Notes DB 91: Divine_Gravitation_2024
Sunday 11 August 2024 - Saturday 17 August 2024
[page 72]
Sunday 11 August 2024
Theology and war are intimately connected by the fact that all the old gods were imperialist warmongers and all the theologians, artists, engineers, [and astrologers] have been employed by them to establish the ideological and physical foundations of their hegemony based on a series of paper tigers built into the nature of evolution, the selective advantage of predation.
Now back to cc18_fixed_points = dogma (fixed by papal/imperial) fiat versus science (fixed by the real divinity).
Having demolished the cosmological constant problem with the distinction between kinematic and dynamic we now push for the idea that quantum mechanically identified fixed points can be energized by gravitation,
Another point to raise is whether we can use the P vs NP argument in the quantum mechanical realm, arguing that quantum mecjanics can identify NP solutions which can be reproduced by P processes. Where does this argument belong?
page 21: Matter and spirit: here we expand on the musical / sound nature of quantum mechanics and maybe there explain how quantum mschanics explains the Lamb shift.
[page 73]
Monday 12 August 2024
. . .
The theme of cc18_fixed_points must be the intelligence of quantum mechanics in picking stationary points out of the chaos of the Hilbert space driven by the idea thaty the basis vectors of the Hilbert space are kinematic rays (frequencies, notes) which can add up to zero like the node of a string carrying a tone and an overtone understood in terms of wavelength. How does 'wavelength' map to frequency in a domain of superposition [when geometric length is absent]? There is a whole story here. [The only variable is "time" and the linearity of quantum mechanical operators means that they can solves a multidimensional problem by changing the weights on vectors in the superposition].
[page 74]
I keep telling myself I should read Nielsen and Huang and I keep trying to wing it by thinking musically, but soon I will have to discipline myself to do a bit of study like a scientist rather than a mythologist. Nielsen & Chuang (2016): Quantum Computation and Quantum Information
In the language of militarism great deeds mean great slaughters and that is what Israel is doing to Gaza now, encouraged by Yahweh's cosmological support for genocide in the Promised Land. Joshua: 10:12-13:
Maybe reading is too easy compared to actual thinking into the unknown. Reading is only helpful if it introduces new knowledge.
Tuesday 13 August 2024
Slowly getting cc18_fixed_points into focus, itself a fixed point where all the incoming rays to a telescope the size of the Earth are precisely superposed. Event Horizon Telescope Collaboration (2019): First M87 Event Horizon Telescope Results. IV: Imaging the Central Supermassive Black Hole
Wednesday 14 August 2024
From notes22m02d22 'A song is a vector fed into a mind for processing to create a feeling'.
cc18_fixed_points: Quantum of action is fundamental fixed point which is set (in effect) by the Lagrangian of the Universe which is set by the fact that the initial
[page 75]
singularity has zero energy so it is the fundamental stationary point and the paradigm of all subsequent fixed points, so we are led to conclude that the quantum of action ≡ god. cf cc03_action, cc08_trinity, cc22 line 851.
Nielsen page 3: '. . . the ability to control single quantum systems is essential if we are to harness the power of quantum mechanics for applications to quantum computation and quantum communication.
page 4: Church-Turing hypothesis: physically implementable algorithm ≡ Universal Turing Machine [we can do it with pencil and paper and a suitable brain].
page 5: efficient = polynomial; inefficient = exponential.
Solvay-Strassen primality algorithm. Solovay–Strassen primality test - Wikipedia
page 6: Any algorithmic process can be simulated efficiently using a probabilistic Turing machine: does probabilistic mean the same as algorithmic? Gödel / Chaitin Gregory J. Chaitin (1982): Gödel's Theorem and Information
page 7: Feynman 1985. Shor and Grover suggest quantum mechanics more powerful than Turing. Richard P. Feynman (1985): Quantum mechanical computers
page 8: No quantum mechanical analogue to Shannon noisy coding theorem.
page 9: Superdense coding: distributed quantum computing.
page 10: Key distribution: observation changed quantum state?
page 11: Public key: entanglement.
page 25: Zurek on measurement: Wojciech Hubert Zurek (2008): Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
[page 76]
Nielsen page 16: ' hidden information' [it is really there or just a mathematical fiction debunked by Bose-Einstein statistics?]
page 17: Bell states: Myrvold, Genovese & Shimony (Stanford Encyclopedia of Philosophy): Bell's Theorem
page 18: Unitarity is the only constraint on quantum 'gates': U†U = 1
Complete revision of CC18_fixed_points (laws and symmetry) to become an essay on quantum computation, ie the space of unitary transformation described by the Schrödinger equation. This will be the quantum mechanical space replacing all the Feynman diagram stuff in quantum field theory providing a foundation for CC24_alternative. If I can pull this off I will consider myself home.
