T(t) − V(t)), where T and V are functions of the kinetic and potential energy of the system. Lagrangian mechanics postulates Hamilton's principle that the actual trajectory taken by a particle whose motion is constrained by T and V coincides with a stationary value of S (a fixed point in the action) which may be found using Euler's calculus of variations. Lagrangian mechanics - Wikipedia, Hamilton's principle - Wikipedia, Calculus of variations - Wikipedia
Lagrangian mechanics is very versatile and serves as a bridge between classical and quantum mechanics, quantum field theory and physical problems in general. On this basis, we might understand mechanics in spacetime as the study of action in the relationship between kinetic and potential energy.
3.4: Max Planck and quantum mechanics
Quantum mechanics began with Planck's discovery, in 1900, that action is quantized and that the quantum of action h is the constant of proportionality between the energy of radiation and its frequency. This is now the fundamental equation of quantum theory, E = ℏω where ℏ is the reduced Planck constant, h / 2π and the frequency is expressed in radians per second, ω, understood as the rate of change of the phase of a quantum state ∂ | φ⟩ / ∂ t. Max Planck (1901): On the Law of Distribution of Energy in the Normal Spectrum
The quantum of action is a now precisely fixed natural constant which is used as a foundation for the natural set of units. We might look upon it as an invariant solution to a Lagrangian variation problem established at the very root of universal structure. NIST: Kilogram, Mass and Planck's Constant
For Aristotle and Aquinas action is a metaphysical term, but here we see that it has a physical realization, providing a bridge between physics and metaphysics in a way analogous to its role in coupling classical and quantum mechanics. Dirac found that this role goes deeper, and Feynman used it to create a new expression of quantum mechanics, the path integral formulation. Path integral formulation - Wikipedia
Quantum mechanics came of age in the 1920's in two versions known as wave mechanics (the Schrödinger equation) and matrix mechanics (first seen by Heisenberg). These were shown to be equivalent by Schrödinger, given a clear abstract symbolic expression by Dirac and a sound mathematical foundation by von Neumann. Dirac notes that the major features of quantum mechanics are linearity and superposition. Schrödinger equation - Wikipedia, Matrix mechanics - Wikipedia, Carlo Rovelli (2021): Helgoland, Paul Dirac (1983): The Principles of Quantum Mechanics, chapter 1, John von Neumann (2014): Mathematical Foundations of Quantum Mechanics
3.5: Action, logic and theology
When modern physicists talk about creating a theory of everything, what they have in mind is a unified theory of the four fundamental forces, gravitation, electromagnetism, the weak force and the strong force. From the theological point of view this is a very limited ambition. A real theory of everything would be a theology, able to describe every detail of both the creator and the creation. Theology itself paints the broad picture, relying on all the other sciences and arts to fill in the details. At present we have a good picture of the development of the Universe since it was about 300 000 years old. Eventually, perhaps, a theological picture will take us back to the beginning.
All the discussion above has assumed the existence of spacetime and is built on our spacetime experiences, but for Aquinas action is the definition of god (actus purus) and the traditional God predates spacetime.
Quantum mechanics in Minkowski spacetime interprets the time rate of action as energy (E = hω) and the spatial rate of action as momentum (p = h / λ for a photon wavelength λ). In the Hilbert space that underlies Minkowski space, the quantum of action behaves as a logical operator. This is represented in the quantum theory of communication and computation as a linear operator which can be represented mathematically as a matrix. Nielsen & Chuang (2016): Quantum Computation and Quantum Information, Matrix (mathematics) - Wikipedia
Each elementary event, like the interaction of an electron and a photon, involves one quantum of action. When an atom emits a photon with spin 1, corresponding to one quantum of action, we understand that the source of the photon is an atomic electron which changes to an orbital with one Plank unit unit less action and a loss of energy which is reflected in the frequency of the photon emitted.
Although this event looks quite simple, the quantum field theory calculation of the energy involved, and therefore the frequency of the emitted photon can be quite complex, and this complexity is represented by the mathematical model of the event. Richard Feynman, one of the inventors of quantum electrodynamics, had this to say about the current form of precise calculations in his Nobel Prize Lecture:
I don’t think we have a completely satisfactory relativistic quantum-mechanical model, even one that doesn’t agree with nature, but, at least, agrees with the logic that the sum of probability of all alternatives has to be 100%. Therefore, I think that the renormalization theory is simply a way to sweep the difficulties of the divergences of electrodynamics under the rug. I am, of course, not sure of that. Richard P. Feynman (1965): Nobel Lecture: The Development of the Space-Time View of Quantum Electrodynamics
The problem facing physicists is that they are trying to explain phenomena in spacetime which are being worked out behind the scenes in a structure which antedates and underlies spacetime. From a theological point of view we may see quantum theory is not so much an arithmetic but as a logical theory. It is therefore closely related to mental function and opens the way for us to consider the physical Universe as the physical mind of God, analogous to our brains that implement our minds. The authors of may have been feeling this when they wrote: So God created man in his own image, in the image of God created he him; male and female created he them (Gn I:27).
