Notes
[Sunday 20 April 2008 - Saturday 26 April 2008]
[Notebook: DB 63 aTheology]
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Sunday 20 April 2008
You have always been a single girl to me means that my view of you is invariant with respect to all your other relationships.
RELATIONSHIP = {CODE. TRUST}
The purpose of the physics section [of this site, Physics] is to set the stage of a living (self moving) Universe. Essential features of life are descent,
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variation and combination and selection. For these we need constraints on resources. These are both provided by the symmetries of physics and broken by communication. In other words, physical symmetries are the protocols of a network of communication that can live and grow. We then graduate from physics to biology to emphasize features of the living and growing Universe.
The essence of gravitation is that communication is attractive and concentrations of communication are more attractive the bigger they get. This is straight bosonic behaviour without mentioning 4-space.
Every intellectual step forward is based on interpretation , which clarifies a previously complex system (diagonalizes it) followed by an explosion of application of the new simplified interpretation to create the next layer of complexity, which will in its turn spawn a new master interpretation and so on.
The invariant step in this process is the cycle interpretation (INSIGHT, SCIENCE) and application (INSIGHT, TECHNOLOGY). This is the cybernetic cycle which carries us from one layer to the next. Lonergan
We study the general process in terms of an abstract computer network. A computer is something that transforms an input vector (ordered string) into an output vector. There are ℵ0 such transformations working in a space of ℵ1 vectors. These we might call computable transformations or computable eigenfunctions.
I feel as though I am very gradually having an insight
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here which has taken 40 years to develop and seems to be going on nicely. The problem is to find the necessary and sufficient representation of this insight. The insight is complete when it can be committed to memory and transmitted to others. This is the wonder of physics.
So what is an insight in network terms? Say it is the development of a communication protocol (an encoding) that enables a set of previously unconnected nodes to connect. [ie the development of an internet] Once two nodes speak the same language they can communicate. The language is the symmetry that unites the,. The first language of the Universe is energy.
Like god, energy knows all because it couples to all, that is it couples to itself and so can be 'critical, as I couple to myself by looking in the mirror, writing, singing or just being consciously aware of myself. And we know that there are a huge number of organic, molecular and atomic couplings within me that keep me moving as a unit and which are all, at the most abstract, channels of energy coupling to itself. What has changed in the strength and variety of the couplings.
UNMODULATED (at a certain level of resolution) = STATIONARY
The book of revelation. Revelation These words record revelations that have come to me as I ponder the theological problem, which at its most general is to identify and understand the source of revelation. The Christians have no ground for thinking that the Bible reveals any more about the source of revelation that any other object in the world. This we might call the 'meaning' cosmological principle that all strings of a given length in a given layer are equally meaningful, ie they are all
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points in one space with one entropy, and therefore one information carrying capacity. Is this true of the letters of the alphabet? We cannot tell because there is an uncertainty principle here induced by the gulf between the statistical definition of source entropy and the letter by letter operation of the source.
Ie all the nodes in a layer are PEERS. The most general specification of peerage is equal entropy = equal variety = equal cardinal number.
Physics thinks of the world in terms of charges and currents.
All the process in a computer can be understood as transformations of a memory, ie the 'tape' in a Turing machine. This statement hopes to be the expression of s symmetry common to all computers.
Communication is the gauge that keeps all the nodes invariant. What does this mean? Every change of state in a network is accompanied by a message representing the change of state. So photons and atomic electrons etc.
If we look at the Hilbert oscillator through the eyes of cardinal numbers alone we get general relativity.
Monday 21 April 2008
Mathematics is itself layered rather like our proposal for the universal network, beginning with the natural numbers and then moving to integers, rational, real, complex, vector, matrix, tensor, [fibre bundle?] and so on. Bernstein & Phillips There is branching in the layering, as for instance real numbers can form the elements of all sorts of different structures and we can assign a cardinal to a layer by counting how many real numbers are required to make that structure, eg how many real numbers in a line, a tensor and so on. The cardinal corresponds to a memory space which determines how many numbers can be kept in play at a given time.
The whole process is built of bricks of spin (which somehow map to the elementary rules of logic) which acquire their strange quantum mechanical [behaviour] when projected into 4D space.
Bernstein and Phillips page 98: 'Physicists have taken the distinctness of spin states and the need for probabilities as being basic postulates of quantum theory.
Probability [symmetry] arises because of lack of requisite variety, leading to a limit in the determination an alphabet can impress on a language. Ashby
So spin 1/2 is up or down, but that can point anywhere in 4D space because the information is not there to say otherwise. This 'theorem' is just as true for the world itself as for statisticians. This is another application of complexity invariance. The rules of logic and communication bind the Universe at all levels.
