Notes
Sunday 17 July 2022 - Saturday 23 July 2022
[Notebook: DB 88: Salvation]
[page 121]
Sunday 17 July 2022
Understanding quantum field theory means mapping it onto a set of synapses in my brain.
Let's think of QCD in terms of Shannon entropy, ie the parallel bandwidth necessary to transmit information around the network space inside the hadron. Curvature of network space follows automatically since all sources are connected to one another and for n sources there are n! paths between any two of them [rather like Feynman's many paths], the longest running in some order through all the other n − 2 sources.
Unitarity demands equal source entropy [for reversibility] Network QCD vs lattice QCD. Network WiFi vs lattice WiFi [systems address each other by sharing a language]. Much of the complexity of QCD comes from seeing messages going through every point in spacetime rather than seeing them carried by messenger particles broadcast like WiFi. There is the germ of an idea here.
Note that we can speak to one another without knowing the implicit mathematical models that make [speech] work, the implicit [tacit] [hardware, out of our control] dimension. A lot of the complexity in physics comes from trying to make the implicit dimension explicit [running from elementary particles to human societies and beyond]. Michael Polanyi (1966, 2009): The Tacit Dimension
It may be that we can greatly simplify our understanding of confinement by accepting that Hilbert space predates Minkowski space. Maybe much of the confusion in field theory comes from the confusion of Hilbert and Minkowski space.
Quantum Field Theory in a Nutshell is about 600 pages. Does the baby universe, with just four dimensional Hilbert space, know all this? Maybe if we think of a qubit |qubit> = a|0> + b|1> where a and b are complex numbers with a2 + b2 = 1, giving us ℵ1 possible states. John von Neumann (2014): Mathematical Foundations of Quantum Mechanics
Maybe an isolated qubit is a just like a real bit [strictly two state] but each out of phase superposition doubles the number of states so the variety of one bit is 2, of 2 bits 4 and so on and all this works by splitting the [complex] circle group into 2, 4, 8, segments - so we have 2 photons and 8 gluons.
[to page 124]
[page 124]
[from page 121]
So time to stop rushing to finish cognitive cosmology and send a month studying physics, QFT in a Nutshell at 20 pages per day [never happened, I am impatient to get on].
Monday 18 July 2022
Monday is a typical morning. Woke in fright. Shower, dress, see a way forward. 2 days to complete cc23_quantum_field and cc24_chromodynamics.
The steps forward:
1. Second quantization mixes hardware (particles [dynamic]) and properties (software [kinetic]) when there is sufficient energy.
2. Deep inelastic scattering: there are moving parts within the proton [life inside it] with peculiar properties, confinement and asymptotic freedom, functions of distance apart [ie the spacetime metric ie Yang-Mills functions].
3. Yang-Mills theory. In QCD messaging is handled by 8 gluons which talk to one another, unlike QED where photons only interact via second quantization via an intermediate particle as in 1. This leads to feedback, providing a cybernetic ground for asymptotic freedom and confinement [screening = negative feedback, antiscreening = positive feedback, reality = cycle of both = wave (phase, the cosmic text message].
4. TBA From Hilbert to Turing to evolution: an imaginary model of the vacuum.
The most remarkable thing is this story slowly assembled itself in my mind and is now floating to the surface out of the kinetic world [where it is supported by a neural substrate, ie its tacit dimension] of thought into the dynamic world of action.
