vol VII: Notes
2018
Notes
Sunday 29 July 2018 - Saturday 14 July 2018
[Notebook: DB 82: Life and Death]
[page 207]
Sunday 29 July 2018
A big question is how is the world implemented. We have our group theoretical model of how gravitation works and we find that it gives the correct results to within the limits of our measurement and computational technology, but the question is how does the
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Universe itself achieve this? Are the universal implementations identical to Einstein's mathematical implementations, and how does the universe perform the calculations that cosmologists perform in order to get the answers cosmologists do?
The network answer, similar to Einstein's answer, is that the overall picture is governed by local events. The ultimate local event is a quantum of action with no specification, completely simple as the traditional God is simple. The creation of the world arises from the interaction of quanta, each being defined and differentiated by their mutual interaction which is imagined in quantum mechanics by measurement, which takes place in the product space [of the Hilbert spaces] of the two systems interacting to give the measurement. This act of communication involves two agents, each acting as a frame of reference or coordinate system for the other, so the interaction itself is self contained and coordinate free. What gravitation does is rename such self contained entities events and then use gaussian and riemannian methods to represent the basic symmetry of events in terms of their energy, thus arriving at the stress-energy tensor which serves as the basic measure of interaction in the global system.
So we equate the Trinity with measurement, two fermions interacting through bosons to give us the fundamental unit of a communication network. We see space as created by the Pauli exclusion principle. There might be a lot going on in my Central Nervous System when I write things like this because
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doing it makes me very tired.
So let us go back to Auyang chapter 3 Relativity and Symmetry Auyang
The study of the history of theology is predominantly the study of the fictions and delusions that people have dreamt up to control one another by devising carrots like heaven and sticks like hell, all under the control of a supreme [being] with which those in power are inclined to identify themselves.
A particle is an event, like a marriage.
Kronecker was right: the continuum is a self-contradictory mathematical fiction. Leopold Kronecker - Wikipedia
Monday 30 July
Tuesday 31 July 2018
I have long thought that there is a close analogy between human insight and quantum measurement. Feynman's path integral formulation of quantum mechanics echoes de Broglie's isight that the permitted orbits of an electron in an atom are those for which the wave motion of the electron has a number of wavelengths that is an integral multiple of the circumference of a stable orbit. Feynman extends the idea to the situation where particles are moving from state A to state B in free space. He presumes that they may follow every possible trajectory, and integrates the phase changes along all these trajectories to find the trajectory with stationary phase that represents (he thinks) the actual path taken by the particle which then becomes input to the vertex of a Feynman diagram.
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Prinz's article on attention contains a similar idea. His AIR theory says 'Consciousness arises when and only when intermediate level representations undergo changes that allow them to become available to working memory.' He then goes on to tell us that in (Prinz forthcoming) 'current evidence points to the conclusions that attention involves an increase in the activity of inhibitory neurons, which result in phase locked oscillations in stimulus encoding pyramidal cells; once synchronised these cells can propagate forward to structures that can maintain neural activity during delay periods (working memory structures). The basic idea is that synchrony allows a population of neurons to produce a signal that can be picked up by other brain areas despite the noisy neuronal environment.' Feynman's idea involves phases (synchrony and asynchrony) across the whole of space-time. It occurred to me that the path integral method can also be applied to phase relationships between neurons in the central nervous system and a similar integration to find stationary (ie synchronous) paths would establish a strong analogy between quantum field theory and neural process. Insight is analogous to the appearance of something in consciousness; quantum theory gives us the probability of the creation and annihilation of particles in the universe. This idea occurred to me while I was doing my homework for Gerard O'Brien's course on naturalizing morality. Throughout the first semester this year I have been wondering which 'ism' to endorse and with William James' help have currently settled on neutral monism sailing under the flag of panpsychism. I solidified this position with an essay for Ant Eagle arguing that God and the Universe are effectively identical. Jesse J. Prinz: Is Attention Necessary and Sufficient for Consciousness?
