Notes
[Notebook: DB 59 Draughts]
[Sunday 11 June 2006 - Saturday 17 June 2006]
[page 10]
Sunday 11 June 2006
Instead of using the introspected working of the mind as an heuristic for the nature of the world, we use the idea of invariance with respect to complexity. When we come to ask how does the Universe increase in entropy, we ask how does a network increase its entropy or how does a village increase its entropy? In each case, we shall say, by copying, by adding a new individual we increase the entropy of the whole by the new communication links so generated by the 1 new one to the n existing ones. We see here a mechanism for the progress of the Universe by going from 1 dimensional (scalar) dust to ordered sets of the dust. Let us consider each grain of dust (in spacetime) to embody quantum o action.
How do we create: by shaping the existing (I am making this reservoir of ink into a series of curly lines on paper).
The theory of everything (x) asserts that the model (x) is true, ie fits the observations.
[page 11]
Gravitation tells us something about the growth and pruning of networks. Special relativity : the effects of delay on the communication between inertial frames; General relativity : the effects of network traffic on the shape of the network. Potential : a new node to communicate with (felt romantically 'across a crowded room'.)
. . .
COMMUNICATION = COPYING
Where best to invest : in increasing the entropy of the elements, or in increasing the number of elements in a string to optimize the error free communication of a given quantity of information? Go for binary (Gatlin?) Gatlin Gatlin
. . .
Stress energy tensor: flow of momentum = flow of entropy/information given Landauer's requirement that all information is encoded physically.
. . .
A neural network is characterized by the algorithms it uses to evolve its states.
[page 11a]
Whatever contribution I might be making to human literature, I at least know that it is a product of my particular instance of the human body and its networks, most importantly my central nervous system.
Gravitation is the ground state, the bottom physical layer of all networks. The constraints on the transmission of meaningless symbols. Then we add further constraints to get the other fields. For afield is a protocol that holds throughout a network, ie electron field, photon field, which in some way constrains the transmission (birth, life and death) of particles. I am a network process with a birth and a death.
Woolf Orlando page 195: 'For what more terrifying revelation can there be than that it is the present moment.' Woolf
LOCAL = HERE & NOW
The gravitation protocol holds for all communications, and subsequent protocols (with much higher coupling constants) are built upon it.
The Christian god, the way it was conceived, has yielded the industrial power of the Christian west underpinned by the huge productivity resulting from fossil fuels and science based design. Noble
Woolf page 201 superposition: 'The selves of which we are built up, one on top of another, are plates piled on a waiter's hand, have attachments elsewhere,
[page 11b]
sympathies, little constitutions and rights of their own, call them what you will (and for many things there is no name) so that one will only come if it is raining, another in a room with green curtains, another when Mrs Jones is not there, another if you can promise it a glass of wine - and so on; for everybody can multiply from his own experience the different terms which his different selves have made with him - and some are too wildly ridiculous to be mentioned in print at all.
What we would like to say is 'Quantum field theory describes network computation'.
Quantum mechanics - 4 postulates
1. state space
2. Unitary evolution
3. measurement
4. Composition.
Monday 12 June 2006
Springel et al, Nature 440:1140 27 April 2006 Springel
Could the 'Lambda Cold Dark Matter' model be wrong in a significant way, requiring a fundamental revision.
'Perhaps the deepest reason to be suspicious of the paradigm is the apparent presence of a dark energy field that contribute ~70% of the Universe's content and has, for the past five billion years or so driven an accelerated cosmic expansion. Dark energy is problematic from a field theoretic point of view. [S Weinberg, The cosmological constant problem, Rev Mod Phys, 61 1-23 (1989)] Weinberg
[page 12]
Springel page 1140: 'The simplest scenario would ascribe a vacuum energy to quantum loop corrections at the Planck scale, hc5/G, which is of the order of 1019 GeV, where gravity should unify with the other fundamental forces. This is more than 120 orders of magnitude larger than the value required by cosmology. Postulating instead a connection to the energy scale of quantum chromodynamics would still leave a discrepancy of some 40 orders of magnitude. A cosmological dark energy field that is so unnaturally small compared with these particle physics scales is a profound mystery.'
Theory of everything must apply at all scales of everything.
Pythagoreans: Tredennick Met I-IX page xv (2) '[The] community of nature between God and the human soul implied an analogy between macrocosm and microcosm; the same principle of order constitutes the essential nature of the Universe (considered as a living organism) and of a particular creature.' Aristotle
'What is' for any entity in the Universe = what is communicated (observed)
Constraints on the nature and frequency of emission and absorption of particles are constraints on communication.
'desire to know' is Aristotle's archetypal potential, carried over into Lonergan, which we see as a consequence of the 'desire to live' cf Wicksteed, Physics I-IV page lxx. Aristotle
Quantum mechanics = set of algorithms for modelling the world : theory of everything.
The particulate nature of communication demonstrated by the
[page 13]
large catalogue of signalling molecules that control the operations of biological life, and the modifications of these molecules and their receptors which constitute the causes of 'molecular diseases'. . . .