Tuesday 19 July 2022
Hi Prof, here is a rerun of my 2019 Thesis translated into a version of quantum mechanics. This year I am celebrating my 60th year on the theological trail. I have started from my early exposure to the medieval theology of Aquinas. I have replaced the classical initial singularity with a quantum of action since in Aquinas + Aristotle god = [omnino simplex + ]actus purus. From there I have let the processions of the Trinity continue ad infinitumproducing a lot of angels (pure forms like mathematics) to be interpreted as the orthogonal basis of a Hilbert space. Using communication theory, I transform this basis into a set of mechanical representations of the computable functions
[page 125]
all of which provides us with enough bits and pieces for a universe like ours to emerge. Since it began from almost nothing, it is not made It makes itself and the evolutionary process by which it makes itsef is a symmetry with respect to complexity that pervades the universe at all levels. In effect a representation of a transfinite computable Lie group. In other words we interpret a set of spacetime points as a network of computer all talking to one another [sometimes relaying messages through chains of sources]. Here I follow the trail from [some introductory hopes to a hypothetical network approach, the next step beyond a lattice (which is a very boring network). In this network the joints of the lattice are computable functions which we can understand as the Fourier inversion of the periodic superpositions of state in Hilbert space.]Stuck on QCD. One can describe the 'traditional' field theoretical account as expressed in Wilczek and Gross. Does my approach offer any advantage. Can I even formulate it. David J Gross & Frank Wilczek: Ultraviolet Behavior of Non-Abelian Gauge Theories
Logical sequences matter more than numerical values and there may be many different logical sequences consistent with a value, say energy [as there are lot of complex narratives recorded in books measured by the kilo].
Wednesday 20 July 2022
Renormalization and scaling. Scaling is a measure of the rate of communication between sources and we imagine there is a function of energy measured as the rate of sending discrete messages (quanta). The rate of communication may be seen as a function of physical distance, or the intensity of love, which may increase with distance, absence makes the heart grow fonder.
Gravitation, being a formless recursive theory without control is prone to collapse, as black holes show. This is a version of positive feedback out of control, whereas the existence of stable particles, that is consistent spaces of dynamic action, show that control in low energy systems is possible.
There are no continua in the formal world. It is of the definition of form that it be the sum of orthogonal vectors of different "length" [or intervals] ie [static, kinetic] or dynamic complexity.
By adding dimensions we are exponentially increasing the size of of the space since each new dimension adds a variable to the space.
The miracuous creation of Minkowski space by the Hilbert space, converting from [potential] into dynamism is the starting point of the world, the point always with us where a form takes life, a combination of Plato's forms and Aristotle's mover. It moves as a linear sequence of spacelike slices of reality which can be stacked to represent paths through space parametrized by time, the fundamental scalar. It is space that is complex, Minkowski Metric 1, -1, -1, -1.
[page 126]
We can think about infinity but infinite things, ie continuous processes do not exist [proton?] . They are approximations to the large number of discrete events that constitute the universe.
Every now and then I get a twinge of the imposter syndrome and I realize that these notes published on the internet are my best defence against that thought, since I have recorded almost every thought along the way to equip myself with a complete trail of responsibility.
[transcription from another source]
Revise cc26_principles adding near the top "Cantor's principle". Apply these principles to the computational model of creation (selected by the application of the no-cloning principle to the primordial Hilbert space). This space is formal and its orthogonality defines the elements of the set that contains them, the set of natural numbers including the empty set. The principle of logical process implies the cardinality of this set and the Cantor principle show how we can grow this dynamically given the principle that processes communicate by sharing a memory location, which means sharing an algorithm, a computable function.The proposed joining process is the fundamental observable process ie we create Minkowski space by breaking the symmetry of Hilbert space, and this break in symmetry is in effect the creation of two orthogonal Hilbert spaces which contain the rules of time and momentum The symbolic indication of this split is embodied in the Minkowski space 1, 1, 1, -1 [or its dual 1, -1, -1, -1] whose functional element, we might say, is the 4D null geodesic made possible by the Minkowsi metric.
[Note Shannon's work shows us how to create orthogonal stares, that is messages that are independent of one another]
All this expression of the fundamental algorithm is what? [evolution: variation and selection]. The vacuum so conceived comprises quanta of action which may act as either sources or sinks of messages, ie creators or annihilators. And every operation is a fixed point in the product of the Hilbert spaces involved. In the formal sense we conceive of each dimension of Hilbert space as a space of particles growing more complex as memory and algorithms are developed and stand in Minkowski space constantly refreshed by the fecundity of action but limited to closure, that is to group behaviour, growing atoms of action. This enormous space of possibility is maintained and grows in Minkowski space, but we consider that the [self consistent and] durable spaces in this system, the stationary states [which] are the ones that can reproduce themselves using the resources available in the Turing vacuum.
