Notes DB 90: Psychogenesis_2024
Sunday 28 January 2024 - Saturday 3 February y 2024
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Sunday 28 January 2024
This site is built on the idea that the Universe evolved, from the parallel idea that the scientific method is an example of evolutionary method, ie we put a few thousand random PhD students on to study thousands of problem at the boundary
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between what is known and what is unknown and rely on the lucky few with names like Dirac, Heisenberg and Einstein to come up wth answers which often open up new perspectives for development. At the physical root of the process is quantum theory which provides a paradigm for creation and scientific method which we imagine to have been set up by the initial singularity discovering Hilbert space through random mappings onto itself and the operation of fixed point theory; and then transformation of this space by the operations of what we now know as quantum mechanics to come up with stationary states which are converted into real physical particles by energy derived by the bifurcation of the initial dynamic gravitation into potential and kinetic energy, equal and opposite, so preserving the structureless symmetry of the initial singularity (see Cognitive Cosmology page 17: Gravitation and quantum theory—in the beginning.
The Hilbert / quantum algorithm having been discovered and encoded in dynamic particles in Minkowski space then continued on its creative way, ultimately appearing in out human minds to which we attribute our experience of consciousness and intelligence. This coincidence we might say is explained by the symmetry with respect to complexity and underlies the claim that the world is cognitive and the hypothesis, embodied in the website cognitive cosmology, which develops the concept that the Universe is divine and all things are children of god. Cognitive Cosmology (2024)
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Although the reality of [engineered] quantum computation is [still] a dot on the horizon, the physical utility of quantum theory more or less proves that the Universe achieved this goal in the first few moments of creation and has continued in this vein for fourteen billion years to convert a structureless but omnipotent initial singularity into the magnificent Universe we are beginning to understand, guided only by the principle that actual contradictions cannot exist. Xavier Waintal (2023_12_29): The Quantum House Of Cards
Waintal page 1: ' At the root of this analysis is the sinple observation that the quantum computer is an analog machine, ie its internal structure is described by a large set of complex numbers that can vary continuously'. I am inclined to reject this and confine the Hilbert space to Cn giving a [countable] set of basis states that can be understood as ℵ0 roots of unity which in [ordered] superposition may give us ℵ1 normalized vectors.
page 2: ' There is no simple path to designing a new quantum algorithm' [although we may suspect that an evolutionary process with sufficient variation in its input may be able to find such an algorithms, and given that we are here, we can probably guarantee that the evolution of the Universe has found a large fraction of the possible algorithms embodied in self-adjoint operators. 'Also, as we shall see, all the known algorithms are very demanding in terms of hardware quality and quantity.' Self-adjoint operator - Wikipedia
page 4: Quantum Error Correction: QEC: 'Russian doll nesting problem transforms the initially simple process of a one qubit gate to thousands, tens of thousands or more physical operations depending
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on the required level of precision. The Russian doll bottleneck excludes all but the fastest hardware from practical applications. Even assuming gates as fast as 1o ns, the overall computation time for a full application often reaches days for a single answer to a single problem.
Waintal page 5: "syndrome bottleneck". The analysis of a syndrome is a difficult (NP complete) problem. For a billion physical qubits quantum computer, the data rate coming from the syndromes is of the order of 1015 bits per second (109 / 10-6). NP-complete - Wikipedia
The last difficulty is that QEC corrects certain types of errors. Others are not corrected and can be fatal to cmputations.
page 6: The simulation of a seminal quantum supremacy experiment, initially assumed by Google to take 10 000 years on the largest supercomputer now requires just 6 seconds according to their own reckoning (an improvement of eleven orders of magnitude on the classical algorithm side).
' The number of processes that are apparently exponentially difficult and that were solved in polynomial time with numerical techniques is quickly growing.'
' The IBM quantum advantage experiment (ref 21) was simulated within days of the article publication (refs 37-39).' Tindall, Fishman, Stoudenmire & Sels: Efficient tensor network simulation of IBM's Eagle kicked Ising experiment (2023)
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Monday 29 January 2024
Spent an hour walking to Bunnings to get bolts and a drill bit to fix my digging fork because I have taken up gardening planting sunflowers. The owner planted the last lot in mid September and they matured in early January. It will be interesting to see of these planted now will mature before winter shuts them down.
