vol VII: Notes
2012
Notes
[Sunday 8 July 2012 - Saturday 14 July 2012]
[Notebook: DB 72 Energaia]
[page 73]
Sunday 8 July 2012
We may say that science as we know it began 2500 years ago with the work of Parmenides, From the fragments of his writing still extant, it appears that he was motivated by the fundamental question of science: how to we capture the nature of a moving world in static text? To answer this question, he split the world into two components: an eternal and complete element to by known by 'the way of truth' and the moving and uncertain elements to be known by the 'way of opinion'. John Palmer - Parmenides
Then Plato, Aristotle, Aquinas, Newton, Einstein, Noether,. In the present day, although we know much more about the world than Parmenides, we still postulate a deterministic world of the quantum state functions which determine the priobabilities of the random events that we observe.
To 'Why is the Universe Quantized?
Gravitation is the fundamental ordering principle of the Universe determining its large scale structure and defining down and up, ie movement toward and away from the centre of mass.
Part of the problem of trying to move into and see the unknown is to guess what one is looking for and how to recognie it when it is found.Insofar as we can talk about it, however, it must be speakable, that is represented in symbols. Bell: Speakable and Unspeakable in Quantum Mechanics
Non-locality of quantum mechanics tells us that there is a layer before space.
[page 103]
Gravitation is a manifestation of entanglement, is the descent of the Universe with modification [from an initial condition].
Hobson page 231: 'We can treat the Newtonian solution [for a general non-circular orbit] as the zeroth order solution of the general relativistic equation of motion.' Does this suggest that Newtonian physics perhaps capture the 1D layer of the Universe with instantaneous ('spooky') action at a distance and just one fixed frame of reference in which not-p represents p and vice versa. Hobson, Efstathiou & Lasenby
E-Theorem may be a relative of the fixed point theorem, taking us down from an infinite set of mappings to a countable set of fixed points. Only computable mappings are allowed, ie locally countable. Khinchin: The Mathematical Foundations of Information Theory
General covariance says there is a 'representational symmetry' insofar as any reference set of coordinate will do if it can be mapped to the Gaussian coordinates of a system. How many dimensions does a computer have? Can we see a computation as a writhing and wrestling of molluscs?
Precession of orbit happens because the orbit cannot close in general relativity as it can in Newtonian physics.
One can see the Christian assumption that God created the Universe in the development of string theory. Although the evolutionary paradigm suggests that the Universe began as something completely simple, string theorists propose more and more complex multi-dimensional and unobservable structures to explain it safe in the knowledge that God established the initial conditions and there is no limit on how precise or complex they may have been.
[page 104]
Hobson page 233: Photons can travel in a circular orbit at r = 3GM/c2
Belief: mental state one is prepared to act upon: I believe that this scaffold will hold me. As the cost of a false action rises, so we would expect a greater certainty of belief, maximized in matters of life and death. Hence the perverse value of martyrdom which suggested that the belief could be stronger than death even if, as history has shown, Christians have been duped in multiple dimensions. page 244: Spin in gravitation.
page 246: Gravity Probe B Stanford University
A solid (n-form) in pace is the reciprocal space of a vector. So we think solids and 3-space are born in unison,, like planes and to space, lines in 1 space and points in 0 space. A point is an 0-space, but it can be placed in an n-space and described by n coordinate parameters, ie it carries this amount of information due to its relationship with a reference frame.
page 250: 'The physically meaningful geometric quantities are the 4-tensors defined at any point of the spacetime manifold.' Which we may remember is comprised of observable points (events)_ which can be labelled using a Gaussian coordinate system.
Every sentence is another little glimmer of light, but how many do we need before everything becomes clear? Photons enable us to see atoms and molecules ad everything with electrons in it. They also serve to make the world by mediating the forces between
[page 105]
electrically charged particles.Action and reaction are equal and opposite: for every action there is a positive and a negative and in a particular peer level they balance, although they may not balance at a higher level, eg matter and antimatter.
