Notes DB 91: Divine_Gravitation_2024
Sunday 22 September 2024 - Saturday 28 September 2024
[page 151]
Sunday 22 September 2024
. . .
Since the Dominican Order expelled me I have considered myself a fringe dweller possessed by an impossible idea, that the universe is divine, that theology can become a real science and that contemporary theology is rubbish. My book, written in my
[page 152]
80th year is a last gasp effort to reenter the mainstream by laying the foundations of a new layer of science and I am convinced that if I can assert some credibility my book might have global implications.
. . .
Monday 23 September 2024'
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Tuesday 24 September 2024
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Wednesday 25 September 2024
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Thursday 26 September 2024
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[page 153]
Move weekend 5-6 October.
Quantum mechanics has misunderstood the quantum — cosmological constant problem; Feynman path integral and de Broglie. Path integral formulation - Wikipedia, Louis de Broglie (1929): Nobel Lecture: The Wave Nature of the Electron
Theology has totally misunderstood god; quantum mechanics has misunderstood the quantum. Perturbation theory homing in on Diophantine analysis. Diophantine equation - Wikipedia
Friday 27 September 2024
I am facing a dream come true. I have argued that theology has misunderstood god and quantum mechanics has misunderstood the quantum. The real meaning of the quantum was expressed by Planck, Bohr and de Broglie. Kinematically it is one execution of a logical operator. Dynamically it is one quantum of angular momentum [spin]. Bohr noted that permissible atomic orbitals are characterized by an integral number of quanta of angular momentum, a stationary integral number of quanta of action consistent with the quantum application of Hamilton's principle. We can say the same thing about Feynman path integral method which tells un in effect that the probability of a certain quantum event is 1, ie it is certain or it happens like an atomic orbital, when it involves a stationary integral number
[page 154]
of quanta of action. The quantum itself is the measure of the smallest possible action. Bohr model - Wikipedia
We understand the application of this idea in the theory of measurement explained by Zurek on page 14: Measurement—the interface between the Minkowski and Hilbert spaces. The application of the Born rule in this situation explains the efficacy of Feynman diagrams in the reconciliation of quantum measurements of various properties through the integration of the frequencies of various events represented by the spectrum of eigenfunctions and corresponding eigenvalues produced by the linear operator acting in a particular measurement. So all possible eigenvalues, weighted by their probabilities are accounted for in a measurement in Minkowski space which is a composite of the countable number of possible paths to the event in question which is analogous to the information theoretical computation of the entropy of a source A with ai paths [in a Feynman diagram] each with a probability of execution of pi.
From a theological point of view we may think of the Universe as a source of revelation of itself which we can observe at various levels of resolution ranging from a catalogue of elementary events to a catalogue of large scale events like wars supernovas, etc, each of which is in my case a network of elementary events.
This approach seems to solve all the problems I have
[page 155]
identified in theology and physics.
First, we get rid of the stupid idea that the so called 'uncertainty principle' is the source of the quasi-infinite energy which constitutes the cosmological constant problem [which is a consequence of confusing the abstract mathematics with the concrete reality. Feynman diagrams may also fall into this category, overthinking simple conversations by heaping a whole conversation into one moment]. Cosmological constant problem - Wikipedia
Second, by founding reality on quantum theory in Hilbert space we enable the pristine linear power of quantum computation and quantum communication without being obscured by the quadratic fog [of cross terms, eliminated by Dirac's gammas] of uncertainty attributed to continuous Minkowski space. Quantum logical operations are sharp, precise and complete, analogous to what we observe in the discrete operations of Turing machines [a linear operator is just like a lot of adding machines (superposers) working in parallel]. Nielsen & Chuang (2016): Quantum Computation and Quantum Information, Dirac equation - Wikipedia
Third, by freeing Feynman's path integral approach to operate in a linear space prior to space and time it makes sense of Feynman's contention that every possible quantum operation must be integrated over the whole of spacetime to make any sense. This works because spacetime does not exist in the Hilbert layer of the Universe, only the abstract kinematic structure of mathematical quantum mechanics, operating as a kinematic version of Plato's forms motivated by divine naked gravitation playing the role of Aristotle's self observing intellectual unmoved mover. Michael Bordt (2011): Why Aristotle's God is not the Unmoved Mover
[page 156]
Hilbert's formal method in mathematics does not create energy. It creates the excited mathematicians and creative people in general that motivates then to art.
Fourth, it reveals the true role of divinity, aka naked gravitation, in the creation of the Universe, itself, analogous to the biological creation of a living creature from a fertilized egg. The metaphysical structure of the initial singularity, expressed by the scholastic dictum that essence and existence are identical in divinity opens the creative power to spanning the complete space of possibility, as we expect of an omnipotent being. Aquinas, Summa, I, 3, 4: Are essence and existence the same in God?