Fortunately my beloved brain rewarded me for this exercise by revealing the following to me. I am developing my Universe in Cognitive Cosmology by analogy with Darwin's theory of evolution. We know that given enough time, every base in every genome in the world has a certain probability of replacement. This means that we can imagine the set of possible genomes in the world to have the cardinal ℵ1 the cardinal of the set of permutations of the set of natural numbers [cardinal ℵ0].
We might guess that the average genome comprises a billion bases, so that we might find any one of (one billion)! species on the planet. Of course a very large proportion of these genomes would not be viable. Species are judged and selected on their ability to survive in their environment, and as environments change species are required to adapt if they are not to become extinct. This system is quite flexible. We have seen 50 tonne dinosaurs mutate into modern 20 gram birds. Jude Coleman (2023): ‘Weird’ dinosaur prompts rethink of bird evolution
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We have noted that the evolution of science is analogous to the evolution of species (see Sunday 28th). Modern quantum field theory is a direct descendent of classical field theory that began its development with Faraday and reached its apogee in Einstein's general theory [and it still contains many traits derived from its parent, particularly continuity and determinism].
The history quantum mechanics has a similar evolution. Planck's discovery of the black body radiation law was something of a shot in the dark. Einstein clarified the picture a little by arguing that Planck's quanta are real particles, photons. Bohr's model of the atom gave some insight into the interaction of photons and atomic electrons. The discovery of quantum mechanics in the late 1920s opened the way for quantum electrodynamics. Schrödinger, Dirac and others united the matrix and wave approaches to quantum mechanics, but Dirac introduced his delta function which at the time seemed rather doubtful, although a mathematical theory of distributions has since been built around it [and has become part of axiomatic quantum theory in the hands of Streater and Wightman]. Albert Einstein (1905c): On a heuristic point of view concerning the production and transformation of light, Streater & Wightman (2000): PCT, Spin, Statistics and All That
Von Neumann avoided Dirac's delta and showed that the natural foundation for quantum mechanics is Hilbert space by realizing that a point in Hilbert's function space was an ideal representative of a quantum physical state. Trouble started when attempts to unite quantum theory and special relativity led to another problematic trick (since naturalized), renormalization. Feynman cast doubt on renormalization in his 1965 Nobel Prize lecture, but Wilson brought it into the fold in his 1982 lecture. Richard P. Feynman (1965): Nobel Lecture: The Development of the Space-Time View of Quantum Electrodynamics,, Kenneth G Wilson (1982): Nobel Lecture: The Renormalisation Group and Critical Phenomena
Maybe this marks the point of extinction of current quantum field theory and points to the need for a new start, [as von Neumann thought was necessary in order to make quantum mechanics mathematically respectable]. The story I have developed here has
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has been developed with the problems of quantum field theory flagged by Kuhlmann in mind. [He concluded (as I quoted in the abstract of Cognitive Cosmology ):
In conclusion one has to recall that one reason why the ontological interpretation of [Quantum Field Theory] is so difficult is the fact that it is exceptionally unclear which parts of the formalism should be taken to represent anything physical in the first place. And it looks as if that problem will persist for quite some time. Meinard Kuhlmann (Stanford Encyclopedia of Philosophy): Quantum Field Theory
He is writing as though the problems of infinity arising from the attempted union with special relativity has been solved by remormalization and the real remaining problems are matters of representation].
It has two foundations. First, we reject continuous mathematics as a nineteenth century mathematical ideal that does not apply to the logical and intelligent physical world [with the sole exception of the initial singularity, see below].
[and second] we reverse the order of Hilbert and Minkowski space, making Hilbert space primary and independent, the source of variation in the evolutionary world, which we introduce under the name of von Neumann vacuum to replace the vacua of traditional quantum field theory which have been totally discredited by the cosmological constant problem. Cosmological constant problem - Wikipedia
The result is the concept that the Universe is divine and cognitive, demanding the union of physics and theology leading to the line of discussion beginning on page 8: The theology of the Trinity and arriving at the relationship between gravitation and quantum mechanics discussed on page 17: Gravitation and quantum theory—in the beginning
Einstein's general theory works because gravitation itself is not quantized but through its transformation into potential and kinetic energy makes the formal fixed points developed by the kinematic operation of quantum theory which gives us the formal stationary points [suggested by Plato] which are converted into real particles [in the Aristotelian model by the attachment of the forms to matter ≡ energy] and real space by the bifurcation of gravitation [into potential and kinetic energy] and the development of Minkowski space by bosons and fermions.