So we wish to show that the transfinite network has features which are to be seen in our world.
Can we say that the Universe moves as it does in order to maximize entropy/energy by cooling and expanding?
ie maximizing the complexity of configurations that can be sustained by a given flow of energy/entropy. So the development of life on earth can be seen as a feature of the expansion of the Universe.
We propose that quantum mechanics and relativity can be unified in entropy space than in energy space.
Inertial frames communicating by exchange of particles are the stuff of quantum field theory, and this paradigm is used to explain attractive rather than repulsive forces. [attraction implies that potential decreases with closeness].
Can we say that Lorentz transformations are themselves quantized because they are performed in nature by something like a Turing machine (deterministic? ish?).
The local structure of the number line is in some ways invariant.
[page 14]
LOCAL ENTROPY is a function of communication rate and entropy density (memory density/access time) Temperature may vary from 1/ℵ0 to ℵ0.
Entropy gains on energy via the ordered set.
The size of a society is measured by the size of the network of trust. And who can you trust? Whoever has an error rate low enough for your system to deal with.
Is the Universe driven by information, energy or both? Energy is the rate of processing information. The fact that the Universe preserves unitarity seems to indicate that entropy is as important as energy, and what we are trying to do in quantum mechanics is find the relationship between them, ie how much energy is associated with a given amount of information.
Tuesday 13 June 2006
. . .
The 'right' to be heard implies (both way, ie identity) the 'duty' to speak. I feel quite good about this, although the grail often seems as distant and unattainable as ever (although when we get it, it will only be a
[page 15]
string of 10 000 or so symbols embracing a central relationship like x' = Lorentz transformation (x(, G = 8 pi T, F = ma, etc.
Consider the electron in a Bohr hydrogen atom. By the time it gets to the [quantum state represented by] n = ℵ0, it has angular momentum ℵ0 x h bar and the energy difference between [successive] states is about 1/ℵ0 (since in the alephs, h bar [planck's constant] is no big deal). Moving between states, it will emit and absorb photons whose wavelength is the size of the Universe. Of course it might have been disturbed well before this (even if it is alone in the Universe) by its own gravitational field or (if not alone) by the photon field in its vicinity.
Particle = message.
gauge theory = the entropy change in emitter and absorber [source] is equal to the entropy of the particle. Is this guaranteed by unitarity of cooperation and annihilation operators? Example the quantum harmonic oscillator.
The Theology Company: founded to research and propagate a plan for the world, or at least a plan for a plan for . . . . Which is really just to apply scientific method instead of warlordism based on some divine mandate. TTC operate at three levels, personal, theological and religious.
How do we measure the entropy of a particle? By looking at its source, to see how big its alphabet is.
Landauer: all information is coded physically and interacts physically. Landauer
[page 16]
Wednesday 14 June 2006
Potential converts (maps) information to energy. So the potential set up by the nucleus of the hydrogen atom determines the energy of the different symbols ([transitions between] energy levels) represented by an electron. Einstein's general covariance tells us that the relationships between a set of general symbols are independent of how we choose to represent thee relationships. So how do we leap from the meaning of the Universe to shape of the Universe : general relativity,
McLuhan: medium is message / message is medium. McLuhan
Gravitation is both medium and message, the fundamental ordering principle of the Universe.
General relativity: conservation of energy
Quantum mechanics: conservation of entropy [unitarity]
In a scalar configuration space energy (action?) = entropy? In more complex configuration space, the relationship is something like entropy > energy.
On these cold mornings, some of my time is spent configuring the fuel in my fireplace so that it burns at the required rate : equivalent to controlling a nuclear reactor by moving the fuel about. What we seek is a chain reaction as a certain rate with zero growth, ie constant power = energy conversion (in my case mostly from chemical into radiant) per second. Ie we are changing the configuration that contains the energy.
[page 17]
The difference between a state of motion and a state of rest (in our analysis at least) is that a state of motion may be considered as a (local) time ordered set of states of rest. A state of rest, from our formal point of view, is that something that can be represented by a state vector, which we here imagine simply as an ordered string of symbols, exactly analogous, for instance, to a word, sentence, book, etc. So our representation of a state of motion is kinematic rather like a movie film. In the kinematic representation the whole film, taken as a unit, is a state of rest. it doe snot move in itself, and can be shipped from theatre to theatre for exhibition. it is exhibited a frame at a time, and because of the way the human visual system works, appears as a continuous flow rather than a flickering of incidents.
IIt is clear from this description that the representations of states of motion are much more complex than representations of states of rest. Symbolically, the creation of states of motion may be imagined as permuting the symbols of a certain alphabet that represents states of rest. If we use the natural numbers as our archetypal states of rest, the continuum that we construct from them may be considered a state of motion. Since Cantor predicted an endless hierarchy of transfinite numbers beyond ℵ1, the 'classical continuum' (but see Cohen), we can go on constructing new states of motion as long as we like. Cohen As with our original film, each subsequent state of motion represents a subsequent instant in local time as Aristotle said, the number of motion with respect to before and after. Aristotle 220a25
[page 18]
Now this discussion sounds a bit like quantum mechanics. Here we represent states of motion (or rest) by little arrows of unit length pointing in different directions in a vector space with finite, countably infinite or a transfinite number of dimensions. Feynman Although the little arrow is a simple thing (electively a point) it carries as much information as the entropy of the space in which we place it.
