volume II: Synopsis
section VI: Divine Dynamics
page 31: Physics
Recognition that the Universe is divine seems to me to be a momumental step forward, but since I seem to spend most of my time worrying about details I miss the big picture. From the marketing point of view, however, it is the big picture that counts.
We are infinitely susceptible to dreams and fairy-tales. We may buy the car or the cigarette because the advertisers have managed to cast such a spell over it that it becomes, for a profitable number of people, something they must have. Many people are disappointed when the stories are revealed to have a down side: the lung cancer that comes with the sexy he-man smoker.
I was taken in by Catholicism, but now I want to make natural religion a must have for everyone on the planet. This means that its formal content must be not only accessible but also desirable to everyone, in other words it has to address our human symmetry. It must also be grounded in reality rather than just a story dreamt up by monarchs to help manage their subjects.
We begin the campaign by choosing the ability to communicate as the fundamental feture of humanity. Our senses are continually pouring information into our systems. We decode this information as best we can and act on the picture thus revealed. By symmetry we mean sameness, the absence of observable difference. We all go about our lives in the same general manner, seeing, thinking, acting. The details break the symmetry. They can be very different from person to person.
Our basic hypothesis is that this communication based symmetry is not peculiar to humanity, but operates at every point in our divine Universe, so we speak of cognitive cosmology. Every point shares symmetries (communication channels) with its environment and shares messages with everything around it. We are not aliens in this world, special creations or chosen people, we are totally embedded in it and our survival implies that it is deeply embedded in us.
A first step toward understanding the Universe is to understand its physical implementation. We are talking about the communication of information, and we assume, with Landauer, that all information is encoded physically. A tear rolling down a cheek says a lot. Rolf Landauer: Information is a Physical Entity
We have now seen physics in two guises: the classical dress first designed by Galileo and Newton; and more recently quantum field theory and gravitation, which model some features of the Universe with outstanding precision although we do not yet fully understand it. Let us turn to our new picture, the transfinite network, and bring it down to Earth. Here we model the Universe as a computer network and attempt to understand everything a set of communication protocols. Computer network - Wikipedia
The general approach to theoretical physics is exemplified by Einstein's slow dance toward general relativity. First came special relativity, inspired by a deep understanding of electrodynamics and Maxwell's equations. This led him to understand inertial frames. But we do not live in an inertial frame - we are glued to Earth by gravitational force. Newton provided a very accurate but philosophically difficult description of gravitation, since his picture demanded instantaneous action at a distance. Abraham Pais: 'Subtle is the Lord...': The Science and Life of Albert Einstein, pp 177-265
Einstein's happiest thought was that freely falling in a gravitational field he would not feel his own weight; he would be in an inertial frame. Free fall became reference point from which to look at gravitation. After much tinkering and many false starts, Einstein's friend Marcel Grossman introduced him to the geometry of curved space. Now he had a body mathematical theory to work with. This turned out to be just what was needed to model gravitation and few years later the general theory was born perfect. Marcel Grossmann, Differentiable manifold - Wikipedia
The plan here is similar, but the execution severely wanting. My mathematical tool is the transfinite computer network. I see it as big and detailed enough to give a formal address to every quantum of action in the Universe. The task now is to fit it to quantum mechanics and special and general relativity. The next pages of this synopsis will summarize some of the ideas I have in this direction. The Development section of this site (Volume III) is the stage where I intend to spend the rest of my conscious life trying to perfect the fit and draw out the consequences for human life in a divine universe. Jeffrey Nicholls: Prolegomenon to Scientific Theology
Like the universe, I begin with nothing, that is the symmetries or conservation laws of physics. These are images of the boundaries imposed on the transfinite network by self-consistency, that is by communication. The formal source of these boundaries boundaries sappear to be the theorems of Gödel and Turing on incompleteness and incomputability. Within these boundaries we have the completeness and computability that underlie natural law. Beyond them we have the uncertainties that not only make creative evolution possible, but add the excitement and pain to our personal lives that drive us toward theology and religion.
For much of its history, physics has been the study of 'dead' matter, and it has been believed that something extra ('soul') must be added to matter to create life. Here we take the view that the whole Universe is alive, and that physics, as we experience it, is simply the conversation of the simpler elements of the Universe. The recursive nature of these converations allows them to build upon one another to form more and more complex entitites, such as those we normally call life, including ourselves.
