vol VII: Notes
2017
Notes
Sunday 3 September 2017 - Saturday 10 September 2017
[Notebook: DB 81: Scientific theology]
[page 135]
Sunday 3 September 2017
When I was young I thought of theology as the study of an impenetrable crystal sphere which promised no successful line of attack. Now, fifty years later, I have little to show except that fixed point theory gives us a window through which to see that a purely simply dynamic divinity must have fixed points and that these fixed points are the world that we see [and are]. This idea penetrates right down to the theory of measurement in quantum mechanics and provides a theological ansatz for the hypothesis that the universe is divine. I can frame this idea with the concept that logical continuity is its own source, bringing logical structure out of the structureless initial singularity.
Farmelo page 336: 'Dyson, "Well, Professor Dirac, what do you think
[page 136]
of the new developments in quantum elecrodynamics?" Dirac: "I might have thought the new ideas were correct if they had not been so ugly." The feature of the new theory that Dirac most loathed was the technique of renormalization. Farmelo: The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom
Farmelo page 354: 'Dirac: "The most important thing about electrons and protons is not what they are but how they move . . . .. Each chessman has a characteristic way of moving that is all that matters about it. The whole game of chess follows from this way of moving the various chesssmen." '
page 359: Dirac: "Physical laws should have mathematical beauty" [perhaps the beauty lies in the logical proofs of the mathematics rather than the mathematics itself].
Can we devise a matrix which is an array of logical operators [ie a program].
page 376: Dirac, Scientific American May 1963 The Evolution of the Physicist's Picture of Nature. P. A. M. Dirac: The Evolution of the Physicists Picture of Nature
page 398: 'The Dirac equation describes the electromagnetic interactions of all the leptons and quarks, each with the same spin as the electron.'
Discrete just means expressed in whole numbers which obey arithmetic. Logical means expressed in symbols (which may be mapped to numbers) which obey the rule of logic [I am such a symbol, with exceedingly complex interior logic which underlies my interactions with the rest of the world]
page 430: 'Michael Atiyah: "No one fully understands spinors. Their algebra is formally understood, but their geometrical significance is mysterious. In a sense they describe the 'square-root' of geometry and, just as the understanding of the square root on -1 took centuries, the same might be true of spinors." [maybe they are a the software of a layer between quantum mechanics and special relativity].' Spinor - Wikipedia
page 436: AdS/CFT AdS/CFT correspondence - Wikipedia
[page 137]
Veltman page xi: Perturbation theory is a perfect fit for the network. Every bit of information I get perturbs me and I react perturbing the world, even if it is only this notebook. Veltman: Diagrammatica: The Path to the Feynman Rules
'Perturbation theory means Feynman diagrams.'
'On what argument rests the assumption that a path integral describes nature? What is the physical idea behind the formalism?' Maupertuis? Maupertuis' principle - Wikipedia
'a particle at rest has four-momentum (0 ,0, 0, iM)
'Lorentz transformations can be understood as rotations in four-dimensional space.'
page 3: 'Compact groups have unitary representations. Lorentz group is non-compact, and its representation is not necessarily unitary.' Unitary operator - Wikipedia
page 4: 'The Lorentz transformation is a six parameter group.
Can we do all of physics by layered symmetries if we start from the quantum of action = structureless event of the same measure as the initial singularity which has no measure because it is alone and isolated, and subject to involution rather than evolution. We are inside God and god is our measure. Permute all these words around enough something might imerge - not-emerge.
Monday 4 September 2017
The theological theory of everything gives us clues to the structure of the world. The notion that the universe is divine is steering me toward a psychological rather than a physical picture of the world, and strengthening my network view by suggesting that the neurophysiological structure of
[page 138]
my mind (and my whole self) is a microcosm, a local system from which I can extrapolate to the world as a whole, ie the whole of God.