Strength of electric charge defines potential which defines quntum energy levels.
Cartan page 59: 'Any continuous linear group can be generated by its infinitesimal elements.' which may mean that there is no more information in the group that in any one of its infinitesimal elements, which seems equivalent to the idea that groups operate at constant entropy. Cartan
We can think of finite an infinite not in terms of size but in terms of determinate (digital) and indeterminate (continuous). Separate particles are finite, but they can become infinite (indeterminate) when they are interacting in contact. (the two shall become one flesh, as Landauer might say). Only finite (orthogonal) signals can carry information without error.
Venn diagrams are geometric representations of logic. We are looking for logical representations of geometry [logical relationships between 'geometric objects']. Venn diagram - Wikipedia
|ψ|2 = p what does this mean?
Monday 9 July 2012
The standard idea that all of spacetime is filled with
[page 105]
dozens of fields is very hard to take if we think of them having been put there when the Universe was very young and (we suppose) very simple. The alternative seems to be some sort of 'logical confinement', a force that works at all places, times and scales. We see it working in the minds of the physicists who cooked up the Standard Model in the first place, a vision that is consistent with our notion that physics is cosmic psychology.
Beatitude : pleasure comes with achievement. So when I wake up early in the morning depressed by the impossible task facing me and then the first insight o the morning brightens me up and convinces me that at least i have taken another step to my distant goal. This goal has two elements: a) a logically and empirically consistent picture of the world; and b) convincing everybody that this new God is fit to take the place of their old (falsish) Gods.
While writing the above, missed another one, now to hunt it down and put it in words.
You tube video: On False Gods. TrueGod.com
Emergence: from infinity to finity: creation, motivation.
How do we translate the Standard Model into software? We are on the way when we write sentence about it, we just have to find a set of sentences that execute themselves to give us the world. All this seems too much to expect from one person, but perhaps I can get the rock rolling!
[page 107]
Familiarity breeds content. A few thousand years of familiarity have made us very much at home with the continuous model, but we have to follow through with the insights of quantum mechanics and the very obvious fact that everything we observe is discrete. Deceived by the flow of motion.
Does quantum mechanics describe a computer network?
Transfinite computer network is a phase space, TFN = {Cantor, Turing}.
Newton assumed instantaneous action at a distance and he justified this assumption by appealing to God, the Creator.
A true God. atruegod.com, .net, .org registered
Where is the Creator? Gamblers know it best!
. . .
A string of processes a) purely random and b) connected to that the current process constrains the choice of future processes.Basically, we have to prove thjt the network gives the same probabilities as the standard model.
INPUT --> PROCESS --> OUTPUT
Quantum mechanics is a version of hydrodynamics where the conserved flow is energy or probability.
[page 108]
A continuum is not observable, like a whiteout.
Although we find orthogonal basis states the simplest and error free we nevertheless have communication between dimensions that has the effect of breaking the orthogonality and introducing curvature into the space. We may think of gravitation in one way as an error signal arising from the overlap of messages which is tantamount to broken orthogonality or curvature [represented by off-diagonal terms in matrices]. Something like this. Communication breaks linearity.
Getting serious : making a larger [emotional] investment.
Tuesday 10 July 2012
Continuity = confinement - arithmetic.
Logical continuity = logical confinement
The connection between trigonometric functions and complex exponentials comes through series expansions, ie a sequence of multiplications and additions. [in the early days, the Universe may have used only the first few terms].
Calculus maps from continuum to continuum, so [there is no information transmitted. (?)]