SPIN ARITHMETIC, spin n + spin m = spin(n + m). with boson or fermion being determined by odd x 1/2 or even x 1/2.
Spin is like gearing, mapping the phases of amplitudes to the phases of wavelike measurements in 4-space.
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Personal security is a sort of Mossbauer effect: the more closely one is bonded to a larger community the safer one may feel, and be.
3D allows 'sourceless' flows as it allows 'complete wiring'.
We can build a computer (and a Universe) from strings of binary numbers or events.
Fibre bundles model projection.
In its own space the spinning electron has two states, but when incorporated into the larger world these states are constrained only be the normalization of probability and in the most likely case, the probabilities of the two states are equal.
PROJECTION - REDUCTIVE / CREATIVE
Creative projections are random by definition because they are non-deterministic.
Bernstein page 102: 'In more general fibre bundles, things are not so simple. For example, if each fibre is a line rather than a pair of points, motion in the base implies motion from fiber to fiber, but it does not specify which point in each fiber is to be traversed. [Things are underdetermined]. To determine an unambiguous path through the total space in such a fibre bundle, additional structure is needed. A procedure that gives a path through the total space lying directly above a path in the base, once a starting point in the total space has been
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specified, is called a path-lifting rule.
Projecting 2D onto 4D, the path lifting rule = random = quantum mechanics?
A digital computer memory can be constructed from any 2-state system like a spin 1/2 particle.
Behind the scenes the quantum mechanics are consistent processes that give meaning to the strings of observations or experience that make up a lifetime. From the lifetime we try to construct the meaning of the life by supposing certain lifting rules.
Bernstein page 105: '. . . to turn the probability amplitudes for a proton field into those for a neutron field and back again, which is in effect to alter continuously the probability that a particle is a neutron or a proton, it is sufficient to shift generalized phases. Phase is scalar.
'For electrically charged particles the magnetic vector potential is a field that acts by shifting phases at each point in space' ie varying the function d theta / dx. 'The vector potential determines the magnetic field; indeed magnetic effects on charged particles can be completely explained in terms of the phase shifts given by the vector potential field. The underlying reason the vector potential field is a gauge field is that a magnetic force acts on a charged particle to change its direction without changing its energy. When an electron enters a magnetic field the frequency of the electron waves therefore remains constant but the spatial pattern of the waves is changed. It is as if the wavelength were to vary from point to point. page 106.
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Bernstein page 109: ' The electric potential and the magnetic potential taken together give a connection that can explain the electromagnetic interactions of charged particles. The curvature of the connection is a tensor with six components corresponding to the three components of the electric field and the three components of the magnetic field.
'Each of the quantum gauge fields can be understood as a connection on a fibre bundle where the base is space-time. The fibre of the bundle is the set of internal symmetry transformations of particles that interact by means of the gauge field.
GAUGE FIELD = METRIC FIELD?
From clarity comes progress.
Fibre bundle and quantum harmonic oscillator: Projection.
Tuesday 22 April 2008
As we go to higher energies in particle physics we are inclined to believe ('the belief angle') that we are getting closer and closer to the initial singularity where we predict infinite temperature and infinite energy density. However if we see kinetic and potential energy as adding up to zero in the whole Universe, this extrapolation is not necessary. Instead we can attribute high localized kinetic energy to a localized potential (like a particle accelerator, artificial or natural) and see high energy physics as something common to all epochs. We can also abandon the need for infinite energy concentrations in the initial
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singularity, unless we say that it has both infinite potential and infinite kinetic energy.
To have no size does not necessarily mean to be infinitesimally small but that the dimensions length, time, mass etc simply do not apply. These dimensions presuppose measurement and therefore a certain complexity in the Universe. Perhaps gravitation antedates measurement, back in the days when pure dimensionless logic was the sole structure.
The funding model for high energy physics is that higher energy scales will yield new phenomenology and in some sense take us closer to the 'mind of god'. The network approach works in the opposite direction, seeing more divinity and complexity in lower energy interactions.
From the information / entropy point of view, high concentrations of energy / potential correspond to high temperature and low entropy, the initial singularity appearing to correspond to infinite temperature (all energy concentrated in one mode [kit ] and zero entropy (. . .). As a betting person, one would see the actual Universe as a superposition of both these views, seeing each network (particle shower) as rooted in a high energy event and increasing its entropy as energy is partitioned (both kinetic and potential) into smaller quanta, ie quanta with longer duration, keeping the product E . tau constant as we follow a path through the tree of network growth. The initial singularity (root) of each network is the fracture of the symmetry of action into kinetic (process) and structural (potential) energy. Gravitation sees only this break in divine symmetry, but the notion of ordering enables
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us (and the Universe), to construct systems with a history.
