Notes
Sunday 15 August 2021 - Saturday 21 August 2021
[Notebook: DB 86: Hilbert / Minkowski]
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Sunday 15 August 2021
One of my principal problems is idiosyncracy which is tantamount to a lack of docility, strongly reflected in my rejection of the religion of my youth, but also creeping into my difficulties with modern physics. I sympathize with Einstein and his feeling that quantum mechanics is incomplete because observers seem to play and important role. This problem is solved by accepting that observers are also quantum systems and observation is just another interaction of two quantum systems which give u a real result [beautifully illustrated by the contrast between real and complex numbers]. The quantum systems in question are carried by particles and their local interaction produces new particles [by superposition in the Hilbert product space of the interacting states]. My problem lies with the complexity of quantum field theory. Relativity and gravitation make sense to me. Field theory with its superpositions of a mass of fields, infinities and other problems sounds more and more like bad dogma of the kind endemic in the Catholic Church which needs to be rooted out and replaced by what? I feel that I have done a good job of replacing the old god with
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the universe, but the foundations of the universe as seen by the physicists seem to be far too complex to be a god like the traditionally absolutely simple god. I have now come to the non-renormalizability of gravitation which is acting as a roadblock to quantizing it and am wondering (and have been since about 2000) whether gravitation even needs to be quantized becasue it carries no information [due to continuity?].We learn that quantum field theory is necessary to explain the creation and annihilation of particles [although every quantum interaction is the creating and annihilation of something]. What about creation and annihilation seen through the lens of [computation] and scale invariance [which involves the creation and annihilation of binary states]. It is described in some detail by the theory of communication, the evolution of deterministic systems of reproduction and error prone systems decay. Do we need quantum field theory for this?
So we can begin the quantum mechanical question all over again by asking why the universe is quantized, whether quantization is necessary for gravitation and what role it plays in particle physics. Back to square 1. In other words my life is all snakes and ladders. Snakes and ladders - Wikipedia
So we bravely ditch the whole quantum field theory thing and imagine that gravitation is a 4D spacetime continuum which reacts to events which we see as the meeting of quantum states in a Hilbert space triggering a real event which appears as a particle in the local Minkowski space. In other words gravitation works beneath the level of spacetime and may be considered to respond at the Hilbert level. The states of the underlying Hilbert space are clones of the initial singularity substantiated by fixed point theory, differentiated by the no cloning theorem and having a sort of semi-existence beneath the surface of spacetime. This is but a dream, but now we can turn to quantum field theory and
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have a few words to say about Feynman's path integral propagator, the field of harmonic oscillators and the reality of the quantum field existing in the pre-space quantum world. The closure of the universe arises from the fact that the quantum world exists in time [/action /energy] alone and is not spatially extended. All open to revision of course, but all we really want is to identify god and the universe and give a few clues about how it might work. From my own point of view I have about twenty years to develop and propagate this story, and given time I hope to bring it and physics closer together.
Monday 16 August 2021
Opening the day in hopeless case mode. I can imagine how the mighty Christian US is feeling having been humbled again by another fundamentalist religious group who believe more in the power of human motivation that the power of overwhelming military weaponry, offering to 'bomb people into the stone age' rather than eternal salvation. Another brick in my motivation to bring religion into the world fo scientific theology, tempered by my efforts to arrive at a plausible transfer from theology based on Aristotle and Aquinas to modern physics. My efforts to simplify physics to a logical and natural foundation often seem to be throwing out too many babies with the bathwater, particularly when it comes to the complexity of the quantum field theoretical explanations that have arisen to provide numerical explanations of the forest of fundamental particles that high energy physics
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has revealed. I can only press on however, using the obvious features of the network model to guide a search for a simple and comprehensive theory of everything. It is time for me to see whether superstrings, wires and geodesics are all manifestations of inherent network structure. The next step is to understand why gravitation is not renormalizable in the present dispensation [which seems to revolve around the existence and nature of the graviton necessary to fit gravitation into quantum field theory]. Physics: Stack Exchange: Why is quantum gravity non-renormalizabe?
Renormalizability has to do with coupling constants.
