Notes
[Sunday 16 March 2008 - Saturday 22 March 2008]
[Notebook: DB 63 aTheology]
[page 39]
Sunday 16 March 2008
page [40]
Natural theology is a purely personal account whose empirical foundation is the observations contained in these notes elaborated into the set pieces in Development, Essays, and History, supported and summarized in About, Synopsis etc.
Opportunism vs substance
About: begin with author. How universal is the Universe, initial fear of stepping out of line to current confidence that I am in a new line heading to a more comprehensive and consistent account of our history and potential future.
So the velocity of light is the speed of processing the simplex messages. It is the speed at which we process things that are no trouble, hard wired in effect, like listening to and speaking our native language once we have learnt it perfectly, say 7 years old.
. . .
Woolf, Orlando: The British Empire a result of population growth at home. page 148. Woolf
It may be God's word, interpreted by science, letting us know the consequences of our actions.
So we might think of the photon as the native tongue of the Universe. The graviton is a more evolved
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product. exiting is 4-space rather than two space, but considered to travel at the velocity of light, ie to have the same complexity as its decoder. 4 channels working in parallel without communication, represented by a diagonal matrix. When there is cross talk between the parallel channels, the matrix becomes more complex, but quantum mechanics tells us that all real messages can be diagonalized by finding the right basis.
The photon and the graviton have infinite range: they are part of the Universe as a whole rather than local phenomena and by this property may be identified as primitive, part of the Universe before the local/global dichotomy became meaningful.
Morality must be based on a knowledge of the consequences of our actions, whether these are 'good' or 'bad'. What happens when you pop your pimples? Should you do it?
Woolf page 158: 'Such is the indomitable nature of the spirit of the age, however, that it batters down anyone who tries to take a stand against it far more effectively than those who bend to its sway.'
The graviton is a more complex product than the photon and its coupling to matter is substantially less. On the other hand it interacts with everything, whereas the photon only couples to electric charges. QED. Feynman
The Hilbert oscillator embraces all possible couplings (Turing machines, particles).
Special relativity and negative pressure Peacock: Peacock
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Both photons and gravitons follow null geodesics, so that no matter how big or old the Universe. their sources and sinks are in contact (co-incident in 4-space). A photon / graviton Universe has in effect no size. At the beginning this might be literally true and by the coevolution of space, time and metric remains so when the Universe differentiates into space and time.
This is the bosonic Universe. With fermions comes space.
Monday 17 March 2008
It is raining and I wanted to work, so back to the books, trying to advance another tiny step.
Classical physics (the geometric view) was wont to set up an independent frame of reference and study its phenomena relative to this frame. This is how astronomy works today. We have set up a frame of reference whose fixed points are the plane of the earth's orbit and the 'fixed stars'. We know that the stars move, but by averaging over the positions of many distant stars and galaxies we get something that varies very little over millions of years. This supports the belief that the Universe is isotropic, the same in every direction. If we assume (as seems to humble thing to do) that everybody sees the same Universe, then it is also homogeneous.
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Peacock page 65.
What we want to do is use the transfinite oscillator to extrapolate from geometric isotropism and homogeneity to noetic homogeneity and isotropism, to that we obtain an analogue of general relativity in human theological space.
Peacock page 65: 'To the relativist, cosmology is the task of finding solutions to Einstein's field equations that are consistent with the large scale matter distribution of the Universe..
'Just as Einstein aimed to write down the simplest possible relativistic generalization of the laws of gravity, so the cosmological investigation began by considering the simplest possible mass distribution, one whose properties are homogeneous (constant density) and isotropic (the same in all dimensions)'
Size is irrelevant, since the equations hold all the way from as small as you like to as big as you like.