(Revised Monday 29 July 2024)
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Notes and references
Further reading
Books
Dirac, P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)
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Dirac (1983), P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)
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Lonergan (1992), Bernard J F, Insight: A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '. . . Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding'
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Lonergan (1997), Bernard J F, and Robert M. Doran, Frederick E. Crowe (eds), Verbum: Word and Idea in Aquinas (Collected Works of Bernard Lonergan volume 2), University of Toronto Press 1997 Jacket: 'Verbum is a product of Lonergan's eleven years of study of the thought of Thomas Aquinas. The work is considered by many to be a breakthrough in the history of Lonergan's theology . . .. Here he interprets aspects in the writing of Aquinas relevant to trinitarian theory and, as in most of Lonergan's work, one of the principal aims is to assist the reader in the search to understand the workings of the human mind.'
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Newton (1729, 1972), Isaac, Philosophiae Naturalis Principia Mathematica, Harvard University Press 1729, 1972 One of the most important contributions to human knowledge. First translated from the Latin by Andrew Motte in 1729,
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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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Rovelli (2021), Carlo, and Erica Segre & Simon Carnell (translators), Helgoland, Allen Lane / Penguin 2021 ' In June 1925, twenty-three-year-old Werner Heisenberg, suffering from hay fever, retreated to a small, treeless island in the North Sea called Helgoland. It was there that he came up with one of the most transformative scientific concepts - quantum theory.
Almost a century later, quantum physics has given us many startling ideas - ghost waves, distant objects that seem magically connected to each other, cats that are both dead and alive. At the same time, countless experiments have led to practical applications that shape our daily lives. Today our understanding of the world around us is based on this theory. And yet it is still profoundly mysterious.
In this enchanting book, Carlo Rovelli, one of our most celebrated scientists, tells the extraordinary story of quantum physics and reveals its deep meaning- a world made of substances is replaced by a world made of relations, each particle responding to another in a never ending game of mirrors.'
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Links
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 |
Aristotle, Metaphysics XII (1072b25-31): God's happiness, 'If, then, the happiness which God always enjoys is as great as that which we enjoy sometimes, it is marvellous; and if it is greater, this is still more marvellous. Nevertheless it is so. Moreover, life belongs to God. For the actuality of thought is life, and God is that actuality; and the essential actuality of God is life most good and eternal. We hold, then, that God is a living being, eternal, most good; and therefore life and a continuous eternal existence belong to God; for that is what God is.' (1072b25-31) back |
Calculus of variations - Wikipedia, Calculus of variations - Wikipedia, the free encylopedia, ' The calculus of variations may be said to begin with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). It immediately occupied the attention of Jakob Bernoulli and the Marquis de l'Hôpital, but Leonhard Euler first elaborated the subject, beginning in 1733. Lagrange was influenced by Euler's work to contribute significantly to the theory. After Euler saw the 1755 work of the 19-year-old Lagrange, Euler dropped his own partly geometric approach in favor of Lagrange's purely analytic approach and renamed the subject the calculus of variations in his 1756 lecture Elementa Calculi Variationum.' back |
Crusades - Wikipedia, Crusades - Wikipedia, the free encyclopedia, ' The Crusades were a series of intermittent military campaigns in the years from 1096 to 1487, sanctioned by various Popes. In 1095 the Byzantine Emperor, Alexios I, sent an ambassador to Pope Urban II requesting military support in the Byzantines' conflict with the westward migrating Turks in Anatolia. The Pope responded by calling Catholics to join what later became known as the First Crusade. One of Urban's stated aims was to guarantee pilgrims access to the holy sites in the Holy Land that were under Muslim control while his wider strategy was to reunite the Eastern and Western branches of Christendom, divided after their split in 1054, and establish himself as head of the united Church. This initiated a complex 200-year struggle in the region.' back |
Cybernetics - Wikipedia, Cybernetics - Wikipedia, the free encyclopedia, ' Cybernetics is a transdisciplinary approach for exploring regulatory systems, their structures, constraints, and possibilities. Cybernetics is relevant to the study of systems, such as mechanical, physical, biological, cognitive, and social systems. Cybernetics is applicable when a system being analyzed is involved in a closed signaling loop; that is, where action by the system generates some change in its environment and that change is reflected in that system in some manner (feedback) that triggers a system change, originally referred to as a "circular causal" relationship.' back |
Galileo affair - Wikipedia, Galileo affair - Wikipedia, the free encyclopedia, ' The Galileo affair (Italian: il processo a Galileo Galilei) began around 1610 and culminated with the trial and condemnation of Galileo Galilei by the Roman Catholic Inquisition in 1633. Galileo was prosecuted for his support of heliocentrism, the astronomical model in which the Earth and planets revolve around the Sun at the centre of the Solar System. ' back |