The fixed points in the general theory are the events which are measured by contact, that is identical Gaussian coordinates. Can we fit a Hilbert space with Gaussian coordinates? How are the dimensions in a Hilbert space addressed? Of Cartesian space? All we say is that they are orthogonal and ordered by the sequence of values in a [composite] vector.
Energy has inertia, it is reluctant to change, is changed by potential and we can see all universal process as an interplay of potential and act, as Aristotle did, but it is its own mover since potential and action are elements of the symmetry of conservation of energy [so the motivation for action is generally entropy, which is s statistical potential, guiding the kinetic action of action].
My feeling is that the real answer to all this stuff is to see the world as a logical system run by quantum logic. The difficulty is to see how to apply this idea. Einstein developed the special theory by finding as new meaning, a new derivation and a new application of the Lorentz transformation first spotted by Voight. My problem is
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how to apply logic to quantum physics, which might require new way of thinking about both logic, physics, insight and intelligence. I am a slow thinker. It took Einstein only ten years from childhood to work out the special theory. Now 54 years after I tried to use information theory to show that the universe is divine I am still in the dark, but, like the initial singularity, beating around the bush trying to find a path, what I have called a generalized geodesic [a simple one dimensional personal path through a curved infinite dimensional manifold which describes the whole world which I now like to see as a transfinite network in Hilbert space].
So take a break away from constructing the world and go back to cognitive cosmology beginning with gravitation which appears to be both where the real genius and the real problem with the current theory lies. Gravitation has two roles, to shape and expand the universe and to compress volumes of gas to cook up the new elements and create planetary system, the precursors of life. Cosmology - Wikipedia
Tuesday 17 August 2021
Always trying to dig deeper into the nature of the universe. Cognitive cosmology is a great ideas, but can we make it stick? The first step is to list the [heuristic principles behind the idea and the] defects with current theology and physics. There is not much to be said about theology, apart from its extra scientific status which means that there is no evidence to support it. The critique of physics can be more concrete and it has a central theme, the use of the fictitious mathematics of continuity to describe a quantum world. This can be broken out into points beginning with the epsilon-delta argument for continuity and then going on to an examination of general relativity and continuous groups. We then backtrack to
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quantum mechanics and von Neumann's treatment of the identity of wave mechanics and matrix mechanics via the symmetry of probability and the [nature of Hilbert space which is a mixture of orthogonality (discreteness) and continuity]. John von Neumann (2014): Mathematical Foundations of Quantum Mechanics
Wednesday 18 August 2021
Action, gravitation, 4D and quantum mechanics may break out simultaneously, another version of the Trinity, the initial quattocracy [in a god with three personal and one time dimensions]
.Thursday 19 August 2021
We are beginning with a quantum of action, potential, kinesis, gravitation, curvature [= dynamics of space] and quantum mechanics, constant entropy [= quantum mechanics], with no input from outside , a group, no input, no output, only growing within itself. The universe is de facto isolated, but contains duality.Another principle: The Universe is all alone. Outside nothing. In side duality.
Gravitation is continuous, the source of all fixed points in the universe. It is a dance. Networks can move dynamically in continuous space [the fixed points, as in general relativity, being the interactions of sources and signals]. [Minkowski] Space is symmetrical with respect to place [Hilbert space is symmetrical with respect to time (?)].
We want physical logic - information is a physical entity, logic is a physical entity. Between logic[al acts, events] there is nothing [to see]. Information and logic are real.
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Time is the first essence. Dance for love; God is love.
Quid est hoc quod est esse? Initial singularity.
We are now inside the initial singularity, inside a quantum of action, inside God and what do we see? The Trinity, Father and Son, fermions distinguished by their relationship which is mediated by two bosons, one going from Father to Son, the other from Son to Father [aka processio and filiatio]. We see something like a hydrogen atom, and we think that a quantum mechanic would describe this by something like the Dirac equation in four dimensions, three of space and 1 of time, derived perhaps, as Dirac did, from the spacetime version of the Schrödinger equation, adjusted to the primitive circumstances where we find ourselves with two atoms of positronium.