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So 24.1 Gravitation and field theory discusses why the general theory works, why gravitation is omnipotent, pure action, neither kinematic nor dynamic, whose only fixed point is general covariance which is not a fixed point. Ie gravitation is identical to the traditional divinity, its essence (form) is identical to its existence (dynamic reality) as discovered by Aristotle, who did not have any superconducting super colliders but a very astute evidence based mind.
24.1 [again] Gravity, field theory, Plato (form) and Aristotle (action)
Quantum field theory is the 50 tonne dinosaur which need to be replaced by the 20 gram bird.
Feynman's diagrams may in fact be the mirror image of the eigenvalues of a quasi infinite dimensional self adjoint operator which has evolved to represent the interaction between a photons and an electron, analogous to the set of operators which have evolved to represent the pairwise interactions of all the elementary particles.
One way to perceive this is that every quantum interaction, because it is a logical interaction, involves precisely one quantum of action. This is obvious in the interactions of photons and electrons [in atoms], and we may attribute some sort of
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quantization to the interactions of photons and electrons in free systems like Compton scattering [since the stationary points in these interactions are the product of multi-dimensional self adjoint operators rather (perhaps) than intersections in Feynman diagrams]. Compton scattering - Wikipedia, Klein-Nishina formula - Wikipedia
The idea here is to go the whole hog and replace quantum field theory with the idea of a spectrum of single quantum interaction that gives the same result as a Feynman diagram approach, to be understood as developed by the evolution of Hermitian operators, with spectra and Born rule type structures that lead to the same results as Feynman. By being logical and single quantum, we expect no problem with infinity and by putting Hilbert before Minkowski we expect no problem with relativity. The Feynman path integral method seems to predict single quantum interactions and our division of processes into kinematic (Hilbert, platonic) and dynamic (energetic, classical) may serve to correct the representation problems that Kuhlmann details. All this development is a bit sudden and will take me a while to absorb, but it is based in two ideas: natural evolution selects self adjoint operators, and symmetry with respect to complexity makes quantum algorithms of superposition apply at all scales particularly in the human mind, and the spectrum and probability structure of self adjoint operator gives us a way to bypass standard quantum field theory [and the symmetry with respect to scale link between human conversation and quantum interaction gives us a new way to explore the nature of quantum interactions (see Cognitive Cosmology Principle 5: Symmetry with respect to complexity]. Path integral formulation - Wikipedia
It may be wrong but it is an interesting deviation.
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A principal objection to the standard model is its complexity. Steven Weinberg takes three volumes to tell us about quantum field theory and a standard work of gravitation, Misner Thorne and Wheeler is aptly called the telephone book, but at the root gravitation is as simple as god, its essence is its existence. Gravitation is a synthesis of stillness and perpetual motion preparing to burst into the dynamic quantum theory and classical stasis, particles. Quantum mechanics is a puppet motivated by gravitation, ie god, the initial singularity, absolutely simple, the foundation of field theory and calculus, not flat but curved, empty, meaningless but omnipotent. The first thing it created, by the action of fixed point theory, is Hilbert space, a kinematic space of ceaseless motion represented by the polar complex plane.
For god and gravitation, essence ≡ existence.
Tuesday 30 January 2024
I wake up doubting my hypothesis of a replacement model for quantum field theory based on the von Neumann vacuum, but realize that it is necessary to write out in detail the ideas sketched above so that they can go into the public domain and attract critical evaluation.
Despite my doubts, I feel very happy with my story so far. Some of my strongest incentives are
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1. That QFT fails with gravitation, because gravitation is not quantized but is a system of overlapping Minkowski spaces described by Einstein with the help of the differential manifold and 'absolute differential calculus', ie tensor analysis that makes reference frames superfluous. Differentiable manifold - Wikipedia
2. The heuristic of simplicity which fits the ideas of a dynamic gravitational singularity with no structure whose essence is identical to its existence so be summarized in [Cognitive Cosmology, page] 24.2 A theological theory of gravitation.
3. The Universe is cognitive and logical so that the application of numerical mathematics to its fundamental quantum computational processes [is a mistake]. This mathematical approach only applies in Minkowski space where rational numbers apply to space and time rates of computational events while telling us very little about the nature of these events. Stationary points in self-adjoint operators are represented by natural numbers (perhaps arising from the rational arguments in complex numbers which we conceive as integral roots of unity, ie just ℵ0 of them in Cn ).
