Notes
[Sunday 8 March 2009 - Saturday 14 March 2009]
[Notebook: DB 66 Turing Field]
[page 1]
Sunday 8 March 2009
Veltman page 38: 'A vector in Hilbert space has no time dependence, but like a movie in a can, all action is contained in that state. In that sense the S matrix is like a cross index register, showing the relation between the two labelling systems [at T-infinity and T+infinity ]. Given
[page 2]
the beginning scene of a movie, the S matrix tells is what the final scene is.'
Assuming that the evolution of the S is deterministic ie that there are no intermediate measurements.
Veltman page 39: Interpolating fields are related to currents, and we interpret a current as a process. [currents flow through Turing machines]
Our heuristic assumption is that embryonic Universes are simpler that grown up ones, and we use the Cantor symmetry to carry us along the universal lifeline ('generalized geodesic').
'Basically all this [theory of interpolating fields] is all just one big assumption. The system is really very complicated even for the simplest cases, as we will see. Only for those simple cases can the . . . equations be solved, and even then only in terms of successive iterations (perturbation theory). Thus the scheme developed below is to a large extent simply determined by the requirement that we can solve it.'
The natural point of coupling between quantum field theory and Turing field theory [is Feynman diagrams].
Veltman page 48: The action of a field is either to start or end a line in a Feynman diagram where the lines represent particles: creation and annihilation. The interaction Hamiltonian density operator script H starts or ends the lines meeting at a vertex.
[page 3]
Veltman page 54 Feynman propagator.
'We can literally say that if the time y0 > y0' then the Feynman propagator represents a physical particles moving from spacetime point y' to space-time point y. In fact the exponential is nothing else but the wave function for a plane wave for a particle leaving y' multiplied by the wave function for a particle of the same mass and momentum arriving at y. This product is the overlap of these functions, something that relates to the probability for this to happen.'
Veltman page 69: 'The fields are operators, that is matrices in Hilbert space.'
Matrices may represent logical operations, as in quantum computation. It seems logical to assume that the whole world is run by quantum computation which seems ultimately isomorphic to Turing computation. To go from the quantum field theoretic world to the Turing field theoretic world we need a little dictionary.
particle: output of a halted Turing machine, ie a completed computation.
We postulate that the observable world operates within the Turing bound.
We have something like the Turing bound on predictable behaviour. Beyond the bound there is not sufficient bandwidth to track reality any more closely. A dynamical version of requisite variety = requisite bandwidth.
Bandwidth is the physical substrate for survival.
[page 4]
The complexity of a Turing field depends on how much memory is available. The world needs a certain amount of space (our footprint) to remember each of us.
Veltman page 70: 'In general what we have is that under a Lorentz transformation two thing happen: first one transforms from one momentum to some other, and secondly spin states are rotated into each other.'
page 71: '. . . spin 1/2 particles with mass.
'With respect to fields, one imagines this as follows. A particle with four states is really nothing else but four different particles, and the fact that a Lorentz transformation may turn one into another [make one look line another] is another matter. Correspondingly, there will be four fields to corresponding to these four particles. Lorentz transformations transform these fields into each other. We are concentrating on the transformation of these fields.'
Veltman page 84: 'The physically important quantities, however, are not the fields but the interaction Hamiltonians. These determine the outcome of physically measurable processes. '
Monday 9 March 2009
Veltman page 68: '4, Particles with Spin'
Back to Lorentz transformations and Hilbert Space.
'Corresponding to [a] Lorentz transformation there will be
[page 5]
a transformation U in Hilbert space such that U applied to a vector corresponding to a state with one (or more) particles with momentum p is transformed into a vector corresponding to a state with one (or more) particles with momentum p' :
This still seems wrong. Lorentz transformations do not change anything local, they merely specify how one reference frame looks from another in relative motion, and the laws of physics, (including what goes on in Hilbert spaces) are not coupled to relative motion.
'With proper normalization, in the limit of infinite volume U [for scalar particles] is unitary, that is U dagger = U -1. However, while U is unitary it is not really like a rotation.' Since a succession of Lorentz transformations from rest do not bring us back to rest.
Veltman page 69: 'It is a know fact in group theory that the unitary representations of non-compact groups are of infinite dimension, what is what we have with U here.'
