Notes
[Sunday 10 February 2008 - Saturday 16 February 2008]
[Notebook: DB 62 Interpretation]
[page 163]
Sunday 10 February 2008
Is there a wave function of the Universe? Everett III, Universal wavefunction - Wikipedia Or (perhaps equivalently) is the whole evolution of the Universe unitary, and (consequently) reversible? Clearly it is not reversible at my level of existence, but is it reversible at some hardware level?
Classical quantum mechanics maintains that a system
[page 164]
involving measurement and a 'collapse of the wave function' can be seen as part of a larger unitary system, although I have yet to understand how this works. It seems , however, to be a part of the many worlds interpretation of quantum mechanics.
Alternatively, the network approach would seem to favour the idea that dynamic deterministic processes may be described by quantum mechanics, but the coupling of such processes occurs by the exchange of real particles which has a random element precisely because of the independence of these processes.
These ideas seem to represent a major departure from the quantum mechanical paradigm which seems to have arisen from my fear of complex mathematics motivating me to take Lorentz transformations out of Hilbert space. The effect of Lorentz transformations is to change the rate of communication between objects in relative motion.
The splitting of the Universe into separate but communicating dynamical processes may remove the difficulty of reconciling the non-locality of quantum mechanics with the locality of relativity and of al communications at finite velocity.
The test of this approach of course is whether it can model the Universe of experience. A big argument in its favour (it seems to me) is Feynman's clear statement that indistinguishable
[page 165]
alternatives interfere. As soon as we observe (or can observe) a system to decide (eg) which hole the electron went through, the quantum interference disappears. The system is no longer a spinning coin or any other dynamic system, but a fixed message conveyed to the observer.
so
DYNAMIC = UNDECIDED = QUANTUM MECHANICS = INVISIBLE
STATIC = DECIDED = CLASSICAL MECHANICS = VISIBLE
So back to Agatha: Until the end of the story we are led to suspect everybody of the crime, but after the denouement we are able to see that the facts and logic point to just one person. The wavefunction has collapsed. The processing by Poirot;s little brain cells is deterministic once he has seen how it all fits together. Christie
DYNAMIC = UNCERTAIN = SEARCH
STATIC = CERTAIN = DISCOVERY
One beauty of this approach is that it is intuitively satisfying. combining both the non-locality of undecided and incomplete processes with the certainty of complete ones, The well defined mathematical distinction between complete and incomplete systems gives a firm direction to time's arrow leading from the past through the incomplete present to the possible future.
Classical quantum mechanics places the observer (a physicist, of course) in the special position of being the one who causes the wave function to collapse. This anthropocentrism seems to violate our cosmological principles and we assume in the network model that wave functions are collapsing all the times, resulting in real messages passing from one
[page 166]
point in real spacetime to another.
The complex mathematics of quantum mechanics is not observable but does serve very well to describe unobservable dynamic prowesses which we are inclined to model with Turing machines. How so?
Agatha p 113: 'Once again, Poirot did not press the question', ie he did not observe which hole the mouse was in, choosing instead letting the situation evolve to its own conclusion. This is an important strategy in human affairs, often overlooked by over eager fools (we think of the US intelligence estimates of Vietnam and Iraq who want to force issues to a (degenerate) conclusion.
Sometimes we sit in silence together following our own trains of thought, sometimes we talk, entraining one another in eachother's thoughts but as a unit remaining private and not communicating with outsiders, following an unobserved collective train of thought. From a neural perspective, my undisturbed musings are the collective result of a billion or so neurons chatting away to one another, and each neuron, insofar as it remains silent, is a hidden process involving countless molecules and so on down to the basic hardware layer, whatever that may be.
Both hardware and software are static rather like mater and form, a la Aristotle. The dynamics arises from their interaction. What we are trying to devise is a formal system to which we can attach some measures which agree with our measurements of the world.
