Abstract
The divine universe creates itself within an eternal, omnipotent, conscious singularity
Here we are exploring the powerful lust for life that drives the creation of the universe and every body in it, including ourselves. We see the universe as a vast collection of discrete particles, bigger ones made of smaller ones and all contained with an initial symmetry whose defining characteristic is consistency.
We follow the definition of omnipotence stated by Aquinas in his Summa theologiae: An omnipotent being is one that can do anything that does not directly involve inconsistency. Aquinas, Summa I, 25, 3: Is God omnipotent?
We fit into this picture. Each of us is a community of about 50 trillion cells, each of which contains billions of molecules. Each molecule is made from a number of atoms ranging from 2 to many thousands. The atoms themselves are made of elementary particles like photons, electrons, gluons and quarks.
We live on Earth, made of atoms and molecules warmed by a star, the Sun, one of the billions of stars in our galaxy which is one of the billions of galaxies in the universe. We imagine that this enormous structure grew within an eternal omnipotent, conscious initial singularity. Our story is briefly outlined on the Home page, 13 steps to a Universe. These steps link to a commentary which explains each one in more detail.
Since the beginning the world creates itself by understanding itself: cognitive cosmogenesis
Our species is about 300 thousand years old. We look back to a dreamtime which created our world and ourselves. Five thousand years ago mathematical and physical ideas began to develop which we associate with large families of creators and historical personalities like Thales, Plato and Aristotle. These ideas reached their maturity at the beginning of the twentieth century. Dreamtime - Wikipedia
The mathematician Euclid summarized much ancient mathematical knowledge in his thirteen books of elements. Much of Euclidean geometry remains fundamental in the 21st century even though the scope of mathematics has increased immensely since Euclid’s time. Euclidean geometry - Wikipedia
We owe the first steps toward modern physics to people like Galileo Galilei, Johannes Kepler and above all Isaac Newton. Newton laid the foundations of classical mechanics. Kepler's laws of planetary motion - Wikipedia, Isaac Newton (1713, 1726, 1972): Philosophiae Naturalis Principia Mathematica, Classical mechanics - Wikipedia
In his book on The Character of Physical Law Richard Feynman explains how Newton was able to develop a Euclidean proof of Kepler’s second law from the simple geometric fact that the force between a planet and the Sun acts along a line joining the planet and the Sun. Richard Feynman (1965): The Character of Physical Law, pp
The difference between continuous and particulate
One component of ancient Greek science was a long debate about whether the world is moving or stationary, smooth or atomic. One of the most significant participants was Zeno of Elea. Zeno supported Parmenides who maintained that motion is an illusion with arguments to show that motion is impossible. One of the best known is a parable about Achilles (the world’s fastest runner) and a tortoise (the epitome of slow motion).
Achilles is handicapped: the tortoise starts in front of him. To catch the tortoise, Zeno says, Achilles must first cover half the distance between himself and the tortoise, by which time the tortoise has moved ahead. So Achilles must cover half the distance to the slowly receding tortoise. This means, says Zeno, that he will never reach the tortoise sine the infinite sum of half-distances never brings him to the tortoise. This argument is obviously wrong in fact, but this and Zeno’s other arguments have garnered much attention over the centuries.
We owe part of the modern solution to Einstein who pointed out that all motion is relative. Analysed from this point of view, we see that Achilles is moving much faster than the tortoise and must soon overtake them.
Mathematics, calculus and continuity
Our concept of continuity comes observations of from smooth motion, like the orbit of a planet, and the invention of calculus reminded us of Zeno.
Newton’s calculus embodied significant mathematical difficulties with the definition of continuity and the definition of a derivative: “For Newton, change was a variable quantity over time and for Leibniz it was the difference ranging over a sequence of infinitely close values.” Given continuity, the derivative is the ratio of two infinitesimal quantities. Since Newton’s time mathematicians has settled on the idea of the limit to settle the problems of calculus, but this may be a red herring. What if spacetime is not continuous and calculus is not applicable? History of calculus - Wikipedia, John L. Bell (Stanford Encyclopedia of Philosophy): Continuity and Infinitesimals
The alternative is proposed by John von Neumann in his book on the Mathematical Foundations of Quantum Mechanics. Recalling advantages of quantum mechanics von Neumann writes:
[. . .] what was fundamentally of greater significance was that the general opinion in theoretical physics had accepted the idea that the principle of continuity (natura non fecit saltus prevailing in the perceived microcosmic world, is merely simulated by an averaging process in a world which in truth is discontinuous in its very nature. [. . .] the levelling law of large numbers completely obscures the nature of the individual processes.Natura non facit saltus - Wikipedia
In the first forty years of his life Einstein made significant contributions to the development of quantum mechanics. He showed that quantization of energy exploited by Max Planck to derive an equation to express the spectral composition of black body radiation points to the existence of the fundamental particles we now know as photons. This radical idea took the Nobel prize Committee nearly 20 years to understand and reward him for this work. Albert Einstein (1905c): On a heuristic point of view concerning the production and transformation of light
Nevertheless, Einstein was never comfortable with quantum mechanics and often tried to expose its weakness. One of his most productive efforts was the paper with Podolsky and Rosen, the ‘EPR’ paper which introduced the idea of entanglement which Einstein called spooky action at a distance. This paper shows beyond doubt that quantum mechanics underlies and creates the apparently continuous Minkowski space in which we live and observe the physical world. The pixellation of this space by the “uncertainty principle” and its metric. This explains why the speed of light is constant for all inertial observers. The details are explained in the commentary attached to the ten steps to the creation of the universe listed on the Home Page.