Friday 20 August 2021
Any progress? The overall plan seems good but the idea of grounding it in physics needs work. Looking back I sometimes feel that I said all that could be said in How Universal 1967, but I still have my heart set on producing something like general relativity that irrefutably couples the physical structure of the universe to a theory of knowledge and intelligence which seems to me now to lie somewhere in the direction of linking quantum computation and quantum communication to the differentiable manifold of general relativity by linking the mathematical concept of a differential to the logical concept of a quantum computation. So I press on with quantum cosmology, hoping to see the light.
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The key idea is that an action by the quantum of action is a logical action and an event orthogonal to all the other events which may be an ordered sequence of events like a computation, rather like a moment in my life which is a superposition of all the processes occurring within me to continue the sequence of my life. Superposition enables us to work from events which involve one Planck quantum of action to the transfinite event which is the lifetime of the universe, a continuum which looks eternal from the outside.
What do the Catholic Church, the Taliban and modern physics have in common? My guess is denial of reality. The are all, along with many of us, living in a fantasy world of their own creation. The fundamental lesson of quantum theory is that what you see depends on how you look. One of the saddest stories in science is that of Albert Einstein, whose total dedication to the notion of objective reality was the source of a lifetime of scepticism about quantum theory which led him, in the last part of his life, to a fruitless search for an alternative. The root of the belief in objective reality lies in the theological notion of an omnipotent and omniscient God in total deterministic control of everything, even human actions understood to be a product of free will. This belief is bolstered by the belied in the eternity of God,who sees everything like the general theory of relativity in one glance embracing past, present and future so that
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the things we see as unpredictable from our perspective locked in time can be seen as fixed history from the eternal point of view.
We might think that the claim that what you see depends on how you look destroys the concept of certain knowledge. The answer to this objection is the central point in Einstein's general theory and all his relativistic work. In order to get an arithmetic grip on the nature of geometry Einstein used Gaussian coordinates which are to a large extent arbitrary, compared for instance to the Cartesian coordinates which impose a fixed metric structure on a Euclidean space. The key to the general theory is, in Einsteins words: 'The Gauss co-ordinate system has to take the place of a body of reference. The following statement corresponds to the fundamental idea of the general principle of relativity: "All Gaussian co-ordinate systems are essentially equivalent for the formulation of the general laws of nature".' The key to getting a deterministic mathematical theory out of this arbitrary coordinate system is that only fixed points and observable points in nature are events and whatever coordinate system we choose must be constrained to give a one to one correspondence between a particular event a particular set of Gaussian coordinates. An observation is an event, so that the foundation of science is equivalent to the foundation of general relativity: all observers, no matter what their perspective must, to make sense, agree on what they actually see: is this person dead or alive? and all equivalent situations commonly understood to be 'facts'. Ultimately, since every event is equivalent to a quantum of action, we can establish a gaussian system of coordinates that embraces all actions by giving identical parameters to identical actions: did
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you hit her, yes or no? and so forth. This notion is not only central to science, it is central to justice and all other quests for local certainty and a foundation for a scientific theology, which is to be a comprehensive theory of every possible event which we comprehend as a universal communication network whose local certainty is time order just as the gaussian system of coordinates depends on the ordered numbering of dimensions of the relevant space so as to make possible the identification of identical events by identical numbers. Beneath [or perhaps within] the layer [cocoon] of certainty reflected in general relativity we have the quantum mechanical layer which introduces uncertainty because it encompasses identical and indistinguishable [particles] which can only be brought into the realm of certainty by 'measurement'. [B]ecause of this creative uncertainty we cannot predict what a measurement will reveal until it happens. This, I feel, is where Einstein went wrong in a misunderstanding of identical quantum states and distinct quantum events. We will encapsulate this idea in a layered network theory, the layer of identifiable observations being the outcome of a layer of unpredictable identities. Gaussian curvature - Wikipedia
Because there is no space in the pure quantum phase / energy world there are identical particles which cannot be distinguished from one another as particles can be distinguished in space-time.
Ballet to music - Hilbert → 4D. Coppelia ABC iview: The Australian Ballet
How do we transform music into action at constant entropy: Serial to parallel, fanout.
Same number of players in the orchestra as dancers on stage/ensemble.
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The musical score is a list of actions coded by frequency, volume and time.
The coupling between the music and the action is probabilistic, not deterministic.
