vol 3: Development
chapter 3: Physics
page 3: The initial singularity
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The initial singularity
I was sitting in a chair in the patent office in Bern when all of a sudden a thought occurred to me: 'If a person falls freely he will not feel his own weight.' I was startled. This thought made a deep impression on me. It impelled me toward a theory of gravitation. Pais, 179
Geodesics and singularities
The logical and mathematical development of Einstein's insight into free fall defines geodesics, paths through the four dimensional space-time manifold. A observer following a geodesic experiences no acceleration. Geodesic - Wikipedia A space-time is said to geodesically complete if all its geodesics have endpoints which are in the space-time manifold.
On the other hand, a singularity is said to exist if we can find a geodesic which does not have an endpoint in the manifold. Hawking & Ellis An observer falling freely along an incomplete geodesic will eventually come to the 'edge' of space-time and perhaps move outside space-time. This is believed to happen when an observer moves through the event horizon of a black hole to the singularity inside. Black hole - Wikipedia
The initial singularity
Black holes occur when the local energy density of the universe becomes sufficiently great. This appears to happen when a large star can no longer maintain its structure against its own gravitation because it has exhausted its nuclear. The big bang may be modelled as a time reversed formation of a black hole. The initial singularity lies at the beginning of a set of geodesics which emerge carrying all the particles of the growing universe.
Why this should happen (when we consider the initial singularity to carry all the energy of the universe and so be absolutely black) is a matter for speculation.
The initial singularity and the classical god
Here we note that from the point of view of an observer in space-time, the initial singularity shares many of the properties of the classical God. This God developed developed from the mutual fertilization of Hebrew, Greek and Christian traditions. The definitive textbook account of this God was produced by Aquinas in the thirteenth century. Thomas Aquinas
Drawing on the work of Aristotle, Aquinas proves that God and the universe are distinct. God is outside spacetime. From this proof, he deduces that God is pure act, and from this conclusion it follows that God is simple, perfect, good, infinite, eternal, omniscient, omnipotent and living. All of these results pertain to natural theology, that is (given certain models) they are consistent with our experience of the world.
The Trinity models a divine universe with many personalities
Christian doctrine adds further revealed features to God, in particular that doctrine of the Trinity, that there are three equally divine Persons, the Father, the Son and the Holy Spirit. This revelation founded on an interpretation of the New testament of the Bible.
It took hundreds of years of debate within the Christian Churches to find a universally agreed expression of the Trinitarian doctrine. Aquinas' modelling of the Trinity is one of the subtlest products of Christian thought. The difficulty lies in reconciling the unity and simplicity of God with the multiplicity of Persons.
On this site, we reject the traditional dichotomy between God and the World by proposing a new model of god which demonstrates their compatibility. On this model, we are not outside god, but inside it, and we can use the modelling of the Trinity as a starting point from which to understand a divine universe with an infinite number of personalities, of which we ourselves are a subset.
Aquinas builds a model of the Trinity on the theory of knowledge and desire developed by Aristotle. Aristotle Aristotle considers that we know by acquiring the form of the known. This form is first captured by the senses, and then passed to the intellect, which discerns the intelligible content of our sensory input.
Such knowledge is not an essential part of our human nature, but something that we acquire after birth. We may express this knowledge in words, and so the intellectual form by which we know something came to be considered as an interior word. Lonergan
This idea is implied in the evangelist John's statement The Word was made flesh (John 1:14) John Using this language, Aquinas models the second person of the Trinity as the Word of God, generated by the Father through His knowledge of Himself. Aquinas 161 Since God's self knowledge is essential to himself, the Son shares in the divine nature. but is to be distinguished from the Father by the real relationships of paternity and 'filiation'.
The third person of the Trinity is understood as the love that exists between the Father and the Son. Aquinas 162
Both the Bible as understood by Christianity and the psychological model of the Trinity limit the number of persons to three. Here, however, we interpret the Trinity as a small network with no limits to its expansion. The function of a network is to copy a message from one source to another, rather as the Father copies himself to create the Son.