4. The trouble with relativity which results from putting the Minkowski cart before the Hilbert horse. This is a carryover from classical field theory in which nobody could imagine a world without a divinely constituted Minkowski space as the foundation of everything. Maybe some imagined Hilbert space as a sort of ether that filled all space to be the foundation of electromagnetic waves, which is in fact truish, as de Broglie recognized. Louis de Broglie (1929): Nobel Lecture: The Wave Nature of the Electron
5. the distinction between form and material reality first introduced by Plato and developed by Aristotle reappears as the distinction between kinematic and dynamic action and clarifies a lot of the representation problems =, like the cosmological constant problem, that Kuhlmann points out in his critique if Quantum field theory. As Einstein points out, special relativity is a kinematic answer to the dynamic problems raised by Maxwell's equations. Kinematics - Wikipedia, Dynamics - Wikipedia, Albert Einstein (1905): On the Electrodynamics of Moving Bodies
[6. Cognitive cosmology: Principle 13: An unmodulated continuum carries no information]
Wednesday 31 January 2024
Plato, Aristotle, Aquinas, Lonergan & von Neumann. One gets the impression,
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reading Lonergan's Insight with his [division of] knowledge into proportionate (to the human intellect) and transcendental (the knowledge possessed by God) that he, like his predecessors, really thought they were onto something. Little did they know that they were deluded by the notion that the key to knowledge and understanding was immateriality when in fact matter is a necessary prerequisite for the representation of knowledge, as Landauer realized, working in the areas of [modern] communication and computation, that [real] information is physical (see ). Bernard Lonergan (1992); Insight: A Study of Human Understanding , Rolf Landauer (1999): Information is a Physical Entity
I also feel that the answer to the delusion lies in the genius of Hilbert and von Neumann. Von Neumann felt that quantum mechanics had to start afresh with Hilbert space to give a consistent mathematical basis to the theory of the world. The key to this is that self-adjoint operators [in Cn space] have rational diagonals, creating a link between Hilbert and Minkowski space. My new physical / theological model of the world takes advantage of this insight which respects the real nature of information.
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The eigenvalue equation may have a countable infinity of solutions, each with a certain probability perhaps related to the Born rule, and the question is does this spectrum of answers in some way resemble the details of the Feynman diagrams, and can we replace the Feynman based quantum field theory with something based on hermitian operators? What we are looking for in quantum encounters is one to one with a single quantum of action at the end of each Feynman path integral which must always end with a superposition that arrives at a full quantum which leads to an event which results in a solution to the eigenvalue equation. Is this a hopeless dream? I have not been drinking. A vague idea, get it right through symmetry with respect to complexity and an examination of human personal relationships.
Thursday 1 February 2024
My personal bouts of insecurity arise because I am taking on the "gods" of physics and theology without really knowing what I am talking about because I rely so much on predigested input from secondary sources. What I am beginning to see is that I need to learn more from von Neumann's revision of quantum theory and his mapping of mathematics onto reality, beginning perhaps with the quantum ergodic theory. This all shows up in my would be tour de
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force, cc24_trans_minkowski, which is in effect my final solution to the "measurement problem", the application of quantum theory to reality. [This] has come round to symmetry with respect to complexity which is the key to my proof that the Universe is divine because it shows that my "spiritual" mind is is quantum mechanical so that physics and theology are united by the "theorem" that quantum theory and god are cognitive. [This is] an epistemological proof that got off to a bad start with Plato, was somewhat resurrected by Aristotle, and finally killed by Aquinas and the militaristic papacy which led to the first Vatican Council to finally [end] the creativity of the Roman Catholic Church. I owe it to myself to get my bloodless revolution right, that power in the [omnipotent divine] Universe was in place at the first moments of creation.
