Notes
Sunday 4 April 2021 - Saturday 10 April 2021
[Notebook: DB 86: Hilbert / Minkowski]
[page 164]
Sunday 4 April 2021
We can create any function using Fourier's method of superposing an infinite spectrum of periodic functions of different frequency, phase and amplitude. This long string of frequencies is rather similar to the strings of Turing machines I have been using to model interactions in the real world. The basic mathematical structure of the elemental machines is boolean algebra. We construct the whole computation process by a suitable network of memories and not and and operators. The functioning of a computer network depends on the phase and frequency of these operations. There is no question of amplitude in the classical sense. Each operation is a quantum of action or an integral number of quanta of action. Here we have a sort of network or coordinate system for converting complex algorithms to simple components via the analogy with the Fourier transform.
Mass seems to be problematic in field theory. We have no idea why the masses of particles take certain fixed values. Newton recognized two aspects of mass, the inertial mass that mediates the relationship between force and acceleration and gravitational mass which is both source snd recipient of the forces which appear to determine the behaviour of the universe.
We wish to remove irresponsible power from the human system. How was it brought under control during the construction of the universe? During the construction of civility?
Edging toward a well developed idea.
[page 165]
Quantum mechanics is not relativistic. Applies in the time domain only [one dimensional field theory].
von Neumann Chapter V General Considerations John von Neumann: The Mathematical Foundations of Quantum Mechanics
'Therefore 2 [undisturbed evolution of quantum state] — like classical mechanics — fails to reproduce one of the most important and striking properties of the real world: namely its irreversibility, the fundamental difference between "future" and "past", the direction of time.
'On the other hand 1 [measurement] does increase entropy and is not reversible.'
page 240: Mechanical energy zero entropy.
Monday 5 April 2021
Ultimately quantum mechanics is like the world, it works but we do not really understand it. We have made a de facto model of the world but it has yet [to] become in some way de jure which means it is ripe for new interpretation.One of the most interesting features of quantum theory is entanglement. This, plus demonstrations of delocalization are evidence for the idea that quantum mechanics is the time / energy / frequency phase domain of signalling which could exist in some way prior to space. Time, we might say, is the home base for quantum mechanics. Without space the only way to differentiate states is by frequency. Phase is represented but the circle group so that all measurements of phase are relative and can be superposed to create new phases whose absolute square turns out to be probability. What is the physics behind this mathematics,
[page 166]
the gateway between amplitude and visibility? So we imagine processes built from superpositions of stats of different frequencies and phases which in their time evolution would perform a sequence of logical (distinguishable) state akin to the operation of a turing machine. Visibility materializes when two of these systems meet, rather like music. Quantum entanglement - Wikipedia
Our mattress is a network of sources (fermions) and messengers (bosons), and we feel no need to model it as an actual continuum limit, since this evokes the continuous symmetry [which] often greatly simplifies things because the law of large numbers translates infinite discrete events into a smoothish functions of time.
By sharply distinguishing the time domain from the space-time domain we isolate the step from time to space-time for careful study. An important foundation here is that every event is precisely measured by the quantum of action but the associated energy can be from close to nothing to close to everything.
Cyndi Lauper. Slowly moving from science to art, from understanding to expression. Maybe I can cleave close enough to quantum field theory to tell my story. The bit I like now is the spirit-amplitude bit, a product of time and eternity which covers most of the points raised by Aquinas in the first part of the Summa from a different point [of view]. Aquinas is the frame of reference for the medieval Catholic god which we are trying to reconstruct by reinterpreting it, combining the wave function of the universe to construct a formal transformation of this frame to fit a divine universe. Cindi Lauper: A Memoir
[page 167]
Lauper page 167: ' "I took a page from Gertrude Stein and tell the press that the three biggest oppressors of women are the church, the family and the government".'
Zee page 17: The basic feed into the path integral is the action so when we set out to go from a single particle to multiple particles and the continuum limit, the function of interest is
Z = ∫ Dq(t)eiS(q)
where S is the action computed by classical methods which indicates that the action here is a function of spacetime, a step ahead [prior to] of the measure of action in the time domain.
Classical to quantum q - Ψ
Tuesday 6 April 2021
What is my role in the universe? To find a consistent set of circumstances in which I can survive. The same as any other particle really. My needs of security, food and shelter are taken care of. The physico-theological milieu is a mess and my outlook is inconsistent with the mainstream which I take to be the doctrines, beliefs and practices of the Roman Catholic Church. I feel the need to modify both our interpretations of physics and theology and bring them into harmony. Bonum ex integro, malum ex quacumque causa. The human world is very poorly integrated. We are a vast number of particles seeking harmony just like the first particles (quanta of action) formed in the universe. Like them I am a quantum of action with a physical presence and a deep formal interior.