Weyl Translator's Note: 'Abbildung which signifies representation is generally rendered equally well by transformation, inasmuch as it denotes a copy of certain elements of one space mapped out or expressed in terms of another space,' page xiii Henry L Brose. Weyl
Feynman Gravitation page ix 'Nowhere else is there a pedagogical account of an unusual approach to the foundations of
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general relativity that was pioneered by Feynman (among others). That approach, presented in lectures 3-6, develops the theory of a massless spin 2 field (the graviton) coupled to the energy momentum tensor of matter, and demonstrates that the effort to make the theory self-consistent leads inevitably to Einstein's general relativity. (It is for this demonstration that the notes have become best known in the physics community, Feynman
So we learn all there is to know about a Universe subject to logical constraint if we know the spin-2 massless field? A la Kauffman, the consistency of the formalism tells us almost all there is to know about the system except how it works out in practice under natural selection. Kauffman The spin-2 particle carries that little bit of extra information which constrain pure logic (transfinite growth) to watch reality, which pays a cost for realizing structure since not all structure can be realized, an interim structure must be selected, the cost being the investment in non-selected structures. Planning reduces these costs by finding the optimum (plan by varying models, not reality as some clients are apt to do, building and knocking down.
The most important feature of gravitation, or any formal model, that that it be self consistent where it can be decided.
This project is formally my child and so I want to maintain control over it until it is old enough to look after itself.
Feynman page x : 'With hindsight, we can arrive at Maxwell's classical electrodynamics by starting with the observation that the photon is a massless spin 1 particle.'
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The photon is a message sent by the field and our window into the field.
'The form of the quantum theory of a massless spin 1 particle coupled to charged matter is highly constrained by fundamental principles such as Lorentz invariance and conservation of probability. The self consistent version of the a quantum theory -- quantum electrodynamics -- is governed, in the classical limit, by Maxwell's classical field equations.'
Consistency is the guide to true theory, self consistency and consistency with experience.
Feynman page xi : 'can we find a sensible quantum field theory describing massless spin 2 quanta (gravitons) coupled to mater in an ordinary flat Minkowski spacetime? The classical limits of such a quantum theory should be governed by Einstein's general relativistic field equations for the classical gravitational field.'
Work rate is closely related to morale. Morale lifts when I seem to be getting somewhere, to be expected since there must be survival value in abandoning dead ends and fatal courses of action.
Feynman: 'One crucial feature of the quantum theory is that the massless spin 2 graviton has just two helicity states. Thus the classical gravitational field must have only two dynamical degrees of freedom. However, the classical field that corresponds to a spin-2 particle is a symmetric tensor hmn with ten components. Actually four of these components ... are non-dynamical constrained variables, to we are left with six
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dynamical components hij to describe the two helicity states. . . .
'To resolve this counting mismatch, it is necessary for the theory to incorporate a redundancy, so that many different classical field configurations describe the same physical state. In other words it must be a gauge theory. For the massless spin-2 field the requisite gauge principle can be shown to be general covariance, which leads to Einstein's theory.'
SPINOR FIELD = MESSAGE FIELD
The message field is mapped out onto fourspace in a manner similar to the physical internet, the difference being that continuum field theory considers the sources and sinks to be dense in spacetime, meaning that the ball around any source intersects the ball around art least one other source. This described the connection between the network and spacetime, but it says nothing about the meaning and volume of traffic on the network, which is the feature which determines the 'shape' of space.
In short what?
Social (network) and geometric (continuum) pictures map only at the cardinal level, and are generally covariant (Einstein gauge sense) in the ordinal domain (ie we cannot generalize much, but have to get down to cases, this action, this planet, etc)
Laws are binding where general covariance (which
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can be understood as the superposition of all possible mappings) is cut down to some fixed mapping by bonding or binding of elements to make a structure or machine that explains some behaviour, ie input / output relationship for an independent element of the Universe (ie closed system)).
Geometry and quantum field theory; geometry and network theory; network theory and quantum field theory. Our triangle Hatfield in Feynman page xxxii.
What is the network principle of equivalence?
Gravity is equivalent to acceleration via force
Attraction / repulsion = correlation - communication.
Relate force, time delay, computation, computational power, bandwidth, communication rate, energy.
The weakness of gravitation shows how weakly energy couples to energy, ie how rarely. Yet energy densities are often so great that gravitation swamps al other forces. Planck density, black hole, breakdown, the Universe of creation.
Communication creates: the exponential structure of ordered sets means that small gains in definition [at the alphabetic level] can be the foundation for exponentially faster communication, ie more frequent communication.
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Hatfield xxxii: 'Feynman certainly felt that the geometrical interpretation of "marvellous" but the fact that a massless spin-2 field could be interpreted as a metric was simply a 'coincidence' that "might be understood as representing some kind of gauge invariance'.
