vol VII: Notes
2012
Notes
[Sunday 4 November 2012 - Saturday 10 November 2012]
[Notebook: DB 73 Spring2012]
[page 141]
Sunday 4 November 2012
Mehra, Feynman Mehra: The Beat of a Different Drum
[page 42]
Why is the probability of an event φφ*?
Mehra page 73: '. . . the variational principle states that the expectation is statinary in the infinitesimal neighbourhood of any of the eigenvalues . . . '
Memory= fixed energy = zero energy.
Monday 5 November 2012
Mehra page 128: We need to male a coupling between the Lagrangian approach to quantum mechanics and the computational approach, which has for a long tome seemed to me to involve optimization of the digital computational algorithm which seems to be represented in standard physics by the difference between kinetic and potential energy.
page 129: Configuration space = memory. A computation converted an initial state of memory to a final state of memory in a given time which is shortest for the most efficient algorithm at a given energy, ie a given rate of processing.
'Today the princial problem o every new fundamental theory is how to find the corresponding Lagrangian [L = T - U]'.
'The principle of least action is perhaps the most basic principle of classical physics, but its full significance lies in quantum physics: one can find it only in Feynman's path-integral formulation of quantum mechanics.'
Our first step, from pure actionto energy, might be made
[page 143]
by dressing up a clock in all the finery of the path integral formulation.
Once we have worked out the quantum mechanics of the not operation, all else will follow, not, nand, . . .
Potential - possible
Kinetic = actual.
For a clock on tick, tock is the potential and vice versa. So we might say that the Lagrangian is tick - tock, which integrated over a discrete cycle is 0. The world we are developing is so simple that it is hard to understand.
The most obvious unexplained feature of the Universe is the increase in entropy, since quantum mechanics operates reversibly, that is at constant entropy.
From 0 to transfinite; from transfinite to 0.
Mathematics explores the boundaries of complexity that lie between each transfinite space. Normally we work between the natural and the real numbers. Quantum mechanics is a mapping from real space through a complex quantum formalism φ and back to real space, < R | φ | R >. We assume that behind each observable change there lies a hidden process. We see this most strongly in our relationships with one another which comprise the observable messages we send to one another and the invisible processes within us which receive and send these messages, We imagine that peer processes throughout the network have the same general structure, discrete observable
[page 144]
messages and hidden processing.
Quantum mechanics is complexity invariant. The energy equation dψ/dt = Hψ is indifferent to the size of the complex vector ψ, which we may think of as a points in a space of 2, 3, . . . , n, . . . aleph(0, ℵ1, . . . dimensions, each set of dimensions forming a complete basis for the process of interest, ie excluding no possibility, however small. Large sets of remote possibilities may nevertheless contribute substantially to the overall integral.
Quantum sources, although normalized, are not statistically flat [and stationary] like the sources of communication theory.
We have a countable set of Turing machines in an uncountable set of possibel functions represented by permutations of the integers. Permiutations of negative numbers oscillate between positive and negative. -2! - -2 x -1 = 2, -3! = -3 x -2 x -1 = -6, etc. Positron hole theory, a step toward {e+, e-} = ∅.
Essence and existence [potential and action].
Hilbert's formalism has taken the mysticism out of mathematics which we see strongly reflected n the ideas of the Pythagoreans, Plato and their contemporaries.
A differential is a discrete representation of a local situation in a continuum.
Feynman was working his way from the continuous classical
[page 145]
exposition of quantum mechanics to the discrete reality of observation.
How does entropy increase? By copying, that is reproduction.
So Feynman begins with two state systems before building up to the continuous space represented by a function space of uncountable dimensions.
Probability deals with discrete events and shows us a version of the relationship between infinite and finite resulting from the low resolution of the infinite by the finite. Kolmogorov
We go from finite to infinite via the doctrine of limits.
Mehra: Feynman trying to remove the infinite degrees of freedom of the field and the infinite self energy of the point particle from quantum theory by the 'action at a distance' (space-time) formulation of quantum mechanics. page 121.