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Wednesday 1 August 2018
As a matter of principle, we might expect the explanation of a natural phenomenon to have approximately the same entropy or complexity as the phenomenon itself. The complexity of explanations is radically reduced by symmetries so (eg) Newton's four laws that occupy less than 1k of text give us a quite complete description of classical dynamics. The detail enters through the application. We can say the same for other classical laws (symmetries) like Maxwell's equations, Minkowski space and Lorentz transformations and general relativity and the complexity comes from applications. We expect a similar symmetrical simplification in particle physics, so, given the simplicity of the early universe, we are justified in seeking very simple symmetries which are nevertheless broken and complexified in applications. So at the heart of QED and all the other fundamental theories we have the simple phase equations represented by the eigenvalue equation and the Born rule. The complex situations we see result from the large numbers of detailed influences that we see on phase, as we see in a raging sea motivated by strong winds. What I want to do (I think) is interpret phase in terms of computational process, beginning with one computer with one clock (source of phases) and building up to a network with transfinite numbers of computers.
Auyang page 27: We take space-time as a given, the passive geometric domain of quantum field theory. I want to make it part of the dynamics of the universe as Einstein did and eliminate the mathematical continuity which casues so much trouble in physics in the region of continuous probabiity amplitudes. The analogy between the brain and quantum field theory developed yesterday looks like a step
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in the right direction.
Auyang pace 26: 'Algebraic topology and algebraic geometry make a topological structure quantifiable by coordinating it to an algebraic structure, for instance the real number system.' Boolean algebra?
'for physical theories, the crucial difference is between finite and infinitesimal geometries, not between Euclidean and non-Euclidian geometries.'
Herman Weyl: ' "The principle of gaining knowledge of the external world from the behaviour of its infinitesimal parts is the mainspring of theory of knowledge in infinitesimal physics as in Riemannian geometry . . . " '
Maybe the artificial symmetry of continuity hides a lot of detail which could be very helpful in simplifying physics. The way forward may be to explain space-time by some logical combination of ℏ, c and quantum measurement / quantum information theory.
A good place to start might be the logical origin of zero point energy, ½ℏω, which seems to suggest that it is not possible for a system to stop communicating entirely, that is to effectively go out of existence, if we interpret energy as rate of action, and action as communication, that is measurement. One cannot see something if it does not communicate in some way with the seer. And what has this got to do with the velocity of light? ½ℏω seems to indicate half a photon? [maybe it takes two to communicate, so each contributes the energy equivalent of half a photon.]
A scientific theory is meant to represent reality.
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Auyang page 27: Cartesian geometry: what is the atom of inertial space - we have coined before the term 'diron', an embodiment of the Dirac equation. The standard assumption is that Euclidean space is continuous and differentiable, but it may be fact be seen as a network of quantum sources whose communications take place at the velocity of light. http://www.naturaltheology.net/Notes/Notes15/notesM11D22.html
Linear because quantum? Length and direction by real inner products, ie classical objects arising from quantum measurements arising from dirons communicating with one another to create events.
A special case covered by a coordinate system, ie linear metric. Are there any real Cartesian spaces — possibly not.
Gauss: dense grid of ordered curves, but arbitrary spacing [nevertheless] dense enough for differentiability. 'Gaussian coordinates individuate but neither relate nor measure.' So we might see them as a good way to individuate dirons.
Auyang page 28: 'Points in a manifold are coordinate free.' So what happened to their differentiation — what is a point in the real world if not an event, ie a [quantum] measurement?
page 29: D2: How do we map a line into a manifold if poits have no identification?D3: Tangent spaces are disjoint (like points) (a fibre bundle on each point?) so we need a curve and a connection to make affine structure. Parallel transport implies the existence of angles, which implies metric, yet not yet implemented?
Connections represent potentials or interaction fields, EM or gravitational.
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D5: Metric tensor is defined over tangent space at each point to give infinitesimal length elements. Tensor field gives metric tensor to each point.
D6: Finite lengths integrals of infinitesimals.
D7: Distance is greatest lower bound of distance between two points
Auyang page 30: 'if a reference frame defined on a tangent space can go from point to point without being rotated, then all the tangent spaces are essentially identical and are identified with the space itsef, and the manifold becomes a Cartesian space.'
'Physical theories parametrized by space-time variables are considered more [basic] than those that are not, but it is often taken for granted because it is so obvious.' And so wrong. We impose the points in our minds, but in fact they do not exist until they are created by a [quantum] event.
page 31: Velocity is a derivative concept in classical physics, but it is, like momentum, a fundamental concept in quantum theory, possibly unanalysable. — 'Special relativity makes the concept of velocity fundamental — for quantum mechanical reasons? The important feature is "proper time".