Léon van Hove (1957) Von Neumann on QM 1927-1929 'work on the mathematical foundations of QM came to a culmination in 1929 with the spectral theorem for hypermaximal symmetric operators in Hilbert space.' Leon van Hove (1957): von Neumann's Contributions to Quantum Theory
page 95: Although vN himself attempted at first, in collaboration with Hilbert and Nordheim, to edify the QM formalism along [Dirac] lines he soon realized that a much more natural framework was provided by the abstract axiomatic theory of Hilbert spaces
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and their linear operators [J. von Neumann, Mathematische Begründung der Quantenmechanik, Nachr. Ges. Wiss. Göttingen (1927) pp. 1-57].
van Hove page 96: 'An essential feature of the Hilbert space formulation of quantum theory is that the most important physical quantities as position, momentum or energy are represented by unbounded hermitian operators. Since the theoretical prediction of measurements make essential use of the spectral resolution of the operators representing physical quantities, vN was in his very first investigation, faced with the problem of extending to the unbounded case the known spectral theory of hermitean operators. He introduced the all important concept of hypermaximal symmetrical operator, being the most general hermitean operator with spectral resolution.'
page 97: Statistical aspects of quantum theory: '. . . he also gave in complete generality the basic statistical rule of interpretation of the theory. The statistical rule, originally proposed by Born in 1926, was for vN the starting point of a mathematical analysis of quantum mechanics in entirely probabilistic terms.' Density matrix. All this is in Mathematical Foundations of Quantum mechanics. Density matrix - Wikipedia
page 99: 1934, 1936 with Jordan, Wigner and Birkoff: ' . . . the question of the algebraic and logical structure of quantum mechanics, looking for possible generalizations.'
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What strikes me here is the emphasis on obtaining results from QM in terms of measurements in terms of classical position, momentum and energy [is] in effect hobbling the power of QM with the connection to classicism. I want to follow Nielsen and Chuang, even though quantum computation is effectively dead. Nielsen & Chuang (2016): Quantum Computation and Quantum Information, Xavier Waintal (2023_12_29): The Quantum House Of Cards
Now to Adrian Heathcote: see Friday
No, Priscilla; and 'the book' Chapter 1: Even omnipotence cannot create contradiction, and the Chritsian god is a contradiction: an omniscient empty mind, the root not of a masterplan but of a glorious wilderness (see page 11: Quantization: the mathematical theory of communication). Priscilla (film) - Wikipedia
Friday 2 February 2024
Evolution is the fundamental process in the Universe and we can see it as a symmetry, the symmetry with respect to complexity which unites variation and selection, that is thought and observation, the interplay between Hilbert and Minkowski spaces. So for instance, every movie, every narrative every myth is a connected sequence f events with random and deterministic events.
Adrian Heathcote: ' The purpose of this note is to exploit some rather surprising philosophical points from the elementary postulates of QM, in particular that the use of unbounded operators leads
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to a kind of incompleteness. Adrian Heathcote: Unbounded operators and the incompleteness of quantum mechanics
Heathcote page 1: |A ψ| ≤ k|ψ|, Ψ ∈ D(A); k ∈ R+, true for bounded operator; unbounded, no such k.
page 2:
(1) < φ, Aψ > = < Aφ, ψ >, for all φ, ψ ∈ D(A).
An operator defined by (1) defined on all H must be bounded. Unbounded, A cannot be defined on all H so, if unbounded, A can only be defined up to a dense subspace of H. A densely defined operator that obeys (1) is Hermitian (symmetric) but not necessarily self adjoint. Domain of operator and adjoint must be the same:
(2) D(A) = D(A∗)
Only self adjoint Hermitian operators generate one parameter unitary groups required for quantum dynamics.
Completeness in QM first defined by EPR. Einstein, Podolsky & Rosen (1935): Can the Quantum Mechanical Description of Physical Reality be Considered Complete?
page 3: EPR: 'As it stands this necessary condition is probably too strong. QM should not be regarded as incomplete for its failure to have a counterpart to Minkowski space-time'.
Incompleteness of QM:
(1) self adjoint operators are required in QM, their being merely Hermitian is not enough. (2) the demain of an unbounded self=adjoint operator cannot be the whole of H.
'Postulate 1: There is a one-to-one correspondence between the possible[page 153]
states of a system and the normed rays of a Hilbert space H, ie |ψ| = eiθ ', ie state is represented by a unit circle on the complex plane, ie it is kinematic.
Heathcote page 4: 'Postulate 2: The observables of the system are represented by self-adjoint operators acting on H. These may be either bounded or unbounded. Examples of unbounded operators that represent observables are the position operator, the momentum operator and the Hamiltonian.' Assuming that spacetime is mathematically continuous, which it is not in the logical picture. The numerical values here are the rate of operation of the relevant operators projected into space-time where there is a rational uncertainty principle granulated by ℏ.
