Notes
[Sunday 3 February 2008 - Saturday 9 February 2008]
[Notebook: DB 62 Interpretation]
[page 147]
Sunday 3 February 2008
The physical processes in the Universe are required to be causally (= logically) connected, ie physical processes cannot affect eachother if they are outside eachother's light cone. [On the other hand, if they share a light cones at the physical level, they are bound to affect one another, hence the complexity of Feynman diagrams?] Quantum mechanics, on the other hand appears to be non local (EPR) so we have to add special relativity to quantum mechanics to get a logical explanation of the world. Einstein, Podolsky & Rosen From this point of view, quantum mechanics precedes space-time. Space-time comes with delay, which comes with complex structure and the need for error free communication.
Because quantum mechanics is non local it does not sit easily with the momentum picture, which involves locality. The quantum field theoretical momentum approach brings representatives of the Lorentz group inside the Hilbert space of quantum theory, and introduces considerable complexity in the process. Can we get around this by disentangling the quantum and relativity picture using the assumption that all interactions take place by contact, ie
[page 148]
at zero spacetime distance (null geodesics) and therefore (?) in the same inertial frame where we do not need Lorentz transformations? As we have it here, the Lorentz delay arises from the need for error free coding, but we do not see this at the quantum mechanical level because the physical layer fills the whole space of its possibility ad so it cannot go wrong. It is only at higher layers where we try to singe out a subset of the possibilities that error correction and so delay and Lorentz transformation enter the picture.
Veltman page 21: 'If the correspondence [between Lorentz transformations and transformations in Hilbert space] is unique, then to the product of two Lorentz transformations L1 and L2 must correspond the product of the two corresponding transformations X1 and X2 in Hilbert space.
In quantum mechanics there is no memory and so there can be no error. As soon as we introduce memory (space) we introduce the possibility of error, and so for space to work consistently we need error correcting code and so delay. Velocity is naturally associated with space.
At the quantum mechanical layer we have only energy. As soon as we introduce space we have two-momentum.
page 22: The trouble starts for quantum field theory when it tries to enforce the requirement of locality on the inherently non-local formalism of quantum mechanics.
Veltman page 22: 'This we hope to achieve by insisting that the operator (matrix) describing a process at
[page 149]
the spacetime point x will commute with a similar operator for the space-time point y if x and y are outside each other's light cone.'
If we are dealing with exact times and places, we have no knowledge of the energy and momentum involved!
. . .
A brief look at any book on quantum field theory is likely to cause pain to anybody without a serious love of mathematics. A more careful look reveals that quantum field theory seems to be bogged deep in a mire of sharp mathematical practices and, by modern standards, serious computational complexity. Yet the Universe is held to have grown from an initial singularity which we might represent mathematically by the empty set. Given the set theoretical Axiom Scheme of Separation, [the empty set] has no elements and therefore no properties: 'If psi is a property (with parameter p), then for any X and p, there exists a set Y = {u is a member of x : psi (u, p)} that contains all those u that have the property psi. The theory of everything thus begins as the theory of nothing. Observation and theory suggest that the Universe we have arose from this simple beginning by a process of complexification, the cardinal of the Universe gradually increasing by creative evolution to its current condition.
Energy ticks but gives no direction to time. The development of space, the layer above energy, which uses energy
[page 150]
provided by the physical layer to carry our its operations, by ordering ticks along a line [establishes] the foundation . . . for time ordered evolution.
Feynman page 16: Space is created by the exclusion principle, ie by antisymmetric interference of identical particles (or vice versa). The Schrödinger equation described the 1D energy world. The Dirac equation the 2D relativistic world (in Minkowski 2-space). We can have 2D and 4D Dirac equations.
page 18: Neutron scattering: exclusive alternatives do not interfered.
Quantum mechanics is not concerned with error because it uses complete sets of basis states all of which are 'correct' and none 'erroneous'.
page 26: Least action, or action, is a function on the domain spacetime which determines the path of a classical particle.