[page 167]
The basic stumbling block to human understanding of the world is our feeling that we are exceptional, a special creation of an alien divinity in some way completely alien to the world in which we find ourselves. The progress of science can be seen as whittling away at this view, slowly removing ourselves from the centre of the world as we see in children gradually developing from almost compete solipsism to citizens of the world able to see and act on the algorithm 'do unto others as you want them to do to you.'
The US delusion that they are the centre of the world, god's chosen ruling by divine right is an example of the two year old stage of development that the more cosmopolitan nations of Europe may have transcended over a few millennia of war and other communication.
The Universe, like god, grows by observing itself: grows = differentiates.
Every now and then as it sit thinking my 'wave function' collapses and I write something in this book, somewhere else, speak or get up and do something.
So we imagine a Universe with little islands of unobserved unitarity (like the tosses of coins) connected to one another by classical communications in 4-space, which communications are described locally in and between inertial frames in 4-space with a Minkowski metric. The energy and momentum of the messages moving between the islands obey Lorentz transformations.
The message is the past. The dynamic is the present.
The past, like god, is eternal. [no memory, no past]
Monday 11 January 2008
High energy systems have a strong tendency to 'decay' into low energy systems, ie entropy and complexity tend to increase. The high energy physics community spends billions trying to reverse this process to see what the very high energy (primitive) (alphabetical) processes of the Universe look like, mainly motivated (at least historically) by the desire to use high energy processes to annihilate their enemies. This enterprise is disguised, of course, as the search for knowledge, knowledge is power after all.
Veltman page 25: Fields are Fourier transforms of creation and annihilation operators.
Continuous range of momentum ==> transfinite creation and annihilation operators.
[page 169]
Tuesday 12 February 2008
The notion of logical confinement is that the Universe will occupy all states logically consistent with some boundary conditions. Boundary conditions are expressed as certain invariants (like conservation of energy) which the system must respect as it goes through its motions. A message serves as a boundary condition on its recipient, so the past, by sending messages to the future constrain the future and so makes it to some extent predictable.
Wednesday 13 February 2008
If the root of the Universe is the classical god, we see quantum mechanics as a description of the emanation of the word. It shows us how the one god splits into a transfinite collection of states and how energy arises from the a priori equiprobability of these states. Because quantum mechanics deals with complete sets of states of any cardinality, the possibility of error does not arise. It is inherently non-local and does not in fact see space and time, only energy. It provides the space in which all other forms of life evolve. It is only when we begin to select out of the transfinite class of possible messages that the possibility of error and therefore the necessity of quantization and finite velocity arises,
so (maybe) phys08 Energy, phys09 Evolution, phys10 Gravitation, phys11 Quantum Field theory, phys12 The solid state.
[page 170]
Christie Shoe 141 '[Poirot] was in a daze - a glorious daze where isolated facts spun wildly around before settling neatly into their appointed places.'
Quantum mechanics describes the energy filled abstract space in which the space and time of experience and all their constituent particles (messages) arise. We only need the continuous formalism to describe the quantum world because there us no possibility of error and so no need for quantization or delay. The postulates of quantum mechanics dealing with measurement rightly belong to quantum field theory which describes the creation and annihilation (transmission and reception) of messages in the cosmic network. So perhaps in the natural order of creation, quantum field theory precedes general relativity. Once again we gain clarity by breaking complex systems down into their alphabetic constituents and the syntax which governs the ordering of these constituents.
Control is only necessary when the variety of a system must be reduced, as, for instance, one is attempting to aim a projectile at a particular target rather than emitting it in a random direction.
The properties of quantum mechanics:
1. complexity invariant
2. non local
3. unitary perpetual motion / complex numbers / continuous
4. frequency invariant
5. not observable
6. complete / metric / inner product, ie isomorphic to Hilbert space.