The origin of space is the origin of history - the origin of memory. We can get no closer to the initial singularity that the beginning of memory, because everything before that is forgotten. No particle can see beyond its own creation. Here we have a statement that applies to the Universe as a whole as well as every particle within it, the cosmological principle we have been looking for.
INVARIANCE with COMPLEXITY (cosmological principle) ==> GRAVITATION. The fanciful plan is to use the transfinite oscillator to unify gravitation and all other physics.
The binary tree (with transfinite overtones) is an adequate model (ie a countable model) of the whole.
We explore the symmetric network by creating comoving models to follow various processes around. Our model is good if it follows the process faithfully. At the work level, our models must be perfect, otherwise things will not work. Here we find an infinity of detail specific to each particular task - how do we fix turbine blades so that they do not come loose when the think is hot and spinning? A serious epistemological issue for plane travellers.
The High Energy Physics community (or any scientific community) is the sort of model I have in mind for the natural theology community, which will grow, like the other scientific communities, from an epistemological principle that we must go with the data, that is
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respect history.
The opposite extreme to a scientific community as the hierarchical community, where guidance is sought from some higher authority . . . .
Our assumption is that the universal network of process and memory gives a place to every event in the Universe. The geometric version of this addressing system is space-time, but there is meaning in the spacetime to which spacetime to which space-time and gravitation are completely blind. The observer and the observed are created in the same break of symmetry. My image in a mirror, no matter how faithful, is not me. Even if it is a clone of me down to the last atom, one is the original, the other the copy. The original is the reference frame to which we refer the copy to test its fidelity.
Physics sets up a reference frame of possible events which are exploited (used) by life to do its thing.
From creation and writing to transcription, rewriting and finally food, read, sleep to begin another day. We re all pretty much on the diurnal cycle, at different phases.
This is a plea to break the institutional hold on theology by reclaiming God for the individual and . . . individual experience away from the needs of an institution and institutional experience. [A continuation of the Reformation.]
Oh pope, you preach human dignity and you practice the opposite, working to subjugate us all to a load of ancient and out moded theory whose sole purpose is to preserve the institution you represent and whose tool you are.
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All revolutions are epistemological: a new way of looking at things suggesting a new mode of action, like universal education, reliable media and democratic steerage on the ship of state, that is a bunch of bosons (which may nevertheless have a lot of fermion structure inside.
Politics: a glimpse of the line of development further along, we see the boson face of humanity forming groups to improve probability of successful reproduction (= survival)
The layered network model sees deeper layers represented recursively in higher layers, so that it takes many atomic events to make a human event.
Geometric views of space so an event as a spacetime point, but in fact events (like myself, the solar system or the emission of a photon by an atom are extended in space and time.
Gravitation is the potential that defined the dynamics of four space as we know it
The world is 4D so that we can see is as a bounded space of anastomosing but not intersecting flow, a source free current, bootstrapping itself.
So the Universe is a source free current of action, something worthy of Aquinas term 'actus purus '. [no boundaries] Aquinas 13
I spent a lot of time in my youth pounding cloisters trying to 'understand' the Trinity, to penetrate the
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mystery as I might have said, or, in Lonergan's terms, have the insight that made it all clear to me. It has become clearer over the years as I have thought more about the concept of generation and its application to the world we know and have generated in.
I get nervous when I am not working. I have got a job to go to when the rain stops (weeks straight now) but I still have to convince myself fully that writing down my speculations is more valuable that digging ditches and will provide me with gainful employment in my old age.
The continuum is essentially invisible (therefore a fiction) because all observations are quantized.
The RCC is a continuous fiction not well represented by its actual history. It is better considered as a set of events whose explanation awaits transcendence of its own explanation of its essence, a fiction in which its power is based.
Ferreting our features of the world: Erez et al, N 452:724 Erez et al
Whenever there is observation there is quantization etc. The only time there is not observation is when there are no observers (critics). This is the initial state of the Universe. The genesis of the Word in Trinitarian theology is similar: the Word is the image of God generated by God observing (reflecting upon) Himself. The Word is identical to the Father but different because of the generative relationship.
Schwinger QED. Schwinger
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Schwinger page vii "The development of quantum mechanics in the years 1925 and 1926 had produced rules for the description of systems of microscopic particles which involved promoting the fundamental dynamical variables of the corresponding classical systems into operators with specified commutators.'
Ie order became important both in the structure and in the application of operators.