Nakahara page 10; 'The gauge principle -- physics should not depend on how we describe it -- is in harmony with the principle of general relativity.' Nakahara
Hatfield xxxiii: 'In quantum field theory of point particles, the force between two particles is mediated by the exchange of virtual (or off-shell) particles coupling to r interacting with the particles that [feel] the force.
'The charge associated with gravity is mass which we expect from special relativity to be equivalent to energy. Sine everything we know has energy, it appears that gravity should couple to everything. The particle that mediates the gravitational force is called the graviton. Since a graviton has energy, gravitons can directly interact with eachother.'
What does a Universe of gravitons look like? [the nearest we can get to empty space?]
'We must recover F = Gm1m2 / r2 by the exchange of a graviton between particles 1 and 2 separated by r in the appropriate limit.'
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Equivalence <--> Gauge invariance
Hatfield page xxxviii 'One way to get improved ultraviolet behaviour is to have more symmetry built into the theory. Thus extensions or modifications to general relativity to improve the quantum behaviour generally are based on additional symmetries. One popular approach is called 'supergravity' . . . . It is based on a symmetry between bosonic and fermionic fields called 'supersymmetry'. When a supersymmetric theory is gauged so that the supersymmetry becomes local (a different supersymmetry transformation is allowed at each point in space-time) the gauge invariance necessarily incorporates the Principle of General Covariance and therefore gravity.'
All messages are the same to gravity. Encode it how you like, gravity only sees the cardinal of the encoding.
The gravitational coupling constant is the proportion of the energy in the cosmic network which is devoted to shaping the network. All the rest of the energy is other traffic on the network shaped by gravitation, ie the physical Universe as we see it, since classical gravitation is a geometric theory that maps readily to geometric space-time.
At the top level of the network all the available symmetries are gone and we are left with the detail of the real which although made meaningful by its history is statistically indistinguishable from noise. As we bore down into the network, however, new symmetries are introduced at each layer until we arrive at the 'totally symmetrical' initial singularity,
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The existing theory, as long as it is in favour, is used for electing and testing applications, and any new development is first tested for consistency with the existing theory before we go to the expense of an experimental or observational test. If we find that it is impossible to extend the old theory to cover a new case which it should be able to explain if it was any good, the time has come to get a new theory. We seem to be in this case with quantum field theory and gravitation. Feynman Gravitation.
Locomotion is somehow not motion, ie not change. Change enters when we consider acceleration which increases the energy (communication rate) of the accelerated body.
Wednesday 19 March 2008
A possible consequence of the large scale adoption of biofuels is that we all turn vegetarian.
The global network is partitioned into subnets by light cones that determine who can and cannot talk to whom, and how long someone will have to wait for a reply when communicating with a distant correspondent. It is no different from the days of letters and sailing ships.
Fourier transform is an encoding which operates between the particle and field representations of the world.
Trying to see the big picture. What is the central message of field theory? Its complicated but it works. There is no central message? The messages are (Fourier) transforms
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of the structure?
Preoccupation with the bomb may seem a little dated now to those whose lived through the worst moments of Cold War and Mutual Assured Destruction. Now we worry about rogue states that might take out a city or two, but the arsenal that can blacken the planet still exists, still ion the control of some semi-psychotic dealers in naked power. Until we get rid of all the bombs 'legitimate' and 'terrorist' we cannot be safe. But we cannot get rid of the bombs until we get rid of all the fears that move us to pay for the. It is erroneous reductionism to blame the wars on the weapons. The wars arise because people fear for their survival, seek preemptive insurance against real or imagine threats to their existence.
Zee page 10: '< q | p > = ei q p . . . . This just says that the momentum eigenstate is a plane wave in the coordinate representation.'
And the geometrical world is the superposition of an infinity of 3D plane waves. Fourier transform this and we get a world of particles being created and annihilated. As we would like to say, a world of messages being transmitted and received.
The main property of a field is that it is local. Veltman page 25. Veltman As with a network, no message is transmitted or received from outside the light cone of the transmitter or receiver. What this might mean is that you can only speak a certain language and get no messages transmitted in other language. Gravity, like God, sees, hears and influences everything.