Least action might arise from two sources: first because there is no real choice, although he mathematical formalism might suggest that there is; and secondly, that there is a choice, but there is also an optimum represented by least action which is selected by an evolutionary process.
Monday 4 February 2008
The time dimension as we know it is an ordered set with a first element which we call the initial
[page 151]
singularity. The space dimensions (at least in flat space)are ordered sets with no upper or lower limits. Given that the real Universe is by definition closed, the spatial dimensions may also be considered closed (that is cyclic). At the beginning it might have been easy to travel right round the Universe if it was static. On the other hand, if its radius was expanding at the speed of light, no particle could circumnavigate the circumference.
The next thing we have to deal with is the velocity of light we might consider to be 'machine infinite' velocity on the grounds that the spacetime interval traversed by a photon (or graviton) is zero. What is the velocity of light in a space-free Universe, ie a 1D space. Can it have any meaning before we introduce space? How does the ordering of time feed into the ordering of space? Think about contact and general covariance.
Waugh Knox page 108: 'Such temptations against the Faith as he suffered - and he was near despair in the year before his reception into the Catholic Church - were total. Either the whole deposit of faith was divinely inspired and protected and developed under divine guidance, or it was false.' Waugh
Christianity, taken literally, is clearly false. But once we make the Universe divine and accept the scientific method, we can happily claim that our knowledge is 'divinely inspired and protected and developed under divine guidance.'
Space and time are connected cardinally by the Minkowski metric; what is the cardinal structure behind this? Can
[page 152]
we get it out of some quantum mechanical matrix? What matrices do is set up a structure which tells us how to apply arithmetic operations (which all come down to addition) just as the accounting structure of an enterprise ('enterprise software') attempts (in most cases) to give a true and faithful representation of the flow of value within the enterprise and between the enterprise and its environment. The situation in the Universe is simplified by the fact that it has no environment.
Poor Ronald Knox is agonizing over his priesthood as I once worried about the truth of my vocation. Looking back now the whole matter is just mystical gobbledegook - nothing anybody says can change bread and wine into meat and blood, it requires an exceedingly complex and partially understood series of metabolic transformations within the human body. Nevertheless, because of the divinity of the Universe, I have no trouble in accepting the real presence of god in all things. The Eucharist is nothing special per se, even if it serves as a symbol in certain (rather misguided) contexts. Waugh, Knox page 146.
What I have wondered about for a long time is a couple of coupled Turing machines, the tape of one being the program of another so that as they work they change one another. To let this system operate for a while and see if it arrives at any stable configurations. This is a model of things talking to one another since my output (what I write to tape) affects your personality (your software).
Nature 451 p vii 'DARPA was to ensure that the US remained
[page 153]
the most advanced military nation.' Herzfeld, Nature editorial, Weinberger
Does this system of entwined Turing machines have anything to do with quantum mechanical computations, particularly the stable states represented by eigenvalues and eigenvectors?
From a transfinite point of view there is just as much information (entropy) in a vector as in a matrix, just as there are as many points in a line or square are there are in any other Cartesian space. The concept of machine infinity seen as machine confinement, carries this transfinite idea over into finite space, since the constraints on a matrix reduce its entropy to that of a vector of the same dimension? So observable operators are diagonal.
Why complex numbers? Because they are closes and energy and the Universe are closed, and therefore cyclic, periodic. In themselves they are a sort of nilpotent recursion, being conserved, like energy, but serving as a foundation for creative recursion by being stretched into spirals of one or many dimensions.
All the Pauli operators are not operators in the sense that XX = YE = ZZ = I.
Tuesday 5 February 2008
Wednesday 6 February 2008
The energy operator is the source of energy and the energy is the source of the energy operator. This is an interpretation of quantum mechanics which connects form (the [operator or potential to process].
[page 154]
Let the Pauli operators be the software for the 'Pauli layer' of the universal network, and show that this Pauli layer can be treated as a 4D real space with a Minkowski metric by somehow setting it up as a computer with three memory locations and clock?