page 20: 'possible to build a single qubit gate using finite set of gates. More generally, an arbitrary quantum computation on any number of qubits can be generated by a finite set of gates said to be universal for quantum computation (section 4.2, page 174). All this is about qubits [2D Hilbert space with arbitrary orthonormal basis states].
page 21: quantum operations reversible, since inverse of unitary matrix is unitary.
page 22: any multiple qubit gate can be composed of CNOT and single qubit gates (Section 4.5 page 188. Measurement 1.5.1, 2.2.3)
Quantum computation is dealing wth two-state spaces, a|0〉 + b|1〉
page 23: Input state to circuit is all |0〉s. No FANIN and no FANOUT.
page 24: No cloning:
|ψ〉|ψ〉 = a2|00〉 + ab|01〉 + ab|10〉 + a2|11〉
[page 77]
page 25: The hidden information in qubit is represened by its phase? We do not see the term ray in Nielsen's index.
page 26: quantum teleportation provides us with a proof that Hilbert space underlies Minkowski space?
A qubit is a superposition of two basis states called computational basis. Any one of these states may be a normalized superposition of any number of basis states of a Hilbert space, ie qm is invariant w.r.t. complexity.
. . .
What we might say us that quantum theory creates structure despite the effects of gravitation and it does it by bifurcating naked gravitation into potential and kinetic energy using the kinetic to transform kinematics structures into dynamic structures but the potential it creates can lead to black holes [which may extinguish the quantum structure].
Photons involve quanta in two ways: Polarization is a phase thing and energy, which belongs to all dynamic particles real E = ℏω
[page 78]
Thursday 15 August 2024
So we are looking for the rebirth of CC18_fixed_points.It seems axiomatic that the primary fixed point is the quantum of action and the scale invariance of quantum mechanics [since we are operating outside space and time] can be anything from the angular momentum difference between two states of an electron to the difference between the existence and non-existence of the Universe, ie we can consider it formally related to god or the Universe. This 'total' fixed point is constructed by nested intervals of physically smaller and smaller fixed points running from eternity to the frequency of the Universe represented in Hilbert space [by a fundamental with a hierarchy of discrete overtones, see note on discreteness of eigenfunctions, Khinchin page 92 below]. This sounds a bit incomprehensible but I want to explain it in CC18 as a preliminary to redesigning the quantum theory of the Universe without using fields which are a product of non-existence mathematical continua. The key may be in Cantor's turnaround from derived sets to transfinite numbers. Dauben Chapter 2. Joseph Warren Dauben (1990): Georg Cantor: His Mathematics and Philosophy of the Infinite
So TSEliot: 'Only those who go too far can possibly find out how far one can go.'
[page 79]
Friday 16 August 2024
The vast amount of social capital invested in theological and religious structured demonstrates the importance of belief over a very long period of human History. Anthony J. I. Clark et al: A Scottish provenance for the Altar Stone of Stonehenge
Still chugging away at CC18_fixed_points - Planck's 'energy units' ie sets of identical photons (ie superposed bosons) decrease exponentially as the factor hν / kT increases in the denominator of the Planck equation.
In physics, the acid test is producing an equation or algorithm (procedure) that fits the facts, ie carries us from a natural starting point to a natural end point as Planck's formula does. Quantum field theory explains quantum electrodynamics by Feynman diagrams and Feynman's path integral formalism. The goal is to replace these results with pure quantum theory and the simplest point of attack is the differentiation of Bose, classical and Fermi statistics. : Aleksandr Yakovlevich Khinchin (1960, 1998): The Mathematical Foundations of Quantum Statistics
[Page numbers here refer to an electronic copy of Khinchin from Google play which lacks equations and symbols from page 130 on so stopped reading it soon after and have wrtten to Google for a complete copy]
Khinchin page 7 Preface: ' . . . I show that a rigorous and systematic mathematical basis of the computational basis of statistical physics . . . may be obtained from an elementary application of the well developed limit theorems of the theory of probability . . . the study of these limits theorems was founded by P L Chebyshev and was developed further by other Russian and Soviet mathematicians. The
[page 80]
fact that these theorems can form an analytical basis for all computational formulas of statistical physics once again demonstrates its value for applications.
Khinchin page 9: Quantum statistics, as distinct from classical theory, is a statistical theory in a double sense of the word. It is very important to distinguish carefully between the concept and computational methods of quantum mechanics on the one hand and of statistical physics on the other. We introduce a special terminology and system of notation for each if these and we rigorously avoid confusing the two sets of ideas since they effectively have nothing in common, except that they are both statistical in nature, ie underdetermined [in the primitive layer of the Universe is structure simply not there to determine things which is why evolution is creative].
page 10: Two new features; 1. Bose-Einstein vs Fermi-Dirac. The transition to the "new" statistics signifies . . . a reduction in the manifold of "accessible" states of the system. " 'Index of symmetry' describes a specific feature of quantum mechanics."