The physical Universe is built upon three fundamental symmetries, called conservation of action, energy and momentum. We connect conservation and symmetry through Noether's theorem. Emmy Noether - Wikipedia, Noether's theorem - Wikipedia, Emmy Noether: Invariant Variation Probems, Neuenschwander
Noether's theorem applies to continuous groups. A group is a set of elements that can interact with one another in pairs, the result of that interaction always being another member of the group. The actions defined in a group never lead outside the group. It is like a closed society and in many ways perfect for physics, which, as the simplest and most deterministic layer in the Universe, is itself closed. Group - Wikipedia
A continuous or Lie group is a group which is also a differentiable manifold. Instead of the elements of the group being conceived as distinct objects, they are modelled as a continuum, like the geometric line, and all operations in the group are smooth. Lie Group - Wikipedia
From an information point of view however, continuity means 'nothing happens': there is no change. Shannon showed that error free communication required messages to be discrete. Continuity denies the presence of discrete changes, and so denies the presence of information. This notion is identical to the notion of symmetry: turn a perfect cube over and it looks just the same. Continuity and symmetry are the absence of observable definition.
Science seeks to document the symmetries of the Universe, those fixed points where nothing happens. Such points ('laws') can be represented in static text, 'the literature'. Mathematics is an important tool for scientists because it connects various fixed points together by theorems, which are 'logical chains' or 'logical continua' binding certain pairs of points in symbolic space.
The symmetries of the Universe tell us the common features of the world. We might say that any symmetry has two states: intact or broken. While a coin is spinning in the air its symmetry is (for practical purposes) intact. One cannot tell which side is up. When it lands and comes to rest, however, the symmetry is broken. One side is up: an indefinite situation has become definite.
In the network model, we identify a symmetry with a communication channel. In communication theory, a channel is an abstract transformation of a string of data designed to ensure that the data coming out of the channel is identical to the data going in. A perfect communication channel is in effect a computer that does nothing: its output is identical to its input. We might say that each channel corresponds to a language or protocol. The Internet Protocol, for instance, binds us all together in the internet.
We represent symmetries by probabilities. In a perfect symmetry, like a fair die, all possibilities are equiprobable. We can use these probabilities to compute the entropy of a symmetry (or source). Actual signals are broken symmetries, the choice of one of the points in the symmetry: once we have withdrawn the ball from the urn, black and white are no longer have a certain probability, we have a black or a white in our hand. The information gained by making the choice is equal to the entropy of the space of possibilities from which the choice was made. So a good communication channel faithfully treats each member of its symbol alphabet equally, transmitting it without error regardless of its specific identity.
This idea is captured by the physical notion of 'gauge symmetry'. Physicists recognise four fundamental forces known as gravitation, electromagnetism, strong, and weak. Each of these is a channel of communication (influence, force) in the physical Universe. These forces are mediated by particles called bosons, and act between fermions. Gauge theory - Wikipedia, Boson - Wikipedia, Fermion - Wikipedia
The transfinite network is layered. Unlike artificial communication networks, which have up to seven layers, the transfinite network may have an infinity of layers, each building on the complexity of the layers beneath it. We propose that lowest, countable layer of the transfinite network corresponds to the quantum mechanical description of the physical world.
The lowest layer of the transfinite network is also that of highest energy per state. One of the discoveries of quantum physics is that many of the internal states of any system do not manifest themselves until one reaches a certain energy level. Thus a hydrogen atom can be treated as a simple particle in interactions less than about 10 eV which do not disturb its internal states. At higher energies, the electron in the hydrogen atom is likely to be moved to a new state, and the atom will behave as a composite object.
The modern trend in particle physics has been toward higher and higher energies, so revealing more and more internal structure in the particles it studies. At the present energy levels, we are faced by a set of particles which appear to have no internal structure, quarks, gluons, electrons, photons, neutrinos. It may be that at very high energies these too will manifest internal structure. However we predict that there will be an energy scale, corresponding to the countable level of the transfinite network, where no further internal structure is manifest.
This scale may be the Planck scale, named for the the quantum of action discovered by Max Planck. We observe that there are no observable event measuring less than a quantum of action. We cannot therefore observe any sub-events within such a one quantum event, since this observation would involve less than a quantum of action. Planck scale - Wikipedia
Some imagine the Planck scale to be the scale of the initial singularity with which the Universe began. This idea implies that space-time and its classical contents, mass, length and time exist at that point. The idea here is that the initial singularity exists in the world that Misner, Thorne and Wheeler call pregeometry, the logical world that is the source of space-time. Misner, Thorne & Wheeler: Gravitation, pp 1203 sqq
The structure of the singularity, an unbroken symmetry, is an element of all more complex structures in the Universe. It corresponds, in modern physics, to the ancient idea of an absolutely simple God. We might say that the initial singularity, represented by the hardware layer of the transfinite network, is the fundamental building block of the Universe.