Saharon Shelah Shelah: Cardinal Arithmetic
The elements of the divine dynamics 'between' the fixed points are traditionally considered to be self consistent and expressions of the divine wisdom, omniscience and power, and we can all go along with that. The fixed points we see are particles, and the current source of the particles is the standard model which is an application of quantum field theory. Although quantum field theory is the best we have, authors like Veltman are not all that enthusiastic about it, saying only that it gets good results. 'There are formalisms that in the end produce the Feynman rules stating from the basic ideas of quantum mechanics. However, these formalisms have flaws and defects, and no derivation exists that can be called satisfactory. The more or less standard formalism, the operator formalism, uses objects that can be proven not to exist. The way that Feynman originally found his diagrams, by using path integrals, can hardly be called satisfactory either.' Veltman page xi.
A path integral is a continuous model of a communication channel, that is a set of error defeating transformations that picks out the route followed by information using the superposition of probability amplitudes which reveal, using Hamiltons principle, the consistent path taken by the information, ie the transform that [is stationary and] has probability 1 (?) [information flows through a computation]
Dirac [Scientific American]: 'I think one is on safe ground if one makes the guess that in the physical picture that we will have at some future stage e and c will be the fundamental quantities and ℏ will be derived.
'If ℏ is derived quantity instead of a fundamental one, our whole set of ideas about uncertainty will be altered . . .. I think one can make a safe guess that uncertainty relations in ther present form will not survive in the physics of the future. . . .
'We would like to think of a vacuum as a region in which we have complete symmetry between the four dimensions of space-time as required by special relativity. . . .
Quantum mechanics depends entirely on the synchronization of frequencies and this happens with amazing precision in some cases, eg atomic clock. The first hint of this came with the Bohr atom where the angular momentum of the electron determined the size of its orbit so that the phase 'joined' at each circuit of the nucleus. Stimulated emission, ordinary emission and absorption and all these things depend upon synchronicity, dynamic logic, as we see in a digital computer where the central clock keeps all the operations synchronized in the phase decided by the designer to make things work. I knew this at school, but it took today's bath to remind me.
Clements page 30: 'The reason for introducing the concept of a gate as a transmission element is that a digital computer can be viewed as a complex network through which information flows and this information is operated on as it flows through the system. Clements: The Principles Of Comuter Hardware
page 23: the two [voltage] states of a typical logic element. Voltages for 0 and 1 are clearly separated to give 'guaranteed noise immunity'.
Tuesday 5 September 2017
and = boson, nand = fermion, basic structure of universe.
Natural theology as I understand it is revealed theology, since
[page 140]
in a divine Universe all experience is experience of god.
On interpreting the Hamiltonian as a network of computers with different clock frequencies, ie different energies.
Particle/wave duality: the process of creating particles is cyclic, like most industrial processes, a sequence of operations to create a house or a baby, for instance. Construction is a cyclic (recursive) process.
Pais page 302: 'The behaviour of electrons, now as particles, then as waves, was still a grave paradox as Bohr and Heisenberg began their dialogue . . . In spite of having a mathematical scheme both from Schrödinger's side and from the matrix side, in spite of seeing that these mathematical schemes are equivalent and consistent and so on, nobody could have known the answer to these questions: "Is the electron now a wave or is it a particle, and how does it behave if I do this and that and so on . . . [Bohr's] strongest impressions were the paradoxes, these hopeless paradoxes that so far nobody [had] been able to answer. These paradoxes were so in the centre of his mind that he just couldn't imagine that anybody could find an answer to the paradoxes even having the nicest mathematical scheme in the world. . . . Bohr would say 'even the mathematical scheme does not help. I first want to understand how nature actually avoids contradiction.' " ' Pais: Niels Bohr's Times, in Physics, Philosophy and Polity
'[Bohr] rather felt, "well, there's one mathematical tool — that's matrix mechanics. Then there's another one — that's wave mechanics. And there may be still other ones. But we must first come to the bottom of the philosophical interpretation." '
Heisenberg: "Still, of course, it made an enormous impression on Bohr that one could now do the calculations. That was definite proof that one had found, a least mathematically, correct solutions." '
Any extended constrained motion must be periodic. The Universe is unconstrained and aperiodic.