[X, Y ] = 2iZ, [Y, Z ] = six, [Z, X ] = ei.
This little scheme needs to be built around a cycle of 'preparation' and 'measurement', each cycle connected to the next by the exchange of a real particle. Will anything every come of this? Hasn't anyone ever done it before?
Perhaps the Pauli space has only 2 real dimensions, L and T, operated by a 4 location (complex) memory, ie a qubit with an induced metric LO - T2 = 0.
Are the particles exchanged in this model photons, to become gravitons when we beef it up to 4D?
Quantum mechanics is one dimensional, dealing with energy alone. It is the invention of space that fragments the energy into different independent dimensions, each of which is an application of quantum mechanics. The simplest form of this space is the natural number line which is the memory of the quantum harmonic oscillator. So we see the quantum harmonic oscillator as a two dimensional object the distribution of energy along a natural line. To make it dynamic we need a way to accommodate transitions which in Planck's historical model involved the
[page 157 (sic)]
interaction of a radiation field and a matter field, ie photons and atoms. We can model this with two photon states and two atom states, which we might see as a set of qubits and a set of operators.
A challenge for DARPA
[A letter to DARPA:
Mr Anthony J Tether,
Director, Defense Advanced Research Projects Agency
DARPA Defense Sciences Office
3701 North Fairfax Drive
Arlington, VA 22203-1714Dear Mr Tether,
A challenge for DARPA: Scientific theology and evidence based religion
My attention was drawn to your organization by some fiftieth anniversary articles in Nature.
I note from your website that DARPA's mission is to maintain the technological superiority of the U.S. military and prevent technological surprise from harming our national security by sponsoring revolutionary, high-payoff research that bridges the gap between fundamental discoveries and their military use.
Further, your site asks: Are you a scientist or engineer with a radical idea (or ideas) that you believe could provide disruptive change for the United States military?
I do not doubt that there are many people in the world who believe that the axis of evil runs precisely through the heart of Washington. Although it is now the sole global superpower, the US seems to steadfastly resist any calls to become a global citizen. Instead it seeks to maintain global hegemony using military means with associated political costs.
As a citizen of a small nation, I see this as a real problem for all of us,
The source of this problem seems to lie in the spiritual heritage of the US. Surveys show the US to be predominantly Christian, a religion two thousand years old. Like its ancient peers around the world, it is out of its depth in modern conditions. Despite its thin evidential base, Christianity is convinced of its own truth and militantly expansionist.
Here we come to DARPA's challenge. Religion is the technology of peace. It is the learned set of protocols which bind a group of unrelated people into a coherent whole, such as a nation. As a consequence religion is also the source of war, since in a world of limited resources, one religious group may expand only at the expense of its neighbours, a situation that guarantees conflict.
From these premisses we can easily deduce that global peace, that is security for everyone (including the US), requires global religion.
The theoretical foundation of religion is theology. Christian theology is fundamentally a collection of ancient stories whose power depends no so much on their scientific content as the fact that they serve the purposes of such large global corporations as the Roman Catholic Church. Other religious stories enjoy similar patronage by established powers.
A fundamental tenet of Christianity is that god, the creator and sustainer of the world, is wholly other and accessible only through ancient texts like the Bible. Christian theology cannot therefore be a science, since it has no empirical foundation. It has little claim to credibility in the modern world.
The alternative hypothesis is that the Universe is itself divine, fully self sufficient and responsible for its own creation and maintenance. If this is so, theology, by observing the Universe, may become a scientific and reliable foundation for evidence based religion, just as physics, chemistry and biology lay the scientific foundations for DARPA's engineering endeavors.
I was once a Catholic, but thoughts along the lines outlined above led me to consider the possibility of scientific theology. My subsequent experience has been that Christianity is so deeply entrenched socially and so totally in control of the theological enterprise academically that it will be a long time before I succeed.