Thursday 21 July 2022
WiFi inside a proton [and outside enabling hadron-hadron interactions]
We learn to understand the proton by learning how it came to be, [ie the evolutionary process, which may have required the whole gamut of computable functions? Remember that these basis vectors - computable functions are discrete quanta, arising from their orthogonality]
Can a continuum make a decision?
QED: We base our computational picture of QED on the four channels of communication revealed by the Dirac equation. We imagine the first generation f these channels which appear when we have the simplest version of the Dirac equation when out primordial Hilbert space has 4 dimensions, enabling two spin channels that deal with plus and minus spin in the photon channel and plus and minus states of the electrons, ie two channels of time and two 3D channels of momentum giving us electrons and positrons. We observe that there are three versions of this momentum channel each of which carries PCT for the three generations of electrons, ie the basic electron and the two heavier electrons. The basic channel is stable; the other two are unstable, tending to decay back from the heavier versions of the electron back to the lightest and stable variety, giving us 2 + 9 channels which may correspond to the 11 dimensional space preferred by the string theorists. We conceive of this in terms of codecs and we seek a set of Turing machines to construct these codecs out of those avaiable from the superposition of 4 qubits yielding 2, 4, 8 and 16 splits of the circle group. We begin with the photon qubit whose operation is not computing not spin up = spin down, not spin down = spin up, and the 8 channes of momentum giving us particle and antiparticle, ie &Plusmn; P, &Plusmn; C and &Plusmn; T, the symmetries that connect particles and antiparticles. We get to these machines by a Fourier transformation of the superpositions if 4 qubits into 16 functions which determine the transformations in the Dirac equation These are computable functions computed by the Turing machines that arise from the fourier inversions of the 4 available basis states of the 4d version of the primordial Hilbert space. Will this fly?
[page 127]
The operators and computations are quantized by the 16 roots of unity corresponding to the sixteen different superpositions of 4 qubits.
Friday 22 July 2022
The wave function of the universe is a rather large matrix which transforms the present into the future. Hugh Everett III (1973): The Many Worlds Interpretation of Quantum Mechanics
The measurement problem arises because we think that the world is doing everything at once [superposed actions] whereas it is really a lot of network atoms doing their own things and communicating with one another. In every event one process begins and ends. A successful algorithm may not represent a mechanical process and may bring problems of its own.Von Neumann's expression of quantum mechanics in terms of complex Hilbert space in which the components of vectors are manipulated in parallel by matrix operators [constrained by unitarity] is very delightful but it brings problems when we come to interpret results in Minkowski space so we have the measurement problem which we deal with by assigning a probability space to the possible outcomes of a measurement and determine probabilities by the inner products of the vectors involved in the measurement. An alternative, provided here, is that we move the probability space to a set of computable functions whose probability of application may be computed by the same Born rule but each of which yields a specific outcome corresponding to these same probability measures.
We can say that all quantum mechanics is relativistic because none of it is relativistic because [we believe that] Hilbert space with its operators and vectors [is] an abstract space where there is no distance or time so no special relativity. Special relativity enters when Minkowski space is created by Hilbert space with the Minkowski metric which makes the transport of quantum states through spacetime by embedding them in null geodesic where the effect of the metrics of time and space is to null one another [an example of zero su bifurcation].
The root of all the problems seems to me to be the abstract Hilbert space designed by von Neumann which has been adjusted with a couple of Weierstrassian axioms which enable it to be mapped onto real Minkowski space, so even though it is an abstract mathematical ideal, giving us things like point electrons with infinite electromagnetic mass and infinite energies induced by infinite frequencies that give us the cosmological constant problem. My cure, outlined above on this site is to see [Hilbert] space as the source of Minkowski space, shedding its infinities
[page 128]
and leaving us with a more manageable digital countable vacuum which I interpret as a complete set of rather tame computers, the Minkowski vacuum explained on this page.
. . .