' From these two elementary postulates we obtain our incompleteness claim (almost) directly. . . . The real problem is that the state is simply not in the domain of the position operator. . . . We now show this by producing a normed function in L2(R) that is not in the domain of the position operator.
Dodgy argument based on a step function in R which assumes that R is continuous which is unphysical because continua carry no information. Cognitive cosmology Principle 13: An unmodulated continuum carries no information.
The uncertainty principle is a measure of the position of a state vector on the circumference of the unit circle on the normalized polar complex plane.
Phone notes: Von Neumann's hypermaximal hermitian operators may have the same entropy as the endless recursion
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of Feynman diagrams and so we might expect the Feynman approach could be mapped onto the vN operator approach. So we can replace Feynman quantum field theory with vN operator theory. Think about it. vN did a lot of work to develop infinite operators that could work on continuous space-time and real numbers [the reason Dirac invented his deltas function], but here we are restricting ourselves to the countable set of rational numbers and moving out into the continuum via Cantor's proof method, ie permutation. This is a consequence of taking the logic computational discrete approach and ditching pointwise continuity as a delusion [on the assumption that the only real continuum in the physical Universe is naked gravitation]. What we need is a spectral set of probabilities identical to the set of probabilities derived from Feynman diagrams. Dirac delta function - Wikipedia
Much of the discussion of quantum mechanics is contained within the constraint of yielding results of position, momentum and energy to suit classical mechanics. In the evolutionary picture the constraint operating on the selected operators is that they shoukd endow their particles with the traits necessary to maximize their probability of survival in the environment in which they find themselves.
We can use experiment to decide whether the probabilities yielded by spectral theory yield the same results as Feynman diagrams in QFT.
There may also be numerical proofs based on the two models but it
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may be hard to work out, although we may find that a normal distribution based on qubits provides a basic connection between the two models, at least to a first approximation.
Quantum mechanics understands emotions and wilderness [because it deals with infinitely multivariate functions, all of the variables which are connected with one another].
Here we see the evolution of fundamental processes progressing. We begin with eternal omnipotent naked gravitation. Because it is continuous, compact and convex we get a countable set of discrete Hilbert basis states all being represented by rays in continuous rotation. Given the emergence of self adjoint operators we get stationary states that are fixed by energy from gravitational potential. This process, like the procession of the trinity generates a set of particles with Hilbert interiors determining their personalities, some fermions and some bosons. Those that fit together to form a group support each other to survive and we eventually end up with the standard model which begins to duplicate itself through Minkowski space and instances of it interact with one another to form more complex structures and so on.
The emergence of fermions and bosons induces the 4D structure of Minkowski space in naked gravitation that generates ther general relativistic structure of the Universe. Albert Einstein (1915): The Field Equations of Gravitation
Another little walk, more phone.
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My mind evolves like the evolving Universe proving the words of Genesis, acted out by Jesus that we are created in the image of god, that is for all practical purposes we are children of gods. All the stories made up here may be wrong in detail but they are in effect authentic replicas of the Universe insofar as they are generated by the same evolutionary process and may or may not have a future depending on whether they are selected to reproduce or not. From this point of view my theory is foolproof insofar as it is an example of what it is trying to say [in scholastic terms, its essence is its existence!].
Although I know a lot of stuff at my advanced age I still cannot really predict what is going to come next unless I am working on some concrete project that physically constrains my behaviour to performing certain necessary acts to carry the task forward [which seems to be happening here as my theological hypothesis generates substance which carries it forward like a partially completed house, maybe a self perpetuating "delusion", like a flying dinosaur].
Each insight leaves me a little bit fatigued and I am inclined to have a little rest like after as a child I had run a race and was puffed out.
Each particle is created with a Hilbert space personality motivated by its kinetic energy and a load of mass / potential energy derived from gravitation both adding up to zero.
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Back to von Neumann, page 6: 'the principle of continuity prevailing in the macroscopic world is merely simulated by an averaging process in a world which in truth is discontinuous by its very nature' [and therefore, as I am learning to understand it, evolves in discrete logical steps each characterized by the multivalued logical operator [encoded in a complex vector] we call the quantum of action].
page 7: ' On the basis of the Born statistical interpretation of the quantum theoretical description of nature, it was possible for Dirac and Jordan to join the two theories into one, "the transformation theory" in which they made possible a grasp of physical problems which was especially simple mathematically' the statistical description being necessary because of the fineness of the material structure that represents the spirit of the Universe: see pages 15: Quantum amplitudes and logical processes are invisible and 21: Matter and spirit.