Mehra page 130: ' "the fundamental problem of the day was that the quantum theory of electricity and magnetism was not completely satisfactory." '
As the Standard Model is now. Standard model - Wikipedia
Feynman: ' "I learned [quantum electrodynamics] from an article by Fermi in the Reviews of Modern Physics later, that there are nothing but a bunch of oscillators and each one of them is a quantum oscillator. What could be simpler? Nothing to it! Why all this hokey-pokey?" '
Quantum oscillator = Turing machine, computer, boson.
[page 146]
Mehra page 122: 'It is here that the theory of action-at-a-distance gives us a different viewpoint. It says that an atom in empty space would, in fact, not radiate. Radiation is a consequence of the interaction with other atoms (namely, those in the matter which absorb the radiation).'
Back to the old 'full duplex' idea explaining ψψ*
Variational principles work in the 'peer zone'.
page 138: 'Feynman invented a completely new formulation of quantum mechanics in terms of classical notions' (helped by Dirac).
page 139: Feynman: ' "In more complicated mechanical systems . . . the state of motion of a system at a particular time is not enough to determined in a simpler manner the way the system will change in time." '
Exit quantum wave function determinism?
Tuesday 6 November 2012
In a way the Trinity has it all: self interaction of the Father gives the Son; interactionof the Father and Son gives the Spirit, and using these two processes repeatedly gives the world we experience as a set of fixed points within the divinity. Reading in Mehra the struggles of Feynman and co to develop a satisfactory quantum electrodynamics one sees a certain similarity, but the great complexity of physical mathematics seems to be so unnecessary and perhaps induced by the attempt to explain all in terms of continuous mathematics which
[page 147]
seems to be the source of the plague of infinites that continues to bedevil the whole business. One the other hand, one despairs of trying to simplify the physics to a discrete model, even if it seems necessary to introduce logical continuity. Feynman and co are attempting to use logical continuity to explain the world in terms of mathematical continuity and getting impossible infinities for their pains.
Photons and electrons are stationary processes, ie algorithms.
An answer to the infinity problem is that the fundamental layers of the Universe are so simple that the local 'machine infinity' is quite finite from the point of view of higher layers, Emergent space is not a continuum in the modern mathematical sense, but a discrete set of interacting algorithms with three degrees of freedom.
From the point of view of algorithmic information theory, that is real information theory, a continuum is nothing, and so it may be meaningless to invoke it in physical computations.
What is my job? I spend my life hitting my head against intractable theological problems.
Rest mass = rate of internal processing = energy = self energy of (eg) electron).
All this continuous mathematics smears out the meaning of the logical processes that underlie the observable world rather like treating the Bible as a lump of paper rather than as a meaningful document. As a meaningful document the Bible is a finite string of symbols (actions) and infinities and infinitesimals are nowhere to be seen.
[page 148]
In a truly atomic Universe infinities, limits and all the paraphenalia of continuity are at best unphysical approximations.Quantum mechanics conceives of the hidden processes of the Universe as arithmetic operations on complex numbers called amplitudes. We want to see them as logical operations involving 'duplex' communications which can to some degree be modelled by continuous complex numbers because of their duality be are in reality encodings and decodings of messages by computations hidden by the invisibility theorem. Shannon's paper on communication in the presence of noise is worked out in a real function space. We might expand this to complex function space by considering any complete act of communication as requiring two applications of the real theory coupled by the Cauchy-Riemann equations to give a complex theory.
Mehra page 259: ' "Rabi told me: 'Just write it up the old way: get it out. You can put the improved technique late on in a more careful paper; but get it out.' " '
page 262: Integration, very common in quantum theory, blots out the artificial detail introduced by differentiation.
Once an electron (or any other particle) is involved in a complex network it is very hard to isolate the personal properties of the particles from the structures induced by its position in the network, person vis a vis role, so although the electron (or the Pope) may be a very simple soul, their social 'dressing' can make them seem very complex,. A proper analysis, however, might eventually be able to distinguish the qualities of the person from the features induced by the role. The
[page 149]
physics of Feynman diagrams points to the inout of the environment to the properties of a specific interaction as perturbations of the behaviour of the particle of interest. We can greatly simplify quantum field theory of we can identify by analysis the letters of its alphabet and distinguish the words and sentences they form from the properties of the letters themselves. The problem of the Standard model as we can see from its Lagrangian, is that it tries to explain everything at one level instead of analysing a level in terms of the levels beneath it.