COMMUTATE = NOT COMMUNICATE WITH (COMMUTATOR = 0)
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'If a system is in a state |c >, then the probability of observing the state | a > [given |c > = alpha | a > + beta |b >] is |<a |c >| 2. This is the fundamental connection between Hilbert space and physical measurements.' Veltman page 30
I have shown a certain resistance to quantum field theory to keep my mind open to the network alternative., but now I am ready to pick the good bits out of quantum field theory and fit them into the network.
The real problem with Christianity is not that it is wrong but that it should maintain that an arbitrary story which bears no particular relationship to reality be enforces as the only acceptable interpretation of our world. One one side we have an ancient book and some (extremely well established) vested interests, on the other the whole world (if we could but see it).
Zee: This fundamental result tells is that to obtain < qfinal | e-i hut | qinitial > we simply integrate over all the paths q(t) such that q(0) = qinitial and q(T) = qfinal .
Very simple. And because exp (-iHT) is periodical many paths cancel to yield something like the classical path. But what really happens? Is the path integral a form of natural selection?
Feynman page 29: 'In the first place, the fact that gravity is found to have a long range automatically means that the interaction energy depends on the separation as 1 / r. There is no other
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possibility in a field theory'. See Zee page 26.
[equation energy integral for inverse squared force.]
Feynman page 32: Propagators connect currents.
Thursday 20 March 2008
Basic idea of field theory: everything is possible except those things rules out by mutual inconsistency: the path integral approach to everything, where inconsistency is represented arithmetically or by measure (integral) rather than logically. This is consistent with the idea that the physical layer is meaningless (has no intrinsic order [is just a count]) and it is up to higher layers to establish order as a condition of their existence - you cannot exist if you [together with your history] have not figured out how to exist.
Infinities are avoided in this scheme because the expectation value of integral exp (-ix) do is zero. It remains in effect zero in the path integral method but one path gets picked out where the infinity of path actually add up to something. Feynman QED and the little arrows. This may be the fundamental form of 'natural' selection.
Good software must deal with every case, or at least 'almost all'. This means that it must not 'hang up' by finding itself in an endless loop which it cannot break out of. Every such infinite loop is an error and must be caught before it gets started or a way found to diagnose its existence and interrupt it. We may think of isolated quantum systems
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as closed loops with a given frequency. It is when these loops are interrupted that we have communication, the 'word' that brought about the interrupt and the word that was returned by the interrupted system, where by word we mean any ordered set of one or more symbols.
To go forever, given the energy, the software must be able to recover from all possible errors, which it does by backing off to higher energy scales where the particles are effectively indifferent to the use being made of them by a higher layer. If a layer develops a loop or contradiction in itself, this will not be apparent to the layer below it but creates a problem for the layer above it which needs its services. Every layer has a vested interest in maintaining control of its relative hardware layer. So I decay back to atoms and small molecules, hard things which know very little of my life, only themselves.
There can be no error without control because without control every state is acceptable. Control partitions every complete set of states into desired states and not desired states, perhaps separated by a no-man's-land of indifference.
Path integral method shoes us control by integrating over a complete set of states to arrive at am amplitude for a given state (a given transition). . . .
What does a 'conservative field' (non-dissipative) like gravitation mean? Conservation of energy. What is
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the mechanism of conservation of energy? Arithmetic / logic / periodicity.
It remains a defect in modern theory that there is such a gulf between the classical and quantum regimes. The network theory would like to bridge this gap by establishing logical continuity rather than topological continuity as the only form of argument sufficiently complex to grasp the complexity of the whole.
From a network / bandwidth point of view we see resolution mapped onto space and time, the minimum pixel being a quantum of action, ie qixel. A quantum can be represented in spacetime by energy and momentum operators, but quanta also occupy the much more complex local Hilbert space, e the Hilbert space corresponding to (part of) the interior of a light cone.
This is the aim of the physical section of this site to understand quantum field theory in terms of communication, bringing our social (network) intuition to bear in preference to our geometrical intuition. It is true that all real communication networks exist in 4D space, but this is of negligible importance in te actual functioning of networks, where computational intensity (energy, mass) gives us a good idea of what is going on, the though behind the messages, encoding and decoding ideas in new alphabets drawn from art and mathematics.