[page 141]
Wednesday 6 September 2017
Pais 326: 'Jeans "[Suppose that] 500 million atoms are due to disintegrate in the next second. What, we may inquire, determines which particular atoms fill the quota? . . . It seems to remove causality from a large part of our picture of the physical world. . . . The new laws merely tell us that one of the atoms is destined to disintegrate today, another tomorrow, and so on. No amount of calculation will tell us which atoms will do this." ' The disintegration is the result of a halted computation which requires phases for all the steps of the computation to line up to give is an inner product of absolute value 1. Jeans: Physics and Philosophy
The order in the world is established and maintained by bonding, and bonding is established and maintained by communication. Communication is made possible by shared protocol or language and theology is the ultimate protocol of everything.
At the moment it happens, the probability of an event is 1. While it is spinning, we can say that the probability of the ball falling into each slot of the roulette wheel is equal, but as things slow down it leans closer and closer to its final resting place and finally the chosen slot is narrowed down to one and the probability of the ball being in it rises to 1. Roulette - Wikipedia, Bayes' theorem - Wikipedia
Thursday 7 September 2017
Pais page 249: 'Feynman QED: "The theory of quantum electrodynamics describes nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept Nature as she is— absurd." ' Feynman We would like to say that the network model is not absurd, it suits our intuitive understanding of gossip, many things talking to one another and[page 143]
perturbing one another.
Pais page 350: Born, Heisenberg, Jordan "The quantum number [n] of a [field] oscillator is equal to the number of quanta with the corresponding [frequency, energy]."
page 351: 1926: Dirac, PRS 112, 661, 1926 P. A. M. Dirac: On the Theory of Quantum Mechanics
A dead day. On board neural network not producing much. Maybe a bath will help.
When we toss a coin we might think of the two faces competing for observability and, because the coin is symmetrical we expect that a large number of tosses will yield ½ heads and ½ tails and these figures will come exact when the number of tosses goes to infinity. Applying the Born rule,we expect the amplitude for each fact to have an absolute value of 1/&sqrt;2. In the quantum mechanical case where we often have coins with an infinite number of sides which are not symmetrical we get a set of observations of varying probabilities whose sum is 1. These probabilities are computed by the inner product of the corresponding basis vectors of the observable operator and the system being observed and given a large enough number of observations, these also approach a fixed limit, which suggests that a deterministic process is computing the 'angles' between the observing and observed states. How does this work?
von Neumann page 3: '. . . what was fundamentally of greater significance, was that the general opinion in theoretical physics has accepted the idea that the principle of continuity (natura non facit saltus) prevailing in the perceived macroscopic world, is merely simulated by an averaging process in a world which in truth is discontinuous by its very nature.'
Friday 8 September 2017
A statement from a fickle politician like Trump is like a short lived particle, like to be annihilated very soon.
From an algorithmic information point of view (or any point of view) a true continuum is nothing and the emergence of fixed points in a continuum could easily pass as creation out of nothing. The problem with the current concept of the vacuum is that the zero pint energy in each of its oscillators is not really zero, giving us the absurdly large cosmological constant suggested by Weinberg. This is a bit like the Catholic concept of the classical God, omnino simplex and therefore a continuum, but nevertheless possessing all possible information and power, omniscient and omnipotent.
von Neumann page 7: 'In both theories we must now learn as much as possible from [the] Hamiltonian function about the true, ie quantum mechanical, behaviour od the system. Primarily, therefore we must determine the possible energy levels, then find out the corresponding "stationary states" and calculate the "transition probabilities" etc.
One is always trying to find a killer argument (like the special theory of relativity) to justify the claim that the world is digital to the core. This would have to be an argument of principle with clear numerical results which seems a big ask. One of my perennial problems with physics is why it yields numerical results in the first place. My thinking usually is that we have a fundamental unit in the quantum of action and want to express al other units in terms of quanta. The next step is to measure the energy in terms of frequency E = hf. We measure frequency as seconds-1 but the second is an arbitrary measure so our measurement of energy is arbitrary and in quantum mechanics and elsewhere we can only speak of relative frequencies and use as standards the transition frequencies between various atomic states.
[page 144]
What we need is a computational model which tells us how many pogical operations at one quantum each it takes to achieve a given process, like moving a hydrogen electron from n = 1 to n = 2.
