Notes DB 91: Divine_Gravitation_2024
Sunday 1 September 2024 - Saturday 7 September 2024
[page 111]
Sunday 1 September 2024
Steady work on cc18 obliterates my worries about homelessness. It is possible that I will have to move by 26 of this month which gives me 25 days to complete the revision of cognitivecosmology.com and then, after a week settling in to the new abode beginning the parallel revision of cogitivecosmogenesis.com and the book derived from that site.
Posted finished version of cc18 to LinkedIn as a proof that evolution solves the P vs NP problem. I love it when the writing clicks together (legolike).
Kinematic = formal = dead, moved by dynamic potentials, the most obvious of which is gravitation, the source of life. <.p>
cc20_memory - revised.
[page 112]
Monday 2 September 2024
Taking time to understand quantum mechanics as the foundation of the Universe as I seek to introduce quantum computation into the model. We will start with a qubit representing an octave, a boson, and then [an overtone] a fermion. Atiyah writes: "The differential operator introduced by Dirac in his study of the quantum theory of the electron turned out to be of fundamental importance for both physics and mathematics. Essentially the operator is the forma square root of the wave operator or, with a different signature, of the Laplacian. In this lecture I will attempt to survey its role in mathematics." Peter Goddard (1998): Paul Dirac, The Man and His Work, Atiyah page 108, Laplace operator - Wikipedia
And I will attempt to glean some ideas about the quantum creation of Minkowski space out of fermions and bosons. Richard Bethiel: The Mystery of Spinors
Spinors matter in physics. The idea that SU(2) gives double cover to SO(3) which gives us [the Euclidean part of] Minkowski space (?).
[page 113]
Ian Duck and E.C.G. Sudarshan (1998): Toward an understanding of the spin-statistics theorem
David Griffiths (2008): Introduction to Elementary Particles
I am having such a hard time with fixed points but hopefully it is improving all the time and the last version finished with the quantum creation of fermions, bosons and Minkowski space which then becomes the foundation for a network and a memory or vice versa.
Linear quantum mechanics is the square root of space and spinors are the double covering that makes space possible like octaves and overtones.
Tuesday 3 September 2024
New big job: revise scientific-theology.com. Site began 4 June 2017. And publish on Patreon?
Wednesday 4 September 2024
[paid ASIC for theologyco]
[page 114]
cc18_fixed_points 18.5: Quantum interactions define relativity and Minkowski space.
The plan to create spacetime from quantum mechanics is based around the creation of a qubit which represents a vibrating string with one overtone at twice the frequency creating a stationary mode in the middle of the string, |0〉 being the basic frequency of the string (which may have any value so that |0〉 is a normalized vector which may have a countable infinity of components and |1〉 is the octave frequency of |0〉 which may be any suitable normalized vector. We then apply the theory of spinors to argue hat these two vectors represent fermions and bosons which between them form the structure of Minkowski space. So watch Behiel again for clues linking the properties of spacetime with the Dirac equation and (perhaps) the Klein-Gordon equation. Richard Behiel: The Mystery of Spinors
First, Feynman on two-state systems. Wave in space: ψ = Aei(ωt - kx)
Feynman page I.48.5: Probability amplitudes for particles. Richard Feynman (2013): Feynman Lectuures on Physics: I_48: Beats
Phase velocity = speed of nodes = ω / k which can be greater than c. Group velocity = speed of modulation dω / dk
[page 115]
ie group velocity is derivative of ω with respect to k.
The drive to connect theology to physics is pushing me to learn things that I never knew before.
So now Feynman III_07: The dependence of amplitudes on time.
But first deal with crashing stock market.
Rest energy vs excited energy : kinematic (conserved) vs dyamic (variable).
Energy swapped between fermions by bosons, fundamentally derived from bifurcation of gravitation to form Minkowski space plus particles.
Why does atom (or anything) decay: entropy, many more states in radiation. Why does radiation have more entropy? Because of space, the principle of individuation. Creative processes tend to move toward increasing entropy, like me!
Three ways to express energy: 1. frequency of amplitude aeiωt; 2. classical energy; 3. ienertia.
Mapping quantum of action onto spacetime gives Δp.Δx ≈ ΔE.Δt ≈ ℏ [ie quantum of action pixellates spacetime making it particulate rather than continuous].
Definite energy = probability constant [within kinematic object] = stationary state. Two different states with different energies give interference.
Fermions are massive, have rest mass (why?); bosons not necessarily so.
Origin of energy scale makes no difference so choose zero in a linear system. So naked gravitation is linear and works by quantum
[page 116]
theory. Non-linearity enters with the creation of rest mass and space? More specifically, the superposition of space and time is a qubit a | space 〉 + b | time 〉, superposed linear + linear = quadratic.
