vol VII: Notes
2012
Notes
[Sunday 2 December 2012 - Saturday 8 December 2012]
[Notebook: DB 74 CREATION]
[page 9]
Sunday 2 December 2012
Plato and Pythagoras senses that mathematics is in some way true throughout space and time and so gives us a window on the Universe. This led ultimately to Einstein's general theory opf space-time dynamics and the Hawking and Ellis mathematical discovery of black holes ands the initial singularity.
Wigner is echoing a thought that seems to be at least 2500 years old. Eugene Wigner
From quantum mechanics we learn that messages (observations) are fixed points in the Universal dynamics.
The complexification takes us to Cantor, stationary points in the mathematical community.
At least some Christians practice (or say we should practice) detachment when religion itself offers the most extreme rewards and punishments, Heaven and Hell, as potentials to steer people in the direction it favours.
Particle = fixed point, independent observable.
Zee page 3: '[The electromagnetic field's] Fourier components are quantized as a collection of harmonic oscillators, leading to creation and annihilation operators for photons.' Zee
page 4: '. . . we can form wave packets by superposing eigenmodes', ie a particle requires a number of different frequencies (processes) to exist, it contains complex linked processes (?).
[page 10]
Zee page 23: 'Physically, S(x) describes the amplitude for a disturbance in the field to propagate from the origin to x.
page 10: '. . . the momentum eigenstate is a plane wave in the coordinate representation.'
page 11: 'This fundamental result tells us that to obtain < qF | e-iHT | qI > we simply integrate over all possible paths q(t) such that q(0) = qI and q(T) = qF.
What does this mean? How do phases add that are spread all over the place. It is because phase relates to time and antedates space. It seems a lot of processing that may be an artefact of trying to represent a digital logical world with a continuum.
Flexibility - bend without breaking, not a common feature of the very old.
A theoretical model of press regulation derived from general relativity and quantum mechanics!
The prospect of poverty puts some pressure on me to succeed.
The long view: the most durable ideas on earth appear to be religion. Christianity has come all the way from the Roman Empire to the present and is still thriving in a wide cross section of cultures.
We wish to do to Christianity what Christianity
[page 11]
did to Judaism, carry it from parochial to truly catholic, Catholic to catholic.
Natural church = catholic Church.
Christianity is a step from magic and craft to science.
What we want to do is couple the collapse of the wave function with human insight and communication.
All digital processes have fixed points which are the digits \, whose individuality is respected by logical process.
Logical continuity is a feature of fixed points which underlain by the dynamics of which the logical symbols are fixed points.
Agatha: Pale Horse 'I don't believe. I know. page 59 Christie
Act - energy - momentum - broken symmetries. First from continuity to ticks of time, each a quantum of action, a plane wave, no entropy or information.
Explain: how does it work, ie a sequence or loop of causality.
Monday 3 December 2012
Tuesday 4 December 2012
A particle is sure to go where its probability is one. The path integral method is a way to identify the path with this probability is realized, ie where all phases add up to one quantum of action (?).
[page 12]
Christie page 129: 'Always envisage the worst. You've no idea how it steadies the nerves. You begin at once to be sure that it can't be as bad as you imagine.'
Mathematics is the fixed point in the infinite dimensional space of the mathematics community, and the 'laws' of physics are the fixed points in the space of the physical world. It is little wonder that these fixed points coincide, as Pythagoras, Plato and Wigner have noted. We now wish to flesh out this concepts with a model to be called the transfinite computer network.
Agatha page 134: 'emotional apprehension'. The skill of authors lies in identifying and naming fixed popints in human dynamics.
page 135: ' " Ritual—a pattern of words and phrases sanctified by time and usage, has an effect on the human spirit. " '
From a physical point of view kinetic energy stands for dynamics and potential energy for fixed points and their some is constant (say 1) whereas in a realized process their difference, the Lagrangian, is 0. so that the action, the time integral of the the Lagrangian, is also 0. Note that |ei0|2 = 1, but |eiθ|2 also equals 1, unless θ is complex.
The ticking of the cosmic clock carries us all along.
Christie page 146: ' "Life is always dangerous—never forget that. In the end, perhaps, not only great natural forces, but the work of our own hands may destroy it. We are very near to that happening at this moment . . . " '
[page 13]
Information in quantum mechanics is carried by the difference of phase.Anne Applebaum: Iron Curtain Another sad tale of human fate. Applebaum
Wednesday 5 December 2012
In many places self 'chosen' people have elected to become outcasts from the society from which they have become chosen.
Let us guess that the Universe is fundamentally democratic in the sense that what happens most frequently happens most frequently and the frequency of an event is proportional to the number of systems that can realize that event.
The horrors of a society gone wrong must motivate the search for how to guide a society rightly.
I convince people by convincing them that I am convinced, in the extreme case accepting martyrdom as proof of my conviction.
The Marxists, like the Christians, totally believed that they were right, which gave them, in their own minds, the right to kill anyone who disagreed with them.