'The light cone structure of special relativity is localized to the tangent space above a single point.' Or does it lie 'beneath' the point — maybe in the diron.
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Localization of light cone is an example of local symmetry — differently oriented light cones in general relativity [so null geodesics followed by light are 'bent'.] Steven Shapiro and Irwin Shapiro: Gravitational deflection of light
Auyang page 32: c is a feature of electromagnetism, and is to be found at all levels, since it is the foundation of the fermion-boson bifurcation.
'Each principle of relativity specifies an equivalence class of coordinate systems which constrains the content of the physical theory.' Why, if coordinates are really irrelevant — more to the point, the physics constrains the coordinates.
page 33: Symmetry → group. Symmetry = difference + identity + relationship.
'The concepts of coordinate functions, coordinate transformations the coordinate free invariant and its coordinate representations constitute an integral coordinate structure underlying all symmetries'. Eg Lonergan: Metaphysics = "integral heuristic structure of proportionate being". Lonergan: Insight
A symmetry reveals the existence of an underlying algorithm. The idea that there is only one electron suggests that there is only one electron algorithm which is instantiated in every electron, just as there is only one photon algorithm which can be expressed in a very simple mathematical form which is instantiated in every photon and so for all the other fundamental particles, 12 algorithms. The four forces are equivalently represented by 4 codecs which encode and decode the messages being passed between the relevant fermions.
page 36: The invariant under the group of Lorentz transformations is the proper time interval [the count of cycles of phase is also invariant under any transformation?].
[page 216]
Auyang page 35: 'If a system is invariant under rotations, its angular momentum is conserved.' So rotations of a Cartesian coordinate system that simply change the identify of the three orthogonal axes conserve angular momentum rather like π/3 rotations of a snowflake. We can imagine spin-flips of an electron as changes of angular momentum so the differences between spin up and spin down correspond to a quantum of angular momentum, so conservation of angular momentum requires that this be achieved with a photon with spin 1.
page 35: Logical symmetry = consistency is the radical symmetry, preserved, we say, by the uncertainty principle.
page 36: 'The phase symmetry in non-reativistic quantum mechanics is global, written as exp(iθ) where θ is a constant'. Here I imagine we are seeing phase changes as propagating as infinite velocity.
'gauge a symmetry group' means to make the phase a function of space-time.'
Poincare transformations become local in general relativity.
Quantum phases transformations localized in quantum field theory, exp[iθ(x)].
A local symmetry is more complicated than a global symmetry because it demands global invariance of the entire system under local transformations' which requires a 'gauge particle' to carry the message from place to place [easy to imagine in a network].
Proper Poincaré group, elements g. Tg are unitary operators on a Hilbert space such that if g = g'g" then Tg = Tg'Tg". The operators Tg
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realize the group elements g as definite transformation on a Hilbert space. Mathematically the Tg form a unitary representation of the Poincarè group.
Thursday 2 August 2018
Maxwell's equations must hold part of the secret of space-time.
Gauss's law - surface integral around a charge is equal to the charge enclosed
Gauss's law for magnetism - net outflow of magnetic field through a closed surface is zero.
Faraday's law - varying magnetic field induces an electric field
Ampere's law with Maxwell's addition - magnetic field [is] generated by electric current, or changing electric field ("Maxwell's addition") — "displacement current".
So: changing magnetic field induces electric field and vice versa. Maxwell's equations - Wikipedia
Maxwell understood the connection between elecromagnetic waves and light in 1861 (imagine how he felt!) - Maxwell's original 20 equations in x, y, z
Vector formulation due to Oliver Heaviside , 1884.
Heaviside in Hunt: S = E ⨯ H - the flow of energy at a point in space is the vector product of the electric and magnetic fields there.
'[this] implied that the energy in an electric current does not flow through a wire like water in a pipe but instead passes through the surrounding field and enters the wire through its sides.' Led to recasting Maxwell's equations — Poynting vector. Bruce Hunt: Oliver Heaviside: A first-rate oddity
'inductive loading' Loading coil - Wikipedia
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Once again early morning malaise cured by intellectual exploration - the joy of insight, analogous to quantum mechanical measurement, orgasm and other creative acts, ie bringing a symbol into the light from the darkness of the continuum.