Hopefully your military mission exempts you from such control and allows you to consider a new, complex technology of world peace that might ultimately complement the creation of superior hardware.
A statement of my work is available at www.naturaltheology.net. This site is by no means complete, consistent or well expressed. I hope, however, that your mathematicians will see that I take the structure of the Universe to be formally equivalent to mathematics, that is without limit and capable of growing from the simplicities of set theory to an unbounded symbolic system.
You are looking for 'disruptive change'. I hope you find the seeds of it here.
Yours sincerely,
Jeffrey Nicholls
Managing Director,
The Theology Company Pty Ltd}
[diagram, complex exponential solution to one dimensional Schrödinger equation]
This setup looks like a photon, but in no way contained, with all frequencies 0=< f < ℵ0. It is only when we introduce space that we start to get constraints on frequency, but what?
Let us say that all communication between systems in the cosmic network takes place through the physical (energy) layer by collapses of wavefunctions. What is happening is entropy is being converted into information and back again rather the same way that kinetic energy goes to potential and back.
Electric and magnetic fields introduce special relativity as soon as we create a spatial dimension. Photon travels at c in every frame regardless of their relative velocity. What does change is the colour / energy / momentum of the photon when spatial movement is introduced.
The whole idea is to simplify quantum field theory by breaking it down into its alphabets, ie its different layers in the network.
[page 158]
Our 'photon' describing the probability of a quantum of action existing in one of two orthogonal states, which in turn describes the probability of communication between the states. At this level of the Universe, the excitation of one state is annihilated to create the other and vice versa so that they do not exist simultaneously. We do not perhaps need quantization at this stage, no error correction, since in such a two state system there is no possibility of error and no delay, a sort of 'pre photon' unobserved and unobservable since there is nothing to observe it. Quantum mechanics as we know it begins when two such systems are used by higher layer to create a qubit?
Veltman Interacting particles page 32. Veltman
'A vector in Hilbert space represents a physical state. . . . physical state is simply a possible physical situation, with particles moving here and there, with dogs chasing cats, with people living and dying, with all kinds of things happening. Often people make the mistake of identifying a physical state with the situation at a given moment, one picture from a movie, but that is not what we call a physical state. The situation at one moment may be seen as a boundary condition: if one knows the whole situation at some moment, and one knows the laws of nature, then in principle one can deduce the rest.'
A Laplacian (?) deterministic view based on the idea that the wave function of the world evolved deterministically in one big Hilbert space. The network picture breaks this down into 'atomic' deterministic processes carried out by Turing machines (which can be seen as deterministically evolving functions) and
[page 159]
indeterministic coupling between the output of one deterministic process and the input of the next.
Quantum field theory is built around accelerator physics and the S matrix which is rather abstract and unrealistic, thought necessary to get to the current state of knowledge. S Matrix - Wikipedia
Thursday 7 February 2008
Finally, the one big vector approach needs to account for Lorentz transformations within the Hilbert space, whereas Lorentz transformation is a creature of observation, that is it is a matter of the coupling between two systems which occurs not on Hilbert space but n the real space of observations, measurements and particles. Merriment involves comparison and the results ore the real eigenvalues of Hermitean operators. Self-adjoint operator
Veltman page 34: '. . . | 0<k, r, s | p,q >in |2 gives the probability of observing three pions of momenta k, r and s at time t = 0 if we know that the system is in a state characterized by the fact that at time t - - infinity there were two pions of momenta p and q.'
Quantum mechanics operates in the realm of superposition, that is overlap and confusion. Real mechanics operates in error free space where there is no overlap or confusion. Everything is orthogonal, and we can imagine the calculations of encoding being analogous to the Gram-Schmidt process which distills orthogonal basis states out of non-orthogonal ones in a Hilbert space of a given dimension. Gram-Schmidt process - Wikipedia
[page 160]
The network admits superposition in the geological sense as well as the quantum mechanical sense. Hence higher strata are, other things being equal, more recent, and the whole tree is rooted in the initial singularity which, like god, has the potential to be everything as is present at every point in the Universe, just as the atomic logical operations of a computer are present in every process executed by the machine. Every operation of the Universe has static and dynamic aspects corresponding to the eternal nature of the initial singularity and the dynamic nature of the processes built on it.
