Notes
[Notebook: DB 61 Warm]
[Sunday 29 April 2007 - Saturday 28 April 2007]
[page 21]
Sunday 29 April 2007
From the Lagrangian of the Standard model we devise a network of processes into which a physicist may intrude so as to become involved at some point of the network. By multiple 'intrusions' (listenings) we hope to build up a picture of the physical layer of the Universe, upon which to base a theory of everything.
A layered network is a natural home for general covariance because each successive layer treats elements of the layer before it as unique discrete processes to which it can give any meaning it likes. The great complexity of the Standard Lagrangian seems to indicate that it tries to take too many layers into account at once.
Physics layers the world by 'energy scales' which are interpreted as spacetime sizes so that the theory of everything is a search for the smallest functional element of the Universe. The thing is riddled with contradictions like point particles which have infinite energy and momentum, but finite action, since the product of energy and duration or momentum and distance has a minimum value, h or 1 quantum of action. So a logical rather than a physical view of the world might reasonably begin with the idea that a quantum of action maps to a quantum of computation and the execution of one 'gate'.
[page 22]
Said all this before but hope by saying is again and again I will slowly clarify in my mind in a way exactly analogous to the slow and repetitive creation of structure in the Universe, an application of symmetry with respect to complexity showing the working of my neural network and that of the cosmic network re essentially identical at a certain level, what we call the physical layers. The difference comes from the meanings given to physical operations by higher peer layers.
What we need are a set of simple logical processes (proofs) and a network communication protocol (modelled on gravitation) that enabled us to compute frequencies for these processes and so yield a model system which behaves like the observed world.
Start with quantum electrodynamics on the grounds of simplicity.
The quantum overlap integral tells us the strength of the connection between two processes represented by state vectors. COMPUTABLE = COMPRESSIBLE
COMPRESSIBLE = SYMMETRICAL
INCOMPRESSIBLE = RANDOM
The transfinite network is a formal (Platonic) construct. Now we can study the properties of communication and computation to see how it realizes itself into us.
Symmetric Universe big sigma + Turing machines [Macro error: Can't evaluate the expression because the name "M" hasn't been defined.] are
[page 23]
two basic ingredients from which to construct a network. Two deterministic Turing machines connected together become relatively indeterministic since the state space of the two machines taken together is a product of the state spaces of the two machines, so that this state space grows exponentially with the size of the cluster of connected machines.
From a formal point of view, quantum of action = quantum of computation.
COMMUNICATION = COMPUTATION (The computation associated with an interrupt). If interrupted, stack present state, deal with interrupt, then go back to old job, but maybe with new information (given that the interrupt related to the job in hand).
DISCRETE = DETERMINATE (1 Turing machine)
CONTINUOUS = INDETERMINATE (Network of TM's)
Why is the Universe quantized: let us speculate. So, Shannon, Turing . . . .
Energy is the time component of 4-momentum which we wish to equate with bandwidth = frequency (E) x word length (3-momentum)
Special relativity establishes a symmetry between energy and mass.
Quantum mechanics creates symmetries between action and energy.time or momentum.distance, so providing common units for the components of 4-momentum.
[page 24]
The transfinite network provides an explanatory foundation for the dimensions mass, length, time and their products and divisions.
A particle of definite momentum occupies all space; with definite energy occupies all time; with definite four momentum (which allows tradeoff of energy and three momentum depending on the frame from which we observe it) ; if it is massive and we observe it in its rest frame it has definite momentum (0) and energy (mc2) which means that in its rest frame it occupies all spacetime. Given that this feature is Lorentz invariant, it is true for observers observing the particle from all inertial frames.
We are not concerned here so much with magnitude as definition, or from another point of view, the more definitely the momentum of a particle is defined (ie the smaller the magnitude of the error) the greater the magnitude of the space in which it may be found, ie close definition of momentum requires a lot of space as close definition of energy requires a lot of time and in quantum mechanics the product of the spatial 'cost' of defining momentum by the definition achieved is Planck's constant.
We can move these ideas from physics to all communication networks by redefining h and c. The local 'velocity of light" is the velocity of communication (eg horses, internet) and the local quantum of action is the energy.time needed to achieve a local unit of momentum.space = local quantum of action.
[page 25]
Veltman page 15: 'A particle with well defined momentum (and energy) is described by a plane wave. This is the true content of the Planck-Einstein relation E = h nu. . . . Thus we do not postulate commutation rules, but we postulate that a particle with well defined momentum and energy will be described by a plane wave.
ie a recursive process occurring with a certain spatial and temporal frequency throughout spacetime.
'The additional quantum mechanical concept is superposition.'
