Notes
Sunday 8 August 2021 - Saturday 14 August 2021
[Notebook: DB 86: Hilbert / Minkowski]
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Sunday 8 August 2021
According to my theory, which I believe, I am these days walking around a fixed point in God. Is it as exciting as I thought heaven would be when I was young? It is hard to remember. I imagine that I was fully deceived by the terminology, eternal bliss. Later I was sucked in by the stories about Aquinas that he had had a mystical vision that led him to stop work and state that his story looked like straw to him. As lot of this was reinforced by the general
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mystical myth that we earn heaven by self abegnation prayer and fasting, not to mention hair shirts for those whose spiritual advisors judged them ready for it. I was pleased to see that earlier this year when I read Dante's Paradiso that he had very little to say about what fun it was and concentrated a lot on bright lights which would have been pretty rare in his day when the best lights were candles and oil lamps. Now looking back all I really miss is the eternal life bit, because I have concluded that heaven as advertised would be deadly boring. The beauty of the divine universe is that it has exciting contrasts between pleasure and pain and the future is wonderfully unpredictable. There is much unnecessary evil in the world that mostly seems to be a consequence of those times and places where survival is a zero sum game and greed and violence have a selective advantage, but it seems that once we establish systems to take care of everybody's physical and psychological needs deliberate violence and the infliction of pain will take on the guise of a disease we need to cure. Dante Alighieri (1986): The Divine Comedy Vol. III: Paradise
Monday 9 August 2021
What have I got to say about QFT and gravitation? Does my much hyped separation of Hilbert from Minkowski space and the use of the velocity of light and contact transformation to explain the emergence of space-time facilitated by null geodesics [actually work]? It is time for a new idea perhaps centred around renormalization, given the idea that the symmetry with respect to complexity characteristic of networks would seem to make renormalization in the Hilbert
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regime superfluous and revealing that the problem lies in making particles of zero size in Minkowski space, thereby introducing unnecessary and unphysical [infinities] that have to be removed by arbitrary subtractions.
Gravity is a potential, a curvature, and so [we] see it in the first bifurcation represented by the Lagrangian
S = ∫ (KE - PE) dt = 0
All my work is part of an antiwar movement [beginning with the theory of peace] Jeffrey Nicholls (1987): A theory of Peace: Lecture 1: Mathematical Theology, Churchill (film) - Wikipedia
Gravitation arrives with the bifurcation of energy into potential and kinetic which we imagine begins as soon as an act acts, revealing its potential and its action, so we have a sort of Dirac delta in the Lagrangian, so KE - PE = 1/ℵ0 × eternity = ℵ0 = 1 quantum of action: S = ∫ (KE - PE) dt = 1. Does this make any sense? — we see gravitation as a conservative field whose role is to honour the fact that the universe is one quantum of action whose energy is nevertheless zero. Somewhere in here potential goes with space, kinetic with time. So we must give some thought to the fact that energy and momentum transform the same way as time and space. It would be good to be intelligent enough to understand this in the way that the universe ≡ god understands it.
Tuesday 10 August 2021
One source of hope for me is a bit like the history of the wheel: the fact that people can miss out on a very simple idea even though it is very close. The special theory of relativity
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is another example. The Lorentz tranformation was well established before Einstein's time but he looked at physics from a new perspective and solved all the old problems, in effect, at a stroke [after ten years of thinking about chasing a light beam] (Voight 1887, Pais pp 121, 131). Abraham Pais (1982): 'Subtle is the Lord...': The Science and Life of Albert Einstein
I am struggling to shine the zero bifurcation and the heuristic of simplicity on the origin of gravitation which we take to be a very early determinant of the shape of spacetime. We have used null geodesics and quantum contact transformations to get from Hilbert space to Minkowski space, but one guess is that we have to see this [realized] in terms of photons, electrons and positrons through the light of the Dirac equation in Minkowski space and this brings in an automatic role for the gamma matrices.
The world is full of wonderful physics, like pressure liquidating ice to make ice-skating possible, not to mention LEDs, lasers, transistors, etc etc, divinity revealed, not to mention life, of course. Sonja Henie - Wikipedia
Dirac equation gives un an entree to 4D and the gamma matrices eliminate cross terms to give us a set of liner orthogonal vectors, fitting special relativity to Hilbert space (?). Dirac equation - Wikipedia
Particles have independent existence and move through space. What does this mean, (or not mean) — inertial motion, a body moves subject to the shape of the space in which it is moving, as the moon around the Earth. I know so little but have such large ambitions.
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Wednesday 11 August 2021
What I like about Einstein is his certainty. He has done the detailed work and is confident in the result, which is why he said the Lord God is subtle, but he is not malicious. This trait did not serve him well at the end because he continued in his attempt to discretize our quantized world with continuous functions. This may have been a consequence of his supreme skill with probabilistic arguments such as his discovery of the photon where his studies of discrete events were carried, by the law of large numbers, into a discussion of continuous functions. Continuous functions are a useful shorthand in this case and their only legitimate use may be in probability theory, as Kolmogorov realised. Andrey Kolmogorov (1956): Foundations of the Theory of Probability
Standing in the garden for my morning application of surplus nitrogen to the soil I realize that the atmosphere is the aether of birdsong, carrying all their sounds by linear superposition from which each listener can pick out the signal relevant to it. Aether (classical element) - Wikipedia
My position seems to be the opposite to Einstein: I am very uncertain because my limited comprehension leads me to skim over things looking for ideas in the same way that I look for books, skimming over their spines many time before my eye finally settles on the one I want. I am quite certain that the universe is divine, which is my radical break from tradition, but I am very uncertain and getting no more guidance from modern science that Aquinas got from Aristotle, but I am hoping that the cumulative effect of my rather groundless speculations will ultimately
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carry weight. My faith us that the Christian story is so ludicrously incredible that anything can be better. My ontological foundation of credibility was severely distorted in my youth and it is slowly coming back onto a credible course as I line things up approximately and then come back to refine them like a sculptor gradually approximating to the desired shape.