[page 168]
I started this project with a business in mind, the theology company. The product then seemed simple and clear, my own first run through the idea of identifying god and the universe. And then the work started, trying to make the fundamental interface between physics and theology, since physics describes the hardware on which theology is built.
Von Neuman unified the two theologies of matrix and wave mechanics by mapping them both onto Hilbert space. Now we are trying to unify physics and theology, repeating Aristotle's discovery in modern terms. Aristotle began with matter and form, went on to define motion as the passage from potential to actuality and using the axiom that no potential can actualize itself to point to the existence of a god, the unmoved mover. What is our parallel path? S. Marc Cohen & C.D.C.Reeve: Aristotle's Metaphysics (Stanford Encyclopedia of Philosophy)
The cats just eat and sleep. Why not me? I am on a mission driven by a dream which seems to be beyond my power but I am convinced that enough small steps will take me to my goal if I can get them properly arranged. We have reified action, What about reifying the wave function, ie seeing it as physical representation of the behaviour of superposition?
Von Neuman joined matrices and waves in Hilbert space. It seems here that I wish to join physics and theology in logical space which I take to be the space of quantum communication and quantum computation. What I am keen to do is to map this idea onto the transfinite computer network to look for a wave function for the universe. Nielsen & Chuang (2000) Quantum Computation and Quantum Information
Wednesday 7 April 2021
[page 169]
Zee page 18: 'We see here the power of imposing a symmetry. Lorentz invariance together with the insistence that the Lagrangian involves at most 2 powers of ∂/∂t immediately tells us that the Lagrangian can only have L = ½(∂ψ)2 - V(ψ) with V some function of ψ. ' This in itself is a symmetry (algorithm) and places the Lagrangian as the difference between 'kinetic' and 'potential' energy right at the heart of the oyster. We see the Lagrangian as a natural outgrowth of the master equation E = hf together with the idea that Δt is the inverse of frequency so we can write Δt = 1/f, hω goes to ΔE.Δt = ℏ. We see a split of action into Et which we can also write ∫ Edt, then bifurcating the potential and kinetic energy whose values are equal and whose sum is 0, is ψ - V = KE - PE so that the two forms of energy can increase without limit as long as they (like charge) balance themselves to zero.
So far, therefore, we are generating an origin story for physics based on the identification of the initial singularity as a quantum of action, that is as an event, a verb. This is consistent so far with the Lagrangian approach to quantum theory and so provides a symmetry or algorithm for generating the universe. It is a mathematical formalism that is 'reified' by cosmic art to give us. In the time domain we might interpret potential energy as low frequency change, storing and transforming over s longer period (like gravitation) while the more dynamic beings dance to its tune. A musical introduction to QED to replace Feynman's screens, although they have obvious computational value, providing a stable model of propagation.
From an abstract point of view a propagator tells us the probability that we will observe a particular spectrum of observations. There is no mention of space.
[page 170]
Here we introduce the idea of evolution as a mechanism for increasing the entropy or complexity of the universe starting from the verb to act, agere. To move on we have to introduce the notions of imperfect but prolific reproduction and selection arising from a finite supply of resources. To be fit is to endure and reproduce. The first is an act of memory, as state that endures through time until it is actively changed. It has a lifetime or period controlled by its encounters with other particles.
In biological evolution the overall structure of an organism has been encoded in its genome, which is passed on from generation to generation in executable form by the organism dividing or producing a fertilized ovum which will grow under suitable circumstances into a mature organism. The variation necessary for evolution is provided either by random errors of copying or the sharing [superposition] of genetic elements from different parents in sexual reproduction. Can these biological ideas be applied in the much less complex context of the big bang?
The role of the quantum of action is to act, but we imagine that it is too simple [to contain some sort of clock] to control the moment of action, so that it acts a random intervals. We call these intervals time and equate the energy of a sequence of actions to the inverse of the interval between actions. The result is a spectrum of energies whose frequencies may range from 1 to ℵ0 where ℵ0 is the first transfinite number, the cardinal of the set of natural numbers (let us say). Every interval in this spectrum may be associated with a certain string of actions which we see as analogous to a propagator, an infinite superposition of paths each constructed as an infinite sequence of products of infinitesimal periods of stasis. We like to think that this idea makes sense, and seek to apply it in an environment
[page 171]
where it may not be legitimate to treat a quantum of action using the technology of calculus.
All of this is to create a story of the universe more in tune with modern science replacing the notion that the universe preexisted in the mind of god, which is tantamount to actually existing. God's consciousness is the reality we experience. Reliving the Aristotelian dream.