Hamilton's principle - Wikipedia, Hamilton's principle - Wikipedia, the free encyclopedia, 'In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action . . . It states that the dynamics of a physical system is determined by a variational problem for a functional based on a single function, the Lagrangian, which contains all physical information concerning the system and the forces acting on it.' back |
Holy See, Code of Canon Law: Canon 252 §3: The formation of Clerics, ' There are to be classes in dogmatic theology, always grounded in the written word of God together with sacred tradition; through these, students are to learn to penetrate more intimately the mysteries of salvation, especially with St. Thomas as a teacher. There are also to be classes in moral and pastoral theology, canon law, liturgy, ecclesiastical history, and other auxiliary and special disciplines, according to the norm of the prescripts of the program of priestly formation.' back |
Hylomorphism - Wikipedia, Hylomorphism - Wikipedia, the free encyclopedia, 'Hylomorphism (Greek ὑλο- hylo-, "wood, matter" + -morphism < Greek μορφή, morphē, "form") is a philosophical theory developed by Aristotle, which analyzes substance into matter and form. Substances are conceived of as compounds of form and matter.' 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 |
Isaac Newton (1726), General Scholium, '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 |
Jeffrey Nicholls (1967), How universal is the universe?, ' 61 The future is beyond our comprehension, but we can get an idea of it and speed its coming by studying what we already have. Contemplating the size and wonder of the universe as it stands in the light of its openness to the future must surely be a powerful incentive to men to love God. We have come a long way since the little world of St Thomas. Ours is open to all things, even participating in god. This is what I mean by universal. ' 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: |
John von Neumann (2014), Mathematical Foundations of Quantum Mechanics, ' Mathematical Foundations of Quantum Mechanics by John von Neumann translated from the German by Robert T. Beyer (New Edition) edited by Nicholas A. Wheeler. Princeton UP Princeton & Oxford. Preface: ' This book is the realization of my long-held intention to someday use the resources of TEX to produce a more easily read version of Robert T. Beyer’s authorized English translation (Princeton University Press, 1955) of John von Neumann’s classic Mathematische Grundlagen der Quantenmechanik (Springer, 1932).'This content downloaded from 129.127.145.240 on Sat, 30 May 2020 22:38:31 UTC back |
Joseph-Louis Lagrange (1811), Mécanique analytique Volume 1, ' On a déjà plusieurs Traités de Mécanique , mais le plan de celui - ci est entièrement neuf . Je me suis proposé de réduire la théorie de cette Science , et l'art de résoudre les problèmes qui s'y rapportent , à des formules générales, dont le simple développement donne toutes les équations nécessaires pour la solution de chaque problème.' 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 |
Matrix (mathematics) - Wikipedia, Matrix (mathematics) - Wikipedia, the free encyclopedia, 'In mathematics, a matrix (plural matrices) is a rectangular array—of numbers, symbols, or expressions, arranged in rows and columns—that is treated in certain prescribed ways. . . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps.' 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 |
Max Planck (1901), On the Law of Distribution of Energy in the Normal Spectrum, Annalen der Physik, vol. 4, p. 553 ff (1901) 'The recent spectral measurements made by O. Lummer and E. Pringsheim and even more notable those by H. Rubens and F. Kurlbaum which together confirmed an earlier result obtained by H. Beckmann show that the law of energy distribution in the normal spectrum, first derived by W. Wien from molecular-kinetic considerations and later by me from the theory of electromagnetic radiation, is not valid generally.' back |
NIST, Kilogram, Mass and Planck's Constant, ' For many observers, the connection between mass on the scale of a liter of water and a constant deriving from the very earliest days of quantum mechanics may not be immediately obvious. The scientific context for that connection is suggested by a deep underlying relationship between two of the most celebrated formulations in physics. One is Einstein's famous E = mc2, where E is energy, m is mass and c is the speed of light. The other expression, less well known to the general public but fundamental to modern science, is E = hν, the first "quantum" expression in history, stated by Max Planck in 1900. Here, E is energy, ν is frequency (the ν is not a “v” but instead the lowercase Greek letter nu), and h is what is now known as the Planck constant.' back |
Path integral formulation - Wikipedia, Path integral formulation - Wikipedia, the free encyclopedia, 'The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a quantum amplitude. . . . This formulation has proved crucial to the subsequent development of theoretical physics, since it provided the basis for the grand synthesis of the 1970s which unified quantum field theory with statistical mechanics. . . . ' back |