I feel that the network model provides a reason for the existence of three dimensional space to yield universal connectivity in a realm where we use continuous wires but what about the world of particles moving through continuous space [where (maybe) orthogonality, like electrical insulation, is established by incommensurable frequencies]. Here we may see another argument arising from Dirac's four dimensional solution to relativistic quantum mechanics where the gamma matrices in some way contribute to to the orthogonality of the four dimensions by eliminating 'cross terms'. Perhaps we are to think of the null geodesics followed by photons as effectively 'wires' that lose their effectiveness if they cross.
Boethius: De consolatione Philosophiae: speculative (Θ) and practical (Π) – rather like potential and kinetic energy. Anicius Manlius Severinus Boethius
Pais page 138: 'Special relativity represents the abandonment of mechanical pictures as an aid to the interpretation of electromagnetism.' But I would really like to substitute a logical picture which must be quantized to the root.
QFT: Light and electrons, giving rise to the infinity problem. Richard Feynman (1988); QED: The Strange Story of Light and Matter
Pais page 151: Planck noted that action is an invariant, not only
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in point mechanics (where is equals the quantity ∫ L dt) but in general. From this he derived that his constant h is a relativistic invariant.
Thursday 12 August 2021
Continuing my scheme of off-label use of modern physics I am exploring the use of Dirac's equation for an explanation of 4D Minkowski spacetime, giving four separate linear descriptions of fermions. This seems reasonable apart form the interaction of antimatter but we can paper over that for the time being, take 4D space as established and go to discuss the network of bosons and fermions and an interpretation of quantum field theory which avoids the traps of continuity, taking advantage of it instead through Noether's theorem and the possible non-quantization of [gravitation].
Loses on the stock market are mildly painful but one can rely on the overall expansion of the economy to save us in the end and meanwhile I have Boethius' Consolations to remind me that every little insight I have into the theology of the divine universe as in a sense worth all the money in the world and I am totally secure under the wing of my benevolent government.
Continuity is where nothing happens, hence Noether's theorem and the structure of space and time, so we see space and time evolving unitarily in quantum mechanics and being pixellated by the continuous unitary evolution of the wave function which is ultimately binary. Featureless space [where nothing happens] is the dual of the quantum of action. Noether's theorem - Wikipedia
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Friday 13 August 2021
A dead end on 4D space via Dirac since we begin there with the assumption that space[time] is 4D and so bring out nothing new. So the best thing I have so far is the need for 3D space to achieve complete electrical connection with uninsulated [1]D wires. Where can we go from here? How does the idea translate into quantum mechanical terms? So let us go off and think about gravitation some more, since it obviously very primordial and curvature of space is expressed by geodesic deviation and geodesics are the nearest thing we have to wires in the theory. Reading physics textbooks with heuristic simplicity in mind is depressing. Gravitational collapse as in black holes is represented by the termination of possible geodesics in a point. How do we make that point sprout a 4D space[time] full of geodesics?
Mark Satta: Orwell: Lion and Unicorn 'The totalitarian idea is that there is no such thing as law, there is only power . . . .. Mark Satta: Orwell’s ideas remain relevant 75 years after ‘Animal Farm’ was published , George Orwell: The Lion and the Unicorn: Socialism and the English Genius
The mathematical details do not seem to be as helpful as the ideas that determine the shape of the mathematics. So the Lorentz transformation is demanded by special relativity to maintain the constancy of the velocity of light in all inertial frames. So what is the idea behind the Dirac equation?
The Suicide Squad (film) - WikipediaWe are now getting to the point where gravitation is the heart of god and the fact that the universe is contained within the initial
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singularity explains the creation of the fixed points in the world which are a little gods like the starfishes spawned by the starfish in the Suicide Squad. The shape of space is determined by its containment in the region of consistency. So we think of gravitation as the source of mind and intelligence which sounds loverly and we can apply fixed point theory in the creation if information as a physical entity. A long shot, but we are working on long shots here. The Suicide Squad (film) - Wikipedia
I had a bad day trying to write about the four dimensions of spacetime but now I can do it as a minimum geometrical requirement for the closure of spacetime (?).
So beautiful that it has to be true according to the Dirac/Einstein principle of truth. Gravitation itself is continuous so it fits a physical [fixed] point theorem and the physical information is the transfinite structure of the universe.
This might be the best outcome of my struggles and it opens a way for the discussion of renormalization and a new Ansatz for quantum field theory to replace the space of harmonic oscillators and infinite Feynman functional derivatives of a propagator which may not explore the whole universe but simply move from a to b.
Saturday 14 August 2020
Can the network model explain why spacetime is 4D? Let us say that evolution by natural selection allows things to become as
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complex as necessary to exist [by reproduction] but no more complex, rather like the paradigm that explanations should be as simple as possible but not oversimplified (Einstein somewhere). Herbert Spencer Lecture. Albert Einstein (1933): On the Method of Theoretical Physics
Gravitational collapse occurs when geodesics get so close together than they merge and disappear. If we think of geodesics as wires and apply the notion that the minimum space necessary to join every point to every other independently is 3D (as the designers of printed circuits know) then we have an approach to evolutionary minimalist approach to the complexity of space.