Zee page 19: 'The dynamic variable in field theory is not position but the field φ. The variable x⃗ is a label, not a dynamical variable. The x⃗ appearing in ψ(t, x⃗) corresponfs to the label a in qa(t) in quantum mechanics. The dynamical variable in field theory is not position but field φ. The variable x⃗ simply specifies which field variable we are talking about (ie is the domain of the field).
So the idea is that the field is a set of purely local events providing a background explanation of events in space-time. Nevertheless the universe is connected together by bosons. If all bosons were massless, they would exist in effect outside spacetime. Mass is contained energy (process) contrasted to uncontained massless photons that can travel the universe from beginning to now to the end. Things do move in spacetime, so we seek to understand the relation between spacetime, fermions and bosons. In other words we want to create a new layer, spacetime, which somehow (through gravitation) constrains the large scale structure of the universe that has emerged within the initial singularity [which we might guess has something to do with fixed point theory, since space acts as the operating system for memory and communication].
'Thus we finally have the path integral formalism defining a scalar field theory in d = (D + 1) dimensional spacetime:
[page 172]
Z = ∫ φ ei∫ ddx(½(∂φ)2 - V(ψ))
Note that (0 + 1) dimensional quantum field theory is just quantum mechanics.
Zee page 20: 'Incidentally the vacuum in quantum field theory is a stormy sea of quantum fluctuations [quantum actions] . . . ' They all say this and it seems to be the essence of a quantum action in action.
Lauper page 239: 'Its really hard to be friends with famous people becasue they are really busy,'
So the earliest foundation of the world is rhythm.
Lauper page 324: 'When these two distinctly separate rhythms were played together it felt like they created a vortex [a Lissajous (?)], one I could sing in the middle of.'
What is potential? What is a source? One might assume that it is an entropic thing, the power of the count. We must begin with gravitational potential. It is embedded in the Lagrangian, has values and can be accounted for, in other words it has a discrete structure, like money.
Thursday 8 April 2021
[page 173]
Zee page 21: 'In particular J(x) can vanish everywhere in spacetime except in some localized regions ([how?] inputs from other regions in the universe)
page 21: '[wave packets'] going off here and there' (see above?) This corresponds precisely to sources and sinks for particles. . . .
page 23; Propagator, D is an integral of the path.
Here we are seeing the fantasy of continuous arithmetic (using infinite superposition to define points) which may be about as trustworthy as Christian theology and causing similar injury to the body politic through unquestioning application.
page 28: ';E = -1/4πr e-mr.
What we have derived here is one of the most celebrated results in twentieth century physics. Yukawa proposed that the attraction between nucleons in the atomic nucleus is doe to their coupling to s filed like the ψ field described here [the sea of activity]'.
page 29: 'That the exchange of a particle can produce a force is one of the most profound advances in physics.'
page 36: 'It is difficult to overstate the importance (not to speak of the beauty) of what we have earned. The exchange of a spin 0 particle produces an attractive force, a spin 1 particle a repulsive force and a spin 2 particle an attractive force
[page 174]
realized in the hadronic strong interaction, the electromagnetic interaction and the gravitational interaction respectively.'
Zee page 37: 'Disturbing the vacuum with a source lowers its energy. Thus it is easy to understand that generically the exchange of particles leads to an attractive force.' On the assumption that the universe wants to decrease energy rather than fix action as an integer.
'but why does the exchange of a spin 1 particle produce a repulsion between the objects. The secret lies in the profundity that space differs from time by a sign.' So? Why? We are not asking these questions, merely reciting the standard model.
Very simply we take the quantum of action, aka god, as the source of the universe and shape our theory as a structure arising from the nature of being [per se ie pure action, beginning completely simple and necessarily complexifying driven by Cantor's theorem, randomness from the past and selection for admission to the future. This is a fresh start. Quantum mechanics has grown from a fork of classical mechanics because it is not a good fit because it uses continuous rather than discrete processes, so excluding logic from its foundations. Classical mechanics uniformed by the long history of theology fails to appreciate the role of discrete logic in the nature of the universe. We 'reify' the quantum of action and see it as the source of the universe, constrained as stated above by the nature of being which is essentially communication and computation. So we go from quantum mechanics to quantum communication and computation and from quantum communication and computation to a logical theory of everything
[page 175]
driven by explosive random force tamed by selection. Out of all the random possibilities the world, de facto, selects those which can in some way reproduce themselves. It feels like making music, saying the same things over and over again. I love the idea of layered development, the lower layers providing the symmetries which are diversified to produce the next layer, with a new crop of symmetries, that is in effect structures that reproduce themselves, the basic property of action.