'. . . electromagnetic radiation contained in an enclosure when considered as a classical dynamical system, was equivalent energetically to a denumerably infinite number of harmonic oscillators.
page vii 'The only real dynamical degrees of freedom are those of the radiation part of the field. Yet one can employ additional degrees of freedom which are suppressed finally by imposing a consistent restriction on the admissible states of the system.
'the complete agreement of [formal quantization and the limitations of the accuracy of simultaneous measurements of two field strengths, produced by known quantum restrictions on the simultaneous measurability of properties of material test bodies] with the formal implications of the operator commutation relations indicated the necessity and consistency of applying the quantum mechanical description to all dynamical systems.'
page ix : 'The replacement of commutators by anti-commutators was found necessary to describe particles, like the electron, that obey Fermi-Dirac statistics. In the latter
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situation there is no reliable physical limit for which the system behaves as a classical field.'
page xiv : 'The evolutionary process by which relativistic field theory was escaping from the confines of its non-relativistic heritage culminated in a complete reconstruction of the foundations of quantum dynamics.'
'[The natural starting point of classical dynamics] is supplied by Hamilton's action principle, and action is a relativistic invariant.' Hamilton's principle - Wikipedia,
'When the action operator is chosen to produce first order differential equations of motion, or field equation, it indeed predicts the existence of two types of dynamical variables with operator properties described by commutators and anti-commutators respectively.'
page xv : 'The practical utility of this quantum dynamical principle stems from its very nature; it supplies the differential equations for the construction of transformation functions that contain all the dynamical properties of the system. It leads in particular to a concise expression of quantum electrodynamics in the form of coupled differential equations for electron and photon propagation functions. '
page xv : '. . . is there a fatal fault in the structure of field theory? Could it not be that the divergences -- apparent symptoms of malignancy -- are only spurious byproducts of an invalid expansion in powers of the coupling constant, and that renormalization, which can change no physical implications of the theory, simply rectifies the mathematical error? This hope disappears on recognizing that the observational basis of quantum electrodynamics is self-contradictory.'
page xvi : 'The localization of charge with indefinite precision requires
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for its realization a coupling with electromagnetic field that can attain arbitrarily large magnitudes. . . . We conclude that a convergent theory cannot be formulated consistently within the framework of present space-time concepts. To limit the magnitude of interactions while retaining the customary coordinate description is contradictory since no mechanism is provided for precisely localized measurements.'
[spacetime is a fictitious continuum upon which quantum logical operations are projected]
Wednesday 23 April 2008
Wake up depressed (common) and cheer up as the fruits of the night's work begin to appear.
The whole point of science (from a practical point of view) is to calculate (predict) as best we can the state of a system at t + delta t, given its state at t. Dirac 1933 hit on a very powerful constraint on the transformation representing the effect of delta t in the Lagrangian L = KE - PE [kinetic energy - potential energy, T - V ]. Dirac
We connect past, present and future by the notion of causality which is expressed in physics by the notion of contact, the opposite of 'action at a distance'. The divine world (being outside space) may be capable of action at a distance but it still requires contact so we say that God is in touch everywhere. Aquinas 39
We can think of the future as a transformation of the past. All the same actors are present but they are doing different things and may have different relationships to one another. Elements of the timeline that remain more or less the same despite these transformations
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are called symmetries. The basic symmetry of physics is conservation of energy which holds even of actors are born and die in the transformation from past to future.
The Lagrangian and the Hamiltonian are symmetries that carry us over the transformation from classical to quantum mechanics. Of these the Lagrangian seems the more powerful because it is more closely related to symmetry by Noether's theorem, and so it is in some sense able to reflect on itself. Emmy Noether
Dirac page 65: 'We must try to take over the ideas of the classical Lagrangian theory, not the equations of the classical Lagrangian theory,
The transition of the Lagrangian from classical to quantum theory gives us two points on a trajectory pointing to the application of the Lagrangian to the Transfinite oscillator.
We are in heavy weather, but not heavy enough to be life threatening.
Poisson bracket. Poisson bracket - Wikipedia
The special feature of quantum theory is that it is inherently ordered so that reversing the order of transformations may lead to a different result eg crack the egg then cook it vs cook it then crack it = fried | boiled.
II am trying to write things which are a true expression of my knowledge and feeling at the time of writing. While my knowledge and feeling are dynamic, writing is static, and so
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the search for written expression is the search for time independent symmetry, ie a search for energy, or something with the time-energy symmetry property. Parmenides Noether's theorem comes in here somewhere as a mathematical property of transformations. Emmy Noether
When Dirac says 'Let f(q) be any function of the q's . . . ' I think he means 'any continuous and sufficiently differentiable function.' Here is the deeply ingrained continuous (geometric) picture that we are trying to expand via quantum mechanics to recursive function theory, where we will write 'let f(q) be any computable function . . . '
Contact transformation expresses symmetries between two dimensional sets of variables pr, or and Pr , Or , and us and Us are independent (an orthogonal basis) so that any function of the dynamical variables can be expressed in terms of them' They are the 'adequate language' which we take to mean a 'computable language'.