[page 171]
It is only when we subject quantum mechanics to the constraints of observation that we begin to get the Universe we observe (a useful tautology). The network model, incorporating geological superposition, tells us that the world is a forest of isolated quantum systems which provide the energetic foundation for the cosmic communication network. Insofar as they are isolated the interiors of these systems are unknown to us. Only when they communicate do we see into them, and insofar as they do communicate they are subject to the constraints of the mathematical theory of communication. Interiorly, they occupy a complete set of basis states completely. When the communicate, these states are constrained by the eigenvalue equation.
I, and every other organism, fit into this paradigm. My interior, undefined at birth but suitably complete and plastic, is shaped by communication with my environment. This is a manifestation of the complexity invariance of quantum mechanics, quantum field theory and the network model.
Aggy again, : 150 'What's the good of manners?
'You'll find they help you along' said Jane. 'I haven't got any myself, but that doesn't matter so much. To begin with I'm rich and I'm moderately good looking, and I've got a lot of influential friends - and none of the unfortunate disabilities they talk about so freely in the advertisements nowadays. I can get along alright without manners.'
In previous pages we have outlined some of the features of quantum mechanics. Now we ask what does quantum mechanics mean? My guess is that it is a mathematical description and model of energy. A physicist would
[page 171]
say that it is energy that makes the world go round. Romantics say that it is love. Quantum mechanics embraces both.
Quantum mechanics is a formal description of energy. No formal description can capture every detail of a dynamic system. Quantum mechanics gets as close as possible to a formal description, that [is] it captures every detail that can be captured.
Mathematically quantum mechanics is described by differential and integral equations in Hilbert space. This space is complete and so a natural home for the calculus, the kinematic view of dynamic processes. Mathematics is the best formal description language of the real world that we have. Here, in the world of free an unconstrained unitary evolution in transfinite function space anything can happen. The continuous world of quantum mechanics describes the energetic foundation of the world. Energy arises from possibility, that is potential. Where potential exists, energy exists as the system cycles through the possibilities. There as no intrinsic clock to quantum mechanics, all we can say [is] that frequency is the measure of energy via the constant h bar, E = h bar omega = h nu. This is a fundamental axiom of quantum mechanical measure.
All we are saying is something tautological: the relative amount of time (or space) a system is found to be in a particular state is the probability of that state. This idea is formalized by mathematical theory of measure. (Kolmogorov) Kolmogorov
[page 173]
Given a source of energy, we can get down to building things, that is structures. Quantum mechanics has no memory, as we see from Feynman's chains of [Stern-Gerlach apparatuses]. Feynman
God went dynamic with the procession of the Son from the Father. The theoretical jewel of Christianity has been hidden in the bureaucratic mire for more than a thousand years as the executive powers of the Church suppress the creative powers. We proceed on this site by treating the theory of the Trinity as real science, a model of reality grounded in fact, albeit a bureaucratically mandated fact. Formally, however, our model is to be judged by its explanatory power. What we are doing is uniting the theory of the trinity with quantum mechanics to explain how god (the initial singularity) became god (the present Universe) and will continue to evolve for some amazing amount of time, measured in human lifetimes.
Quantum mechanics by a dummy.
Quantum mechanics is the source of energy. We deal with the cosmological constant problem by allowing that at the level of pure energy there is no memory and the only structure is that imposed by the immediate logic of a dynamic system. A simple expression of this idea is . . . hydrodynamics, which describes the flow of fluids with various properties like density, viscosity, etc.
Quantum mechanics describes the vacuum. Not an energy vacuum but a structure vacuum, a system with no memory, no space, no mass, no momentum, no velocity,
[page 174]
Nothing but energy arising from possibility. Possibility arising from formalism.
Quantum mechanics so derived is a dream, something independent of reality. To get reality, we have to introduce memory. Memory is a stationary state. Quantum mechanics tells us that we get stationary states as soon as we impose constraints. The quantum constraint which applies when 'the wave function collapses' is that the exchange of action in any process is measured by an integral number of quanta of action h bar whose classical dimensions are energy.time, ie frequency x time (interval) = 1. We measure happenings in the Universe by how many quanta of action were exchanged. The energy of the interaction tells us the duration of the action: more energy (frequency) completes processes more quickly, jut like a computer (other things being equal).