Thus we see the initial singularity as a point communicating with itself, talking about itself (since it has nothing else to say). This idea is already present in the ancient theory of the divine Trinity. We begin to model this, following Gödel, with arithmetic talking about arithmetic. Cantor's theorem shows us that, to avoid contradiction, it is necessary for this to grow into a Universe of unlimited complexity. Physics leads us toward the low entropy layers of the Universe, where the energy per state is high. We now turn to metaphysics, the high entropy layers of the Universe, where the energy per state is low. Big Bang - Wikipedia, Trinity - Wikipedia
(revised 5 April 2020)
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Further readingBooks
Cantor, Georg, Contributions to the Founding of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain), Dover 1895, 1897, 1955 Jacket: 'One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc, as well as the entire field of modern logic.'
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Capra, Fritjof, The Tao of Physics: An exploration of the parallels between modern physics and Eastern mysticism, Shambala 1991 'First published in 1975, The Tao of Physics rode the wave of fascination in exotic East Asian philosophies. Decades later, it still stands up to scrutiny, explicating not only Eastern philosophies but also how modern physics forces us into conceptions that have remarkable parallels. Covering over 3,000 years of widely divergent traditions across Asia, Capra can't help but blur lines in his generalizations. But the big picture is enough to see the value in them of experiential knowledge, the limits of objectivity, the absence of foundational matter, the interrelation of all things and events, and the fact that process is primary, not things. Capra finds the same notions in modern physics. Those approaching Eastern thought from a background of Western science will find reliable introductions here to Hinduism, Buddhism, and Taoism and learn how commonalities among these systems of thought can offer a sort of philosophical underpinning for modern science. And those approaching modern physics from a background in Eastern mysticism will find precise yet comprehensible descriptions of a Western science that may reinvigorate a hope in the positive potential of scientific knowledge. Whatever your background, The Tao of Physics is a brilliant essay on the meeting of East and West, and on the invaluable possibilities that such a union promises.' Brian Bruya
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Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. . . . In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands
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Misner, Charles W, and Kip S Thorne, John Archibald Wheeler, Gravitation, Freeman 1973 Jacket: 'Einstein's description of gravitation as curvature of spacetime led directly to that greatest of all predictions of his theory, that the universe itself is dynamic. Physics still has far to go to come to terms with this amazing fact and what it means for man and his relation to the universe. John Archibald Wheeler. . . . this is a book on Einstein's theory of gravity. . . . '
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Neuenschwander, Dwight E, Emmy Noether's Wonderful Theorem, Johns Hopkins University Press 2011 Jacket: A beautiful piece of mathematics, Noether's therem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space or rotation will obey the laws of conservation of energy, linear momentum or angular momentum respectively. This exciting result offers a rich unifying principle for all of physics.'
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Pais, Abraham, 'Subtle is the Lord...': The Science and Life of Albert Einstein, Oxford UP 1982 Jacket: In this . . . major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire ouvre. . . . Running through the book is a completely non-scientific biography . . . including many letters which appear in English for the first time, as well as other information not published before.'
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Weinberg, Steven, The First Three Minutes: A Modern View of the Origin of the Universe, Basic Books 1993 Preface: 'The present book is concerned with the early unvierse, and in particular with the new understanding of the early universe that has grown out of the discovery of the cosmic microwave radiation background in 1965.'
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Weinberg, 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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Links
Big Bang - Wikipedia, Big Bang - Wikipedia, the free encyclopedia, 'The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in its present continuously expanding state. According to the most recent measurements and observations, this original state existed approximately 13.7 billion years ago, which is considered the age of the Universe and the time the Big Bang occurred. ' 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 |
Computer network - Wikipedia, Computer network - Wikipedia the free encyclopedia, 'A computer network, or simply a network, is a collection of computers and network hardware interconnected by communication channels that allow sharing of resources and information. . . . The best known computer network is the Internet. . . . Computer networking can be considered a branch of electrical engineering, telecommunications, computer science, information technology or computer engineering, since it relies upon the theoretical and practical application of the related disciplines.' back |
Differentiable manifold - Wikipedia, Differentiable manifold - Wikipedia, the free encyclopedia, 'In mathematics, a differentiable manifold is a type of manifold that is locally similar enough to a linear space to allow one to do calculus. Any manifold can be described by a collection of charts, also known as an atlas. One may then apply ideas from calculus while working within the individual charts, since each chart lies within a linear 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 |
Emmy Noether, Invariant Variation Probems (English Translation), M. A. Tavel’s English translation of “Invariante Variation
sprobleme,”
Nachr. d. K ̈onig. Gesellsch.
d. Wiss. zu G ̈ottingen, Math-phys. Klasse
, 235–257 (1918), which originally appeared in
Transport
Theory and Statistical Physics,1
(3), 183–207 (1971).
'The problems in variation here concerned are such as to admit
a continuous group (in Lie’s
sense); the conclusions that emerge from the corresponding
differential equations find their most
general expression in the theorems formulated in Section 1 a
nd proved in following sections.