Fifth, as in the case of Newton and Darwin, we do not need to know the actual details of the evolutionary creative processes to postulate their existence and to argue back from the existence of rabbits, fermions and bosons and Minkowski space to the possibility of their creation by quantum theoretically consistent processes. As Streater and Wightman write: ' the quantum theory of fields never reached the stage where one could say with confidence that it was free of internal contradictions, nor the converse.' Streater & Wightman(2000): PCT, Spin, Statistics and All That
Sixth. We greatly simplify the structure of the Universe with the assumption that all conversations between elementary particles are one on one, fermions communicating through bosons, one word or letter at a time from their respective vocabularies. This is an approach to calculating cross sections that seems parallel to Feynman diagrams without the mysterious influences of quantum fluctuations, where are absent in logic.
[page 157]
S&W page 2: ' The task of the first chapter is to provide a language in which physical states with simple transformation properties have a simple description. For example the concepts of bare mass and bare vacuum have not been introduced.'
States in physical systems are represented by unit rays since the computation of probabilities by squared inner products is unaffected by multiplication of the vectors involved by complex factors of absolute value 1, ei θ
Super-selection rules (S&W p 5); Things never produced: superposition of different charges; every physically realizable state must be an eigenstate of B, the Baryon number, and (-1)F where F is an even integer for states of integer spin and an odd integer for states of half odd integer spin. Operator (-1)F arises because the invariance of results of experiment under rotation of 2π around any axis.
page 7: It should be ephasized that the . . .
seventh: superselection rules for Q, B and (-1)F, like all the laws of physics, depend upon experiment [but all these observations are in Minkowski space and are therefore perhaps constrained [to be] below the capability of pure quantum mechanics, as we might find in a pure Schrödinger equation in [an independent] Hilbert space].
Eighth - Symmetry
Action: Schwinger Nobel and Dirac on action [Lagrangian]. Julian Schwinger (1965): Nobel Lecture: Relativistic Quantum Field Theory, P. A. M. Dirac (1933): The Lagrangian in Quantum Mechanics
[page 158]
Ninth - 'The strange story of light and matter - Feynman.' The path integral method serves as a proof for the independence of Hilbert space, although there are no paths, no time and phase is just an abstract parameter representing what? page 13: Is Hilbert space independent of Minkowski space?. Physics only talks about things that work. Cosmological constant does not work.
A combination of quantum wave mechanics with the Nyquist-Shannon digitization theorem effectively makes a quantum computer equivalent to a Turing machine. The big advantage attributed to [quantum] computation is that linear operators working on vectors are believed to work in parallel, but this might be a delusion arising from the superposing large numbers of discrete operations as though the collapse of the wave function did not happen. Schrödinger equation - Wikipedia, Nyquist-Shannon sampling theorem - Wikipedia, Shor's algorithm - Wikipedia
Saturday 28 September 2024
Action at a distance. Physics and theology are big mistakes. Isaac Newton produced a wonderful theory of the Solar system but it had one massive flaw [according to many commentators] - action at a distance.
What is the answer to quantum field theory: the theological answer. The cognitive answer? The remedy to large language models answer? The theologically icompatible?
[page 159]
Struggling to find the thing? I hope the empty space in my brain is going to be filled soon with a clear and distinct idea - Minkowski space.
Dirac Lagrangian: ' We must therefore seek to take over the ideas of the classical Lagrangian theory, not the equations of the classical Lagrangian theory: Action is the time integral of the Lagrangian - no cocordinates and velocities in quantum mechanics.
Say the same thing in a different language - Large Language Model.
What is my alternative: reverse the order of Minkowski and Hilbert.
The output of the Lagrangian is very simple: each quantum process takes precisely one quantum of action. QED. Must write it tomorrow.
The book has slowly developed an alternative to quantum field theory. I don't have to say it all on the alternative chapter, just summarize the general idea and note its advantages: page 24: Is there an alternative to field theory?
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Further readingBooks
Nielsen (2016), Michael A., and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2016 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002.
Amazon
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Streater (2000), Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2000 Amazon product description: 'PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.'
Amazon
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Links
Alexandra Petri (2024_09_25), Opinion: It is so much nicer being a woman in Trump’s world, “You will no longer be abandoned, lonely or scared. You will no longer be in danger. You’re not gonna be in danger any longer. You will no longer have anxiety from all of the problems our country has today. You will be protected, and I will be your protector. Women will be happy, healthy, confident and free. You will no longer be thinking about abortion.” Donald Trump's teleprompter at a campaign rally in Pennsylvania on Monday back |
Aquinas, Summa, I, 3, 4, Are essence and existence the same in God?, 'I answer that, God is not only His own essence, as shown in the preceding article, but also His own existence. This may be shown in several ways.