With the advent of quantum computation theory we may think of quantum mechanics as logic, operating in logical space prior to physical space.
Space-time is an abstract representation of the logical processes that underlie the Universe. In other words there are many more logical processes (implements by the transfinite symmetric network outlined above [Physics] than there are points in spacetime, which are events (the transmission of a message).
[page 6]
We model the interior of the initial singularity. Let us say that this interior begins as a perfect continuum, a perfectly featureless space in which all points, insofar as they can be identified, are in some way identical. Here we come up against the basic conundrum of identity (meaning sameness) and identity (meaning individuality). This works like the uncertainty principle and the actual state of the whole population can be modelled as a superposition running from 'one people' to 'a dust of individuals.'
The expansionist creative process in the Universe is a loop that leads through addressing precision to increasing memory size to increased addressing precision, to the quantum limit.
Steane N 399:124 13 May 1999 Steane
'Quantum computers are based on the controlled manipulation of entangled quantum states, which are extremely sensitive to noise and imprecision. Active correction of errors must therefore be implemented without causing loss of coherence.
Quantum mechanics lies at the boundary of the primordial continuum and the expanding discretum, that is the entropy of memory.
Information flows like water, the unit is the bit. And this flow is a stream of action (ie energy) flowing between different parts of the Universe. But the big question now is how do we get from the n fundamental particles driven from outside spacetime to the thing we see now, space-time and all. We fall back on the old idea, that 3D space is
[page 7]
the smallest space in which we can connect every point without crossing. [ie it is the smallest space in which coherence can be maintained?]
Our notions of coding and decoding tell us that that we can say the same thing in many different languages as well as many different things in one language.
The first axioms of quantum mechanics describe the interior of the initial singularity.
Insofar as the statistics of a quantum source are stationary, we imagine that the past is not influencing the future, or perhaps, because the messages appear random, having the greatest possible effect on the future by maximizing past/future bandwidth.
Steane page 124: 'Here I report a general technique for circumventing the trade off between the achieved noise tolerance and the scale up in computer size that is required to realize the error correction. I adapt the recovery operation (the process by which noise is suppressed through error detection and correction) to simultaneously correct errors and perform a useful measurement that drives the computation.'
'However, these methods [cited] are not in themselves sufficient, because the greater complexity of the operations lowers the error tolerance, offsetting the gain in coding efficiency.'
Tuesday 10 March 2009
The books all tell us that quantum field theory is concerned with the creation and annihilation of particles because special relativity equates mass and energy, and the uncertainty principle relates energy uncertainty and time so that a particle of mass m may exist ('virtually') for approximately t = h/mc2 seconds.
The argument leading to mc2 derives from the Lorentz invariance which itself is a consequence of the fixed finite velocity of light for all observers.
We design things going from the general to the specific. Every designed object is in effect a transformer that changes physical states. So the function of a shelter is to transform extremes of natural climate into a gentle draft free warmth. By further developing a shelter into a home, we add more and more tools to simplify and enrich life, like hot and cold running water, cooking equipment, sleeping and entertainment arrangements and so on. Le Corbusier - Wikipedia So the design of a house begins with a long list of requirements related to our needs and behaviours and is gradually refined until we can begin construction with a clear idea of the order and shape of proceedings.
My theological project is very closely related to my building projects, and it seemed to have reached the point where the general ideas are settled and now we can begin [to go] through the details one by one in a logical manner defined by the overall picture and myriad measurements and calculations and specific dimensions modelling it so it will all
[page 9]
fit together. In general we begin with the infinite, continuous ad completely featureless system described by the first three postulates of quantum mechanics. Quantum mechanics Then we show how structure develops in such a system when we impose the constraints of communication. Zurek The constraints of communication are embodied in quantum mechanics. The interior of the initial singularity is like a whiteout in free fall.
QUANTUM MECHANICS is isomorphic to FORMALLY REALIZED NETWORK.
Quantum mechanics lies at the most abstract level of the Universe, a theory of theory. And our basic assumption is that insofar as it is formal, this system is totally mathematically static and therefore it represents the fixed points in the universal flow of action. A major design feature here is that the 'velocity of light' in pure formalism is infinite (and we take formalism seriously as a reality). What I am doing now, embodying formalism for transmission to you, is real, and the ideas are as real as the ink and paper. To say that the velocity of light is infinite is to say that space does not exist.