To kill for an idea, an ephemeral content of mind.
Insofar as politics is a numbers game, quantum mechanics and politics are isomorphic (?).
[page 14]
Mistakes (errors) make the process longer so the cheapest route is the error free route, gained at minimal cost by coding according to Shannon. Claude Shannon
Pinker is in effect describing the effects of good religion. Pinker: The Better Angels of Our Nature
Thursday 6 December 2012
In the two slit experiment, particles are thought to 'interfere' with themselves, so guiding themselves to particular points on the screen which can be computed by superposing 'waves' that come through both of the slits. This must tell us something about how space-time guides quantum communication, and can be expanded to Dirac or Feynman's path integral formulation.
Friday 7 December 2012
Feynman & Hibbs Path Integral Feynman
Integration implies the existence of some continuous function which we are integrating which we cook up in the path integral approach by dividing each path into infinitesimal pieces < j | i >, multiplying them together to get the whole path < J | I > and then adding all the paths, on the rather outrageous assumption that this all happens in reality.
Applebaum page 192: 'Between the signing of the Yalta treaty, with its promise of elections in Eastern Europe, and Winston Churchill's " Iron Curtain " speech which foretold the rise of totalitarianism, a year elapse.
[page 25]
During that year a great many changes took place,. The Red Army brought Moscow trained secret policemen into every occupied country, put local communists in control of national radio stations, and began dismantling youth groups and other civic organizations. They arrested, murdered, and deported people whom they believed to be anti-Soviet and they brutally enforced a policy of ethnic cleansing.'
All while I was a baby!
Bringing religion back into the fold. The separation of Church and State has been necessary because the Church is so uncivilized, but given scientific theology [and evidence based religion] the Churches may eventually begin to fit in with the universal reality and give useful guidance to the political process.
The two slit experiment is representative of the very primitive and simple state of the Universe, and there is a symmetry there which defies explanation because it is effectively random, without fixed points.
Let us imagine that we can describe the initial singularity by the wuantum mechanics of a one dimensional Hilbert space, a one state system whose state vector is a complex scalar (?) The complexity is already a duality, the spawn of some previous symmetry breaking which we assume to be the bifurcation ofg pure action into potential and kinetic energy.
We imagine the complex vector having two extremities of opposite [maybe π / 2] phase and we name them the kinetic and potential
[page 16]
forms of energy, in logical terms memory and processing. Processes change memory but a memory may stay in the same state for a long period, that is a great number of elapsed operations of some clock. From a dynamic point of view, all that matters is the transition of the clock, and there is no way to measure how long the eternities between the actions last. This writing is such an eternity, a static system (form) that may be propagated through space and time in any suitable physical embodiment [and read anywhere and any time after it is published].
God = one state system = actus purus [Aristotle, Metaphysics, 1071b20] Aristotle
Feynman & Hibbs Preface viii 'During some conversations with a visiting European physicist, Feynman learned of a paper in which Dirac had suggested that the exponential function of iε was analogous to a transformation function for the quantum-mechanical wave function in that the wave function at one moment could be related to the wave function at the next moment (a time interval ε later) by multipying with such an exponential function.
Duality requires differentiation and one of the most interesting differences between mathematical entities is the differentiation between real and complex [or imaginary] numbers. Complex numbers can solve problems that real numbers cannot do. Every complex matrix has an eigenspectrum (?) Eigenvalues and eigenvectors - Wikipedia
F&H page 2: '[Quantum mechanics] asserts that there are experiments for which the exact outcome is fundamentally unpredictable and that in these cases one has to be satisfied with computing probabilities of various outcomes. But far
[page 17]
more fundamental was the discovery that in nature the laws of combining probabilities were not those of the classical probability theory of Laplace.'
The bifurcation of action into kinetic and potential energy is equivalent to the emergence of time, the characteristic of a two state system. The theory of the one state system was developed in some detail in ancient times and eventually became the classical model of the One, God. This developed from the conviction that this enormously complex and varied world can be traced down to a single source. Parmenides, Plato, Aristotle, Aquinas.
Behind the Iron Curtain Stalin set out to grind people to dust, to destroy all interpersonal relationships leaving only the individual and the state, the individuals being powerless before the state because all their connections to sources of power had been severed.
The notion of state antecedes [is more general, abstract than] the notions of space and time (or momentum and energy), but nevertheless we can describe states using spacetime as our independent variable.
The classical harmonic oscillator (like a pendulum) oscillates between potential and kinetic energy, in such a way as to keep their sum constant and there difference oscillating between + and - 1, but integrated over time = 0, ie action = 0 = + action + - action (creator and annihilator) both working at one to create PE by annihilating KE and vice versa. What about the quantum harmonic oscillator?
[page 18]
Saturday 8 December 2012
ψ(t + ε) = ψ(t) . eiε(T-V), L = T - V,.