Pais page 205: 'This is the dawn of the correct formulation of equivalence as a principle that holds only locally', ie in time alone, not space-time?
page 206: 'By the spring of 1912 Einstein knew that the source of gravitation was not just ponderable matter but also field energy. He realized that gravitational energy is to be included as a source and that the gravitational field equations were therefore bound to be nonlinear. He saw that the equivalence principle held only locally. As yet he had no theory of gravitation, but he had learnt a lot of physics.'
Pais page 211: (see also Notes 2003/04/20 and 1983/08/07) 'If accelerated systems are equivalent then euclidean geometry cannot hold in all of them. . . . Gauss's theory of surfaces holds the key to unlocking this mystery . . . I realized the foundations of geometry have physical significance.'
Saturday 21 August 2020
I live in a sea of doubt which first threatened to drown me in my youth. This is a consequence of the failure of the two sources of certainty I was brought up to believe in: theology and[page 342]
physics. The first to fail was theology. I went to Catholic schools beginning in a small rural town where my teachers were relatively unsophisticated nuns and brothers, strong in their faith but far from the mainstream of theology. [Then we moved to the city and] my last two years of school were taught by well educated Catholic priests, members of the Dominican Order. This ancient order was founded by Dominic Guzman and approved by Pope Honorius III in 1216 by the papal bull Religiosam Vitam. Religiosam vitam - Wikipedia
This order was fortunate to be home to many leading theologians including the star of them all, Thomas Aquinas (1225-1275) whose work remains officially approved in Canon Law, the Constitution of the Roman Catholic Church. By some mysterious process I was judged to have religious vocation and entered the order on my 18th birthday, 12 January 1963 to be trained as a priest. I did well in my studies and found the Summa of Aquinas particularly exciting but saw that much of Aquinas' work, which was based on the work of Aristotle, was inconsistent with the physics I had learnt at school. Thomas Aquinas - Wikipedia
In time I began to feel that the five ways Aquinas used to prove that God is not the world did not convince me and that a firmer foundation for real scientific theology would be to assume the identity of God and the Universe. I expressed this view in an essay which was deemed to be heretical and asked to leave, my solemn vows of poverty, chastity and obedience annulled by papal rescript. This was 1967. Jeffrey Nicholls (1967): How Universal is the Universe?
Like a fish out of water I gradually adapted to secular life but kept on reading theology and physics and in 1987 I went public with a series of lectures on 2BOB radio which were received without
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murmur. I was now 42 and began to think more seriously of establishing a union between physics and theology to give substance to my theological hypothesis. I this process I learned that the state of physics is no more credible that the state of theology [although both enjoy practical and popular success] and began to write essays on the subject, my most recent work in progress being called Cognitive Cosmology which purports to show that it is reasonable to understand the universe as the mind of God. My problem with physics is that the current doctrines of quantum field theory are riddled with mathematical problems, perhaps the most egregious of which is the computation of a value known as the cosmological constant which differs from the observed value by something in the region of 100 orders of magnitude. Jeffrey Nicholls (1987): A theory of Peace, Meinard Kuhlmann: Quantum Field Theory, Cosmological constant problem - Wikipedia
Cognitive cosmology is an attempt to find some firm physical and theological ground before I die by reconciling what we know about our universal habitat with what we know about ourselves so that i can feel at home in the world. This essay currently has the following elements. First, statement of my program, along the lines expressed here; second a set of principle to guide the work; third critique of the current theological and political positions of the Roman Catholic Church; fourth a similar critique of modern physics; and fifth an attempted reconstruction of theology and physics beginning with the one body of theory which seems to be both logically and mathematically consistent and very closely aligned to astronomical and cosmological observation, Einstein's general theory of relativity. This theory provides us with a picture of the overall structure of the universe. I then invoke the theory of fixed points in dynamical systems to lay the foundation
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for a quantum mechanical theory of fundamental particles consistent with the theory of relativity and go on from there to speculate about the evolution of the universe from the initial singularity predicted by relativity which I identify with the classical Thomistic divinity.
My state remains a sea of doubt, but like Boethius, I have some consolation from the philosophy developed in this essay and hope that it may serve as a foundation for the next twenty years of my theological development. Anicius Manlius Severinus Boethius (1983): The Consolation of Philosophy
To new notebook DB 87: Cognitive Cosmology
