Notes
[Notebook: DB 62 Interpretation]
[Sunday 30 September 2007 - Saturday 29 September 2007]
[page 13]
Sunday 30 September 2007
Organizations perform to what they are measured by'. N 449:159 Butler
There is only one abstract Hilbert space for each 0 < i > aleph(n).
UNITARY EVOLUTION = THOUGHT
MEASUREMENT = COMMUNICATION
UNINTERRUPTED = DETERMINISTIC
The mathematical machinery of quantum mechanics is deterministic, or as deterministic as arithmetic as mathematical analysis can make it. But is the continuity defined by classical analysis trustworthy? In particular, what are we to make of 'the argument from continuity'. The answer lies in the history and process of mathematics. As far as I know, the mathematical consensus is that the transformations in Hilbert space we use to model the mechanism behind events are continuous, deterministic and reversible, that
[page 14]
is they take place at constant entropy or cardinality
TECHNOLOGY = MANIPULATING POSSIBILITIES.
SYMMETRY = BLINDNESS The energy of a system is blind to time, invariant with respect to time not controlled by or correlated with time, but a quantity conserved (remaining the same) no matter what the time.
Feynman: 'The old, deep mystery of quantum mechanics - the interference (pointwise addition] of amplitudes' III 5-10 Feynman
Monday 1 October 2007
How does it work. We see no formal difference between a text with rules expressed in text and a machine a la Turing.
Interference (in physics) = addition = voting. The greatest amplitude occurs where most are in favour and least against (subtraction). Complex system exhibit vector (term by term) addition. Such systems are linear (no meaning or power). Power corrupts voting system by giving more weight to powerful voters than the rest.
We control the world by creating an environment to increase the probability of the desired outcome, whether this environment be a silicon chip or a global regulatory environment for health care. Danzon, N 449:176. Danzon
Tuesday 2 October 2007
Dreaming Dragons Damien Broderick Broderick
Wednesday 3 October 2007
Entropy increases -> count of states increases -> count
[page 16]
of possibilities increases -> potential increases. This fct seems to vbe taken for granted. Why does entropy increase? How does enbtropy incrase? Why are there always nmore states becoming posible?
Is it a natural consequence of reversible computation, since every step of a reversible computation has to maintain its input while generating output? Feynman Computation page ?
In othe words, entropy increases when we keep the history without erasure.
But certain hitories can be compresses and stored as an algorithm which may then be expanded to compute the whole hitory in quetion. So the history we see i the compressible history, compressed by the laws of nature.
Feynman: 'In order to have the probabilities change in time, we have to have the interference of two amplitudes at two different frequencies, and that means that we cannot know what the energy is. The object will have one amplitude to be in a state of one energy and another amplitude to be in a state of another energy. That's the quantum mechanical description of something when its behaviour depends on time.'
ie there are adequate features in the behavioiur to enable it to be mapped onto a sequence of times. TIME is the DOMAIN of behviour. If it does
[page 17]
nothing, it cannot be mapped onto time, except to say that at all times it is the same, an algorithm that compresses all the history of an eternal object into a very short statement, f(t) = a constant!
At its simplest, the state of the world is the superposition of every possible frquency, that is every possible energy, . . .
All this applies to amplitudes which inhabit the complex domain.
What we see (as traffic frequencies in the network) is the variation of the squared amplitudes (possibilities) with time, ie watching myself writing this
17-3 'The choice of origin for our energy scale makes no difference: we can measure energy from any zero we want.' But the rest energy of an electron is still 0.511 MeV.
The coupling between amplitudes in Hilbert space and probabilities in 4-space is fraught with difficulty.
[page 18]
Thursday 4 October 2007
To talk about thing we must name them. The configuration space of any system is the dictionary from which we draw our names, and the rules for using the names constitute a language.
Language gives infinite possibility with finite resources. This is how entropy is created, in discrete tranfinite steps.
The fittings and pipes are a finite alphabet from which one can create an infinity of plumbing systems.
Quantum mechanics is a finite mathamtical alphabet which decribes the flow of probability (entropy?, information, numbers) through the cosmic pipework.
Friday 5 October 2007
INFINITESIMAL = LOCAL
The method of physics is to extrapolate from the local (diuffeential) to the glbal (integral) using local observations to constrain a set of differential equations. Feynman on the S matrix, III 8-8 sqq.
The Universe is very convenently paritioned into space and time. This allows a digital kinematic vision of the world as a series of time slices (spaces) ordered in
[page 19]
time. Dynamics is the study of the variation of spaces with respect to time with an eye to finding elements that do not vary with time as a basis for understanding and prediction of the future.
Feynman III 8-10 'i hbar d Ci (t) / dt = SUMj Hij (t) Cj (t) (8.39) : This equation is then the quantum mechanical law for the dynamics of the world.
(We should say that we will always take a set of base states which are fixed, and do not vary with time . . .)'
Eigenstates = eigenfunctions = eigenTuring machines = computable functions.
The evolution predicted by (8.39) is a parallel computation whose size varies roughly as n2, where n is the dimension of the space in which the model is being run. By running n2 paralel processes, quantum processes become time invariant with respect to compolexity. Of course we could put more energy in and make them run faster.
Does the inevitability of death constrain our lives?
Hamiltonian == energy matrix, which decribes the allocation of bandwidth to pairs of states represented by the indices i and j in the symbol Hij.
[page 20]
'This follows from the condition that the total probability of the system to be in some state does not change.'
At every scale some parts of the world vary more slowly than others. We use the slowest ones to get the greatest certainty.
Creation and annihilation mean that energy states are defined only to a certain precision.
Everything we observe is error free, so we suppose nature has some error correcting mechanism that picks a 'correct' state out of an infinite superposition of possible states.
The basic problem is that there are people in the world like the Burmese military junta and George Bush and other terrorists, who believe that it is quite permissible to kill people indiscriminately for political [purposes]: so we arrive at the height of evil, heavily armed troops massacring unarmed civilians.
Feynman: conservation of strangeness (III 1-13) blocks certain otherwise expected transformations.
[page 21]
What we need to produce is a mapping from quantum mechanics to a network of Turing machines which communicate with one another at rates determined in some way by quantum mechanical amplitudes.
So now we replace the bit in "how Universal" with the quibit in the model of God, our lowest order (two states) model. Expansion from two to the Cantor Universe via the tensor product is 'obvious'. I just have to learn to write it out in the language of the trade. For some reason I maintain my outsider status, neither a qualified plumber nor a qualified academic. A lone wolf with big (possibly posthumous) ambitions.
The formal equivalent of a message a proof that a (a space) is b (a point in a).
F III 11-21 Determinant is a polynomial. Feynman
Vectors of different energy are orthogonal.