Matthew 13:12 Matthew 13:12
Feeling is essentially dynamic, but can be aroused by static elements like pictures, music, words, personalities.
Our heuristic principle is that the Universe started off with zero entropy and gradually complexified to its present condition through the evolution of fixed (stable) points. The advantage of a fixed point is that it reproduces the same dynamics to reproduce itself and so becomes more probable than random points in the dynamics.
The simplest system we can imagine may be the interaction of a photon and an electron in one dimension. Insofar as an electron has rest mass, we can see it as a closed process interacting with itself at a certain rate, dS/dt = E = mc2
Wednesday 7 November 2012
We consider a quantum system as a message source and
[page 150]
use quantum theory to predict the output of the source given its input, ie quantum theory is a codec, a reversible coding / decoding algorithm.
The Lagrangian of a logical function like not-p depends on the initial and final states p and not-p and integrates to be exactly 1 quantum of action, as does any computation whose output is different from its input, ie it moves from p to not-p (true of any non-null process).
Mehra page 284: Feynman: ' "by forsaking the Hamiltonian method the wedding of relativity and quantum mechanics can be achieved most naturally." '
My daily battle with intractable theological problems s offset by my practical successes in modifying the deity to improve my habitat and those of other people.
Hamre A Threat to National Security: 'The greatest threat we face today is not external but internal. Our inability as a nation to reach a durable consensus on plans to match our national goals with our financial resources is, in my judgement, the greatest National Security risk.
We need scientific courage to take on false theologies.
Steven Pinker: The Better Angels of Our Nature Pinker
Thursday 9 November 2012
Analysis and synthesis. Newton set science in
[page 151]
spacetime . . . on its way by analysing motion down to infinitesimals and integrating back up to orbits, a procedure that has borne enormous fruit ever since through Einstein to the quantum mechanics and on to the present. Feynman analyzed complex events down to a network of simple events via his diagrams, each interaction of which is itself analyzed thrugh calculus. It seems (Mehra) that Feynman's particular genius was for clear visualization and complex integration [with lots of tricks], In theology we analyze reality down to a completely simple God and then 'integrate' God logically to give is the Universe of experience which we model as a transfinite layered network of events all of which are ultimately made from the 'infinitesimal' of pure action [here we are measuring size by entropy, not mass, length or time]. Network integration. From this point of view the God is both the ultimate ingredient and the ultimate whole.Physics is still mainly using space-time as the domain for its analysis and the other science build upon messages (particles) moving in space and time but the notion that everything is built on the continuous background of space and time leads to many difficulties of dividing by zero and infinite frequencies that require what appear to be cumbersome cutoffs and renormalizations that appear to amount to defocussing the Dirac delta function. Shannon shows how this works in the untization of an abstract continuous space to give error free messaging, What I appear to be trying to do is to do away with continuity and construct spacetime logically, beginning from the observation that the world is quantized or pixellated by the quantum of action and that the quantum of action is isomorphic to the deity which is pure action,. The fixed point theorems (themselves proved in continuous space) provide my latest tool for doing this.
[page 152]
marketdesigner.blogspot.com
onezoom.org
Mehra page 292: Feynman rules.
A photon never rests and in this sense is not a fixed point but on the other ahdn it has (in flat space) a definite energy so conservation of energy is its fixed point,. This is not so on curved (dynamic) space. Here might be a clue.
Mehra page 337: '[Feynman] started off by defining science as an understanding of the behaviour of nature.
God is an integer, ie there is but one God and continuity in the mathematical sense does not apply to God or to any part of it.
In physics derivation = (numerical) explanation. Can i derive anything with the netork model? Not so far, except by treating quanta of action as meaningless units in general relativity, ie energy.time.
Merhra page 368: Insight: Feynman ' "I cannot remember exactly how it happened. I was walking along the street . . . and zing, I understood it. The form (of the wave function) had to look like this." '
So here we se an insight as the detection of a fit. just as the eigenfunction of an operator is something that fits the operator, like a Bohr orbit where the de Broglie wavelengths exactly fit the circumference of the orbit. A 'digital' fit.