2. . . . ergodic approach is impossible: ergodic theorems state that on the average a system whose evolution in time is generated by equations of motion, remains in different parts of a given manifold of constant energy for fractions of the total time which are proportional to these parts [because deterministic equations of energy, space and time do not exist in the quantum domain].
[page 81]
Khinchin page 12: 'In quantum mechanics the situation is completely different.'
page 13: '. . . local limit theorems for sums of identically distributed random variables that can assume only non-negative integral values.
Chapter II: Preliminary Concepts of Quantum Mechanics
Chapter III: General Principles of Quantum Statistics
Systems with definite total energy? We consider such systems kinematic weith energy defined formally as E = hν
page 15: fundamental eigenfunctions/ fundamental states.
page 16: Chapter 4 Bosons; Chapter 5 fermions (massive).
page 17: Chapter 6 defines entropy and the second law of thermodynamics.
Saturday 17 August 2024
cc18_fixed-points laws and symmetry
cc18.1 Divine law, human law and natural law
My days on the natural religion project seem to follow a familiar pattern, wake in fright, wondering what I am doing, whether I will actually achieve anything Lie in bed thinking about it until a course of action emerged, feel better, get up and get on with it. My only guide to the future is the past, and so I go back over my story and try to work out what next. This page, cc18, I see as a transition from the theory developed up to now to an outline of the practical consequences of the theory and the principal principle is that in a divine Universe, natural law
[page 82]
and divine law are equivalent and human law, if we are to survive in the closes possible approximation to peace and happiness requires that we conform to the divine / natural law.
The key to natural law seems to be quantum mechanics, and at the moment I am thinking about Planck's first step into quantum mechanics which amounted to correcting a disparity between classical theory and laboratory observation by a breakthrough in the relationship between energy and entropy which amounted to the application of Bose-Einstein statistics, even though details of this theory did not become clear for another quarter of a century. Abraham Pais (1982): 'Subtle is the Lord...': The Science and Life of Albert Einstein, Chapter 19: The Light–Quantum
. . .
As a background to al this, in the back of my mind, I am always seeking ways to steep the Roman Catholic Church away from its fictitious divine law into realistic human law. My life in a nutshell. So now
[page 83]
read the news and have a cup of coffee before I settle down into conversation with Khinchin 1960, written at the same time as my rather spotty theological career began at a school run by Catholic priests.
Khinchin page 22: Chapter 1 - Preliminary Concepts
Most important formulas established by limit theorems. Limit theorems of the type we require first prove by V Gndenko and students. Boris Vladimirovich Gnedenko - Wikipedia
page 25: Probability of an n dimensional random vector is the probability that all n conditions realized.
page 28: limit theorem designed to embrace wide range of possibilities. DeMoivre and Laplace study of errors led to normal distribution - Bernoulli trials, two values, 0 and 1.
page 29: Chebyshev was the first to try to formulate a general limit theorem, work completed after his death by Markov.
page 30: For quantum mechanics only local limit theorems for integral valued random variables required.
This is why the fiction of renormalization is required when field theory attempted to describe the world with continuous functions [because it confuses the discrete logical mathematical of quantum theory with the continuum assumed to exist in Minkowski space].
Skip to Chapter II: Preliminary concepts of quantum mechanics.
page 75: In QM the state of a system is described by U = U(q1 . . . qs) of the coordinates qi alone, also known as the 'wave function'.
[page 84]
'A knowledge of the function U describing the a state of the system does not in general make it possible to determine the Hamiltonian variables qi, pi. In the most favourable case, knowing the function U, we can determine the value of some of these variables, but all 2s can never be completely determined. The reason is that qi and pi (for the same i cannot both have defined values in the same state. . . . In QM, prescribing the function U determines the distribution laws of the physical quantitites but not their values.'
' In particular, if the system is in the state U, the probability of the qi belonging to a region V of the configuration space (ie the Euclidean space of s dimensions with rectangular coordinates qi is given by ∫V |U|2 / ∫ |U|2 where the denominator is taken over the whole 3D space.'
page 77: ∫ |U|2 = 1, normalized. This introduces scale invariance since the probability of any set of specific outcomes, considered as a comunication source, is always 1.
page 78: Superposition: If U1 and U2v describe possible states of a system, U = λ1U1 + λ2U2 (λ arbitrary complex coefficients, λ1 + λ2 > 0) is also a state of the system, and can be extened to an infinite series.
page 79: Probability of an event = relative frequency of occurrence. Assertions regarding probabilities can only be precise if conditions stated precisely.