So my chief belief is that the observable world is demanded to be discrete by Shannon's theory of observation ≡ communication.E is a vector field; B is a pseudovector field.
ε0 is permittivity of free space; μ0 is permeability of free space.
c = 1 /√ε0μ0
When devising a mathematical treatment of an hypothesis one needs first a clear understanding of the hypothesis.
Auyang page 37: Let S and S' be coordinate systems and |&psiS> and |&psiS'> be quantum states. S and S' be connected by Poincaré [transformation g so S' = gS. So transformation of the unitary operator Tg is completely determined by the coordinate transformation (?). How does this work? Hilbert space and its transformations would appear to be independent of Poincaré transformation.
So take another look at Veltman. Veltman: Diagrammatica: The Path to the Feynman Rules
Veltman page xii: '[Physicist] must know how Lorentz invariance, conservation of probability, renormalizability reflect themselves in Feynman rules.'
We transform between numbers and logic by counting operations [so all the measurements of physics are counts of operations or rations of operations] . So how do we arrive at the number c = 1 / √ε0μ0
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Veltman page 3: Compact groups have unitary reprentations. Lorentz group is non-compact. Compact = linear (?) α1 + α1 = 2α1.
Auyang page 37 (continued): 'This correspondence is established between the transformations of coordinate systems and the transformations of quantum states. The state transformations preserve the inner product or the probability of states.' Which is consistent with the notion that Poincaré transformations have no effect on operations in Hilbert space, which is consistent with the notion that the quantum layer lies beneath (ie is symmetrical with respect to) the space-time layer. It is the pure energy-time layer.
Wigner on elementary particles: 'A free electron should be a free electron in all relativistic frames. Any two states of a free elementary particle should be connectible by the transformation of the Poincaré group. Thus all states are representable by the superposition of states obtained by the relativistic transformations of a single state. In other words there must be no relativistically invariant subspaces of the state space of a free elementary particle, otherwise we would call the invariant subspaces elementary. The state space of a free elementary particle is the Hilbert space for an irreducible representation of the Poincaré group.'
Compare Veltman page 15: 'In a quantum mechanical description the state of a free spinless particle is completely specified by its three-momentum. The energy follows from the energy-momentum relations. Location in space and time is completely unknown.' ie there is no coupling between Hilbert space and spacetime (?)
'A particle with well defined momentum is described by a plane wave.'
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Veltman page 17: 'This plague, having to abandon Lorentz invariance in order to define the formalism, seems common to all approaches to quantum field theory. One always needs some kind of grid.' Comment ~2000 ce: 'because you apply Lorentz transformation to amplitudes where they are in appropriate.'
Is this true? Does quantum formalism 'predate' space?
Field theory thinks that there is a global field (with local features) which evolves deterministically and determines the probability of the creation and annihilation of various species of particles. The network theory, on the other hand, sees everything in terms of pairwise local interactions of individual particles, rather like the pairwise interaction of people in a society. The probability amplitudes and Hilbert spaces (ie minds) of the interacting particles are local to them, so we do not have one field for the whole world but local discrete 'fields' which are represented by the products of the fields of the pairwise interacting particles. So special relativity applies to the real particles, not to the complex amplitudes that we use to model the local interactions that lie behind the communication of particles. The analogue is between the minds of people in conversation acting as the complex processors controlling the physical interaction between the people. There is no more global quantum field than there is a global human mind. Our minds act like Hilbert spaces, our interaction are real [ie there is no telepathic communication]. This is getting closer to to what I have been trying to say at least since I bought Veltman in 2000.
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At the university I am back in the monastery, developing a point of view which I want to convince the management to accept. We are taught that philosophy proceeds by the pure light of human reason, and I am trying to convince L.P. Fitzgerald OP that this is not enough any more, we have to add the pure light of science to the pure light of reason which means that if we really want to know about God we have to identify God and the Universe and study God by the empirical methods that this made possible. No dice, and I am expelled as a heretic. Now fifty years later I find myself in a university where the philosophers are moving toward embracing science as well as looking into the scientific space. So after 50 years in the wilderness I am coming home.