Richard P. Feynman (1965), Nobel Lecture: The Development of the Space-Time View of Quantum Electrodynamics, Nobel Lecture, December 11, 1965: We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover all the tracks, to not worry about the blind alleys or to describe how you had the wrong idea first, and so on. So there isn’t any place to publish, in a dignified manner, what you actually did in order to get to do the work, although, there has been in these days, some interest in this kind of thing. Since winning the prize is a personal thing, I thought I could be excused in this particular situation, if I were to talk personally about my relationship to quantum electrodynamics, rather than to discuss the subject itself in a refined and finished fashion. Furthermore, since there are three people who have won the prize in physics, if they are all going to be talking about quantum electrodynamics itself, one might become bored with the subject. So, what I would like to tell you about today are the sequence of events, really the sequence of ideas, which occurred, and by which I finally came out the other end with an unsolved problem for which I ultimately received a prize.' back |
Rolf Landauer (1991), The physical nature of information, Abstract Physics Letters A 217 (1996) 188-193 The physical nature of information Rolf Landauer 1 IBM T.J. Watson Research Center, P.O. Box 218. Yorktown Heights, NY 10598, USA Received 9 May 1996 Communicated by V.M.Agranovich 15 July 1996 Information is inevitably tied to a physical representation and therefore to restrictions and possibilities related to the laws of physics and the parts available in the universe. Quantum mechanical superpositions of information bearing states can be used, and the real utility of that needs to be understood. Quantum parallelism in computation is one possibility and will be assessed pessimistically. The energy dissipation requirements of computation, of measurement and of the communications link are discussed. The insights gained from the analysis of computation has caused a reappraisal of the perceived wisdom in the other two fields. A concluding section speculates about the nature of the laws of physics, which are algorithms for the handling of information, and must be executable in our real physical universe.' back |
Schrödinger equation - Wikipedia, Schrödinger equation - Wikipedia, the free encyclopedia, ' In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a quantum system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger. . . . In classical mechanics Newton's second law, (F = ma), is used to mathematically predict what a given system will do at any time after a known initial condition. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). It is not a simple algebraic equation, but in general a linear partial differential equation, describing the time-evolution of the system's wave function (also called a "state function").' back |
Second Vatican Council (1965), Dogmatic Constitution on Divine Revelation 'Dei Verbum', Solemnly promulgated by His Holiness Pope Paul VI on November 18, 1965. ' Preface: 1. Hearing the word of God with reverence and proclaiming it with faith, the sacred synod takes its direction from these words of St. John: "We announce to you the eternal life which dwelt with the Father and was made visible to us. What we have seen and heard we announce to you, so that you may have fellowship with us and our common fellowship be with the Father and His Son Jesus Christ" (1 John 1:2-3). Therefore, following in the footsteps of the Council of Trent and of the First Vatican Council, this present council wishes to set forth authentic doctrine on divine revelation and how it is handed on, so that by hearing the message of salvation the whole world may believe, by believing it may hope, and by hoping it may love.' back |
Theory of Forms - Wikipedia, Theory of Forms - Wikipedia, the free encyclopedia, 'Plato's theory of Forms or theory of Ideas asserts that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality. When used in this sense, the word form or idea is often capitalized. Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggest that these Forms are the only true objects of study that can provide us with genuine knowledge; thus even apart from the very controversial status of the theory, Plato's own views are much in doubt. Plato spoke of Forms in formulating a possible solution to the problem of universals.' back |
Thomas Ainsworth (Stanford Encyclopedia of Philosophy), Form vs. Matter, 'Aristotle famously contends that every physical object is a compound of matter and form. This doctrine has been dubbed “hylomorphism”, a portmanteau of the Greek words for matter (hulê) and form (eidos or morphê). Highly influential in the development of Medieval philosophy, Aristotle’s hylomorphism has also enjoyed something of a renaissance in contemporary metaphysics.' back |
Thomas Aquinas, Commentary on Aristotle De Anima 430a10-430a25, ' § 731. The reason why Aristotle came to postulate an agent intellect was his rejection of Plato’s theory that the essences of sensible things existed apart from matter, in a state of actual intelligibility. For Plato there was clearly no need to posit an agent intellect. But Aristotle, who regarded the essences of sensible things as existing in matter with only a potential intelligibility, had to invoke some abstractive principle in the mind itself to render these essences actually intelligible. . . .. § 732. Next, at ‘And this etc.’, he states four qualities or conditions of the agent intellect: first, its separation from matter; second, its impassibility; third, its purity, by which he means that it is neither made up of bodily natures nor conjoined with a bodily organ. Now these three qualities are also found in the potential intellect; but the fourth is proper to the agent intellect, and consists in its being essentially in act; whereas, the potential intellect is essentially potential and comes to act only by receiving an intelligible object.' 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 |
Zeno's paradoxes - Wikipedia, Zeno's paradoxes - Wikipedia, the free encyclopedia, 'Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.' 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 |