To see how this works in more detail, we turn to quantum mechanics. Quantum mechanics
(revised 22 October 2008)
Further reading
Books
| Aquinas, Thomas, and (edited by Angeli M Pirotta), In Aristotelis librum de Anima Commentarium, Marietti 1959 William of Moerbeke's latin text of Aristotle's On the Soul (a brilliant little treatise on life written 2300 years ago) together with a latin commentary by the Angelic Doctor Thomas Aquinas. Here is an ancient foundation for the Christian belief in the immortality of the soul.back |
| Aristotle, and (translated by W S Hett), On the Soul, Parva Naturalia, On Breath, Harvard University Press (USA) ; William Heinemann Ltd (UK) 1975 Introduction: 'This collection of treatises belongs to subjects on the borderline between bodily and mental. Aristotle was the son of a doctor and himself a biologist, who believed in experiment and dissection as a means of collecting evidence. Thus his views on the soul are influenced by his physiology. Yet he never falls into the meshes of materialism, and appears quite certainn that the body cannot possibly explain the mind. ...' Amazon back |
| Einstein, 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 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 simplext and most intelligible form, and on the whole, in the sequence and connectionin which they actually originated.' page 3 Amazon back |
| Hawking, Steven W, and G F R Ellis, The Large Scale Structure of Space-Time , Cambridge UP 1975 Preface: Einstein's General Theory of Relativity ... leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.' Amazon back |
| Lonergan, 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.' Amazon back |
| 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.' Amazon back |
Papers
| Bromley, B C and W A Miller, V I Pariev, "The inner edge of the accretion disk around a supermassive black hole", Nature, 391, 6662, 1 January 1998, page 54. Letters to Nature: 'Massive black holes are generally thought to exist at the centres of galaxies, but an unambiguous identification of a black hole has been impeded by lack of evidence for the strong field relativistic effects expected in the vicinity of such an object. ... Here we present an analysis of the iron line emission from MCG 6-30-15 ... We find that the inner edge of the disk material giving rise to the line is within 2.6 +- 0.3 times the Schwarzschild radius - the event horizon of a non-rotating black hole - at the 95% confidence level.' . back |
Links
| Aquinas 161 Whether any procession in God can be called geenration? 'I answer that, The procession of the Word in God is called generation. . . . the procession of the Word in God is generation; for He proceeds by way of intelligible action, which is a vital operation:--from a conjoined principle (as above described):--by way of similitude, inasmuch as the concept of the intellect is a likeness of the object conceived:--and exists in the same nature, because in God the act of understanding and His existence are the same, as shown above (14, 4). Hence the procession of the Word in God is called generation; and the Word Himself proceeding is called the Son.' back |
| Aquinas 162 Whether any other procession exists in God besides that of the wWord? 'I answer that, There are two processions in God; the procession of the Word, and another. In evidence whereof we must observe that procession exists in God, only according to an action which does not tend to anything external, but remains in the agent itself. Such an action in an intellectual nature is that of the intellect, and of the will. The procession of the Word is by way of an intelligible operation. The operation of the will within ourselves involves also another procession, that of love, whereby the object loved is in the lover; as, by the conception of the word, the object spoken of or understood is in the intelligent agent. Hence, besides the procession of the Word in God, there exists in Him another procession called the procession of love.' back |
| Aquinas 168 Whether in God there are only four real relations -- paternity, filiation, spiration and procession. ' . . . a real relation in God can be based only on action. Such relations are not based on the actions of God according to any extrinsic procession, forasmuch as the relations of God to creatures are not real in Him (13, 7). Hence, it follows that real relations in God can be understood only in regard to those actions according to which there are internal, and not external, processions in God. These processions are two only, as above explained (27, 5), one derived from the action of the intellect, the procession of the Word; and the other from the action of the will, the procession of love. In respect of each of these processions two opposite relations arise; one of which is the relation of the person proceeding from the principle; the other is the relation of the principle Himself. . . . ' back |
| Black hole - Wikipedia Black hole - Wikipedia, the free encyclopedia 'A black hole is a region of space in which the gravitational field is so powerful that nothing can escape after having fallen past the event horizon. The name comes from the fact that even electromagnetic radiation (e.g. light) is unable to escape, rendering the interior invisible. However, black holes can be detected if they interact with matter outside the event horizon, for example by drawing in gas from an orbiting star. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation in the process. . . . ' back |
| Eugene Wigner The Unreasonable Effectiveness of Mathematics in the Natural Sciences 'The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories.' back |
| Geodesic - Wikipedia Geodesic - Wikipedia, the free encyclopedia 'In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. In the presence of an affine connection, geodesics are defined to be curves whose tangent vectors remain parallel if they are transported along it. The term "geodesic" comes from geodesy, the science of measuring the size and shape of Earth; in the original sense, a geodesic was the shortest route between two points on the Earth's surface, namely, a segment of a great circle. The term has been generalized to include measurements in much more general mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. Geodesics are of particular importance in general relativity.' back |
| Geodesic - Wolfram Geodesic - - from Wolfram MathWorld 'A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight lines. On the sphere, the geodesics are great circles (like the equator). The geodesics in a space depend on the Riemannian metric, which affects the notions of distance and acceleration.' back |
| Hubblesite.org Hubblesite: Black Holes: Gravity's Relentless Pull 'Black holes are places where ordinary gravity has become so extreme that it overwhelms all other forces in the Universe. Once inside, nothing can escape a black hole's gravity -- not even light. . . . For a fully interactive multimedia experience, click Journey to a Black Hole (fast internet connection recommended). For an in-depth study of black holes that presents the site's contents conveniently sorted by topic, click Black Hole Encyclopedia.' back |
| Sloan Digital Sky Survey The Expanding Universe 'The Sloan Digital Sky Survey (SDSS) is a joint project of The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Princeton University, the United States Naval Observatory, and the University of Washington. Apache Point Observatory, site of the SDSS telescopes, is operated by the Astrophysical Research Consortium (ARC).' back |
| Thomas Aquinas Summa Theologica Thomas Aquinas: The medieval theological classic online. :'Because the doctor of Catholic truth ought not only to teach the proficient, but also to instruct beginners (according to the Apostle: As unto little ones in Christ, I gave you milk to drink, not meat -- 1 Cor. 3:1-2), we purpose in this book to treat of whatever belongs to the Christian religion, in such a way as may tend to the instruction of beginners. We have considered that students in this doctrine have not seldom been hampered by what they have found written by other authors, partly on account of the multiplication of useless questions, articles, and arguments, partly also because those things that are needful for them to know are not taught according to the order of the subject matter, but according as the plan of the book might require, or the occasion of the argument offer, partly, too, because frequent repetition brought weariness and confusion to the minds of readers.' back |
| University of Southampton Gravitational Collapse 'The modern theory of black holes begins with the 1939 paper by Oppenheimer and Snyder entitled `On continued gravitational contraction'. Their paper showed that if a stars collapsing core had sufficient mass, then even the neutron pressure would be insufficient to prevent further collapse to a black hole. This paper has strong claims to being one of the most prophetic ever written in this field of research. Today, 60 years later, this paper needs little revision - even the terminology is undated!' back |
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