Pais, Inward page 121: 'Thus radioactivity represents one instance among many of situations in which physicists of earlier day were unwittingly dealing with quantum effects.'
'. . . radioactive decays were contrary to the traditional concepts of cause and effect. During the first two decades of this century, physicists had no reason to suspect that these paradoxes were not by any means typical of radiation only.'
The wave theory of physics is a law of large numbers thing. We do not know exactly what the underlying processes are but if we observe enough of them we can see how common they are and try to make theories to explain these probabilities. Can we make such a theory with logical continua, ie computers, in a network?
Digital to the core means beginning with the first digit which may be taken as the representation of a single lone act, the apophatic God. Symbols only come in pairs, the p and the not-p, image and ground. So we come to the next digits, 1, 2, ect etc through he transfinite space never coming to an end.
Fixed point theorems and Cantor's theorem drive the complexificationof the Universe. The number of fixed points generated in a space is equal to the number of mappings possible in that space, so the fixed points of the mappings of the numbers onto themselves, all ℵ0 of them, have the cardinal ℵ1 [?]. Of course, in the early days,
[page 145]
ℵ0 = 0, and things began to grow after that, the Cantor explosion that models the big bang [which was an explosion of space and particles?]
I want to reproduce my mind? Why? Because I think it s god and would like to set it out in print where people can look at it and judge.
Saturday 9 September 2017
What happens when something happens? Is this the question?
von Neumann I:4 The matrix and wave theories united by the fact that in both cases the sum of the probabilities of the symbols emitted by a quantum system may be normalized to 1.We can explain how things mathematically because we just define them to be so. But how do they actually happen when the symbols are physical.
Fixed point in a continuous topological manifold defined by f(x) = x, but how do we define x This whole business reeks of bootstrapping but how does the universe create itself? Because God is pure eternal act and so both completely simple and has no energy because no time and therefore no zero point energy. Here we are taking over old theological ideas for the cosmological constant problem.
Holland page xvii: 'Complete specification of the state of an individual system requires both aspects: not wave or particle, but wave and particle. The wave particle composite continuously evolves according to a set of deterministic laws. Holland: The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics
The wave is the periodic computation process that produces the particle
[page 146]
when it halts ?
The aim of the de Broglie-Bohm theory is not an attempt to return to classical physics, or even particularly to invent a deterministic theory. Its goal is a complete description of an individual real situation as it exists independently of acts of observation. According to Einstein, that is the programmatic aim of physics.' We think he is wrong. The network model tells us that all events are observations. To be is to be observed which is the whole point of being beautiful and explains the trade in super-models.
Holland page 2: '. . . insofar as it only predicts the outcome of measurements performed on statistical aggregates of physical systems, quantum mechanics does not in itself provide an explanation of the experimental facts. What is missing is a description of the actual individual events of experience of which statistical phenomena would be functions.'
Quantization replaces classical dynamical variables with operators.
Holland page 8: Bohr in Jammer 1974 page 204: 'There is no quantum world, there is only an abstract quantum physical description. It is wrong to think the task of physics is to find out how nature is Physics concerns what we can say about nature [and do]. Jammer: The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective
Theology concerns what we can say and do about God.
Holland page 11: 'In the following the important issue is not so much the denial of causality in the processes governed by quantum mechanics, but the claim that no model at all can be constructed of an individual system.'
page 13: 'In [Einstein's] view, the indeterministic aspect of quantum mechanics follows from the failure to provide a complete description
[page 147]
and not because it is an intrinsic characteristic of matter.'
Read Holland in 1993. 24 years have passed, and what progress have I made? One new child and assisted the upbringing of the first three. . . .
Holland page 15: 'It seems to have been regarded as almost axiomatic that the trajectory concept of classical mechanics is incompatible with wave mechanics.' But consider the path integral method. Now the trajectory is the logical execution of a computation process.
page 17: Bohm: quantum potential, which we would like to see as logical potential, ie a convincing argument.
It has taken me fifty years to discover that I am never going to get very far, but I do enjoy reading and writing.