Just one death from AIDS that might have been prevented by the use of condoms puts the Vatical in the same class as the Taliban, people condoning death as a consequence of an arbitrary (and counterfactual) legal fiction. For us the founding legal fiction is that the sovereign owns all the land [including all its inhabitants] and can deal with it as it wishes, subject only to the possibility of losing its sovereignty. Holy See - Wikipedia, Taliban - Wikipedia
[page 109]
Democracy swaps sovereignty from the root of the tree to the leaves and is the natural situation, since the root cannot control the leaves of the transfinite tree. ['requisite variety' Ashby Ashby: Cybernetics]
Requisite variety enables us to swap uncertainty for determinism. An engine confines air and fuel in such a way as to produce macroscopic mechanical energy from the microscopic kinetic energy of moving molecules. This process works, and so we can work out the complexity of an engine from the number of degrees of fredom it contols: pressure, volume, temperature. Since these are related by a definite (probabilistic) function, asnhy two will do.
THERMODYNAMICS = CYBERNETICS Brillouin
Both these disciplines work in terms of simple arithmetic whose symmetry is exploited by using continuous functions. An engine picks one state out of the f(n!) states of a hot body and deposits the rest of the states in a cold body.
Cybernetics = thermodynamics - communication theory - probability
Probability: We have had n years experience with big power reactors and two maximal errors in that period. Chernobyl disaster - Wikipedia, Fukushima Daiichi nuclear disaster - Wikipedia
Probability and public health - stateistics.
We assess everything in terms of probabilities. The purpose of theory is to guide the computation of probability.
Feynman diagrams tell us that if we want to improve our assessment of the probability of an event, we must visit wider
[page 110]
and wider areas of the network that send occasional messages to the locality we are studying. So the National Security Agencies travel far and wide to find the sources of the messages that are coming to their suspects. Eric Lichtblau
I have started with a million piece jigsaw but by assembling patches of it I am beginning to get ideas about the completed picture.
All our statistical models are built up from the behaviour of individuals like coins and dice [this is analogous to physicists integrating a picture of the world from local infinitesimals.]
After such s long struggle, one wants to explode on the scene with the answer.
The algorithmic complexity of a continuous function is the length of the algorithm needed to compute it. We might see all continuous functions as computable since their variety is so low.
Transfinite arithmetic tells us that it is time, that is the exponent, that counts.
The power set P(S) is the set of all subsets of s. The empty set has no subsets, and its power is 0 [1?]. When the empty set splits in 2 (internally) to give us p and not-p we have a power of 2, the first (second?) transfinite number at this level of resolution.
Error free communication = perfect resolution of symbols.
[page 111]
The only arithmetic operation that gets us anywhere in the transfinite domain is exponentiation.
We must take physics out into the field of meta-mathmatics to see the whole picture. Using the transfinite computer network makes this obvious.
The Gaussian, measure theory and the identity of infinitesimals. Measure (mathematics) - Wikipedia
What is gravitation giving us the probability of? The path of a photon.
the 'naked gate' is a symmetry which is broken by clothing the gate with other gates to make a computer. A 'memory' is a latching gate with a set of states, ai, the letters of the state's alphabet.
Transfinite computable manifold? No, not continuous, but symmetrical subsets of the transfinite computer network can be approximated (as to probable outcomes) with a continuous manifold.
An unmodulated plane wave carries no information, Δp 0 (ie exact frequency) Δx = ∞, no spatial information.
A general proof of the applicability of discrete mathematics where continuous is currently used comes from the fact that all of our proofs for properties of continua begin with the discrete values and then seek the continuous limit if it exists, that is if the function of interest is differentiable. . . . [T]his process depends on the fact that the infinitesimals are linearly additive, that is integrable, a fundamental assumption of the theory of measure - all the points in a line
[page 112]
are of the same size. Information theory and measure theory - Wikipedia
This essay is in effect a philosopher's eye view of the current difficulties in physics.It seems logical that discrete events should have discrete (rather than) continuous operations. However here we encounter the problem of 'action at a distance' and introduce the concept of logical continuity. How does the Universe cover the 'distance' between discrete entities named by different numbers, n and m.