Now we want to make the transition from formal system, in which all states are equal, to a dynamic system where some states are attractive, some repulsive and maybe none completely neutral, for everywhere we go there is gravitation.
Dynamics introduces relativity and causality. We can only see movement if we have distinct objects in relative motion. There is no perceptible movement in a whiteout.
[page 10]
Self awareness brought on by sheltering from the weather. One lovely phrase like 'Turing field' or 'whiteout in free fall' every few days is good going.
Feynman I 15-1: 'Newton's Second Law, which we have expressed by the equation F d(mv) / dt was stated with the tacit assumption that m is a constant, but we know now that this is not true, and that the mass of a body [appears to increase] increases with velocity. In Einstein's corrected formula
where the 'rest mass' m0 represents the mass of a body that is not moving . . .' . Feynman
'For those who want to learn just enough about it so that they can solve problems, that is all there is to the theory of relativity -- it just changes Newton's laws by introducing a correction factor for the mass.'
Mass seems to be the big conundrum in physics. Everyone hopes the LHC will find the Higgs system and so explain (to standard modellers) how massless particles become massive. Here is what I would like to say: mass is the manifestation of energy which is itself a measure of the time rate of flow of action in the system. We model the system as memory being changed by action. Assuming that it takes one quantum of action to change one unity of memory, the rate of memory change is E / h = nu units per second. Given
[page 11]
a system with cardinal complexity n, (ie a system of n memory units) will take n / nu seconds to change completely. So we introduce momentum.
Quantum mechanics itself is not dynamic. It is mathematics that happens to track the fundamental constraint imposed on the Universe by the fact that it is a deeply layered communication network.
Feynman 15-1 : Newtonian relativity: 'The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line', ie in an inertial frame.
An inertial frame, attached to a particle, has zero velocity relative to the particle and 'sees it as it is'. Observers in other particle frames see it differently, in other words particles see each other differently when they are in relative motion.
At stake is the whole of western theory, from theology to physics.
Wigner constructs a Universe by relative motion: Somewhere, Wigner. Wigner (page 70, Appendix I)
Dynamics introduces causality. We want to know why things move analogously to our own awareness of our own motivations.
Motion = change of space. Type of motion = type of change of space; geometrical; logical.
Right now we are trying to generate the observed 4-D Universe
[page 12]
with the logical model built from quantum mechanics but as yet outside space. Space comes with distinction of memory, communication, error and coding delay.
So for space we need two independent memory units; communication between them, symbolized by the pendulum. Two states two motions but an infinite spectrum of frequencies. No definite energy, no stationary states.
All we have to do is prove that quantum mechanics is an expression of the constraints placed on observed reality by the theories of communication and computation. How many times have I said this before? Search. But each time with more experience and conviction.
The proof: quantum information and quantum communication are universal, ie as powerful as the universal Turing machine, which is all we want. But this does not quite answer the question. Here we are dealing with a system which has gone from one dimension of time to one dimension of space and one dimension of time, ie it has 2-momentum (p0, p1 ) and a Lorentz transformation which implements energy/momentum conservation.
Momentum is a consequence of having memory which can only be changed by a force that motivates action, the result of a potential or desire to move. Momentum is the cardinal of change / energy is the cardinal of change. The cardinal remains the same when the pure energy Universe bifurcated into the energy - momentum Universe.
Feynman page 15-15 Poincare? A complete conspiracy is a law of nature.
[page 13]
There is no way to determine an absolute velocity.
Only relative velocity has meaning, a tautology since meaning <==> correspondence <==> twoness.
Computation sees 'inertial' mass. Mass is a pure scalar, and a feature of a system where action . time = energy has mass.
The quantum mechanical formalism (and its possible isomorph, communication theory) is the hardware of the Universe.
We might think of two dimensional space-time as two representations of the same data which are in some way superposed, and oscillating as we would expect in a Hilbert space one of whose dimensions represented space and the other time. So we have a space basis and a time basis, a parallel basis and a serial basis, so to speak.
Practically, space-time is a set of events. An event is relative to an observer, something that an observer sees that changes the state of the observer. So we need a set of observers corresponding to our set of observers, The orderings that exist among events and observers we call spacetime. These orderings are established by logic and communication.