Quantum harmonic oscillator = computer. Pendulum is simplest classical computer, transforming kinetic energy to potential and back.
Quantum mechanical processes take place 'behind' space and are projected onto space, rather as a computer works 'behind' the memory space, reading it and writing to it in an observable way. So we read the two slits and write a diffraction pattern.
I m rather bogged in the quantum mechanical problem although it seems in a way one can express the theology without solving the quantum mechanics, but then it would be rather like Christianity, theology by arbitrary assertion rather than by explanation. What I am basically looking for is a mechanism for creation, but must accept that insofar as a mechanism is deterministic it is not creative, and insofar as it is truly creative it is not deterministic and not therefore amenable to a casual explanation. The answer so far lies in symmetry and symmetry breaking, like the spinning and halting of a tossed coin.
What is random in quantum mechanics are not the eigenfunctions of the [measurement] operator, which are analogous to the faces of a die, but the choice of which eigenfunction to execute, analogous to breaking the symmetry of the die when one face lands uppermost. One
[page 19]
might say a deterministic process occurring at random, like mating.
Each swing of the quantum pendulum is a quantum of action and the rate of swinging is the energy the pendulum, E = hf.
What to do next. In some cases this is a predetermined part of a larger task like making a cake - now we crack the eggs. In other cases, when one has 'free time' it is a matter of somewhat random choice from a range of possibilities, make tea visit neighbours, unload car, etc nothing pressing. Each of these operations is an algorithm, but choice of algorithm is not algorithmic.
The root of it all is the quantum mechanical computation of probabilities constrained by what? Unitarity: the source emits one symbol ai at a time, constrained by the equation Σ pi = 1. | eiθ |2 = 1.
Then comes an outside event which determines the next step.
One gathers from the struggles of the mystics that 'understanding' or 'experiencing' absolute simplicity is not easy. On the other hand the statement that God is a one or zero dimensional [isolated] quantum system has some sort of mathematical meaning, we 'extrapolate' down from to to 1 to 0 dimensions.
What the mystics are trying to do is quiet their own consciousness down to their idea of simplicity, ie to experience nothing rather than to simply understand
[page 20]
nothing. The nothing of experience is pure act, that is everything and nothing, essence identical to existence, ie essence is esse. The nothing of knowledge is simply the empty set, like the first element of an ordered set. As we can set our zero of energy anywhere (in physics) so we can choose how empty our empty set is, ie using general covariance, map any set to the empty set.
Forms generate passion, as I experience every time I see her, ie potential generates kinetic. The reverse also happens, in that kinetic energy can be converted into potential, creating a higher resolution representation of the form [creation]. A pendulum, like a quantum system, operates at constant entropy.
Over the last few decades it has become clear that we can represent physical processes as computations and a lot of scientific and technological effort is going into the development o quantum communication and quantum computation. At the quantum level, we need not distinguish communication and computation.
One dimension. Time is like half a dimension, only moving one way, or more to the point, having no direction, not so much a line as a dynamic point, a two state system. The use of complex numbers in quantum mechanics means that there are in effect, twice as many basis states as the dimension of the relevant Hilbert space. So all the state in the Hilbert space are 'split' by the duality of complex numbers.
[page 21]
Let us try to understand the fundamental processes in the Universe through addition. Multiplication is repeated addition, exponentiation is repeated multiplication. In order to make this system complete and reversible we need complex numbers, unitarity and the
Polya and Latta page 75: 'A complex function of a complex variable is equivalent to a pair of real functions of two real variables; only if the pair is exceptionally well assorted can we differentiate the complex function. Such well associated pairs of real functions have remarkable properties and are represented by mappings and vector fields of exceptional geometrical and physical importance. Polya & Latta
Derivative: ratio of output to input of continuous function.
Polya page 80: '. . . practically all real functions of a real variable that intervene in geometrical and physical problems possess a derivative. In the complex domain, differentiability is exceptional.
page 83: 'We now know under which conditions a pair of real functions u and v is well assorted and forms a differentiable complex function u + iv: the functions u and v must satisfy the Cauchy- Riemann equations [
∂u / ∂x = ∂v / ∂y, ∂u / ∂y = -∂v / ∂x].
A pair of functions so assorted is called a pair of conjugate functions.
A vector rotating in the complex plane models a two state system whose states are (say) i and 1.
[page 22]
Alternatively (page 82) ∂w / ∂x = 1/i ∂w / ∂y = -i ∂w / ∂y.
The inverse of i is its negative -i, -i . i = 1.
The complex domain is logically consistent but not observable.
Is potential energy positive or negative? Kinetic is considered positive, and we usually consider the potential at infinity to be zero and negative closer to home, ie we live in a potential well, as do electrons and all other bound (bonded) particles.
Theology is the theory of everything, fitting all the other sciences into a unified point of view, showing how the world is both many and consistently one.
Fundamental logical fixed points NOT and AND can be combined to create a universal computers. We say this often, but are we making any progress?