The ideas recorded here appear in my mind as discrete states which I then try to capture in a few sentenced. From myposition as observe of my mind I cannot tell where they come from or where they go, but as a biologist and a physicists I am pretty sure that these mental states are the output of transparent network operations at all levels down to the initial singularity.
Gravitation sees the physical flow of information but takes no notice of its meaning [coordinate or context free].
We might think of a computer as a continuum whose input is a set of initial conditions and whole output or solution is a set o consequences of the initial conditions given [the structure of the computer]
All this, of course, is about myself, Where did I come from? What am I doing here? What is the future, etc.
[page 113]
Wednesday 11 July 2012
Kinema ; we represent a moving image by a series of snapshots. The link between these snapshots lies in the reality photographed rather than the snapshots themselves. The casual link is in reality.
CONTINUITY = CAUSALITY
We begin with velocity as an unanalysed entity which becomes a ratio of distance and time once space and time emerge from their 'hardware' which we take to be energy. The split into space and time is isopmorphic to the spit into potential and kinetic energy [, and into energy and momentum,] an act of creation.
So to justify calling the Universe divine we need a model of creation which we derive from Lonergan's insight. So we work from a microcosm, the working of my mind, to the macrocosm, the working of the divine mind. The origin of science corresponds to the origin of consciousness, which is the emergence of a layer of self control [internalized community control]. We have to work with what is given to us by evolution. So to understand creation we understand evolution., So this idea incorporates the work of Heraclitus, Aristotle, Darwin, Jaynes, [Lonergan] Heraclitus - Wikipedia, Aristotle - Wikipedia, Charles Darwin - Wikipedia, Julian Jaynes - Wikipedia, Bernard Lonergan - Wikipedia
So we ask : how does the phase space create itself, following Einstein's lead that we understand 'forces' as the property of space itself, not something working 'in' space, as the standard model assumes. This idea is already present in field theory if we consider the fields not so much as functions of space-time as in some way space=time itself.
[page 114]
Abstract : We understand things by comparing them to known frames of reference or 'reference bodies (Einstein ref). Newton formalized this approach by studying the motions of the heavenly bodies in an absolute space and time which he understood to be established and maintained by the creator (Newton, Scholium). Einstein assumed that frames of reference are defined for our own convenience, and reality goes its own way independently of how we look at it, so that all frames of reference are equivalent, the principle of general covariance. Nevertheless, following Riemann, he introduced 'self reference' into space through the mechanism of reciprocal spaces about an event connected by a metric which represented what was actually happening. In this way he understood gravitation as a geometric property of spacetime. Quantum mechanics was emerging in he same period as General relativity,. Relativistic spacetime has become the domain of quantum theory, and we model the life of the Universe using a set of continuous fields imagined to exist throughout space-time,. Following the Born rule, these fields predict the probability of creation and annihilation of particles corresponding to the fields. This scenario works quite well but there is a deep problem associated with the using the assumption that spacetime is mathematically continuous to describe the behaviour of a Universe which is observed to be completely discrete. The continuous approach leads to many series without limits, which appear to be unphysical. To deal with this problem, we propose a new 'phase space' with which to describe the Universe. This space, based on the technology of computer networks, is able to create itself, and so may describe the Universe from thhe initial point to its current state and beyond. Einstein, General Scholium - Wikipedia, Born rule - WikipediaGeneral covariance - Wikipedia
[page 115]
Now I am happy again. Something like childbirth, a painful time getting the baby out, the joy.Old men, past their prime, like to impose celibacy on the youth in order to control them and get more output, undistracted by love [the real foundation of our existence].
Hilbert space / space of phases / space of processes in progress.
Reciprocal spaces, tensors and forms, n=tensors and n=forms. [?]
We replace the duality of reciprocal spaces with the duality of memory and content, ie dimension and parameter. [?]
The complex conjugate of z is the image of z in the 'real' axis.