Einstein’s best known contribution is the general theory of relativity which explains the overall structure of the universe. This theory is a triumphant application of calculus which can overlook quantum mechanics because the enormous difference between the size of the universe and the fundamental particles from which it is made means that it can be effectively treated as continuous. Einstein hoped to develop a unified theory of the universe on the basis of his general theory but was stymied for the last 30 years of his life because he could find no way to develop a theory of particles using a continuous mathematical field theory. Large numbers can take us from particles to cosmic space, but not vice versa
By far the most radical recent revision in theology and science was wrought by Darwin’s study of evolution. His work contests two ancient beliefs. First, that reality is deterministic; and second, that mind and matter are absolutely disjoint categories of reality. With these two fictitious constraints out of the way, the path is open to a comprehensive unification of physics and theology. Charles Darwin & Ernst Mayr (1859, 2001); On the Origin of Species: A Facsimile of the First Edition
Given that nothing comes from nothing, we must assume that the source of the universe is eternal. The evidence for biological evolution is overwhelming. The strongest evidence for the prebiotic evolution of the universe arises from the finite velocity of light and its relationship to gravitation. We observe the cosmic microwave background radiation which was created soon after the beginning and use the ubiquity and redshift of radiation from distant sources to extrapolate the expanding universe back to a postulated initial singularity. Precise measurement of this radiation interpreted using Einstein’s general relativity indicate that the current structure began to emerge from a singularity fourteen billion years ago. Cosmic microwave background - Wikipedia
Here we develop a concise picture of this history consistent with the evidence by blending the altogether simple (omnino simplex) Christian god described by Aquinas, the structureless gravitation described by Einstein, and quantum physics which describes the emergence of spacetime and matter. Aquinas, Summa, I, 3, 7: Is God altogether simple?, Albert Einstein (1915): The Field Equations of Gravitation, John von Neumann (2018): The Mathematical Foundations of Quantum Mechanics
We assume that the fundamental formal structure of the world can be represented in the abstract Hilbert space defined axiomatically by von Neumann. We imagine the singularity as the entity of pure action developed by Aristotle and Aquinas to account for all the action in the world. It creates random bases for Hilbert space as a consequence of Brouwer’s fixed point theorem when it maps itself onto itself. The invisible operations that control the world are described by quantum mechanics as mappings of Hilbert space onto itself by hermitian operators. The random products of these operations are analogous to genes in biological evolution. Unmoved mover - Wikipedia, Self-adjoint operator - Wikipedia
We imagine that the energy enters this system by the bifurcation gravitation into positive kinetic and negative potential energy, a phenomenon suggested by the pendulum. The positive energy plays the role of matter in Aristotle’s hylomorphism converting quantum forms into real physical particles. Hylomorphism - Wikipedia
A century of laboratory observation has revealed a set of 61 elementary particles which together construct the world. These particles fall into two categories, fermions and bosons whose agency, independence and constructive ability define the world we experience in Minkowski space. The potential component of the energy created from gravitation binds these structures. Elementary particle - Wikipedia
The conclusions I seek follow from the symmetry of quantum mechanics with respect to complexity. The rules of quantum mechanics are the same in Hilbert spaces of any dimension from two to a countable infinity. This range embraces elementary particles, our human being and the universe as a whole. It is sufficient to establish that the structural consequences of quantum theory support the freedom, agency and communication of discrete entities at all scales. This structure provides a firm foundation for theology, religion and politics.