So while space is metrically pretty homogeneous, most masses binding it but little, the energy that makes that mass is subdivided into a vast network of channels of action
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whose details are the life of the Universe, but whose symmetries are the stuff of physics. All hydrogen atoms are the same and yet we can say that at any one moment each one is playing a unique role in the life of the Universe. That we can measure these rates statistically does not detract from their uniqueness.
Quantum field theory integrates over the uniqueness, smearing it out into a statistical distribution.
Phase is the affine parameter of the quantum Universe. Relative phase is observable. Phase is monotonically increasing, continuous and unobservable. Superposing all the phases in the Universe, however, yields observable concentrations of energy,
ENERGY IS VERY FINELY DIVIDED INTO PARTICLES
Quantum field theory accepts space as something with a Minkowski metric, but expects trouble at the Planck length, when particles retreat inside their Schwartzchild radii and communicate only by gravitation. So some expect to find the quantum theory of gravitation on the other side of the 'Planck barrier' (event horizon).
Current - amplitude - probability.
Friday 21 March 2008
Good Friday. - the day (in my old religion) on which we remember (in LITURGY) that the creatures killed
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their God, the Son of their Creator, but he came alive again a few days later. We may take this as the dramatic (human social) expression of an idea that we would today like to capture in abstract symbolic language.
From a scientific point of view, we are looking at a retrospective expression of a paradigm change seen from the perspective of the new paradigm which eventually came to be called Christianity. If we see Christianity as a result of the 'symmetrizing' effect of Roman imperial conquest that threw people together who would never have met otherwise and made it necessary for people broaden their horizons on humanity, language, behaviour etc. This was seen by Augustine as a New City of God, something wonderful, a miracle in fact, a Heaven at the end of this life of considerable difficulty. An idea that has served as a goal ever since, to live without turning a finger.
Since each life has inherent in its structure a modicum of processing (a quantum of action) to keep itself alive, some can live without effort only by imposing the requisite effort on other, either by violence (slavery) or spending an inheritance or becoming wealthy by one's own efforts, thus earning an effortless retirement. This is part of my dream, to bring in enough revenue to live on the internet.
PEERAGE = we all do a fair share of the work and get a fair share of the reward.
The hardship associated with natural religion is learning to respect the world, as Christianity taught us to love one another,
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to treat all people as peers (a prescription heavily modified by the practical politics of survival, ie war), so natural religion is based on the complete implementation of human peerage (symmetry) so as to tackle the question of universal or environmental peerage. Protons and us are equally real although playing very different roles in the social network.
Social network implies peer trade in all available forms and regulations to balance the load on people and their share of the common goods.
One consequence of human symmetry is that life is beyond value (or at least life can only be valued in terms of life) so that we will go to extremes to save a life whether it be a accident victim or a lost yachtie.
Biology applies universally in that it is the study of the process of creating life both phylo- and onto-genetically. We say physics establishes the conditions for evolution and after that all is biology, including mathematical physics as practised socially.
Karl said 'From each according to his (sic?) abilities, to each according to his needs'. This is open to the elitist interpretation favoured by some Party members who consider that their abilities and needs are especially great. So we need to impose human symmetry on this statement,
Zee page 17: 'The modern view, which I will call Landau-Ginzberg, is that we start with the desired symmetry, say Lorentz invariance if we want to do particle physics, decide
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on the fields we want by specifying how they transforms under the symmetry . . . and then write down the action involving no more than two time derivatives (because we don't know how to quantize actions with more than two time derivatives).'
Say this in network:
1. The symmetry tells us who are the users who obey the protocol associated with the symmetry, ie all HTTP servers and clients. So Lorentz invariance = {everybody communicating at the velocity of light}
2. Field = language = space of all possible messages. The same message may be transformed into many different linguistic representations (Einstein's general covariance). The complexity of the operators working these transformations is symbolically unbounded. One realization is the human mind capable of translating ideas between human languages.
3. The action related to the processing required to perform transformations. The action is the time integral of the Lagrangian. The Lagrangian at any moment is kinetic energy - potential energy. Both these quantities are relative to some zero, so we can adjust them so the : = 0 at any moment. So what s energy? Simply the frequency of action.