Sacks Musicophilia page xi: 'The inexpressible depth of music, so easy to understand and yet so inexplicable, is due to the fact that it reproduces all the emotions of our innermost being but entirely without its reality and remote from its pain. . . . Music expresses the quintessence of life and of its events, never these themselves.' Schopenhauer. Sacks
WILL - POTENTIAL / INTELLECT - KINETIC
The dynamics arises between two static versions of the initial singularity, separated but maintaining their unity by communication which is tantamount to exchange of quanta of action (messages) whose frequency of exchange becomes a measure of energy. What we seem to be doing is trying to express the mystery of the Trinity as Aquinas expressed it in quantum mechanical terms.
Friday 8 February 2008
All elements of the cosmic tree share the attribute of existence which the traditions of both external and internal creation attribute to god as source.
Sacks page 37: 'Music can have wonderful, formal, quasi-mathematical perfection and it can have heartbreaking tenderness, poignancy, and beauty (Bach of course was a master at combining these(. But it does not have any 'meaning' whatever.'
Verbally expressible meaning that is, but obviously it is a message from composer / performer to audience which acts to create a force of attraction (or repulsion) between them.
Our brain is a network subject to various upsets as detailed by Sacks in his books and the whole neurological | psychological | psychiatric literature.
Sacks page 77: 'hallucinations in the sane.'
'. . . if there is a critical deficiency of input from the sense organs, this will facilitate backflow, producing hallucinations psychologically and subjectively indistinguishable from perceptions.' Jerzy Konorsky. . . . 'Konorski's theory provided a simple and beautiful explanation of what came to be called de-afferentation. Such an explanation now seems obvious, almost tautological - but it required originality and audacity to propose in the 1960s.' page 78.
[page 162]
The vacuum: meaningless or random traffic on the network.
The denser the coding, the more completely random it looks until all symbols become equiprobable. Chaitin
Sacks page 80: 'Musical hallucinations tend to reflect the taste of the times rather than the tastes of the individual.'
Saturday 9 February 2008
We would like to assume that all interactions take place in a rest frame. This would be analogous to the observation that the velocity of light is the same in all frames, regardless of their relative motion. The idea being that the energy of particles interacting depends on where they come from, and since quantum mechanics is concerned with energy alone, this determines the outcome of the interaction. The chosen frame is the 'centre of momentum' frame where total momentum is zero (ie rest frame) and all Lorentz transformations of incoming and outgoing particles are computed relative to this frame to determine the energy which they are bringing to the table. This paradigm is suggested by the fact that Hilbert space does not 'see' real space and time, only energy. Space, time and momentum are added later to convert non-local quantum mechanics into local 'quantum field theory'.
From a quantum mechanical point of view, the state of a free particle is stationary. This is an extension of Newton;s first law: 'A body remains in its state of
[page 163]
rest or motion unless it is acted upon by a force'. Momentum does not come into existence until space comes into existence.
In any given system the total energy may be assigned a probability of one and the probability of constituent event in the system is then proportional to their energy (frequency) so that the sum of energies corresponds to the sum of probabilities = 1.
Frequency is a purely probabilistic term. Probabilistic frequency is normalized to one in the case of one event (one throw of the die) but by increasing the frequency of throws, we increase the frequency of the various outcomes in proportion. So the total frequency of the Universe may be seen as 1 (one Universe) or ℵ0, ℵ0 discrete events.
But Veltman page 38: 'A vector in Hilbert space has no time dependence, but like a movie, all action is contained in that state. In that sense, the S matrix is a cross index register, showing the relation between the two labelling systems [in and out]. Given the beginning scene of the movie, the S matrix tells us what the final scene is.
-->