vol VII: Notes
2017
Notes
Sunday 27 August 2017 - Saturday 2 September 2017
[Notebook: DB 81: Scientific theology]
[page 118]
Sunday 27 August 2017
Zurek: Decoherence: This looks like an unnaturally long and complex attempt to explain the transition between 'quantum' and 'classical' states, ie states represented by a complex number or function ψ [and a real number]. The equivalence between vectors and functions [is shown] by the fact that a vector is a mapping from the natural numbers, which index the components of the vector, to the complex numbers, the value of the probability amplitude represented by each [element of the] vector. The mapping from the natural numbers to the complex numbers is dynamic, changing (in the Schrödinger picture that we assume here, one view of the relativity of vectors and operators) in a way determined by the wave equation, so we see no problem in principle to modelling eigenvectors as Turing machines, ie computers. This suggests that the cardinal of the set of eigenvectors is equivalent to the cardinality of the set of computers, ie ℵ0. Wojciech H Zurek: Decoherence, Einselection, and the Existential Interpretation (the Rough Guide), Schroedinger picture - Wikipedia
[page 119]
We close the gap between continuous and discrete by recognising that the discrete, ie the logical, is much more powerful than the continuous since all the properties of the continuum are established by discrete arguments (theorems) which can be represented by turing machines. Every valid deterministic computation is a proof. The eigenvectors are the computer that evaluate the eigenvalues, and there is little empirical doubt that these values are computed by deterministic processes. It may be claimed, through the doctrine that continuous arithmetic is just as deterministic as digital arithmetic, but this is not possible since we cannot make a deterministic continuous (ie analogue) computer precise because of the uncertainty introduced into mathematics by Gödel and Turing. Getting there, a bit like sex, looks like there might be an orgasm (halted computation emitting an eigenvalue) to come.
As we lay out the mathematics of the transfinite computer network we model it with the results of quantum field theory, based on the idea that quantum mechanics describes a communication network. We describe this first in the transfinite world of Gödel and Turing and then bring it back to earth beginning with the assumption that ℵ0 = 0, 1, 2, 3, . . . in succession as the world complexifies.
einselection Einselection - Wikipedia
My writing is conformal to wrestling for orgasm, ie struggling to bring a computation to a halt, yielding observable output as a consequence of the hidden [but felt] process generating fixed points.
Each dimension in a Hilbert space may be considered as a source represented by a basis vector. Each of them progresses at its own phase velocity [frequency].
The mapping of computers onto wave functions has something to do
[page 120]
with the Born rule.
The rotation of an orthonormal base must proceed by infinitesimal breaks of orthonormality in the basis vectors, and the whole rotation group is then constructed by integration, but can this be physically realized? Lie Group - Wikipedia
The geometry of orthogonality and rotation is built around the Pythagorean theorem [a fixed point in any Euclidean space].
How do we logically - computationally represent the various group operations that play a role in physics? We may think of an algorithm as a vector in a space which the process follows element by element, or as a box in which everything has to find its natural eigenfunctions, so that they can all live together in harmony. The best known family is the vibrating string. String vibration - Wikipedia
Clebsch-Gordan coefficients for SU(3). Special Unitary Group. Clebsch-Gordan coefficients - Wikipedia, Special unitary group - Wikipedia
Monday 28 August 2017
Is this work or self indulgence? What is the difference? In effect we work to indulge ourselves, the purpose of work being directly or indirectly to improve our physical and spiritual condition. Somewhere in my upbringing [or my evolution] I was oriented toward doing good [cooperating] or trying to make the world a better place as an alternative to solipsistic self indulgence, and I still feel this and feel that my theoretical quest is a work in this direction, giving us a scientific understanding or our nature and role in the world and bringing to light the peacemaking power of divine creativity. The challenge, in terms of effective propagation, is to write something that inspires readers to develop and propagate the ideas expressed, that is to create a field of study and action. I like to think I am onto something and want to keep the little flame going until it finds suitable fuel, or potential (in the minds of readers) that will be released by the ideas proposed.