Newton [and theology] James Force and Richard H Popkin: Stephen David Snobelen. Stephen David Snobelen
Veltman: back to the old question, do we apply the Lorentz transformations inside the Hilbert space or do we wait till the quantum system 'collapses' into a real particle and then apply the Lorentz transformation to the particle. The latter seems easier, taking things in stages instead of cooking up rather complex Lorentz invariant state equations [in the unobservable real of complex amplitudes].
The big question is not so much the mathematics (which is all, hopefully, computable) but how to interpret it'
[page 116]
If we apply Lorentz after the collapse, this implies that all the quantum mechanical stuff takes place 'outside' space, consistent with the idea that quantum mechanics is itself a one dimensional (line based [cardinal ?]) field theory.
Already 4-space is in effect 'applied relativity', a structure created out of 2D sections of space-time. Time does not make sense unless it is contrasted with space as change has no meaning unless something changes.
Special relativity: points come into coincidence after a delay which depends on the initial distance between them and the speed at which one travels relative to the other. Address and memory are dual and there are no duplicates, giving us fermions.Veltman page 15: '.. . we postulate that a particle with a well defined momentum and energy is described by a plane wave', ie a clock. Veltman
page 16: 'A generalization of quantum mechanics is that wavs may be complex and that the probability is not the square but the absolute value squared of the amplitude.'
How do we make this look like a network or vice versa? First the only information a wave carries is energy = rate of change of phase x ħ = ħω. There is minimal structure here at all, but we can treat it as a series of actions, that is transmissions of information without loss. A wave oscillates between duals, which are in some way represented
[page 117]
by φ and φ*. The space of duals in the basic case has an entropy of one bit, like the spin flip of an electron.
Looking at the way spins behave, one can almost se a computational paradigm emerging.
The real is the potential, the imaginary is the kinetic, and we see them transforming one into the other as the phase vector rotates.
By the time I was 20 I was firmly on the path to a divine Universe.
Veltman page 16: 'Planck-Einstein relation E = hν
The additional quantum mechanical concept is superposition' linearity.
Superposition is boson-like behaviour, simple addition and subtraction in two dimensions.
The metric in quantum mechanics is probabilities, and all the probabilities in a given event must sum to q, a fundamental constraint that can be realized mechanically [by eg, a coin].
The mechanism of the Universe is logical, not simply energetic. The energy determines the rate at which the logic is executed.
QUANTUM = OBJECT [=ACTION]
The set of distinct quanta is countably infinite.
What does the square of the amplitude mean? Probability, but how do φ and φ* work together to make a probability?
Veltman page 17 quote again: 'This plague, having to abandon Lorentz invariance in order to define the formalism seems common to all approaches to quantum field thoery. One always needs some sort of grid.' a suasio toward digitalism.
MEMORY / DYNAMICS FIXED POINTS / DYNAMIC POINTS
The Universe is Divine : a single concepts with many ramifications, most relating to the creation and annihilation of states. Hitler and his friends created the Nazi State, a point that could be represented in a sufficiently complete [space].Creation: we generate by breaking symmetry. Deals are done when the potential difference is zero, buyer and seller both agree on a price (cross at a point).
What we want to know is 'how do amplitudes exist, and what makes the square important? The guess is that every observation is a two way street and is not complete until the circuit is closed by a reply to the original message (action and reaction = φ, φ*)
Quantum mechanics assumes that it can integrate over all space.
Veltman page 21: 'Under a translation the state |p> goes over into the stateeipb|p>
[page 119]
which shows explicitly how the transformation of the vectors in Hilbert space differs from what happens in ordinary space. Note that the vector |p> just gets a phase factor, in other words it stays normalized and represents, physically speaking, the same state.
We only see the messages and must guess the dynamics that lie behind the messages,. We do this in human situations by watching our own expressions of our dynamics (feelings) and attributing them, with suitable transformations, to the other people we meet.