Space is orthogonal to time: time moves without affecting space, which thus plays the role of memory. But this orthogonality is not relationship invariant. Instead we have the relationship
[page 14]
a Pythagorean thing defining an invariant interval which we might take to be equivalent to an integral number of quanta of action, an elaboration of ds 2 = dt 2 in one dimensional space, dt = h / dE..
Imaginary interval is spacelike; imaginary mass is momentum-like, real interval is timelike. real mass is energylike.
E 2 - p 2 =
m02 = E' 2 -
p' 2
t 2 - x 2 = s
2 = t' 2 - x' 2
Makes us think that mass is a squared interval between value of E and p or t and x. Since Lorentz transformations represent different relative velocities, they represent different energies and momenta, but both the interval s and the rest mass mo are relativistically invariant.
Feynman p 17-8: Minkowski: 'Space and time of itself will sink into mere shadows, and only a kind of union between them will survive,'
On the contrary space and time were just one thing which we call energy or flow of action, and then they bifurcated, giving us energy / momentum and space / time as a later stage in the generation of the Universe.
Space is the world of memory and wiring that forms the durable hardware of the world and so we are inclined to think of space as prior to time, insofar as memory shapes
[page 15]
activity. But also vice versa. Space and time go together like momentum and energy, or potential and kinetic energy. For massless particles, E = +-p, since E 2 = p 2.
The eternal god imagined by Parmenides and Plato is to us the world of formalism. Physics deals with dynamic formalism where the rules of formalism are applied to formalism itself (as Gödel, Turing and Shannon have) giving us certain dynamic limitation which, we hope, describe the world as we know it.
Reading Veltman (or any other field theory book) it seems to be too complicated to be true, and the source of the complexity seems to be the effort to make the particles Lorentz invariant by making the fields Lorentz invariant. My preference would be to let the quantum mechanics be local, separate spaces communicating by the exchange of particles outside geometric space, and only the particles appearing in space be Lorentz invariant, all this done with real numbers. But how to make it work? First we need to draw a network diagram of all the known fundamental particles.
Is there any hope for this program, constructing the Universe from first principles'? There is if the current baroque complexity of the particle zoo is a pretty late stage in the development of the Universe, representing a complex low energy manifestation of high energy foundations. On the other hand, from a computer software point of view the energy (ie rate) of a process makes no intrinsic difference, only completes the processes more quickly. How does this fit in with the apparently different energy scales of the Universe?
[page 16]
Wednesday 11 March 2009
Rain and despair. But of course the Turing field model has no shortage of complexity, and can easily embrace anything the Universe can come up with. We do not mind the complexity so much as the ad hocery that appears to be present in the standard model. What is needed here is a clear statement of the effect of applying the Lorentz transformations after the quantum mechanics and not before which is a (the) question of how to map the computing model onto 3D space. At present we do it with the continuous machinery of vectors and tensors and transformations in both Hilbert and real space.
The Minkowski metric gives us a way to get 'outside' real space, a wormhole into the space free logical space via the 'null vectors', the set of zero space-time intervals between events connected by massless particles like the emission and absorption of a photon. Insofar as the logical network operates masslessly at the velocity of light, it is 'outside' spacetime. Once we get to high enough energies, every particle, no matter how high its rest mass, is effectively travelling at c.
Energy has inertia. Gravitation couples to itself.
We feel potential. Its name is emotion, and like physical potentials, it moves particles coupled to it, and we are strongly coupled to emotion. Some of us like to think that we are also coupled to science and reason. Although these couplings, like gravity, might prevail in the long run they are very weak in everyday life, which tends to be just one thing after another
[page 17]
reacting to traffic, disgruntled children, personal issues and everything else under the sun from moment to moment dawn to dark. Not that it might not be fun, but life is rather unrelenting. Coupled to reality, we might say, through the medium of feeling.
Feelings are learnt. There are still a lot of people in the world whose lives are devoted to hacking up their enemies, although this seems rather pointless these days where there are so many other options available under the general head of negotiated peace and prosperity. And we assume that this is what fundamental particles are doing as well. Partitioning out the energy available in the ecosystem in a complex way that guarantees the survival of many species [and unfit particles have very short lifetimes, so that their integrated share of the communal energy is small].