Superposition is made possible by arithmetic addition and subtraction.
page 16: 'A generalization of quantum mechanics is that the waves may be complex and that the probability is not the square but the absolute value squared of the amplitude. What follows below is the mathematical implementation of these statements.
The unity of action is broken into energy and momentum when it is projected onto spacetime.
. . .
page 16: 'Vectors are orthogonal if the corresponding states are mutually exclusive' 'Degree of orthogonality = 'degree of exclusivity'.
Orthogonal = exclusive = no error = deterministic = Turing
[page 26]
The complexity of a process is a function of time x bandwidth.
Every channel to the future has a bandwidth and between them they all add up to the bandwidth of the Universe.
Processes in the logical space of quantum mechanics present their results in Minkowski space. The definitive version of these results is that observed by an observer at rest in the rest (local) frame of that event.
Distant and moving events will appear transformed by the appropriate Lorentz and Einstein equations. We can only see distant events by communicating with them through the network and delay on the network induces Lorentz transformations. How does the network become curved?
Veltman page 20: 'Thus corresponding to a Lorentz transformation, there is a complicated big transformation in Hilbert space.' Is this so, or should we consider Hilbert space to be 'outside' [orthogonal to] or 'hidden behind' Minkowski space? Since we do not observe the Hilbert space but only events whose probability is calculated by arithmetic in Hilbert space. [The definitions and conventions of the space decide which pairs of values are to interact.] This arithmetic will (ideally) reproduce the observed pattern of events all of which will be the same to an observer sharing a Hilbert space with the event, and whose appearance to distant observers merely requires transformation of the results (the events), not the computations, which are locally linked to the events.
An observation exists in the product space of observer
[page 27]
and observed (which are in fact completely symmetrical, entering into a joint state with one another) ? [at the physical level]. See von Neumann pp 417-445. von Neumann
Klir and Valach page 21: 'A system is a set of interrelated elements'. [ie a network] Klir and Valach
String theory diversifies its particles by different vibrations in the strings. We might do it by associating different algorithms with different particles which execute in different times.
Veltman page 21: 'To every Lorentz transformation . . . corresponds a transformation in Hilbert space. Since we want physics to be unique we will insist that there is a one-one correspondence.'
But is physics unique, or is it generally covariant, allowing any transformation between two points in 'space'. So if the Hilbert space is independent of the 4-space we can have he same Hilbert space associated with many different points in 4-space and vice versa. Then Lorentz invariance may hold in 4-space but be irrelevant in Hilbert space, which is inherently local, a computation 'at a point' (in a point, system, organism).
4-space is the user interface of the physical world in which we see all more complex systems (like ourselves) operating.
The meanings of energy, momentum and action are different in the two orthogonal (independent) spaces.
[page 28]
Quantum mechanics: deterministic evolution of probabilities followed by discontinuous 'jump' into one of the states whose probability has been evolving.
Logical mechanics: random network of deterministic Turing machines yielding the same result as the above system with improved credibility.
Monday 30 April 2007
Our first heuristic principle is that the Universe is expanding. This expansion is manifest both in spacetime and in entropy or complexity ('complexification' Teilhard de Chardin). Teilhard de Chardin We couple this heuristic principle (for modelling purposes) to the Cantor Universe, the ever complexifying hierarchy of transfinite numbers.
Our second heuristic principle is that some things do not expand or contract, they are conserved. Without these elements of the Universe, the term expansion would be meaningless. It is the constancy of wavelengths of certain photons, the constant size of atoms, and all sorts of other constant features that give us the stable heart of our expanding and complexifying Universe.
NOOSPHERE & the INTERNET Rev. Phillip J. Cunningham, C.S.P
The internet is a physical foundation of the noosphere (like books, phone calls and all other forms of communication)
Complexification : f(number of symbols in the alphabet,
[page 29]
length of symbolic strings).
Hypotheses non fingo : the world is the way it is because God wanted it so, and this gives us faith that it is knowable if only we interpret the evidence right.[ Newton, Principia, General Scholium ad finem]. Newton The first thing we notice is that god both does and does not play dice, depending on how we look at it.
graviton = metric (?) spin 2 = 5 states. gmn has ten degrees of freedom.
To build quantum mechanics, or to build a quantum mechanical world, we can start with Hilbert spaces of each natural number of dimensions and then create products and entanglements of these states. The particles that result ultimately make the relevant Lagrangians stationary at (let us say) minimum action.
Seeking the best buy re polio. S316/362. Roberts
Tuesday 1 May 2007
The whole world is not a clumpy material thing, but a living system. A divine living system.
Proof = logical continuum. There is no half-proof.