Copyright:
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Notes and references
Further reading
Books
Darwin (1859, 2001), Charles, and Ernst Mayr, On the Origin of Species: A Facsimile of the First Edition, Harvard University Press 2001 Amazon review: 'It was a very happy idea to publish a facsimile of the first edition of On the Origin of Species; the price of copies of the original edition has reached the thousand dollar bracket, and in contemporary literature all page-references are to the original pagination, which was not followed in previous reprints of the first edition. Now, with this very reasonably priced and beautifully produced book, not only historians of science but also biologists will have the opportunity of following the fascinating thought-trails, still far from fully explored, of that remarkable man Darwin. Few if any persons are so well qualified as Harvard's Ernst Mayr to execute so helpfully and gracefully the delicate task of writing a worthy foreword to such a classic.'
--Sir Gavin de Beer (Science )
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von Neumann (2018), John, and Nicholas A. Wheeler (editor), Robert T Beyer (translator), The Mathematical Foundations of Quantum Mechanics, Princeton University Press 2018 ' Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics--a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. In this new edition of this classic work, mathematical physicist Nicholas Wheeler has completely reset the book in TeX, making the text and equations far easier to read. He has also corrected a handful of typographic errors, revised some sentences for clarity and readability, provided an index for the first time, and added prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson. The result brings new life to an essential work in theoretical physics and mathematics.'
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Links
Albert Einstein (1915), The Field Equations of Gravitation, ' In two recently published papers I have shown how to obtain field equations of gravitation that comply with the postulate of general relativity, i.e., which in their general formulation are covariant under arbitrary substitutions of space-time variables. [. . .] With this, we have finally completed the general theory of relativity as a logical structure. The postulate of relativity in its most general formulation (which makes space-time coordinates into physically meaningless parameters) leads with compelling necessity to a very specific theory of gravitation that also explains the movement of the perihelion of Mercury. However, the postulate of general relativity cannot reveal to us anything new and different about the essence of the various processes in nature than what the special theory of relativity taught us already. The opinions I recently voiced here in this regard have been in error. Every physical theory that complies with the special theory of relativity can, by means of the absolute differential calculus, be integrated into the system of general relativity theory — without the latter providing any criteria about the admissibility of such physical theory' back |
Aquinas, Summa, I, 3, 7, Is God altogether simple?, 'I answer that, The absolute simplicity of God may be shown in many ways. First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His "suppositum"; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple. . . . ' back |
Cosmic microwave background - Wikipedia, Cosmic microwave background - Wikipedia, the free encyclopedia, 'The cosmic microwave background (CMB) is the thermal radiation left over from the time of recombination in Big Bang cosmology. . . . The CMB is a snapshot of the oldest light in our Universe, imprinted on the sky when the Universe was just 380,000 years old. It shows tiny temperature fluctuations that correspond to regions of slightly different densities, representing the seeds of all future structure: the stars and galaxies of today.' back |
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 |
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 |
legislation.gov.uk, Commonwealth of Australia Constitution Act 1900, ' WHEREAS the people of New South Wales, Victoria, South Australia, Queensland, and Tasmania, humbly relying on the blessing of Almighty God, have agreed to unite in one indissoluble Federal Commonwealth under the Crown of the United Kingdom of Great Britain and Ireland, and under the Constitution hereby established:
And whereas it is expedient to provide for the admission into the Commonwealth of other Australasian Colonies and possessions of the Queen:
Be it therefore enacted by the Queen's most Excellent Majesty, by and with the advice and consent of the Lords Spiritual and Temporal, and Commons, in this present Parliament assembled, and by the authority of the same, as follows:[. . .] |
Self-adjoint operator - Wikipedia, Self-adjoint operator - Wikipedia, the free encyclopedia, ' In mathematics, a self-adjoint operator on a complex vector space V with inner product ⟨ ⋅ , ⋅ ⟩ is a linear map A (from V to itself) that is its own adjoint. That is, ⟨ A x , y ⟩ = ⟨ x , A y ⟩ = for all x , y ∊ V. If V is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of A is a Hermitian matrix, i.e., equal to its conjugate transpose A∗. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this basis is a diagonal matrix with entries in the real numbers. . . . Self-adjoint operators are used in functional analysis and quantum mechanics. In quantum mechanics their importance lies in the Dirac–von Neumann formulation of quantum mechanics, in which physical observables such as position, momentum, angular momentum and spin are represented by self-adjoint operators on a Hilbert space.' 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 |
William Bristow (Stanford Encyclopedia of Philosophy), Enlightenment, ' The Enlightenment is often associated with its political revolutions and ideals, especially the French Revolution of 1789. The energy created and expressed by the intellectual foment of Enlightenment thinkers contributes to the growing wave of social unrest in France in the eighteenth century. The social unrest comes to a head in the violent political upheaval which sweeps away the traditionally and hierarchically structured ancien régime (the monarchy, the privileges of the nobility, the political power of the Catholic Church). The French revolutionaries meant to establish in place of the ancien régime a new reason-based order instituting the Enlightenment ideals of liberty and equality.' back |