First, whatever a thing has besides its essence must be caused either by the constituent principles of that essence (like a property that necessarily accompanies the species--as the faculty of laughing is proper to a man--and is caused by the constituent principles of the species), or by some exterior agent--as heat is caused in water by fire. Therefore, if the existence of a thing differs from its essence, this existence must be caused either by some exterior agent or by its essential principles. Now it is impossible for a thing's existence to be caused by its essential constituent principles, for nothing can be the sufficient cause of its own existence, if its existence is caused. Therefore that thing, whose existence differs from its essence, must have its existence caused by another. But this cannot be true of God; because we call God the first efficient cause. Therefore it is impossible that in God His existence should differ from His essence.' back |
Aquinas, Summa, I, 3, 4, Are essence and existence the same in God?, ' I answer that, God is not only His own essence, as shown in the preceding article, but also His own existence. This may be shown in several ways.
First, whatever a thing has besides its essence must be caused either by the constituent principles of that essence (like a property that necessarily accompanies the species — as the faculty of laughing is proper to a man — and is caused by the constituent principles of the species), or by some exterior agent — as heat is caused in water by fire. Therefore, if the existence of a thing differs from its essence, this existence must be caused either by some exterior agent or by its essential principles. Now it is impossible for a thing's existence to be caused by its essential constituent principles, for nothing can be the sufficient cause of its own existence, if its existence is caused. Therefore that thing, whose existence differs from its essence, must have its existence caused by another. But this cannot be true of God; because we call God the first efficient cause. Therefore it is impossible that in God His existence should differ from His essence.' back |
Bohr model - Wikipedia, Bohr model - Wikipedia, the free encyclopedia, 'In atomic physics, the Rutherford–Bohr model or Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with attraction provided by electrostatic forces rather than gravity.' back |
Cosmological constant problem - Wikipedia, Cosmological constant problem - Wikipedia, the free encyclopedia, ' In cosmology, the cosmological constant problem or vacuum catastrophe is the disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and theoretical large value of zero-point energy suggested by quantum field theory.
Depending on the Planck energy cutoff and other factors, the discrepancy is as high as 120 orders of magnitude, a state of affairs described by physicists as "the largest discrepancy between theory and experiment in all of science" and "the worst theoretical prediction in the history of physics".' back |
Diophantine equation - Wikipedia, Diophantine equation - Wikipedia, the free encyclopedia, 'In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values). A linear Diophantine equation is an equation between two sums of monomials of degree zero or one. An exponential Diophantine equation is one in which exponents on terms can be unknowns.
Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic surface, or more general object, and ask about the lattice points on it.' back |
Dirac equation - Wikipedia, Dirac equation - Wikipedia, the free encyclopedia, 'In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1⁄2 massive particles such as electrons and quarks, for which parity is a symmetry, and is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It accounted for the fine details of the hydrogen spectrum in a completely rigorous way.' back |
Julian Schwinger (1965), Nobel Lecture: Relativistic Quantum Field Theory, ' Following the establishment of the theory of relativity and quantum mechanics, an initial relativistic theory was formulated for the interaction between charged particles and electromagnetic fields. However, partly because the electron’s magnetic moment proved to be somewhat larger than expected, the theory had to be reformulated. Julian Schwinger solved this problem in 1948 through “renormalization” and thereby contributed to a new quantum electrodynamics.' back |
Lexin Zhou et al (2024_09_25), Larger and more instructable language models become less reliable, ' Abstract: The prevailing methods to make large language models more powerful and amenable have been based on continuous scaling up (that is, increasing their size, data volume and computational resources) and bespoke shaping up (including post-filtering, fine tuning or use of human feedback). However, larger and more instructable large language models may have become less reliable. By studying the relationship between difficulty concordance, task avoidance and prompting stability of several language model families, here we show that easy instances for human participants are also easy for the models, but scaled-up, shaped-up models do not secure areas of low difficulty in which either the model does not err or human supervision can spot the errors. We also find that early models often avoid user questions but scaled-up, shaped-up models tend to give an apparently sensible yet wrong answer much more often, including errors on difficult questions that human supervisors frequently overlook. Moreover, we observe that stability to different natural phrasings of the same question is improved by scaling-up and shaping-up interventions, but pockets of variability persist across difficulty levels. These findings highlight the need for a fundamental shift in the design and development of general-purpose artificial intelligence, particularly in high-stakes areas for which a predictable distribution of errors is paramount.' back |
Louis de Broglie (1929), Nobel Lecture: The Wave Nature of the Electron, ' The necessity of assuming for light two contradictory theories-that of waves and that of corpuscles - and the inability to understand why, among the infinity of motions which an electron ought to be able to have in the atom according to classical concepts, only certain ones were possible: such were the enigmas confronting physicists at the time I resumed my studies of theoretical physics.