[page 85]
Khinchin page 80: ' The fact that the statistical predictions of QM are independent of all supplementary conditions is one of the most general principles of the theory and gives the predictions real statistical meaning.'
' linear self adjoint operator' - 'operator a assigns to each element U of the complex Hilbert space a definite element aU of the same space.'
We might call this the fundamental principle of natural ≡ divine law and our task is to convert this into a fundamental principle of human law, ie the linear superposition of some feature of 'humanity'.
Linear a(λ1U1 + λ2U2) = λ1aU1 + λ2aU2.
We can define a 'human hamiltonian' in an infinite dimensional space of human activity comprising discrete actions. This becomes the fundamental law of the 'supreme court'.
page 81: ' In QM a linear self-adjoint operator a is assigned to each physical quantity x. The statistics of this quantity are established for each state U of the system by means of this operator.'
So probability of an electron in the state U is defined by the electron operator e which also defines the nature of the electron, eigenvector and eigenfunction.
[page 86]
The salient point of reality is communication = observation which is in some sense the control or lack of control of communication. Quantum mechanics is music because sound in air like waves in water is linear although non-linearity arises through viscosity, ie communication.
page 84: Self-adjoint property of momentum operator depends in an essential way on the presence of the imaginary unit, i.
page 85: '. . . the problem of assigning an operator to a given physical quantity x cannot always be solved by simple general methods' [which is why, in nature, the set of operators that define the world has arisen through evolutionary trial and selection].
page 92: ' The spectrum of an operator is discrete as a consequence of very general conditions imposed on eigenfunctions. This is similar to the theory of one oscillating string in which the discreteness of the sequence if possible modes of vibration follows from the boundary conditions imposed.'
page 93: confine ourselves to examining the set of eigenfunctions which belong to a single eigenvalue ak. Linearity means that if Uk1 and Uk2 are two eigenfunctions belonging to ak then λ1k1 + λ2Uk2 will also be an eigenfunction of the same eigenvalue, ie the set of eigenfunctions is a linear manifold.
[page 87]
Khinchin page 97: Given eigenfunction (eigenvalue) ak we can choose an infinite orthogonal system of elements U of a complex Hilbert space.
page 102 § 4: Evolution of the state of a system in time. Classically we need to know the time evolution of all 2s variables in the Hamiltonian - classical casuality.
In quantum mechanics causality means wave finction U retains the same form which means that statistical properties remain the same through time.
page 106: Laws of QM that determine the change of state with time: the Schrödinger equation first order in t [which may not necessarily be physical time, but a continuous monotonic kinematic variable]. The norm (U, U) is an invariant integral of the S equation.
page 108: Stationary states : conservation of energy - results in the bifurcation of naked gravitation. Search on "naked gravitation" brings up cognitive cosmogenesis. I love it!
page 110: 'In a stationary state the statistics of physical quantities are independent of time.' I am a stationary state.
page 111: 'We must now determine the physical quantities in QM which are integrals of the motion'. In QM such integrals are quantities whose distribution does not change in time.
[page 88]
Khinchin page 112: Lemma: Let x and y be two self-adjoint operators with discrete spectra and let xy = yx Then there exists a complete orthogonal system of eigenfunctions of the operator xwhich are simultaneously eigenfunctions of the operator y.
page 118: General principles of quantum statistics.
The state of a gas is uniquely determined in classical statistical theory only when the positions and velocities of all the particles are given vs phenomenological theory when the volume and temperature are constant.
page 121: phenomenological theory must depend symmetrically on the states of the particles in the statistical theory, and depends on principle of averaging.
page 124: § Microcanonical averages
page 127: Distinguish microcanonical average from mathematical expectation, and 'mean value' = microcanonical average.
page 128: microcanonical average is arithmetical average over an orthonormal basis in which identical weights are ascribed to each term.
129 §3; Complete, symmetric and antisymmetric statistics.
page 130: As a rule, quantum systems cannot attain all the states which are described by the eigenfunctions of an operator x
[book becomes unreadable here]
[page 89]
corresponding to its eigenvalue E. Only an insignificant fraction of these states can be attained. A valid averaging system must be different from a microcanonical one.
'System n identical and completely indistinguishable particles, qi, pi, Hamiltonian variables of particle i must be symetrical because indistinguishable.
page 135: Photons symmetric, fermions antisymmetric.
page 136: particles are given an "index of symmetry": 0 complete, 1 symmetric, -1 antisymmetric.
page 164: Chapter VI: Foundations of statistics of photons.