Thursday 12 July 2012
Veltman page 36 'A physical state in Hilbert space is a like a movie in a can. It is the whole movie, not just the opening scene, even if the movies is labelled that way, Seeing things this way it becomes hopefully clear that a progressing physical situation is not s vector in Hilbert space (such as |pq>in rotating to another state (|pq>out in the course of time,. A vector in Hilbert space has no time dependence, but, like a movie, all the action is contained in that state, In that dense the S-matrix is a cross index register, showing the relation between two labelling systems, Given the beginning scene of a movie, the S-matrix tells us what the final scene is.' Or at least gives us a probability distribution of possible final scenes.
A movie is a read only memory, an ordered string of symbols (images) which we read in order, in time, to realize the appearance of a dynamic situation.
[page 120]
Turing machines: read only, read and copy, read and transform.
Continuous functions either add or subtract 1 at each move (where 1 stands for some infinitesimal), so their variation can be said to be continuous, We guess that there are ℵ0 such continuous functions that can be mapped to the ℵ0 Turing machines. These functions are an infinitsimal fragment of the ℵ1 mapings of ℵ0 symbols onto themselves.
Following the Einstein path, we set up a gigantic space (the differentiable manfold), transfinite computer network.
The transfinite numbers are a static, Platonic structure.
The history of science is beginning to reveal that many of the sources os substantial scientific insights were theologically motivated, seeking to project a consistent picture of the world. Newton was content to explain the kinematics of the world and made no hypothesis about how it actually worked, except the assumption that God made it and kept it under control.
Veltman's picture is a typical 'accelerator physicist' scenario with free particles going into and coming out of an interaction or event and the modeller trying to match the statistics of many repetition of this event which have almost identical inputs. In reality the particles of the world have never been compkletely free but are entangled with one another by common descent.
We bgin with some finite permutations and then let them go to infinity.
[page 21]
Mathematics is a set of stationary points in the dynamic system we call the mathematics community.
We interpret the Cantor Universe as an ordering of computation processes, each with minimal action h.
The creative bootstrap works by layer (n+1) being able to control layer n so as to maintain all the systems it needs for survival. This means a) having an efficient algorithm and b) controlling errors.
We construct this in the transfinite network, growing in resolution as it grows in complexity
I do not understand quantum field theory but it is necessary that I should if I am to create a digital analogue of the standard model.
Creation means the emergence of new stationary points in the same dynamic system, rather like the creation of turbulence down to the scale of Planck's constant.
We start with the large scale structure of the Universe, since at one point early on we assume that the large scale structure was smaller than the smallest structures we currently see with our largest machines, We don't need a big machine to see an electron, which is felt to have zero size.
The Transfinite computer network sketched so far is Platonic.
Creation = emergence of higher cardinals.
[page 122]
Quantum mechanics converts from energies (frequencies of actions) to frequencies of events. Some frequencies are favoured by harmonies, standing waves. Like Turing's delay line computer.
Graham Greene Brighton Rock: 'Its a good world of you don't weaken.'
Friday 13 July 2012
The perennial question, which hits me almost every morning in the predawn darkness is 'does this project have any chance of success?' The fact that I go on with it despite my conscious misgivings seems to be evidence in favour. The principle seems good. A stable network must have error free communication, meaning digital communication, and since computer is effectively a network, digital communication. This coupled with the evidence that the world is discrete from the quantum of action on up seems to put this part of the picture on firm ground, The layered nature of computer networks and the desire for unlimited size seems to put the transfinite numbers in the frame.
I am a bit stuck when it come to the actual algorithms used in the Universal network, but the assumption that it starts very simple and complexifies seems well founded, so we expect the initial algorithms to be things like not, and or, which can by built up to do anything computable.
Our basic quantum field theory is built out of quantum mechanics and special relativity. We can follow
[page 123]
this path, generating digital versions of quantum mechanics and special (and general) relativity and then combining these digitally to get a theory of everything, So press on. The beauty of the current situation is that I have a steady income and the children are pretty much grown up, so I can spend a lot of energy on the project and hopefully contribute something to planetary peace and happiness while adding to my income and the property I can pass on to my descendants.