The environent of the Universe is the interior of the initial singularity, that is god. In the evolution of the Universe each layer of development in the history of the Universe is hardware for the layer above it. And in a dynamic network, all the hardware layers in their logical, historical and temporal ordering are nevertheless part of the present, since every current communication is passes down to the lowest hardware layer for transmission.
So we need to layer the fundamental particles, to find what is prerequisite for what. [order U(1), SU(2), SU(3)]
We might think of the muon and the tau as processes that do the same job as the electron, but less efficiently [hence their short lifetimes and large masses]
Thursday 12 March 2009
[page 18]
The photon is a two dimensional object which we see in four dimensions, like a needle of zero diameter, and from the observer's point of view, zero length. It attributes are number (energy, frequency) and polarization).
This story starts about 40 years ago. Then, after studying philosophy and theology in Latin in a Catholic monastery, my eyes were opened by Bernard Lonergan's Insight. Lonergan Lonergan, following in the footsteps of Thomas Aquinas, tries to argue that the perfect God must be other than the visible world because the visible world is defective. In particular, it contains unintelligible data which he calls empirical residue. Since his understanding of the world seemed exactly wrong from a quantum mechanical point of view, it occurred to me very forcefully that there was no reason why God and the Universe should not be identical. I voiced this opinion, and was, or course, dismissed from the Order.
In the intervening time I have worked incessantly to study this position in detail after overcoming the revulsion from the world that has been drilled into me since birth as part of my Catholic faith.
My first breakthrough came in the realm of size: God is infinite, they say, the world is finite. Quantum mechanically, no. Quantum mechanics works in Hilbert space. You can make Hilbert space as infinite as you like it. It is the sort of space described by Georg Cantor's transfinite Universe. Cantor
[page 19]
started with the net of all the natural numbers, {0, 1, 2, . . . n . . . }. From this infinite set Cantor showed to to build an infinite hierarchy of even greater infinities. Hilbert was a mathematical prodigy of the early twentieth century, who seized on Cantor's ideas to develop 'Hilbert space'. He did it just in time for John von Neumann to find that this massively infinite space and the mathematics within it was just the language needed to make sense of quantum mechanics.
That was about 30 years ago. It got me so excited that I eventually made a set of radio program about it called A Theory of Peace. A Theory of Peace The cold war ended soon afterwards, but there was no response to the theory.
By the early nineties I was sufficiently convinced of my idea to use it for political purposes. This came in the form of a submission into an inquiry into the logging of NSW forests. The idea of the submission was that in a divine Universe we should treat the forests and all of nature as our own flesh and blood. When the matter came to court, of course, there was no mention of these theological matters, but much evidence about the value of the forest as a going concern and the need to think deeply (the precautionary principle) before we started destroying our own habitat. I still feel that the divinity of the Universe is the spiritual part of the 'green' movement. Ultimately a significant fraction of the disputed land has since become National Park.
The next step in the process was my growing feeling that quantum mechanics was a representation of a universal communication network. We are well into the internet era now, and most of us are practically if not theoretically aware of the behaviour of networks: everything from totally frustrating to divine.
The technicalities of networks are deep and wide and known to us intuitively since we are natural networkers endowed with the gift of language to communicate with all which speak the same tongue as ourselves. But the theory of networks allows an infinity of languages within the same paradigm. From the network point of view, the conversation between a proton and an electron in an atom is pretty much the same as the conversation between two people or two nations.
Or two Gods. Over the last few year I have realized that the ancients knew quite a lot about how the world worked precisely because of the deep analogies between human networks and all other networks.
Western Christianity began among the Hebrews of Palestine. They invented the One God who because the paradigm of the Christian God the Father. But Christianity, when it finally settled its belief system, found that God, while remaining 1 had split into three personalities, Father, Son and Holy Spirit. And Aquinas perfecting work of Augustine, explained how this could be. The Father reflecting upon Himself, bears the Son, and the love of the Father for the Son is the Holy Spirit.