Concerning these differential equations that arise from pro
blems of variation, far more precise
statements can be made than about arbitrary differential equ
ations admitting of a group, which
are the subject of Lie’s researches. What is to follow, there
fore, represents a combination of
the methods of the formal calculus of variations with those o
f Lie’s group theory.' back |
Emmy Noether - Wikipedia, Emmy Noether - Wikipedia, the free encyclopedia, 'Amalie Emmy Noether, . . . (23 March 1882 – 14 April 1935) was a German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of rings, fields, and algebras. In physics, Noether's theorem explains the fundamental connection between symmetry and conservation laws.' 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 |
Gauge theory - Wikipedia, Gauge theory - Wikipedia, the free encyclopedia, 'In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations. . . .
The term gauge refers to redundant degrees of freedom in the Lagrangian. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field.' back |
Group (mathematics) - Wikipedia, Group (mathematics) - Wikipedia, the free encyclopedia, 'In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity and invertibility. Many familiar mathematical structures such as number systems obey these axioms: for example, the integers endowed with the addition operation form a group. However, the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way, while retaining their essential structural aspects. The ubiquity of groups in numerous areas within and outside mathematics makes them a central organizing principle of contemporary mathematics.' back |
Internet Protocol - Wikipedia, Internet Protocol - Wikipedia, the free encyclopedia, 'The Internet Protocol (IP) is the principal communications protocol used for relaying datagrams (packets) across an internetwork using the Internet Protocol Suite. Responsible for routing packets across network boundaries, it is the primary protocol that establishes the Internet.
IP is the primary protocol in the Internet Layer of the Internet Protocol Suite and has the task of delivering datagrams from the source host to the destination host solely based on their addresses. For this purpose, IP defines addressing methods and structures for datagram encapsulation.' back |
Jeffrey Nicholls, Prolegomenon to Scientific Theology, ' This thesis is an attempt to carry speculative theology beyond the apogee it reached in the medieval work of Thomas Aquinas into the world of empirical science (Aquinas 2019). Since the time of Aquinas, our understanding of the Universe has increased enormously. The ancient theologians not only conceived a perfect
God, but they also saw the world as a very imperfect place. Their reaction was to place God outside the world.
I will argue that we live in a Universe which approaches infinity in size and complexity, is as perfect as can be, and fulfils all the roles traditionally attributed to God, creator, lawmaker and judge.' back |
Lie Group - Wikipedia, Lie Group - Wikipedia, the free encyclopedia, 'In mathematics, a Lie group . . . is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Norwegian mathematician Sophus Lie, who laid the foundations of the theory of continuous transformation groups.
Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. . . . One of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its "infinitesimal group" and which has since become known as its Lie algebra.' back |
Marcel Grossman - Wikipedia, Marcel Grossman - Wikipedia, the free encyclopedia, ' Albert Einstein's friendship with Grossmann began with their school days in Zurich. Grossmann's careful and complete lecture notes at the Federal Polytechnic School proved to be a salvation for Einstein, who missed many lectures . . . It was Grossmann who emphasized the importance of a non-Euclidean geometry called Riemannian geometry (also elliptic geometry) to Einstein, which was a necessary step in the development of Einstein's general theory of relativity. Abraham Pais's book on Einstein suggests that Grossmann mentored Einstein in tensor theory as well. Grossmann introduced Einstein to the absolute differential calculus, started by Christoffel and fully developed by Ricci-Curbastro and Levi-Civita. Grossmann facilitated Einstein's unique synthesis of mathematical and theoretical physics in what is still today considered the most elegant and powerful theory of gravity: the general theory of relativity.' back |
Noether's theorem - Wikipedia, Noether's theorem - Wikipedia, the free encyclopedia, 'Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.' back |
Planck scale - Wikipedia, Planck scale - Wikipedia, the free encyclopedia, In particle physics and physical cosmology, the Planck scale is an energy scale around GeV (corresponding to the Planck mass) at which quantum effects of gravity become strong. At this scale, the description of sub-atomic particle interactions in terms of quantum field theory breaks down (due to the non-renormalizability of gravity). That is; although physicists have a fairly good understanding of the other fundamental interactions or forces on the quantum level, gravity is problematic, and cannot be integrated with quantum mechanics (at high energies) using the usual framework of quantum field theory. . . . ' back |
Rolf Landauer, Information is a Physical Entity, 'Abstract: This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that on the ultimate nature of the laws of physics are included.' back |
Trinity - Wikipedia, Trinity - Wikipedia, the free encyclopedia, 'The Christian doctrine of the Trinity (from Latin trinitas "triad", from trinus "threefold") defines God as three consubstantial persons, expressions, or hypostases: the Father, the Son (Jesus Christ), and the Holy Spirit; "one God in three persons". The three persons are distinct, yet are one "substance, essence or nature" homoousios). In this context, a "nature" is what one is, while a "person" is who one is.' back |
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