FREQUENCY - VELOCITY
PERIOD = 1/ENERGY.
Proofs via continuity are logically correct when we advert to the fundamental property of the continuum. It is fully symmetric -
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nothing changes as we move through it so that we cannot tell that we are moving through it : it is an (the?) inertial frame. We do not know we are moving until we experience a potential and we cannot experience a potential unless we have two fields, one pulling us off the geodesic defined by the other, eg gravitation and the quantum forces that keep the earth and our bodies together.
The rules of arithmetic are well defined so that we can do arithmetic without knowing what it means. The mapping between arithmetic and unites of value (accountancy) is probably the first and greatest scientific discovery ever made, since it underlies all the other like physics where we account for particles, currents of particles, amplitudes etc etc.
Feynman Gravitation page 66: 'If we compare the differential equations of particles in electric and gravitational fields we find that the gravitational equation has a qualitatively distinct new feature: not only the gradients, but also the potentials themselves appear in the equations of motion.'
Because the potentials are energy, and gravity couples to energy.
Feynman page 67: 'This would seem to say that the effect of a constant potential is like a change in the scale of time to make physical processes run more slowly in regions of lower gravitational potential.
So (maybe) clock rate of initial singularity = 0, or at Schwartzchild radius and on in.
Acceleration is a local phenomenon. We can feel it (in the interaction of my bottom and my support).
I 'know where I am' by local interactions, so when
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there are none (free fall) I do not know where I am: fixed momentum, infinite space dp dx = h bar.
Feynman page 71: 'In a vacuum, two equal photons heading toward one another do nothing special until the wavelength is less than 2 pi 3.68 x 10-11 cm when pairs of electrons can be produced. How do the photons 'know' what their wavelength is in absolute units into decide whether to make pairs? Each volume of space must contain a natural measure of space (or time).'
page 72: 'We therefore suppose that the natural scale of time -- the size of h bar / mc2 (or any other combination for other fundamental particles - we suppose that are all proportional to some unit of length) -- is determined by the distant nebulae.'
'Mach's principle is equivalent to the statement that the fundamental units of length and time at a point are the result of the influence of the nebulae.
page 68: 'Gravitational potentials are negative so clocks [go slower] as they come nearer to a massive object such as a star . . . the man on top of the mountain is living and aging faster and we see him moving faster.'
'The clocks which run more slowly in this case are the nuclear mechanisms which produce photons at definite frequencies.
page 75: '. . . another example of a rule of thumb about theories of physics: theories not coming from some kind of variational principle, such as least action, may be expected to eventually led to trouble and inconsistencies.
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Evolution by natural selection naturally eliminates inconsistencies because the inconsistent ones are dead.
Feynman page 81: 'There is apparently no successful theory which is not derivable from a variational principle which starts from a Lagrangian or Hamiltonian functional (which are equivalent).
'It is not certain whether the failures of non-Lagrangian theories reflect some fundamental truth about nature.' Evolution again. 'It is possible that the fundamental truth may be that processes occur according to principle of minimum phase, and that the actions of classical physics or quantum physics are expressions of this phase which are correct to some approximation.
Time = phase is of the essence in a survival context, where may explain the importance of energy.
Action - Lagrangian integrated over time while survival says minimize, or perhaps make stationary (keeping the status quo rather than evolving).
EVOLUTION = ACCELERATION (Selective pressure = selective force per unit 'area').
Gravity automatically generates complexity by coupling to itself. This is similar to the self-reference problem (sets not members of themselves) in logic.
page 87: 'Einstein himself, of course, arrived at the same Lagrangian but without the help of a developed field theory, and I must admit that I have no idea how he
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ever guessed the final result -- but I feel as though he has done it while swimming underwater blindfolded and with his hands tied behind his back.'
Feynman page 89: 'One feels that the idea uppermost in Einstein's mind as he developed his theories was that all branches of physics need to be consistent.'
page 90: Weightlessness is satellites, which is a cancellation of gravitational forces by acceleration.
TURING MACHINE = fully constrained transformation.
The gauge is orthogonal to realty and so does not have observable consequences.