[page 21]
A simple, powerful model, beautifully reflected in quantum mechanics. Quantum mechanics sees no need to limit God's personalities to three, however. In our quantum mechanical world we have an infinity of personalities, free and independent sources of action, like ourselves, all the other plants and animals, atoms, in fact every independent entity in the Universe, all engaged in the gigantic conversation we call god. This is just another example of the well known habit of mathematicians taking ideas from a few cases and ultimately proving theorems that apply to an infinity of cases.
So, at least in principle, we can see god everywhere in the world. Not always nice. One has only to read the Book of Job to see that this is nothing new. Job The old God could be a total bastard to his people, particularly when showing off to the devil. And the whole story is just made up anyway, like this story.
With a difference. The old theologies were made up by a ruling elite determined to keep their power. Since the ideas have minimal foundation in reality, they have to be preserved by fire and sword. But of the Universe is divine, every human experience is experience of the divinity, and we can build our own theology based on this facts, just as physics and biology have been built. No more popes and ayatollahs to push us around. And what's more, since god is one and the world is one all honest students will eventually come to the same theological and religious vision, the sine qua non in my book, for peace on earth.
[page 22]
Photon cannot be transformed to rest. Why? Because it, like the graviton (?) dates from an era when rest had no more meaning than motion, ie the space-time bifurcation has yet to become part of the software of the universal network. For photons, the Universe has no size. ds 2 = 0.
What is the difference between photon-photon coupling and gravitation?
The interpretation of a model requires the establishment of correspondences between elements of the model and elements of reality. So we say that E = h nu means that the energy we measure in a photon is a product of its frequency nu by Planck's constant h, things that can also be measured that is expressed by ratios of standard masses, lengths and times.
Perhaps photons existed before space but they do come in two sorts of opposite polarization. In space the polarization vector is parallel or anti parallel to the momentum vector, but before space comes to exist they have only energy say left handed and right handed, and once a photon is born with a given polarization it cannot be changed, ostensibly because it has no rest frame. From the beginning all photons travel at c in all inertial frames. Since electrons have rest frames they have some sort of space. Following the network paradigm, if electrons and positrons come after photons, the electrons must in some way use the photons as an ecosystem to maintain their own existence.
[page 23]
Not only does L Universe = T Universe - V Universe globally but we have the local requirement that the Lagrangian density script L = script T- script V most also be zero at every point, so that the energy scale of the initial singularity need not be the energy of the Universe as we know it now but, the absolute value of the local script L, script T or script V.
Quantum field theory merely provides us with the probability that a photon with a certain energy will appear at a point in space-time. It considers the a random and unpredictable event within the bounds of the computed property. Some might claim that the Universe is rather random, but others, noting that an ideally coded message is indistinguishable from noise, may not be so sure.
Massive means has a rest frame which means can process itself without moving. The only process available to a photon is to move to couple energy from A to B. Photon is the most basic particulate energy carrier and the whole Universe is its oyster, unlike other fundamental particles which are somewhat localized [graviton?]. If photons occupy 2D space-time we might think electrons and positrons between them make 4D spacetime. When they interact they revert to photons. What is the cross section of interaction between free photons and free electrons, the Compton effect?
Friday 13 March 2009
Driving home I have one of the best ideas but by the time I get here they are gone. But the message is that
[page 24]
consciousness is quantized, one event following another and some of them are impressed on memory. But we can't access the whole memory because it all takes time and we must live in the present as well as the past, with limited bandwidth, bandwidth limited to the energy of my life. And history shows that different people have vastly different energy as we see when we compare Joan of Arc to the average 'maid' or Stalin to the average altar boy. Joan of Arc - Wikipedia, Joseph Stalin - Wikipedia
In the end, it is the engineering details that decide whether the dream can be realized or not. The Catholic dream cannot be realized. Proof?
Prolegomena to the settlement of the Arab-Israeli conflict. . . . speaking from a broad Australia perspective, I think religious conflict is crap because all the religions in conflict are crap, not worthy of humanity. All these religions were founded by self-serving cliques of powerful people.
PAIN ==> ERROR
Saturday 14 March 2009
My God, ie god as I imagine it, god for me. Jesus may have been expressing deep delusion when he (allegedly) said 'My god, my god, why have you forsaken me.' [Matthew 27:46, Mark 15:34] Matthew, Mark, Peter Kirby My god is my world and my hope is to show every one that this can be true for them too.
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