The logical approach, executed in Hilbert space as a medium of communication and computation prior to the processes in Minkowski space, means that size, infinity etc do not matter. The electron, even if it has zero size embodies a Hilbert space algorithm or algorithms driven by its mass / energy which determines how it presents itself in the [observable] physical world much as my personality hidden in my mind controls how I present myself to the world.
von Neumann page 8 (cont) 'In both theories we must learn as much as possible from the Hamiltonian function about the true, ie quantum mechanical, behaviour of the system. Primarily then we must determine the possible energy levels, then find out the corresponding "stationary
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states" and calculate the "transition probabilities" etc.' On the assumption that the entropy of the quantum system is far greater than the entropy of the classical Hamiltonian system, we may not have enough information to determine the quantum mechanical behaviour of the world [which seems to be the case given the assumption that the wave function "collapses"].
von Neumann: page 9: Matrix calculation rules:
page 10: 'It is important that only hermitian matrices be permitted, ie such matrices A = {amn} for which amn =
Anm
holds identically.
Wave mechanics rules:
page 11: Schrodinger equation: eigenvalues are discrete and continuous energy levels and eigenfunctions describe corresponding stationary states of the system. [Two systems can communicate (Zurek) when they share a stationary state: see page 14.4: Zurek: observations involve interactions in Hilbert space.
page 12: Schrodinger stationary states are time dependent but different times differ by absolute value 1 (ray) so same state.
page 13: The transformation theory: the equivalence of the two theories.
How is the logical approach going to deal with the (pseudo) infinite self energy of the electron [let us say it is kinematic, like Hilbert vacuum energy, so it is not dynamic] ?
Saturday 3 February 2024
If we look behind Minkowski space we will find a very simple Universe of [sometimes very big] hermitian operators. Does
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Minkowski (Lorentz) transformation destroy the Hermitean property of operators (Veltmann page 20)? Martinus Veltman (1994: Diagrammatica: The Path to the Feynman Rules
Minkowski space is unified by the time vector ie null geodesic which has zero ingterval so reproducing quality of the Hilbert space from which it came. I have to learn my way around Hilbert space from vN.
My ignorance, like the ignorance of god, frees me to think unthinkable things. Can kinematics create contradictions? By time division, like traffic lights,
Normalization of vectors in Hilbert space controls their statistical implication. Every junction in a Feynman diagram (calculated by the path integral(?)) can only be activated by a whole value of the quantum logical operator [so its statistics arises from the periods between operations, not from the size of the operations].
If both Feynman and hermitian operators have a countable infinity of possibilities and are normalized and normally distributed they are in effect isomorphic [so we can replace Feynman QFT with von Neumann QFT (?)].
Nicholas R Micinski & Kelsey Norman: Funding for refugees has long been politicized − punitive action against UNRWA and Palestinians fits that pattern, Al Jazeera: Upfront (2023_02_03): ‘It’s immoral’: UN special rapporteur on UNRWA funding cuts
Benediction: I wish I could put more passion into this work and make it go faster but I am going as hard as I can and stepping forward every day. The dream of peace that I made in 1987 is coming closer and the theory of peace is deepening as I see the symmetry of love swooping from the initial singularity to a planet of peace. It may take centuries,
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but I hope the necessary theory will be in place before I die. Jeffrey Nicholls (1987): A theory of Peace, Benediction (film) - Wikipedia
Ghost Riders in the Sky. "Why Catholicism, Father?". (Ghost) Riders in the Sky: A Cowboy Legend - Wikipedia
Siegfried, do you renounce Satan and all his works and all his pomps. . . . Siegfried go in peace and the Lord be with you (00:14:24).
We need enough entropy to make war unnecessary, which is the role of Cantor [and the only way to get enough entropy is for each person to govern themselves, in just the same way as every other particle, atom and molecule govern themselves as long as they live].
30:33: The love that cannot speak its name,
Wilfrid Owen Wilfred Owen - Wikipedia
Siegfried Sassoon. Siegfried Sassoon - Wikipedia