Gravitation = selective pressure.
page 91: Newton (F(action) - -F(reaction).
page 92: '
we can get rid of gravity at any one point and at any one time
'By considering the transformations, eg (7.1.3) over infinitesimal regions, we expect to learn how to describe the situation in differential forms; only then shall we worry about boundary conditions, or the description of gravity over large regions of space.'
page 96: 'We see that the requirement that proper times should be a maximum is equivalent to the principle of least action in the
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classical limit.
page 97: Constructing the invariant interval, the basic symbol, the proper time
page 99: 'The central idea is that since matter is physical, whereas coordinate systems are not, matter must be described such a way that the results of solving the equations of motion are independent of the particular choice of coordinates.'
The network model does not need coordinates because each act of communication is specified in terms of its two sources.
page 115: Gravity is that field which corresponds to gauge invariance with respect to displacement transformations.
Saturday 22 March 2008
Feynman page 136: 'Proper time is a scalar invariant'. The backbone of the Universe to which we refer all life from birth to death.
I have spent 40 years struggling with the proposition 'the Universe is divine' to convince myself that it is true and that in my religious tradition (Order of Preachers) I can begin to preach it not as an arbitrary administrative decision (and death to those who disagree) but as 'J's theory of Divinity' analogous to 'Einstein's theory of Relativity'. Don't want to get too personal, because this is (in its
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own mind) the fundamental symmetry from which all else can be seen to arise. The Universe is divine; divine creates; therefore the Universe creates. Why? We can only talk about this formally, picking out fixed points in the dynamics like Cantor's theorem which, given certain axioms. ordains continuous formal creation. By creation we mean the evolution of more and more structure, or, in general, space. A space is what we have left when we abstract from the details of its points and just consider how they interact, make love, annihilate, whatever.
space = {points, protocols}
Does preaching begin with Capitalized Terms? I am still inclined to avoid capitals but seem to have been using them lately. But let God be the name of the traditional god and god be the natural god, whose total symmetry (and so commonality) is represented by small g.
Perhaps more to the point, preaching brings in artistic considerations of the kind familiar to advertising agencies trying to give the product an aura of very human desirability. So we reach back into the past to find the forces that shape our desires. In the evolutionary picture, all these desires are for the food, leading the balanced desirer toward survival. This picture diverges
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sharply from many religious tendencies which see desire as something to be controlled, repressed and even killed.
So we develop a cybernetic theory of desire and the errors than can invade a system of desire, particularly by 'going too far', having sex with children, consuming absurdly large amounts of materials mined from the earth and so on. As Aristotle notes, we seek the mean, and we can use control theory to search for a consistent set of means that guarantee adequate material life with sustainable global consumption. The general problem arises because we evolved in a space where almost every resource was limited to that there was no need to set an upper limit when everybody's eyes were on the lower limit. We have to impose upper limits on ourselves of eventually it will be imposed upon us in a manner not of our choosing.
Preaching: I have made my initial solar feelings into a religion of poverty, chastity and obedience. In each case these are given operative definitions: poverty = don't consume too much; chastity = don't produce too many offspring; obedience = look to the divine structure and behave accordingly. Love your neighbour, treat as you would be treated, etc.
For me the blackest part of Christianity was the suppression rather than the channeling of my desires. I still fear pleasure in some way because once it was sinful and self abegnation was the go. Am over it theoretically and trying [not] to pass it on to the next generation while using the discrepancies between my former self and my new ideal as sources of comment which might echo in other minds.
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Do I address the reader in these books? No. They are a log, noting features of the journey.
We see gravity a a network of gravitons. All nodes are identical in this network, since gravitons see only energy. They also carry energy, so they see themselves and so form a network with only gravitons for nodes? Gravitons, since they see only energy look just like energy to eachother, and so we are led to the view that the general theory is a set of mathematical constraints on the spacetime distribution of energy and, in the network view, of the framework of the universal network.