Now a purely corpuscular theory does not contain any
element permitting the definition of frequency. This also renders it necessary in the case of light to introduce simultaneously the corpuscle concept and the concept of periodicity.
On the other hand the determination of the stable motions of the electrons in the atom involves whole numbers, and so far the only phenomena in which whole numbers were involved in physics were those of interference and of eigenvibrations. That suggested the idea to me that electrons themselves could not be represented as simple corpuscles either, but that a periodicity had also to be assigned to them too. . . .
Thus to describe the properties of matter as well as those of light, waves and corpuscles have to be referred to at one and the same time. The electron can no longer be conceived as a single, small granule of electricity; it must be associated with a wave and this wave is no myth; its wavelength can be measured and its interferences predicted.
It has thus been possible to predicta whole group of phenomena without their actually having been discovered. And it is on this concept of the duality of waves and corpuscles in Nature, expressed in a more or less abstract form, that the whole recent development of theoretical physics has been founded and that all future development of this science will apparently have to be founded.' back |
Michael Bordt (2011), Why Aristotle's God is not the Unmoved Mover, ' The aim of this essay is to show that the view—popular among
certain philosophers and theologians—that Aristotle’s God is the
unmoved mover is incorrect, or at least leads to serious misunderstanding. In a nutshell: among other things, the project of the twelfth book of the Metaphysics is to determine what the first ousia is. This first ousia is not identified with God in so far as it is an unmoved mover, but in so far as it is the actual activity (energeia) of thinking. To put matters differently, the actual activity of the first ousia does not consist in moving anything. Its activity rather consists in the exercise of reason, in thinking. Since, however, thinking is without qualification the best activity, and since God is that being who just does engage in the best activity, the first ousia, in so far as it is the same as the activity of thinking, must be God. Thus we perhaps expect that, at the summit of ontology, God himself will be the object of this first philosophy. Metaphysics Λ meets such an expectation only in a very limited way.
The limitation is the following: that which, so to speak, stands at
the summit of metaphysics is not God, but the activity of reason.
While this activity is identified with God, it is not so identified directly or immediately, but only as mediated by way of the conception of the best possible life. The twelfth book of the Metaphysics thus provides to an even lesser extent than is usually assumed the outlines of a theology. By way of recompense, however, Aristotle offers us a truly breathtaking metaphysics.' back |
Nyquist-Shannon sampling theorem - Wikipedia, Nyquist-Shannon sampling theorem - Wikipedia, the free encyclopedia, ' In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called "analog signals") and discrete-time signals (often called "digital signals"). It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.' back |
P. A. M. Dirac (1933), The Lagrangian in Quantum Mechanics, ' . . . there is an alternative formulation [to the Hamiltonian] in classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulation are closely related but there are reasons for believing that the Lagrangian one is more fundamental. . . . Secondly the lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; . . .. ' [This article was first published in Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933), pp. 64–72.] back |
Path integral formulation - Wikipedia, Path integral formulation - Wikipedia, the free encyclopedia, 'The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a quantum amplitude. . . . This formulation has proved crucial to the subsequent development of theoretical physics, since it provided the basis for the grand synthesis of the 1970s which unified quantum field theory with statistical mechanics. . . . ' back |
Schrödinger equation - Wikipedia, Schrödinger equation - Wikipedia, the free encyclopedia, ' In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a quantum system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger. . . .
In classical mechanics Newton's second law, (F = ma), is used to mathematically predict what a given system will do at any time after a known initial condition. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). It is not a simple algebraic equation, but in general a linear partial differential equation, describing the time-evolution of the system's wave function (also called a "state function").' back |
Shor's algorithm - Wikipedia, Shor's algorithm - Wikipedia, the free encyclopedia, ' Shor's algorithm is a polynomial-time quantum computer algorithm for integer factorization. Informally, it solves the following problem: Given an integer N, find its prime factors. It was invented in 1994 by the American mathematician Peter Shor. . . . If a quantum computer with a sufficient number of qubits could operate without succumbing to quantum noise and other quantum-decoherence phenomena, then Shor's algorithm could be used to break public-key cryptography schemes, such as the widely used RSA scheme. RSA is based on the assumption that factoring large integers is computationally intractable.' back |
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