The opening into quantum mechanics is via the Turing machine, We assume that a complete computation corresponds to a quantum of action, We further assume that a complete computation corresponds to a complete cycle of phase, something that fits very naturally with the design of digital computers which proceed one step per clock cycle. Quantum mechanics proceeds by the addition and multiplication of phases represented by complex numbers, whose rate of rotation is strictly proportional to energy. A complete computation corresponds to the emission of as particle which can be observed, The Born rule suggest that what we see at any moment is an event with a probability of 1, that is a computation completed at the moment of observation.
Relativity is all about communication delay, and so it has input into the relative phases of processes communicating over a distance, which modulates the probability of outcomes, so this piece of the picture also looks good, The last step in the process is to describe creation, that is the generation and maintenance of new stationary points in the global dynamics, complexification [and annihilation, the decay or 'corruption' of a stationary point].
[page 124]
So now the sun is almost up and the fire is burning I feel better about the whole project and like Pascal see that the payoff is so great if I am on the right track that there is a good reason to plod on and hopefullycapitalize on the insights of the last fifty years. A mission from God,
Our starting point is the classical God of pure action which is conceived as the fixed point from which all else emanates. The task of the physics section is to show the compatibility of this God with the [Universe that we observe].
Epistemology : cosmic psychology. The structure of the website rflects the structure of God, beginning with a template that with the aid of a few vriables whose values are set by the environment in which it is rendered, beginning with the home page and applying to all the pages in the tree.
A spacelike slice is the set ofall the leaves of the cosmic tree which have the same proper interval from the root, the initial singularity.
Our first task is to explain the structure of Minkowski space beginning from the constant four velocity of every particle in the Universe, so that we can say of the Universe itself moving through proper time, ie proper phase, Proper energy measures the rate of processing associated with the march of proper time, ie the ratio between action and time, dS/dτ.
Saturday 14 July 2012
[page 125]
What we need now is a 'digital field theory' and the starting point might be an algorithmic Lagrangian. If we suppose potential energy is characteristic of memory and kinetic energy is characteristic of change of memory, and that each act of digital processing is associated with a quantum of action, we might guess that the action is stationary when there is a particular relationship between memory and computation, We may do a 'computation' in two general ways, either by using a look-up table (ie using a lot of memory) or by computing everything from scratch (ie using a lot of computation). We imagine some optimum algorithmic efficiency between these two extremes and hope to identify it with stationary action.
Veltman frequently notes that the computational methods used in the Standard model are pretty flaky, but that the results are better than the theory that leads to them, eg page 17: 'What we are doing here is quite horrible: we are violating Lorentz invariance'.
Given that quantum field theory is a blend of quantum mechanics and relativity, we should digitize these first, and given that quantum mechanics works in the one dimension of time, looks like it is the foundation of relativity since relativity requires space as well as time. We might guess that quantum mechanics does not need memory since each event appear to be a rather random consequence of the event before. Quantum mechanics in itself has no memory, only the equation E = hν.
Physics is a forest of equations, each of which asserts the numerical equivalence of certain strings of symbols, eg E = hν. What does this point to in reality? The symbols on each side of the equation are mapped to certain measurable quantities, that is quantities that bear come relationship to a standard. In
[page 126]
classical Newtonian dynamics the standards we use are intervals of mass, length and time, which eventually come down to the properties of something like atoms, which have a symmetry of mass, size and frequency.
Frequency is a fundamental measurement which can be made by phase locking between a certain standard and the frequency of interest. From frequency we move to energy and via special relativity to mass. From mass and frequency we get momentum and a measure of distance,
NOP is an action that does not change memory. Given binary digital memory, NOT.NOT = NOP, where here the equality speaks not so much of a quantity measured by a number, but of a state, where we say that |a> = |b> iff both vectors are identical, same basis, same coefficients.