From the point of view of quantum mechanics, the Universe is a frictionless perpetual motion machine. Quantum mechanical amplitudes vary at a frequency E / h bar, where h bar is exceedingly small. Different states with different energies vary t different rates, and they all superpose to give the world we've got. The energy of this system remains constant, energy as such being neither created nor destroyed, is the total probability of the Universe remains at one, even though the number of formal sates grows transfinitely.
Quantum mechanics is the most abstract and general description we can give of consistent dynamic system
[page 175]
with a compete set of solutions (no dead ends).
Quantum Field Theory = Quantum Mechanics + MEMORY (Quantum mechanics has no memory beyond one cycle).
Where does this view of quantum mechanics leave us with respect to quantum computation. Quantum computation comes from the boundary conditions we place on the flow of energy in our computer. A message is a boundary condition,. It (to some extent) controls behaviour, ie reduces its entropy.
The principle of superposition tells us that only relative frequency matters, so it does not matter where we put our zero of energy.
Thursday 14 February 2008
Sacks page 252: Novartis: 'Every disease is a musical problem; every cure is a musical solution.' Sacks
Friday 15 February 2008
Much of the specification of structure arises from constraint. So I have spent 40 years filling my head with my understanding (and misunderstanding) of everything relevant to this site, which, since theology is the theory of everything includes everything in my life, and I am trying to fit it all into one model. The transfinite network covers all the possibilities, but for the theory to be of any help, it needs to narrow this down a bit, at least locally. The local constraints are local history: as the
[page 176]
song says, you've got to play the hand that's dealt you.
Sacks' books emphasize the division of labour in the neural network and often the plasticity of the network if certain workers are damaged or killed by disease of trauma. An effect of networking is to differentiate the participants so that each has a specific role in the overall picture. If I find someone doing the same thing I communicate with them until our common task becomes clear and then share the load by differentiating, eg you take that end and I will take this end for a simply lift and carry task.
Let us say that the fundamental constraint on the Universe is that it can only be in one state at a time. This forces time division multiplexing if the Universe is to have many states, and the rate of change of states might be in proportion to the number of states available to it, and since the rate of change of state is equal to kinetic energy, we would expect the kinetic energy to vary as the number of states. Since the differentiation of states creates potential energy, the negative of [kinetic] energy, we can see that the total number of states may increase to ℵ0 while the kinetic and potential energy increase of +1 ℵ0. This paragraph has a certain feeling of deja vu attached to it which I might be able to check with Google now that many pages of my notes are electronically published and searchable.
Energy is abstract music? 'Nietzsche . . . spoke of the "dynamic" or propulsive powers of music - its ability to elicit, to drive and to regulate movement. Rhythm, he felt, could propel and articulate the stream of movement (and
[page 177]
the stream of emotion and thought which he saw as no less dynamic or motoric than the purely muscular." Sacks page 257.
[Nietzsche] called his own philosophizing 'dancing in chains' and he thought the strongly rhythmic music of Bizet as ideally suited to this. Sacks page 258.
Saturday 16 February 2008
Sacks page 314: More recently evolved brain functions seem to inhibit the more primitive. This is the key to Catholic morality, suppressing natural desires in the guise of promoting higher spirituality. The network model supports this idea, the higher layers of the network needing to control 'noise' and error in the lower layers if they are to function correctly. Similarly we might imagine that isolated quantum systems fill the entire function space and it is only when the begin to communicate that their outputs are restricted to orthonormality. Zurek
page 316: 'One must wonder about the 'Grandma Moses' phenomenon - the unexpected and sometimes sudden appearance of artistic or musical powers in old age. Without speaking of 'pathology' (perhaps indeed one should speak of 'health' here), there may be a variety of inhibitions - psychological, neurological and social - which may for one reason or another relax in one's later years and allow a creativity as surprising to oneself as to others.'
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