Electron charge |1| is 3D, quark charge |2/3| is 2D and quark charge |1/3| is 1-D?
Wednesday 2 May 2007
[page 30]
The role of religion is to take the long view, to see the world sub specie aeternitatis. The dominant 'long view' in the western world is that of Christianity, a moral story of creation, fall, redemption and ultimate reward or punishment.
Although Christianity controls most of the world's wealth there are other great religions more or less in conflict with it in their quest to get a fair share of the world's goods. Our hypothesis here is that religion is behind all war because only religion is powerful enough to sanction the death of my friends and fellows in pursuit of some goal.
Natural religion preaches that god is all around us and we best guarantee our survival by looking carefully at god to see what it wants. We no longer need guru's to tell us what god wants, only scientists to see how it works so we can deal with our problems.
The scientific long view sees a Universe of finite age evolving from non structure to structure, often at an explosive rate. It sees us and planet earth having evolved in this cosmic milieu for some five billion years.
Angular momentum = action. Torque = processing load. Power = torque x angular velocity. Energy = action/time = power x time.
Processing load = number of logical operations / cycle.
[page 31]
From a recursive function theoretical point of view 'angular dynamics' would seem to be the best starting point to move from the classical 'mass points in a continuum' point of view to the logical 'recursive signal processing' point of view.
Thursday 3 May 2007
Friday 4 May 2007
COMMUNICATION = DECISION
Nonlocally -- non-realism -- non-definition.
The Roman Catholic Church is a political organization: toe the line or be sacked.
As one might expect from these ideas, my conviction is part discrete (logical) and part continuous (emotional). Evolution itself is underlain by discrete processes, but they are so complex they look continuous from the point of view of reason.
. . .
[think of the vast amount of neural processing required to write these few words.]
Does my 'subconscious' (all that processing that I am not aware of) really run my life and not tell me?
Various ploys have been dreamt up to explain the collapse of the wave function, non=locality, non-reality and other conundrums of quantum mechanics, but none are very satisfactory, requiring ideas like many worlds. Quantum mechanics remains recalcitrant and backed by experiment. So
[page 32]
perhaps we are looking at it the wrong way. The prescription offered here is a revision of the nation of continuity and conception of our world as analogous to a layered computer network, albeit a transfinite one.
The natural numbers are an alphabet for the reals. We can express any real number as a (possibly infinite) string of natural numbers. Cantor's hierarchy does not sop there but sees the reals (so defined) as an alphabet for the next level of communication, and so on without end.
And gravitation: could it be that 4-D spacetime is the simplest space in which a network can exist? All points can connect without the wires crossing. Relativity tells us that there are sufficient degrees of freedom for a gravitational field to exist in empty space. We might imagine this as the hardware layer of the cosmic network, in existence whether or not it is carrying messages. Turned off, one might sat. We turn the network on by introducing quantum field theory which predicts the content and frequency of the messages (events) transmitted over the network. This traffic causes rewiring of the hardware network in a manner predicted by the general theory.
It may seem a bit extreme to invoke the transfinite numbers do describe a manifestly finite Universe. One the one hand, we can plead that it has already been done, under the guise of the function theory that forms the mathematical foundation of quantum mechanics. The Universe is observed to be expanding and
[page 33]
consequently was once much smaller, perhaps beginning from the initial singularity which we may model as a mathematical point. How does it expand? Here we get a clue from medieval theology which in effect studies the initial singularity under the name God and modelled how that God could differentiate into a Trinity by generation and relationship. So we can exploit the creative ability of networks, beginning with a network conceived as a space where ℵ0 = 2. To an inhabitant of this space, 2 = infinity (think 'machine infinity' and any attempt t talk about 2 may lead to paradox, as we find with the set of all sets. We, looking from a space where ℵ0 > 2 can see the limitations of the smaller space without able to see the limitations of our own.
How do networks expand themselves? By reproducing nodes which share common hardware (so 'material creation' is not involved), common software but, through communication with the rest of the network gradually builds up unique 'personal' memories which define a new personality on the network.
Out of the continuum of work to the measurement of hours, materials, rates, ie concocting a bill, reducing it all to money (or some other payment medium). The less concrete the service one renders, the more bullshit goes into this operation. Lawyers charge more than plumbers. Plumbers charge more than unskilled labourers? What do we think of this. As a labourer, I am not happy, yet I charge what the local market will bear. For bigger money I have to go further afield, and this does not seem worth it.
[page 34]
Groblacher: 'A special case deserving comment is Bohm's theory. There the non-local correlations are a consequence of the non-local quantum potential, which exerts a suitable torque on the particles, leading to experimental results compliant with quantum mechanics'. N446:872 Groblacher