We associate the mass of a particle with its energy, that is the rate of internal processing,. On this picture, massless particles like photons have no 'internal' process, ie their whole reality is visible from the outside, and they cannot interact without annihilation, but we might think that massive particles (like myself) can communicate without losing their identity, by, for instance, emitting and absorbing photons.
We might further guess that the basic source of numbers in the Universe is a count of quanta of action, and the size of a process is measured by the number of actions needed to complete it, as we might measure the size of a pain job by the number of brushstrokes it takes.
We can develop and understand the network model by mapping
[page 127]
it to the world, beginning with a count of actions which are the units we get to get the cardinal of a process.
We can express logic as Venn diagrams where 'contains' = implies. We can think of containment dualistically: I contain atoms spatially, but the atoms contain me dynamically. I am a memory full of atoms. The atoms make me go.
All the complex mathematics of quantum field theory is designed to yield frequencies of events by estimating the overlap of various initial and final conditions. We can interpret the overlap in terms of s 'channel' or process, whose frequency of completion is a function of the larger process in which it is embedded. The calculation of event frequencies thus becomes analogous to the estimation of the number of times a particular subroutine is called as part of a larger computation. In the case of the Universe, we build up the main routine out of subroutines beginning with the routine that operates the clock, NOT, whose frequency is the greatest of all and, since there is nothing to compare it to is assumed to be constant with a constant interval of proper time between every tick. As the railways served to synchronise the clocks of England, we assume that the time division multiplexing of the universal process introduces 'lines' into the spectrum of the initial singularity.
Essence and existence are the stationary and dynamic aspects of God and because of the divine simplicity are initially indistinguishable, since both the essence and the existence are both fixed and moving.
[page 128]
The mathematical foundation of quantum mechanics bears heavily on complex numbers which are isomorphic to two dimensional space with the real dimension orthogonal to the complex dimension and we might guess that they contain all the information available in the 2D layer of the Universe. To digitize, we can divide the phase angle into discrete units of 2π/n and do our calculation s with the complex roots of unity. Somewhere in here we may be able to explain the Born rule as the outcome of a process that complete the full circle from start to finish which we may think of as encoding, transmitting and decoding a message. So a clock in effect talks to itself, the tick eliciting the reply tock and tock, tick.
The relationships between real and imaginary numbers are induced by the operations of squaring and taking square toots,. What does this mean when mapped onto reality?Physicists hope to create a theory of everything by learning the alphabet of the book of nature, Theologians, on the other hand see the theory of everything as the study of all the things that can be written with the alphabet of the Universe by stringing the alphabet of fundamental operations into sentences, paragraphs, books, literatures and so on. The realm of theology is therefore mathematical logic, transfinite numbers and all that ilk. The transfinite computer network is beg enough to do this, since it contains all of set theory, all of mathematics, all of group theory and so on. It is a representation of mathematics.
History teaches that the big developments in physics often have a theological foundation (ref Newton, Einstein).
[page 129]
The Universe is always concrete but it has symmetries an invariants which are the foundations of knowledge.
Via negativa - fermions - wave function changes sign on permutation.
We build extended structure out of fermions which we understand to be orthogonal degrees of freedom, ie orthogonal processes, ie not communicating. When electrons do communicate by exchanging photons they can maintain their identity while changing their state.
What does path integral method mean? It describes a sequence of processes: crack eggs, mix, cook, eat etc, or maybe a sequence of identical operations, step, step, step, . . .
One gets the impression from older quantum mechanical literature that the wave function only collapses and emits as particle when there is a physicist 'observing'.
Feynman's path integral method is simply the canonical formalism somewhat dressed up. The canonical formalism is itself based on the time honoured method of deducing a differential equation from local infinitesimals and then integrating it. Feynman's method following this rack creates a high infinity of different paths that must be added to find the path of stationary action, The computational method, on the other hand, imagines a finite number of computational steps between initial and final states which may branch with a certain probability to give the observed distribution of outcomes from a given initial situation.