At rest, magnitude of amplitude is constant, phase depends on time. The generation of space depends on freezing time, x = ct, c constant, time determined by atomic frequencies, and so we have a measure of distance, x
Feynman 7.2: Uniform motion: here he uses Lorentz transformation to explain phase. We we want to use phase (ie qubit) to explain Lorentz transformation, ie Minkowski space, quadratic relationship ds2 = ds2 - dt2 In other words, Feynman is assuming changes in Minkowski space cause changes in Hilbert space; we want to go the other way, from linear to quadratic rather than quadratic to linear.
Superposing fermions and bosons is as difficult as superposing physics and theology, but bosons are superposed with fermions when they are interacting [and when they are observed to come apart, we observe a fermion and a boson, just as we only ever observe a |0〉 and a |1〉 when we observe a qubit, so is a qubit a tensor product as in Zurek on page 14: Measurement—the interface between the Minkowski and Hilbert spaces?].
Feynman couples space to amplitude via the relativity of time.
' If we have several amplitudes for pure energy states of nearly the same energy then interference gives ' lumps' in the probability that move through space with the velocity of the classical particle with that energy.'
7.3: Potential and energy conservation
[page 117]
Constant potential makes no difference as zero of energy makes no difference.
. . .
'spin up' and 'spin down' are basis states in 3D space, the space of a spinor in 3D space.
Feynman I_49 Modes; 49.1: Reflection of waves.
' the most far reaching principle in mathematical physicsL Any motion of a linear system can analyzed by assuming that it is the sum of the all different modes, combined with appropriate amplitudes and phases, eg a superposition [of synapses] on a neuron. This is in effect 1 dimension.
Wave reaching the clamped end of a string reflected with change of sign. String can have a sinusoidal motion, but only at certain frequencies: the frequencies are fixed points.
Mouth is a terribly complex resonator.
Coupled pendula
49.5: Linear systems:
In quantum mechanics the vibrating object or the thing that varies
[page 118]
in space is the amplitude of the probability function that gives the probability of finding an electron or a system of electrons in a given configuration. frequency = energy: de Broglie: all comes down to frequency and superposition BUT topology in Hilbert space is a source of fixed points, space growing out of time.
Feynman III_08 The Hamiltonian Matrix
Throughout here we distinguish between kinematic 'energy' E = ℏ
8.3 What are the base states of the world: any state is a superposition of base states, eg spinor =
| |0〉| |
| |1〉| |
Spinor [has] 2 states (but what are they on reality?)
Complete description of an electron = {momentum, spin} expressed in Hilbert — so we make a Hilbert space with classical bases.
Spinors are the linear square root of quadratic spacetime. This is the broad argument. We should
[page 119]
be able to find then in the topology of complex Hilbert space and guess the spinors are vectors with two complex dimensions which have enough entropy to describe 4D space.
8.3 (continued): 'We don't really know what the correct representation is for the world'. What about the "guts" of the proton. Does the proton have interior parts?' He was writing this before QED was 'completed'. So what is the Universe made of? Following Plato we say formalism. Following Whitehead and Russell we say [kinematic] logical formalism. [Following myself I say [kinematic] logical formalism energized by bifurcation of naked gravitation into Einstein gravitation with potential and kinetic energy].
A very old question for me. If the Universe is a computer, what hardware does it run on? My answer, since way back, has been that whatever the hardware is it is 'logically confined', cannot contradict itself. The beauty of logical confinement is that because it is logical higher energy just speeds it up but the processes are the same, as in slow and fast computers.
8.4:How states change with time.
S matrix: 〈−∞| A | +∞〉
The Hamiltonian matrix describes the topology of the transforming Hilbert space and maybe we can do it all with spinors in 2D complex space. Quantum dynamics
iℏdCi(t) / dt = Σj Hij(t)Cj)
Variation of state is the sum of the variations in the basis states [linearity].
[page 120]
. . .
All the states of the ammonia molecule are split in two by the N atom tunnelling between the triangle of H atoms. Feynman, Leighton & Sands: FLP III:9 The Ammonia Maser
Back to Behiel [ref page 112]:
[notes on video] . . .
[page 121]
Thursday 5 September 2024
As I struggle with my theological dream the mathematics
[page 122]
of SU(2) looks a bit like my salvation. I will now be able to show (I think) that Hilbert space is the foundation of the Universe and gravitation is the source of both quantum theory and energy, so fittingly named the footprint (vestigium) of divinity. It is remarkable how the promise of progress raises my spirits and provides material for a PhD somewhere.
Auntie day, chocolate cake in the bag.
How do you get from SU(2) to Minkowski spacetime?
[cc18_fixed_points] 18.4 Classical physics and mathematical fiction
18.5: Classical computation and evolution - P vs NP
18.6: Quantum interactions define special relativity and Minkowski space
18.7: The cosmological constant problem
So another revision:
cc18_fixed_points finishes with the cosmological constant problem that kills quantum field theory.