[page 121]
Libertarian solipsism versus cooperative parallel processing of the human state, rotating the state vector of humanity toward peace, ie complete human symmetry [and consequent harmony?].
Feynman III:3: 'When a particle goes by a particular route the amplitude for that route can be written as a product of the amplitude to go part of the way with the amplitude to go the rest of the way. So [if the ampliitude] for a particle to go from a to b is ψ, to go from b to a is ψ*, then the probability of the round trip is ψψ*, ie |ψ|2 = p. Feynman, Leighton & Sands FLP III:03: Chapter 3: Probability Amplitudes
<r2|r1> = eipr12/h / r12 where p is the momentum which is related to the energy by the relativistic equation p2c2 = E2 - (m0c2)2 or the non-relativistic equation KE = p2/2m.
'Provided that the particles do not interact, the amplitude that one particle will do one thing and the other something else is the product of the two amplitudes that the two particles would do the two things separately.'
'Suppose we didn't know where the particles [approaching the holes] came from before arriving at holes 1 and 2 of the first wall. We can still make a prediction of what will happen beyond the wall . . . provided that we are given two numbers: the amplitude to have arrived at 1 and the amplitude to have arrived at 2. In other words, because of the fact that the amplitude for successive events multiplies, . . . , all you need to know to continue the analysis is two numbers — in this case < 1| s > and < 2| s >. These two complex numbers are enough to predict all the future. That is really what makes quantum mechanics so easy.
[page 122]
'You must never add amplitudes for different and distinct final states. . . . by "final" we mean at that moment tje probability is desired—that is when the experiment is "finished".
'. . . we must be careful not to attribute too much reality to the waves in space. They are useful for certain problems but not for all.'
FLP Chapter 4: Identical particles: 'If a process involves two particles that are identical, reversing which one arrives at a counter is an alternative that cannot be distinguished [not revealed] and—like all cases of alternatives that cannot be distinguished interferes with the original unexchanged case. The amplitude for an event is then the sum of the two interfering amplitudes; but, interestingly enough, the interference is in some cases with the same phase, and in other with the opposite phase.' Feynman, Leighton & Sands FLP III:04: Chapter 4: Identical Particles
'Why is it that particles with half-integral spin are Fermi particles whose amplitudes add with a minus sign, whereas particles with integral spin are Bose particles whose amplitudes add with a positive sign? An explanation has been worked out by Pauli . . . The explanation is deep down in relativistic quantum mechanics. That probably means that we do not have a complete understanding of the fundamental principle involved.' Spin-statistics theorem - Wikipedia, Ian Duck and E.C.G. Sudarshan: Toward an understanding of the spin-statistics theorem
'It is generally true in quantum mechanics that the amplitude to get from any condition φ to any condition χ is the complex conjugate of the amplitude to get from χ to φ, < φ | χ > = < χ | φ >*.
Any state can be decribed in a set of base states by giving the amplitudes to be in each of the base states.'
[page 123]
FLP Chapter 7: 'Why does an atom radiate light? The answer has to do with entropy. When the energy is in the electromagnetic field there are so many different ways is could be—so many different places where it can wander—that if we look for the equilibrium condition, we find it in the most probable situation the field is excited with a photon and the atom is de-excited.' Feynman, Leighton & Sands FLP III:07: Chapter 7: The Dependence of Amplitudes Upon Time
'You may be thinking that it is strange to think of a "particle" which has equal amplitudes to be found throughout all space [perhaps because quantum mechanics dates from an epoch before space]. After all, we usually think of a "particle" as a small object located "somewhere". But don't forget the uncertainty principle. If a particle has definite energy it also has definite momentum. If the uncertainty of momentum is zero, the uncertainty relation ΔtΔx = ℏ tells us that the uncertainty in position must be infinite, and that is just what we are saying when we say that there is the same amplitude to find the particle at all points in space.
'Although the amplitudes vary with time, if the energy is definite they vary as an imaginary exponential, and the absolute value does not change.'
'. . . we can measure energy from any zero we want.'