A key point is orthogonality, the condition that marks a degree of freedom, able to move inertially without effecting its environment. So events on the East-West line have no element of north-south. The basic creative power is the power to create orthogonality because, at its simplest, the software in the quantum of action is the instruction not which when applied to an entity p creates not-p, transforming |1> into |0>, |p> into |not-p>, orthogonal to |p>.
Friday 9 April 2021
Zee page 62: 'The anharmonic term [is] the interaction term in quantum field theory.'
Every event in the universe is associated with a quantum of action and a certain amount of energy which can by calculated by quantum field theory.
Zee page 77: ' "internal symmetry" '. We might imagine that Hilbert space is the internal symmetry of the world.
Must learn to think mathematically again. Managed for a while near the
[page 176]
end of school and then branched out into the dreamworld of philosophy and theology. Now I have to come the full circle and must learn to understand QFT.
Zee page 83: 'What exactly are energy and momentum anyway? Energy and momentum are what gravitation listens to.'
page 88: 'QFT is not that difficult; it just consists in doing one big integral
Z(J) = ∫ D ei∫ d(D + 1)S. . . .
That is just about all there is to quantum field theory.'
Saturday 10 April 2020
There is a true god that makes everything work. It is not in the sky, it is everything itself, the thing an sich (per se?)
Think like Dirac. This is what we are trying to do about everybody, understand the mechanism behind their behaviour. Dirac found that space and time are identical at the linear level. The purpose of physics is to operationalize this mathematical algorithm as a constraint on the actual physical structure of the world, so there is truth there. The Einstein Jesus - the core message is in the stable formalism.
[page 177]
So we are now reifying mathematics by removing the original sin of continuity and opening the way for dynamic logical structure, ie computation. What we have to explain to ourselves is the hardware on which the universe runs and we understand this to be the fixed points in the universal dynamics which have been selected out of an infinity of possibilities like Feynman's path. So we shift the quantum mechanical path integral equation to a quantum mechanical communication and computation network (layered) whose physical hardware is logically defined fixed points in the transfinite logical structure [which we guess to be those features of the universe that are defined by closed recursive structures, ie groups].
Quantum of action: just do it, ie execute a string of events that makes it happen.
Zee page 94: The Dirac equation: 'some linear combination of ∂μ acting on some field φ equal to some constant times the field, rate of change proportinal to the fied, both measured in energy.
The Dirac Key (selector) {γμ γν} = 2ημν.
This led to (∂2 + m2)φ = 0, particle mass m, sothe Dirac equation (iγμ∂μ)φ = 0, the fixed point of a differential operator like eigenvalues of a matrix?
The puzzle: find iγμ that anticommute with eachother.
page 95: ' . . . the mysterious Dirac equation is no more and no less than a
[page 178]
projection that gets rid of unwanted degrees of freedom. . . . Our discussion provides a unified view of the equations of motion in relativistic physics. Just roject out the unphysical components.' The paths untravelled, so mathematics can describe what does happen and what does not happen since it has degrees of freedom by fiat. Let us assume . . .
Why does mass play such a large role?
Zee page 120: Every electron in the universe is an excitation of one and the same electron filed ψ (so where did this field come from?).
page 121: 'This fact, charge quantization, can only be deduced by embedding quantum electrodynamics in a larger structure such as the grand unified theory . . . ' Following requisite variety, we cannot see how the initial singularity could represent all the details of the grand unified theory.
I have been drawn on a particular course since I was baptized into the Catholic Church. First, like air it was part of the environment and not particularly visible to a child apart from the need to be well behaved in church [so as not to embarrass my mother by crawling off under the pews]. I continued in that vein until my early 20s when the idea occurred to me that everything could be much simpler if we accepted that the universe plays all the roles traditionally attributed to god. We might say that the universe is theologically complete, able to achieve anything possible which does not involve contradiction. I have followed this insight to the limits of my understanding and creativity ad now, reading through Zee I see little flashes of possibility in the application of quantum theory to theological questions. It appears to be simply applied logic, after all.
[page 179]
I think the strongest personal indicator that I am on a fruitful line of inquiry is that it has remained fruitful since about 1966 and is gradually becoming inevitable in my mind and leaves me quite relaxed, feeling that the creative effort is over and now we are up to mopping up and documentation on the web.
Agatha Christie: Mrs McGinty: an observable representation of human events surrounding a murder. Agatha Christie: Mrs. McGinty's Dead: A Hercule Poirot Mystery
What is a piece of information? It is relative to a particular hearer and has meaning for them, maybe leading to action.