Then a rewrite of cc20_network (cooperation and bonding) to conclude the formation of Minkowski space and the classical particle networks, ie the whole of reality. New title
[page 123]
cc19_networks: quantum to Minkowski via SU(2) and spinors [?]: Page 19: Networks: cooperation and bonding
Friday 6 September 2024
cc18_fixed_points uploaded without the section titled.
Now cc19_network. We begin with the Universe as a normalized communication source according to communication theory which means that the diagonal of the density operator is 1.But what do I want to say? The task of this page is to produce classical Minkowski space and classical communication out of the Hilbert space basis and we will do it with qubits and SU(2) operators maybe, bosons and fermions.
From a final cause point of view the case for Minkowski space is basically a matter of entropy. An atomic electron emits a photon because the possibilities in the EM field are very much greater than the possibilities in the atom. Entropy attracts, love attracts, potential attracts.
In the Trinity three identical persons are identified by different locations in space. In choirs of angels, angels are differentiated by species because they have no differentiating matter or energy. How do we swap specificity for space?
What do we mean by positive and negative charge; matter and antimatter; spinup spin down, qubit 2D fermion/boson. Fermion 4π to come home, bosons 2π to come home.
[page 124]
It is depressing when ideas do not come, but that is the downside of randomness - one needs savings to get across the dry periods, but I just have to go back to the spinors for inspiration. Can I get my linear mind to follow the linear operators that convert photons to electrons? What is the zero sum bifurcation at the particle level that gives us Minkowski space? Has it got something to do with dark matter? Neutrinos and anti-neutrinos, electroweak interactions? The baryon symmetry problem, do gravitons exist in Minkowski space? We are trying to exploit the heuristic of simplicity to get the first step after naked gravitation, but we want null geodesics and massless spin 0 bosons? Spin 0 plus neutral spin ½ would be enough, built on a qubit. Dark matter.
One does not need charge to create the exclusion principle; it resides down at the level of wave functions. Then we have new bifurcations which may be coupled: matter / antimatter, positive negative, left right, up down, all to arise from wave topology? Does matter have to be particulate? Why does rest mass preclude the velocity of light? Is rest mass a consequence of internal energy / motion / action.time? The quantum of action is connected to one revolution of a radius vector / ray [and appears in Minkowski space as angular momentum].
I am amazed at all the stuff instrument making scientists do and I would like my physical theology to contribute to this effort. My struggle to make Minkowski space out of Hilbert space might help.
[page 125]
[Back to Behiel Spinors]
. . . .
[page 126]
Why are spinor valued wave functions asymmetric under particle exchange? [is this a feature of Hilbert or Minkowski space, or pure evolution?]
The whle page on networks could be devoted to this:
Part I: Hilbert to Minkowki.
Part II:Minkowski to transfinity.
We expect that the answer lies in the well understood Nicholls ansatz which is based on the zero sum bifurcation of spinor mapings to 4D Minkowski space - we wish.
Saturday 7 September 2024
Love, entropy and a great leap forward.
What is cc19_network trying to say? I wrote the core ideas in 2 essays in 1992 when I was probably at my most intelligent aged 47, An esssay on the divinity of money (May 1992) and An essay on value (November 1992) which came as consequences of my Theory of Peace (1987) which was motivated by my discovery of transfinite numbers and their application to the expsnsion of hums=an cognitive space as a means to stop war by showing that we can make our mental space large snough to ensble us all to live together in peace. This spawned the idea of network creation which formed the subject of my 2019 Honours Thesis and now I am coming to the same
[page 127]
psychological moment in the creation of the world that I am describing in cognitive cosmology at the point where the Universe is going for a massive increase in entropy by inventing Minkowski space and real particles that are capable of networking to form a Universe. We have come in effect to the big bang. Jeffrey Nicholls (1992): An esssay on the divinity of money, Jeffrey Nicholls (1992a): An essay on value, Jeffrey Nicholls (1987): A theory of Peace
Behiel Dirac equation Richard Behiel: Deriving the Dirac Equation
Klein Gordon Equation - mass shell again, energy, quantum + mass. So Hilbert space ignores the mass shell; Einstein and Minkowsko bring it in. Klein Gordon just putsd time and momentum opertators into the mass shell. It yields negative energy but no anti-matter. Richard Berhiel: Relativistic Quantum Waves (Klein-Gordon Equation)
All this has got wave function mixed up with mass shell.
[page 128]
Spin is a thing - yet the quantum of action is a logical operator. So there is no relativity in Hilbert space only quantum mechanics and [linear] operators, which can be modelled by matrices or differentials. Slowly beginning to take my cart / horse idea seriously.
What can the initial singularity do? Create space by creating Minkowski space. Music without matter. The development of Minkowski space feeds the Hilbert and they multiply into transfinite space.