Chapter 8 The Hamiltonian Matrix
'The complete description of an electron, so far as we know, requires only that the base states be described by momentum and spin. Feynman, Leighton & Sands FLP III:08: Chapter 8: The Hamiltonian Marix
'Because the operation of waiting is especially important, we call it U instead of A.
'. . . we can analyze any time interval if we can analyze a series of short time intervals in between.' Provided calculus applies.
To apply calculus we imagine some plausible behaviour at an infinitesimal level, perhaps defined by a function and then integrate this to arrive at the big picture. Perhaps the most audacious application
[page 124]
of this idea is Feynman's path integral. But where does this get us? Is there any [more] information in the integral than there was already in the infinitesimal? So why not (on the logical paradigm) simply apply a logical function directly (if you can find it) to the situation in hand as a software engineer would do if she wanted to transform the state of the machine from a> to b. Feynman & Hibbs: Quantum Mechanics and Path Integrals
Feynman lecture 8: [In accelerator experiments] there is no experimental evidence on the details of the process, only what goes in and what goes out.' Feynman, Leighton & Sands FLP III:08: Chapter 8: The Hamiltonian Matrix
Chapter 10: '. . . s "virtual exchange" means that the phenomenon involves a quantum mechanical interference between and exchanged and a nonexchanged state. Feynman, Leighton & Sands FLP III:10: Chapter 10: Other Two=State Systems
In the "particle" theory of electromagnetism, the process of a virtual photon exchange gives rise to all the phenomena of electrostatics.
Tuesday 29 August 2017
The outputs of a [classical] communication source and a quantum source have the same characteristics. Now compare mechanisms — every [measurement] operator is a codec. Codec - Wikipedia
A message is vector; a function is vector, in function space
A computer is a vector in function space mapping from a program counter to a string of logical operations.
Feynman chapter 8: 'We have discovered that any state in the world can be represented as a superposition—a linear combination with suitable coefficients—of base states.
Fields devised to avoid action at a distance which the network does
[page 125]
using particles to carry messages through spacetime. The messages exist and travel by logical processes that antecede the space-time metric.
'Prepare a state' - put a system through a filter, eg Stern-Gerlach. Stern-Gerlach experiment - Wikipedia
The basis vectors of an operator are orthogonal and (we guess) it takes a quantum of action to transform one into another.
In the Shannon word noise is controlled by packaging information into lumps. In the physical world where information is physical this packaging is achieved by bonding which is explained in quantum mechanics by energy (physics) and entropy (psychology).
I look at all the structures I have build and appreciate the power of just plodding along realizing a design, gradually dealing with all the devilish details encountered in the realization. Now that I have given up building for writing, similar algorithms apply. These notes are intended to serve as a log of the process of building natural theology and using it as a set of principles to design a natural religion, seeking the perfect balance between fermionic behaviour (solipsism, libertarianism) and bosonic behaviour (totalitarianism, cloning into one state.
Is Hilbert space compact and convex?
Identical particles - identical messages, but at different points in spacetime.
Phase change distinguishing fermions from bosons is a sort of square wave, π difference, ψ + ψ vs ψ − ψ.
Feynman III:7: Amplitudes are dependent upon (aware of) time.
[page 126]
Stern-Gerlach: '. . . only one component of a particle's spin can be measured at one time, meaning that the measurement of the spin along the z axis destroys information about the particle's spin along the x and y axis.' Does this mean sin exists in 2D space-time?
Let us imagine that only one electron exists in the pre-space epoch and it is somehow reproduced to make a vast number of electrons as the space expands and the same for all the other fundamental particles that are essentially points built out of the code implicit in space. So photons and electrons exist in time but are multiplied by the emergence of space. ?
Wednesday 30 August 2017
One of the assumptions of the application of calculus in physics is that infinitesimals are linear, that is very short pieces of curves can be assumed to be straight. This works in the geometric world but not in the logical world where all the functions [except identity] are [discrete] steps [as in a proof].
We might say that there are no things only messages, which, in the form of particles ranging from atoms to galaxies and beyond, are the only things we observe.
I have written the same things many times, always looking for a succinct, comprehensive and stable text [writing is like software for the mind].