In the classical world we then find
Here S is acting as the invariant relating the pr to the or and Pr to the Or .
Dirac page 314: 'In the quantum theory we may take a representation in which the q's are diagonal and a second representation in which the Q's are diagonal. There will be a transformation function
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[Turing machine] (q' | Q' ) connecting the two representations. We shall show that this transformation function is the quantum analogue of e is/h .'
In physics the computers all work in unary notation, so that we represent the number 10 with ten items whose total mass is 10 m where m is the mass of one item. Mass - weight - force. Different coupling constants give different weights to different items. The gravitational coupling is the measure of meaningless self reflection. Coupling constants get stronger as systems become more complex and selective.
Dirac page 314: 'The equations of motion of the classical theory cause the dynamical variables to vary in such a way that their values at it , put at any time t are connected to their values it , put at any other time T by a contact transformation . . . .
This process is analytic and deterministic in the classical picture.
' . . . which may be put into put into the form (1) with q , p = it , put and Q, P = it , put and S equal to the time integral of the Lagrangian over the time T to t.'
page 316 '. . . we ought to consider the classical Lagrangian, not as a function of coordinates and velocities, but rather as a function of the coordinates at time t and the coordinates at time t + do. '
Time is not a degree of freedom. It flows inevitably and we cannot change it in our local frame. It is the one dimensional version of the 2D quantity velocity.
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Contact sport. Transform the opponent in some optimal way (from the agent's point of view).
I have been fairly certain (based on quantum mechanical formalism) that the Universe is transfinite for ten or more years. Now I am slowly working my year from this cardinal insight to its cardinal features.
Physics talks at a high level of abstraction because the things it talks about are very simple: an electron has spin, momentum and a charge, two vectors and a scalar; a photon merely spin +- and energy. The complications arise when these simple beings interact in the complex present way world. The network model with its layer may help us to see the buildup of the Universe more simply, in that we try to look at a layer without taking uses into account, only its intrinsic properties which it manifests by using the layer beneath it.
The layers of the Universe are parametrized by time and complexity. Each layer is a 'rolled up dimension' but we are inside the space-time layer which is 'rolled up' by the curvature of the Universe.
The world makes best sense when viewed socially, as a layered network. Physics comes to grief in the mapping between quantum mechanics and spacetime. This is fixed by renormalization. Gravity is unrenormalizable, which suggests that quantum mechanics plays no part in it. The beginning of quantum mechanics at the layer of stationary states. The only stationary state in gravitation is the Universe as a whole.
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What does the Lagrangian men, L = T - V? Kinetic energy is energy of motion and depends quadratically on relative velocity, T = 1/2 mv2. Potential energy is energy of position and depends linearly on distance, being F . s = = partial d phi . s. We say that for the Universe V + T = 0, so V = = T and L = IT or -TV for the whole Universe. This does not constrain the amount of energy in the Universe as long as V +T = 0. The action integral L do = integral T do - integral V do = 2 integral IT do where the 'event' is the life of the Universe.
Can we imitate QED with networks of Turing machines? Should be possible if QED is computable. Then all we have to do is find the actual topology of the network and the algorithms in the machines. Instead of analyzing the world into infinitesimal units of space and time we analyze it into atomic logical operations, ie executions of Turing machines or acts.
Thursday 24 April 2008
'We are faced with insurmountable opportunities.' Pais, Inward page 624. Pais
A complete cycle of phase (= a completed process) corresponds to a quantum of action. The simplest Turing machines corresponds to a plane wave and the superposition of more and more plane waves corresponds to more complex Turing machines whose period (execution time) corresponds to the longest wave (the slowest change of phase = the lowest energy). So high energy processes are nested inside low energy processes, as we would expect. Dirac's (and Feynman's) path integral method consists in breaking a path down into small chunks of time or action (subroutines)
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which taken together describe the whole process of getting from one spacetime state (the input) to the output spacelike state.
STATIONARY ACTION = FIXED (OPTIMAL?) ALGORITHM
Classical physics sees the world moving through time as a braided network of continuous flows. We see it as a network of logic which looks like the classical picture if we ignore the meaning of the logic (as a computer does, having no idea whether it is running a dating agency or a climate model).