Friday 3 August 2018
Quantum field theory holds the universe together with a superposition of a number of 'fields', perhaps 12 fermions plus 4 bosons plus their antiparticles less the photon antiparticle which gives us a total of 15 + 16 = 31 fields. These fields are all imagined to evolve deterministically. Veltman's summary of the standard model and the relevant Feynman diagrams occupies 23 pages and shows how complex this field system has grown in the attempt to summarise all the details of fundamental particle behaviour in one big picture. I admit that I do not really understand it and have not the first idea how to calculate with it and fit it to the data pouring out of the LHC and the enormous flock of lesser accelerators that precede and augment it. So I am inclined to take the Heaviside approach. Heaviside said he could not understand Maxwell's treatise until he had recast it in his own language and reduced it from a forest of variables and equations written in three dimensional language to a relatively simple set of vector algebraic expressions that were easy to understand and apply
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and which served him to develop many new ideas in the technology of communication. The field approach takes the view that the invisible and complex fields are the reality and the particles just epiphenomena, the manifestations of excited states of the fields.
I wish to reconceive all this in terms of the network model which has been rattling around in my mind since time immemorial. Here the particles become central and are conceived as carriers of messages from point to point in space-time, which is in itself simply a message space. A guiding principle in the development of this model is symmetry with respect to complexity, based on the symmetry that Cantor exploited to generate the transfinite numbers. One consequence of this symmetry is the analogy between human consciousness and quantum measurement or observation. The idea had its roots in my readings of Lonergan's Insight during my time in the Wahroonga house of the Dominicans in 1965. This suggests that the subconscious workings of our mind which bring subconscious structures into consciousness by the act of insight is analogous to the invisible processes in Hilbert space which bring particles into reality by measurement. We should note that no information is lost by thinking of particles rather than fields because one is mathematically a fourier transform of the other and fourier transforms are reversible, that is they conserve entropy and play the role of codecs in information theory. Codec - Wikipedia, Fourier transform - Wikipedia
I am so happy with this I do not feel like writing any more. Sort of post orgasmic lassitude, but the show must go on, So we look at this network from the panpsychical point of view, going back once more to the Trinity and the word of god as an early version
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of the atomic network event, modelled more formally by Zurek, where we have two minds (Hilbert spaces) meeting to form a product space from which emerges a particle which is in effect a message between the two particles taking part in the conversation. So we throw a hadron at another hadron (in the Large Hadron Collider) and look at all the messages that emerge from the interaction of these two complex particles. We decode all this in terms of the individual properties of the quarks and gluons involved using fragments of the process represented by Feynman diagrams each of which involves two fermions and a boson coupling them. The network approach loses none of the complexity of the standard approach, but it does enable us to break it down into simple pieces which have a layered or hierarchic ordering reflected in the general idea that large actions are built from small actions. What I have been looking for for a long time is the order of emergence of the layers of complexity in the universe starting from the primordial actus purus and building up to more complex actions like myself, stars, galaxies, planets and so on.
Saturday 4 August 2018
Circling around the Teillhard de Chardin point of view that things have an interior and an exterior, mind and body, wave function and particles etc. The next big step is to study the Dirac equation in detail and compare it to Maxwell's equation and see if these ideas can reproduce the results of quantum electrodynamics, something that seems beyond my powers but plays the role of the pons asinorum in my world of dreams. Teilhard de Chardin: The Phenomenon of Man
First continue with Auyang:
page 37: Wigner: ' . . . there are two characteristics that are invariant under relativistic transformations . . . mass and spin.' mass (?)
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'. . . pure relativistic considerations single out mass and spin as indices for the classification of various fee elementary particles and put certain constraints on their values.'
Auyang page 38: Three symmetry principles a) special; b) general; c) gauge = network.
all physical theories are 'field theories with local symmetries'.
each has two symmetry groups: a: spatio-temporal and b) local group, intimately connected with reaction dynamics.
'The possession of two groups distinguishes [quantum theories[ from special relativity which has only one symmetry group, the spatio-temporal group, and which is not concerned with interactions.' You say, so flat space is a completely passive background to the world. Very unlikely [the wave nature of momentum suggests that particles step their way through space, so maybe there are some steps].