Art Hobson: There are no particles only fields Art Hobson: There are no particles, there are only fields
Hobson page 2: 'Based on standard non-relativistic and relativistic quantum physics, do experiment and theory lead us to conclude that the universe is ultimately made of fields, or particles, or both or neither?
[page 127]
Hobson page 2: Wilczek: ' " uniquely (so far as I know) among physicists of high stature, Feynman hoped to remove the field-particle dualism by getting rid of the field." '
page 5: '[Faraday] saw lines of force as space-filling physical entitites that could move, expand and contract. He concluded that magnetic lines of force, in particular, are physical conditions of "mere space" (ie space containing no material substance). Today this description of fields as "conditions of space" is standard.'
'if energy is emitted here and now, and received there later, then where was it in the meantime? Clearly in the field [or just as clearly in a swarm of particles!].
page 6: 'For Einstein, there was no material support ether to support light waves. Instead the "medium" for light was space itself. [Now we are saying that it is a field]
'The implication of special relativity that energy has inertia further reinforces both Einstein's rejection of the ether and the signficance of fields. Since fields have energy they have inertia and so should be considered "substance like" themselves rather than simply states of some substance such as ether.' or space-time?
page : '. . . fields are inherently extended in space and don't have specific positions', ie they exist in a layer 'under' space [somewhere between the initial singularity and space].
'. . . the radiation field's quantum states exist in a Hilbert space of variable N called Fock space. . . . the full state of |ψ> is (in general) a superposition of states having a definite number of quanta [one quantum of action = 1 cycle per second of energy?]. Fock space - Wikipedia
page 11: 'Quantum fields have one particle-like property that classical fields don't have: they are made of countable quanta.'
page 12: 'The superposition principle should have been a dead giveaway: a sum of quantum states is a quantum state. Such superpositions are characteristic of all linear wave theories and at odds with the generally non-linear
[page 128]
nature of Newtonian particle physics.'
Hobson page 12: A benefit of QFT is that all quanta of a given field must be identical because they are all excitations of the same field, . . .. ' How does this field fill all space if it can not grow with the space rather that spilling into it and spreading?
page 12: 'When a field changes its energy by a single quantum it must do so instantaneously, because a non-continuous change would imply that, part way through the change, the field had gained or lost only a fraction of a quantum. . . . a quantum is a unified entity even though its energy might be spread over light years—a feature that raises issues of non-locality intrinsic to the quantum puzzle [also, we presume, the change in the field must propagate superluminally].
page 14: Two slit experiment explained by extended field, not localized particle. Dirac: 'Each photon interferes only with itself '.
page 18: Two slit: 'only spatial fields must be postulated to form the fundamental objects to be quantized . . . while apparent particles are a mere consequence of decoherence [ie localization by the detection process]'. So how does the detection process decide where to localize to give the observed interference pattern?
page 20: 'even under a broadly inclusive definition of "particle" quantum particles conflict with Einstein causality.'
page 20: QFT vacuum phenomena that are difficult to reconcile with particle, ie Casimir effect, Lamb shift, electron [anomalous] magnetic moment. Casimir effect - Wikipedia, Lamb shift - Wikipedia, Anomalous magnetic dipole moment - Wikipedia
We do not yet understand the quantum vacuum. The most telling demonstration of this is that the most plausible theoretical estimate
[page 129]
of the QFT estimate of the energy density of the vacuum implies a value pf the cosmolgical constant that is some 120 orders of magnitude greater than the upper bound placed on this parameter by astronomical observations.' Stephen Weinberg: The Cosmological Constant Problems
So we won't let this worry us, since QFT in QED gives results accurate to one part in 108ish.
The trouble lies in the uncertainty princilpe which is really just telling is that we cannot know what s going on between the natural numbers and our development of real numbers to fill this gap is unphysical. Every measurement is digital, and the least uncertainty is the gap between the least significant digits, eg millimetres in the construction business
page 22: Unruh / Sokolov-Ternov effect. Sokolov-Ternov effect - Wikipedia
'The Unruh effect is counter-intuitive for a particle ontology, as it seems to show that the particle concept isobserver-dependent. Of course it is, a particleis a message.