In quantum mechanics, the little arrows rotate at a frequency proportional to the energy of the state they represent. A state of zero energy is completely static (formal) and may be taken as the equivalent of a state of rest (no matter how complex, ie no matter how many states of motion are encoded within it.
We have given a kinematic description of motion and stillness, now we turn to dynamics, which explains why things change. We model dynamics by letting the little arrows (vectors or functions in Hilbert space) interact. We may find that dynamics constrains the set of kinematically representable states to a certain subset. Kinematically, a film of pure noise (like an unturned TV) is indistinguishable from a passionate love story. We who feel the dynamics behind the image, know what is really going on when all those atoms move as they do,
Quantum mechanics rests on four postulates. Nielsen and Chuang 1> state space (discussed) 2. unitary evolution 3. 'measurement' 4. composition . . .
[page 19]
Gravitation describes a dynamic Universe that has grown from a point to unlimited size, rather like the transfinite numbers. As Shannon pointed out, increased structure puts things further apart, making them more clearly defined so that more structure can be built on them. Pierce
We stop motion by making the space bigger. The kinematic view of motion embodied in differential and integral calculus has been the key to physics since Newton (1642 -1727), Who we may represent as an arrow rotating in an environment with a cross section to communicate with the environment going 0 - 1 - 0 [ie not alive, alive, not alive] The cross section for interaction is 1 when the target particle envelops one like a sphere, or any other closed surface.
Every state is embodied in a particle, a state of motion by a set of particles in motion, eg hydrogen molecule.
Lo page 37: Every entangled state, of any number n of remote subsystems, is nonlocal.' Lo, Popescu and Spiller
May be a . . . gone. Maybe it will come back.
Particle: born, propagates, dies.
What are the dynamic constraints: conservation of energy, momentum, angular momentum and entropy [unitarity]. The Universe we see is random input constrained by these (and other) symmetries.
Hilbert space --> coding --> spacetime --> Hilbert space.
[page 20]
. . .
Shannon: error free = no confusion = no overlap = orthogonal.
Veltman page 35: 'Now that we are clear about the meaning of states and their representation in Hilbert space we can now process and postulate equations that Will describe particles in interactions. Experiments must then decide which equations describe nature. Of course whatever we postulate, it will be within the framework of Lorentz invariant quantum mechanics. Only a limited degree of freedom is left.' Veltman
Lagrangians, Feynman diagrams etc are all algorithms or protocols for communication between fundamental particles.
. . .
Thursday 15 June 2006
Friday 16 June 2006
Saturday 17 June 2006
We represent the world with vectors and matrices. In practical terms, a Lorentz transformation is a matrix. Put a 4-vector in and you get another one out: what the local state would look like if . . . it was moving at a certain velocity relative to us.
[page 21]
Null geodesic in spacetime is the distance between any two points communicating at the velocity of light: they are in effect in the same place. The same, we say, is true of all other communications when we substitute the relevant velocity of communication for c.
What doe the masslessness of the photon mean? We assume that
particles with mass have internal process whose bandwidth is a
function of their mass H = mc2/
h.
Bandwidth = entropy / time. Entropy is a scalar, so the unit of bandwidth is 'per time' = frequency.
Rest mass implies velocity < velocity of light. There exists a Lorentz transformation which brings a massive photon to rest. No so for the massless photon. There is no rest frame for a photon.
Veltman: 'There is a more explicit difference [between massless and massive particles]. A photon is a particle with spin one, and in its rest frame such a massive particle has three polarization states. By suitable rotations any state can be rotated into any other. A massless photon has only two polarization states, namely along or opposite the direction of motion. Moreover, they are independent. One cannot rotate one into the other. To rotate one into the other requires an axis of rotation perpendicular to the direction of motion of the photon; such a rotation, however, also reverses the direction of motion of the photon and spin along that direction remains spin along that direction. In conclusion the massive and massless case are vastly different.'
The photon has no internal pressing. It is not, then, an independent particle, but a manifestation of the universal
[page 22]
system at work.
General covariance : every explanation requires a frame of reference.
One may surmise that Parmenides, Plato and their ilk were led to postulate an unchanging reality in order to retain the possibility of certain human knowledge.
The dynamic point of view changes that. Now we require (Nyquist's theorem) that our knowledge is updated at twice the maximum frequency of change of the known for the knowledge to adequately track reality and so remain 'true'. Nyquist This brings Einstein's relativity into the centre of the theory of knowledge, not just for people, but for all the other particles which guide their behaviour by knowledge of their environment, eg atoms, bacteria, galaxies, everything.