[page 153]
Fit by measure, fit by logic, fit by harmony / rhythm, phase locked loop, [fit by order], etc. Feynman's path integral method.For my own safety is would like to establish 'theological licence' which allows theological abuse of mathematics to be greater than the physical abuse of mathematics.
Fit and fixed: things like atomic orbitals or nations) become fixed when they fit their environment. So the complex waves that describe electronic orbitals fit together in various ways each of which is represented by an eigenfunction of the operator use to observe the atom. At the other end of the scale a nation or a person is a hugely complex organism which must, if it is to survive, fit the environment [be able to speak the language and do the actions].
As this idea develops, I feel more pressure to make it public. Here the idea is a gradually strengthening potential increasing the probability of certain actions. I think the subject is so complex that is is best communicated in writing, and I am gradually trying to organize my life so as to maximize my time of writing,. As for what to write, we must advance on both the scientific and political fronts, attracting money from the public to pursue research which stands to yield considerable public benefit, or at least I think so. My faith these days is to give the book of nature absolute priority over the Bible, which is a good book, but carries but an infinitesimal amount of the information about the nature of God compared to the book of nature within which we live and work and are. To be is to communicate and we have continuous broadband communication with our environment through the forest of sensory receptors that keep us in touch with our world.
[page 154]
Compared to this even Facebook is nothing.
Merhra page 437: Feynman: ' "Can a man write his own wave function?" '
Friday 9 November 2012
New Yorker: Fit and Fixed,
We have a challenge here for the scientific establishment, to bring theology into the fold of science.
Mathematics is communicated in words and symbols that pass between mathematicians as they learn and explore the possibilities of mathematical structure. Georg Cantor laid the foundations for twentieth century mathematics by inventing set theory and transfinite numbers, The beauty of set theory is that most of it is intuitively obvious and we can picture it in various sorts of geometric diagrams, the most complex of which are the function spaces in which we model quantum phenomena. By model we mean establishing a correspondence between mathematical symbols (eg the sound 'one') and physical events like eggs. We say the egg is an event because it has a lifetime.
Science has got a bad name for itself by getting into bed with the military and the big money, but some of the income derived from these shady sources has been well spent in revealing to us the nature of the world at both the physical and stretegic / political level.
[page 155]
Here we are users of mathematics rather than pure mathematicians. Pure mathematics trusts things that can be logically derived from some fairly obvious starting pins. Users trust mathematics because it works throughout their daily lives in trade and design.
Theorems not about the numbers themselves but using the numbers as code to describe a multi-dimensional structure like a Hilbert space. Each dimension has a name and a parameter, one real, one complex number.
Prophecy, a dream it do it thing. But to be doable, dreams must be consistent with the health of the Earth and here we find many discrepancies between reality and the ideas of economics, a discipline that has freed itself from too much worry about the planetary consequences of its conclusions and recommendations.
Bandwith = frequency range = energy uncertainty = non=stationarity.
Quantum field theory is built on spacetime but it may have made false assumptions about the continuity of space and time. We have to correct this by seeing how spacetime is constructed from basic physically embodied logical connections.
Fit / love
Photon / electron as algorithms. What does a photon do? Carries energy, action and momentum between electrons. What does an electron do? Emits
[page 156]
and absorbs photon. Each of the quantities carried by a photon is countable in units of h, E/f - h
The 'digitization' of the Universe is expressed by the orthogonality of the basis states in Hilbert space.
Saturday 10 November 2012
The first step towards scientific theology is to abandon the hypothesis that God is other than the world.
Change measures the
- rate
Mehra page 490: Feynman's 'digital' hypothesis: 'Everything is made of atoms."
page 500: QUD: 'photon goes from one place to another, electron goes from one place to another, and the electron emits or absorbs a photon.'
Encased in hot water, I love you.
Can I do it is always the first question. Should I the second.
[page 157]
We imagine the Universe as a communication network. This is easy to do because we are all born communicators and networkers with central nervous systems devoted to integrating and interpreting the vast flow of information coming from our sensual interface with the rest of the world. We know (because we are here with all the rest of the structure of the Universe) that this hypothetical networks hypothetically works, which we understand to mean that it communicates with sufficient fidelity to maintain this gigantic structure. Shannon showed us how we (and by extensions, the Universe) can communicate without error, and so quantization.