All the mathematical work on quantum theory that I have seen treats action as a continuous quantity differentiating and integrating happily, as a consequence. But it is not, and so the whole basis of the formalism may be brought into question. [but we must explain why it is quite successful].
ALGORITHM = an itinerary through logically deterministic space, ie space that can be reduced to atomic logical operations.
Our fundamental assumption is that apart from gravitation, the Universe works the same way as we do so the scientific method comes into play as soon as we have space = memory.
Action is quantized, but this does not necessarily mean that energy and time, or momentum and space, which are multiplies to give action are quantized, since E / omega = h bar = 1, E = omega as real numbers.
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Friday 25 April 2008
Feynman 1948: 'The formulation to be presented contains as an essential idea the concept of a probability amplitude associated with a completely specified motion as a function of time. . . . We shall examine the essential changes in physical outlook required by the transition from classical to quantum physics.' Schwinger page 322, Feynman
Path integral = Two slit experiment.
Schwinger page 323: '. . . the chance of finding a particle going from a to c through several different routes (values of b) may, if no attempt is made to determine the route, be represented as the square of a sum of several complex quantities - one for each available route.'
page 325: Postulate I: 'If an ideal measurement is performed to determine whether a particle has a path lying in a region of space-time, then the probability that the result will be affirmative is the absolute square of a sum of complex contributions, one from each path of the region.'
Let us say that an early bifurcation of the Universe is from real to complex numbers, whose absolute value is real and whose values are constrained by the requirement that |z| = sqrt (x 2 + y 2) where z is represented by the vector equation z = x + ivy. We also have |z | = z z bar. How do we explain this situation? Perhaps is is the only way to break the symmetry of the real numbers. What if we calculate the Lagrangian of the reals and see if it equates to the equivalent Lagrangian of the complex numbers. We imagine that the bifurcation from real to complex introduces energy which bifurcates into
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potential and kinetic at the next (spin) step of development, action remaining at all times invariant. [one act converts an electron from spin up to spin down]
Feynman postulate II: 'The paths contribute equally in magnitude, but the phase of their contribution is the classical action (in units of h bar), ie the time integral of the Lagrangian taken along the path' page 325.
L is the time integral of the difference between kinetic and potential energy = action. If they can, things move to equilibrium, where both potential and kinetic energy are 0, and so is L.
'That is to say, the contribution phi [x (t )] from a given path x(t) is proportional to exp (i/h S [x (t )]), where the action S [x (t )] = integral L (... ) do is the time integral of the classical Lagrangian L(v, t) taken along the path in question.
We still have a classical continuous L in here whereas the full quantum treatment should restrict the action S to values no, which may have some effect on the result. However, we can allow frequency, energy, distance, momentum etc to be continuous as long as their products with the dimensions of action (ie ML2T-1), are discrete.
e (a + b) = e a e b . This conversion of a sum into a product must indicate a transformation from one layer to another layer via an exponential function. The hint might be that the transfinite transitions is (from a cardinal point of view) an exponential (or logarithmic) function.
The transfinite transition is the fundamental mode of the Hilbert oscillator, and we like to compare it to CREATION (=
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producing different orderings of the letters of the alphabet) and INSIGHT (= determining the alphabet (ie the diagonal representation) of a transformation).
KNOWLEDGE = {INSIGHT, DATA}
Multiplying Hilbert spaces (tensor product) is also an exponential operation.
Let us guess that each quantum of action adds a dimension to the Hilbert space of the Universe, so the whole thing is growing at exp (S = ℵ0 h )
Theology is the study of God in order to arrange our own relationship with God as advantageously as possible. Study of God means communication with God.
The Roman Catholic Church is reminiscent of the unscientific world of business where knowledge (= intellectual property) is private, hidden, protected.
Theological knowledge is just as important as any other knowledge, like hunting or child bearing, and we will find theological elements in any culture, buy which I mean the totality of postnatal adaptations to survival in an environment. The most remarkable product of human mental adaptability is shown by our acquisition of the cultures necessary to live on a very wide range of global conditions, so our range is global.
This range is the complete set of basis states upon which we can build our existence.
The finite velocity of light limits the data going into and coming out of an event = finite rate of communication = bandwidth.
How does bandwidth relate to the velocity of light? c is the transformation
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constant between space and time so it has space and time dimensions c = L /T = LT-1 If we make c dimensionless, we find that LT-1 = 1, ie L = T (when c = 1). Bandwidth then becomes a matter of how finely we divide our length or time, it corresponds to spatial and temporal frequency, ie MARKING.
Any function needs memory, but the memory needed for a recursive function is used most efficiently. Something that can be done again and again mechanically is capital = machine = algorithm.