'I argue that general invariance concerns the spatio-temporal group, and is conceptually similar t special relativity, while general covariance concerns the local group and is similar to gauge field theories.
The network theory likes to think that fat space-time is closely related to the quantum theories [representations] of energy and momentum since these transform in the same way as time ad space and another name for space-time is momentum-energy. All we have to figure out us how this is put together, going from the linearity of quantum mechanics to the quadratic behaviour of space-time.
My guess, given the simplicity of the early universe, is that the explanation we are seeking here is also very simple, but, like the wheel,
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not obvious until you see it; I write this to make myself feel more confident of success. Wheel - Wikipedia
We see space as a communication network that carries messages through time. My ability to move depends upon the ability of space to transmit me. On the other hand we are inclined to think of space as nothing but a void. Space is a carrier [vehicle] and the simplest thing it carries is a photon.
Michelson and Morley established that no mechanical scaffold is necessary to implement electromagnetic laws - nothing is waving except perhaps a probability amplitude. Michelson and Morley: On the relative motion of the earth and the lumeniferous etherGleick page 261 (speaking for Schwinger): 'When you talk about fields you presume that you can describe, and somehow experience, exactly what goes on at every point in space at every time; when you talk about particles, you merely sample the field with measurement at occasional instants. . . . the essence of renormalization is to make the transition from one level of description to the next. When you being with field equations, you operate at a level where the particles are not there from the start. It is when you solve the field equations that you see the emergence of particles.' Gleick: Genius: Richard Feynman and modern physics
Time and space are properties emerging from God by complexification, ie by god reflecting on itself and interacting with the reflection [this may be made easier by the fact that space is in a quadratic form the inverse of time]. Quantum field theory finds these reflections and consequence self interactions to be infinite because it operates in continuous space. Here in the digital world, we do not have infinities and renormalizations but self interaction is the rule by which ore complex structures come into being, just as all this writing flows from me because I am reflecting on what I know (ie what I am) and trying to build it into a consistent theory of the emergence of the emergence of the observable world from god.
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Auyang page 44: 'Fritz London worked out the local phase invariance of elecromagnetism and derived the electromagnetic coupling from symmetry considerations.'
Photons are not charged and are massless, unlike quanta of weak, strong and gravitational forces.
Auyang: 'The fundamental ontology of the world is a set of interacting fields [don't like this at all; the field don't interact directly, they do it by communicating through particles,which are messages that can travel through space-time].
12 matter fields + 12 antifuleds; 12 interxtion fields + antifields Photon, W, gluons.
Auyang page 46: 'there is no sourceless electromagnetic fieds' - what about Maxwell field?
Interactions occur at a point [another rather dodgy claim that gives us dirac deltas and other headaches].
page 47: 'The world of fields is full, in contrast to the mechanistic world in which particles are separated by empty spaces across which forces act instantaneously at a distance.' The Newtonian story. Particles may also travel through space, meet and interact.
A field is a continuous dynamical system with infinite degrees of freedom whose domain is space-time.
page 48: 'A fundamental field of physics is a freestanding and undecomposable unit by itself, it cannot be taken apart materially.' So just lke the ether really!
page 49: Electromagnetic field F(xμ). 'Ye field is not "waving" in some kind of ether and it needs no support of a propagating medium. F is a tensor.' Too abstract to be true. All information is physical, but field described here is pure formalism [and ignores finite size of quantum of action].
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Auyang page 50: Dirac and Klein-Gordon equations give negative energies and other problems.
'The difficulties disappear if the variables ψ(x) of the relativistic equations are interpreted not as single particle wavefunctions but as dynamical variables for continuous systems, or simply, fields. . . . the single particle interpretation does not work.
'We go from classical to quantum mechanics by replacing the classical mechanical variables for position and momentum by quantum operators Q and P that obey the commutation relation [Q, P] = QP - PQ = iℏ'
'Quantum fields are obtained by replacing the classical field variable ψ(x) and its conjugate π(x) by [operators] obeying certain commutation relations'.
'Continuous systems constitute the basic ontology of the world according to contemporary physics.' Here is where I would like to differ, since I think that the basic ontology of the world is error free, ie quantized, communication. How to implement this in a way that gives the same numerical results as continuous field theories I have no clue other than a desire to find out.