The Universe I experience is a fixed point in the dynamics of God.
Insight / fit.Fredkin gate (Mehra page 532) 3 lines in, 3 lines out. Fredkin gate - Wikipedia
Why do I want to digitize the world? - to get all those incomputable degrees of freedom. Why am I dissatisfied with quantum computation? because it misunderstands continuity.
Historically our best representation of the unity of a state is the unity of its sovereign Lord which we imitate in modern times by the role of head of state filled by a person who often has only symbolic power, although there are plenty of old time sovereign dictators like the Pope who are still able to exert considerable force on their subjects to keep them from their natural tendencies and [lead them to] contribute to the power of their Sovereign.
[page 158]
Literary eternity:
'. . . But thy eternal summer shall not fade,
Nor lose possession of that fair thou ow'st,
Nor shall death brag thou wander'st in his shade,
When in eternal lines to time thou grow'st,
So long as men can breathe, or eyes can see,
So long lives this, and this gives life to thee.'
William Shakespeare Sonnet 18
Religion is applied theology. What we are looking for is the application of the theology of creation, a faith or doctrine that gives hope by exploring the powers of cooperation which is founded in love, self love extending to love of the community that supports the self. I have long been supported by the community and have a desire to repay this support (trading on time, extended credit) by identifying [a] clear new foundation for theology.
The simplest quantum mechanical picture shows a two state system which may be described in terms of two orthogonal basis vectors in Hilbert space. This is well established and my interest is in extending it to systems as complex as human communities.
The ultimate steady state of humanity may be imagined as a state of constant energy in quantum terms. This is a state of continuous creation and annihilation of human beings and al other personalities in the Universe.
We like to call all entities persons or sources. Sources can also receive and respond in detail to input rather than [act simply] as actors doing their thing from memory on cue.
[page 159]
So Fit and Fixed must bring in death as well as life. This is the hardest part of breaking away from Christianity, accepting that death is real rather than a transformation from one form of life (Earthly?) to a new form (Heavenly?)
Natural war (brought on by shortage of resources) vs ideological war (brought on by a need to change people's culture). What is a suitbale name for the the totality of learned information? Like phenotype, but nootype or psychotype [culture?].
What we seek is to emphasize the pleasures of creation over the pains of annihilation (death, recycling, writing off).
Theology does not determine particular religions [any more than] physics determines the design of bridges. There are an infinity of possibilities consistent with the constraints ultimately imposed by the consistency of the universal dynamics communicated to us through the consistency of the fixed points we observe in the world.
I can bore myself into writing. It is too wet to build and the internet has gone off, so no distractions there.
An 'atom' of space-time comprises 4 memories and various transformations between them. It is measured by action, ℏ. We start with one state or memory, the initial singularity and then go to 2, 3, 4. Then we get a multiplication of 4D space from a single atom of space to the current Universe. Atoms of 4 space-time can execute the five species of covariant transforms represented by the gamma matrices which can themselves be constructed from Pauli matrices. [see also Davis, quadruples Davis]
[page 160]
Veltman page 3: 'Compact groups have unitary representations. The Lorentz group is non-compact and its representations are not necessarily unitary.
Creation: symmetry breaking: every atom within me has a distinct role.
In general, all that goes on in a four space atom can be imagined as represented by the rotation matrices.
Atoms of space communicate by gravitons?
The role of each atom may be mapped to its space-time coordinates in my body, so that general covariance is in a way broken because local relative positions must be retained for proper functioning and are maintained by bonding.
atoms of spacetime isomorphic to atoms of momentum-energy, measured by quanta of action.
The adventures of X = interactions of X and environment.
Space must expand by copying itself. It is not a continuum but a power network of entities with no particular structure. Each unit of space is an inertial frame. The actions of space are build on the clock of time, multiplexed so as so serve every atom of space, sharing energy and momentum like time and space.
[page 161]
We want to upgrade spacetime from a differentiable and integrable manifold to a computable manifold., the simplest instance of which is a two state memory and a process for changing the state from p to not-p, underlies all process and appears to us as time and energy. We then expect this system to grow like the transfinite numbers to give us the manifold of events that we experience and are.