CAPITAL = MACHINE = ALGORITHM
So it looks like the communication rate has nothing to do with the velocity of light but that there is an equivalence between serial and parallel storage of data and relativity shows us how to dynamically transform a set of points in the same place at different places into a set of points which exist at the same time in different places, or anything in between.
So the split from 1D to 2D is serial to parallel [and one can be transformed into the other].
Logically the serial parallel trip is done in communication between memories. All elements of a string exist simultaneously in memory (so that ut can have random access to itself) and when we read them out one by one and transmit them in a serial stream (whose elements may include memories, ie complex particles) to another memory, which stores them in a spatial order relating to the logical addressing of its physical bits.
The construction of a differential equation. Feynman [Quantum mechanics] pages 8-7 to 8-10.
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The key to quantum mechanics is commutation, and we see this at its simplest in the equation <x |y > = <y |x >*.
Quantum mechanics says 'We have discovered that any state in the world can be represented as a superposition -- a linear combination with suitable coefficients -- of base states'. Feynman 8-5
Post quantum mechanics, ie discrete or quantum quantum mechanics would say almost the same, that any state in the world can be represented by a permutation of permutations of . . . of a set of base states.
The base states of a motor vehicle are its parts which are coupled to eachother in different ways (welds, bolts, bearings) to make a car. There is sufficient in formation in the parts of a car to unambiguously construct a car (apart from a few adjustments), but this need not be so for many constructs.
E =h omega, E /omega = 1, so as E goes to infinity, so does omega, so they stay in step with one another. There are no ultraviolet of infra red divergences in action, S = E / omega . The computation (action) approach circumvents renormalization? So we see the electron mass as an invariant related to other properties of the world by constants like e and h.
STATE = SPACE = MEMORY holding a certain VALUE = MEMORY + VALUE
A memory is a stable state that can only be changed by an action, and the minimum such action is measured by the quantum of action.
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Two time ordered states are two states of memory, the same space of addresses with content changed by dynamical processes that realize Landauer's idea that all information is represented (and processed) physically. Landauer
What does physical mean? Geometric, continuous? The physical layer is the continuous layer, the transparent and amorphous optic fibre transmitting information from terminal to terminal. In any context, the physical layers is continuous (gravitation) and ...
Feynman (Schwinger) page 373: 'The Lagrangian is a function only of positions and velocities' in the non-relativistic space-time formalism, we might say classical quantum mechanics.
'The quantity psi depends only on the region R' previous to t and is completely defined if that region is known. [past light cone] It does not depend, in any way, on what will be done to the system after time t. This latter information is contained is chi. Thus with psi and chi have separated the past history from the future experiences of the system. This permits us to speak of the relation of past and future in the conventional manner'.
We may generalize this from regions of spacetime to space-time states of a network.
The past hands a complex number to the future at every point in space and time. This complex number is a 2D paradigm of all the messages passing from past to future, like this writing.
Everything we have to say is about communication and so may be exemplified by the act of communication starting in me
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(region R' ) and finishing in you (region R'') displaced in both space and time from one another.
'[the wave function] [ determined by the past] contains all that is needed to predict future possibilities.
Complete action = 2 pi phase = closure = there and back again.
Feynman (Schwinger) page 378: 'The close analogy between <x' |x > and the quantity exp (is(x', x )/h ) has been pointed out on several occasions by Dirac.'
Schwinger (1951) page 914 in Schwinger page 342: 'Quantum mechanics involves two distinct sets of hypotheses -- the general mathematical scheme of linear operators and state vectors with its associated probability interpretation, and the commutation relations and equations of motion for specific dynamical systems.'
page 915: 'The problem of constructing a complete set of commuting operators that is of simultaneously measurable physical quantities necessarily involves specific properties of the fields. Nevertheless, as a general principle associated with relativistic arguments, we must expect such mutually commuting operators be be formed from field equations at physically independent space-time points, that is points which cannot be connected, even by light signals. A continuous set of such points form a spacelike surface [ie a continuous memory] . . . A change of representation will correspond, in general, to the introduction of another set of commuting operators on a different spacelike surface [another memory in communication with the
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first.]' [precision placement of the symbols .]' is important]
Fuck off Pope! Dissent. Dissent
Not very nice thing to say to someone who has come around the world to see us, but I mean it, and I'll tell you why.