We have modelled pure energy as a closed or isolated quantum system whose Hamiltonian is unknown precisely because it is unobserved. From a Platonic or formal point of view, we consider it to be a transfinite function space. Now we let different isolated systems of pure energy communicate in the only way they can, by exchanging energy. What differentiates them? Look to the Trinity and the network for a plausible formal explanation. Spacetime then becomes the symmetry necessary for consistent exchange of energy, three dimensions to avoid conflict and one (of time) to sequence the messages. The fundamental tautology is that insofar as the Universe is complex, it is structured. The ancient model of God did not comprehend this so we are left with a point that carried no representation of its own details, the 'omnino simplex' model of god. Aquinas 20 Formally god is complex (ie in the messages that we see) dynamically it is one. The formal fixed points are not outside the dynamics, but communicable parts of it which serve both as expressions of and constraints on the dynamics.
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Personally the crucial thing is to enjoy the realities and responsibilities of divinity. A party of one which, like a boson state, wants to attract another and another until the human race gets to something like a superfluid state where our interactions are frictionless.
So the theory of gravitation asks nothing about the details of the energy, only its quantity. This level of communication does not communicate any information except a count and so cannot go wrong or need coding like more complex messages. The gravitational structure of the Universe evolves out of an isolated quantum system.
Climate change (and all other global changes) are natural religious problems because we are all in it, although some would like to use their wealth to opt out and transfer the load to others.
Feynman page 137: 'the general expression for the invariant volume element is square root -g d4x' because the metric tensor is symmetric and so can be rotated into diagonal form.'
From the geometric view of gravitation, the world is made up of infinitesimals like the invariant volume element which serve as fixed points in the relevant universal set.
Why is space four dimensional? Because this is the smallest space that is 'source free' so all is flow. To be source free is to be topologically periodic. In a sense source free means every point is a source and a sink, the first
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appearance of quantum structure. More prosaically, 3D space enables us to join every pair of points without crossed wires.
Gravitation is purely Platonic - formal because we can only observe the formal (fixed) points of the Universe And so on at every level of complexity.
Gravitation is a generally covariant network protocol meaning any points can communicate with any other at any time without interfering with the communication between other pairs of points.
Ie gravitation is the interference free background for quantum interference.
Feynman page 137: 'The quantity square root -g is a scalar density' ie the 'weight' of a point.
'The proofs that we offer are not rigorous, we don't bother with rigor because it is the facts that matter and not the proofs. Physics can progress without the proofs, but we can't go on without the facts. The proofs are useful in that they are good exercises; if the facts are right, then the proofs are a matter of playing round with the algebra correctly.'
ie programming the Turing machine that will execute the proof.
SOURCE = DIVERGENCE
pager 139: 'Thus we see that the invariance of an action results in the construction of a tensor density which is automatically divergenceless. No source, no sink, no communication, or, all communication via logical
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confinement. Continuous confinement = the set of properties that define a quantity (variable) (measurable) as continuous.
So we see 3D bundles of wires appearing and disappearing all the time as different pairs are connected, like the telephone system (MTW) without the constraint that phone numbers map continuously onto the geometry. Misner, Thorne and Wheeler A sort of string (and two cans) theory. Spacetime is equivalent to the idea that the closer we are together, the more frequently we communicate.
Feynman page 143: '. . . In gravitation theory the conservation of energy and momentum hold, but this does not suffice to determine the motions of the planets and the moon, for they are not points, and laws of physics other than the conservation of energy are required to elucidate their behaviour in a gravitational field.'
The layered approach sees more complex systems as users of the less complex. Gravity, by its universality, seems to be the least complex structure possible, one that allows for a closed frictionless sourceless flow such as Heracleitus would have loved. The rest of the Universe is built on this flow.
dy / dx is a formal bearing, measuring how x slides over y.
Gravitons see only energy, so why is their particle, spin-2 graviton, so complex. Perhaps this is because gravitons, which in the wild state are simply structureless quanta of energy, become more detailed when placed in 4-space where the
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communication protocol is shaped by quantum mechanics.
Gravitation sees energy simpliciter. Quantum mechanics only sees energy differences, ie between members of a set of states described by a Hamiltonian.
Integration and differentiation of a flow give us total volume and rate of slow which are both conserved if we find the right way to measure them.
Equation of state relates pressure and density, p = f(rho). Can we write an equation of state for human populations, and see how social changes affect the equation. One such change is to put people in rooms so that the number of individual people per unit volume can be increased (the density) without increasing the pressure (the stress felt by an individual, liquefaction, solidification.
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