But first, I do not know Joseph Alois Ratzinger, who is currently fulfilling the role, and I have nothing against him personally, but I'm dead against the role. Pope Benedict XVI - Wikipedia
The Pope is the mother of all monarchs, pushing a product called Salvation. The pope is entrusted with Supreme and infallible power as the Absolute Head of a vast and ancient Institution, the Roman Catholic Church (RCC). The Holy See Over its history, the Church has been an instrument of pain to about the same number of people as the Emperors of China and their successors. Billions of people over thousands of years. These people have put up with it because they have known no other, because the spin has been perfected over many centuries and because dissidents are made to suffer. Even the Chinese, as far as I know, did not burn people at the stake. Execution by burning - Wikipedia
Saturday 26 April 2008
Proper time is not a variable in the sense that we can change it arbitrarily -- it is the inevitable spinning of the cosmic wheel, the irreversible increase in phase that all systems experience.
Empirical residue implies arbitrary creation, since
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there are meaningless facts (empirical residue) put there by the creator.
The march of proper time may be the fundamental confinement of the Universe from which all structures arise. Periodicity (vibration) is consequence of confinement (eg string trapped at the ends).
OSCILLATOR = STATIONARY STATE.
BINDING ENERGY
Physicists are inclined to hold that both energy and probability are positive. Phenomenologically, however, of we associate potential energy with structure, se can associate the negative nature of potential energy with the negative probability of the structure. A train without tracks (structure, confinement), we might imagine, has equal probability of moving in any direction. The rails, however, confine the train so that it can only go in two directions. If we count trains for a long time on a time between two cities, we will see that the two directions have a probability of 1/2 each. The rails has moved the infinite set of possible directions and their associated probability density into two directions, up and down. [just like an electron].
We may thing of quantum mechanics as a closed plumbing system containing a frictionless and incompressible fluid in perpetual motion. This fluid is probability. It takes a while to see probability as a fluid.
tau (proper time) has only positive values by definition. Since it is the basic immeasurable constant. Each of us carries a clock reading our own time, our proper time, our comoving clock. The passage of time is the 'dynamical denominator' by which all other processes are measured. Quantum mechanics tells us
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that this clock ticks at a rate determined by our local mass. This rate is given by the formula f = mc2 / h, where m is our proper mass, h is the quantum of action and c is the velocity of light. This equation tells us that each tick is equivalent to a quantum of action.
We may thing of phase, probability and time as incompressible frictionless fluids flowing in space. If we think in terms of pipes for a moment (I have been working all my life toward the plumbing analogy), the only topology that can accommodate such a flow is a circular pipe, and the fluid can only flow round the pipe in one direction. From a human point of view the fluid in the pipe is time, our basic resource. In real life we divide our time [between a multitude of tasks].
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Every day I pick my garden of ideas, which grows overnight as well as during the day. The unprocessed produce goes here, for later classification, processing and perhaps cooking to produce the end products which I wish to trade. For my own use, I consume everything and it becomes part of myself. In Dawkins' world, I am a selfish angel, feeding on the world and myself to keep myself in equilibrium. For it is painful not to do this. Many ideas are bursting to be put into action, by writing, planting, building and all the other operations that we need to keep ourselves happy.
Pope: morals: The drive of proper time propels us to do all sorts of things, some ultimately self destructive. We can be told what and what not to do by a higher authority but this can be ultimately self destructive is the authority deviates too far from reality. In that case the only way for the underlings to survive is to exert their own independence.
The development of monotheism and personal responsibility go hand in hand. I must respond to unstoppable environmental forces by saying out of harm's way. The existence of an intelligent, loving and all powerful god means that this is possible, since such a God would not create dead ends in time where doom is inevitable. But it can be taken too far. The Catholics has appropriated God for their own use and thus sent God into prostitution, the golden goose of a lot of theatrical old men who enjoy their power too much to let it go., the College of Cardinal of whom the first and infallible leader is the Pope, College of Cardinals - Wikipedia Read the Canons. Holy See The Code of Canon Law is the Constitution of the Roman Catholic Church as a human institution. It has all been designed over thousands of years, beginning with the Roman Monarchy as a self perpetuating centre of power over the masses.
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The Catholic Church goes too far when it says that its infallible definitions are irreformable, because they may be wrong. The Eucharist may not really be Jesus' body. This idea is based on attributing a self contradictory power to God, and above all (for a monotheist) . . .
For instance, the postwar generation has rebranded sex as an exciting game rather than a social duty, partly because rising standards of living have removed the need to breed as fast as we can to survive. For the old men of the church, however, sex is still for breeding, and any fun must be purely incidental (ref).
In a nutshell, the Pope's role is to be Vicar of Christ on earth, which means roughly that he is the Governor General when God is Queen.
Stationary points in a motion are represented by differential equations.
Memory gives order to time.
. . .
The computer has liberated us from the continuous analytic function and taken us into the world of logical functions, ie permutations and combinations constrained by the rules of logic, ie by computability.
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