'Non-locality is pervasive, the characteristic quantum phenomenon.'
E. Lombardi, F. Sciarrino, S. Popescu, and F. De Martini E. Lombardi, F. Sciarrino, S. Popescu, and F. De Martini: Teleportation of a Vacuum-One-Photon Qubit
Our central nervous system is literally a microcosm, a subnet of the universal network.
Thursday 31 August 2017
Can I really establish that the universe is digital, ie
[page 130]
logic driven, and what is the point if I do? This development seems essential of we are to consider the Universe to be divine so that we replace physics based on the notion of continuity which can be seen to be essentially meaningless, since a continuum carries no information, with the notions of logic and psychology, which break the symmetry of the continuum with events. Energy is a measure of the rate of events, the time frequency of quanta of action.
Friday 1 Septembrt 2017
Feynman maintains that we get the same results on the wave and particle picture, they are duals. Hobson, Weinberg and co want to go all the way with fields but it looks a bit problematic to me but I have yet to have the vision that enables me to see digital to the core enabling calculations. It is clear, however, that we can consider things like the Lamb shift to be the work of channels with relatively low energy / frequency.
The one thing we know is that every event involves a quantum of action. The problem is to map from quanta of action to energy levels which we measure by establishing harmonies with known frequencies. Because we have no fixed zero of energy all these frequencies are expressed as energy differences. The wave functions are a set of potentials which control the motions (including creation and annihilation) of the particles as the gravitational potentials control the motions of the planets and every other thing.
We start with de Broglie who proposed that periodic potentials apply to all forms of energy, so the frequency of the potential determined the energy of the event. Harmonic computation. The clock in a computer controls the superposition of the potentials that drive the execution of computations. The potentials are invisible and manifest themselves in the behaviour of the particles. Quantum field theory is in effect quantum potential theory and the particles and potentials are duals, two representations of the same
[page 131]
information, one is not the other. How does this fit with bosons and fermions? The layering of the software beginning with the initial singularity seems to be a good paradigm and is perhaps the central point of e19_gravitation, inspired by the ancient idea of the Trinity which need not be mentioned in the physical paper but is central to the theology in e17_scientific_theology. We might se gravitation and particles as fixed points in a differentiable manifold that describes gravitation. Louis de Broglie - Wikipedia
Invisibility. What is going on inside god? Model: page 6 Invisibility
In a photon each cycle of the wave is a quantum of action to the energy of the photon is proportional to its frequency.
I have a headful of bits and pieces of quantum mechanics, information processing, etc etc but have yet to boil all these down to a consistent picture that deals with all the problems I see in our current theological and physical pictures of the world. All the time I am looking for a logical or psycho-logical picture of the world because it seems more consistent with my own mind and the mind of god.
How do we explain the linear superposition of potentials? Vector sum of potentials from a distribution of masses / 'charged' particles.
FLP III:1 Heisenberg ' "It is impossible to design an apparatus to determine which hole electron passes through that will not at the same time disturb the electron enough to destroy the interference pattern.
'One might still ask: "How does it work? What is the machinery behind the law?" No one has found any machinery behind the law. No one can "explain" any more than we have "explained". No one will give you any deeper representation of the situation. We have no ideas about a more basic mechanism from which these results can be deduced.' Feynman, Leighton & Sands FLP III:01: Chapter 1: Quantum behaviour, §7
[page 132]
Feynman III 1-8 The uncertainty principle: 'This is the way Heisenberg stated the uncertainty principle originally: If you make the measurement of any object and you can determine the x component of its momentum with an uncertainty Δp, you cannot, at the same time, know its x-position more accurately that Δx ≥ ℏ/2Δp, where ℏ is a definite fixed number given by nature. . . . the more general startement was that one cannot design equipment in any way to determine which os two alternatives is taken without, at the same time, destroying the pattern of interference.'The uncertainty principle "protects" quantum mechanics. Heisenberg recognised that if it is possible to measure momentum and position simultaneously with greater accuracy, the quantum mechanics would collapse. So he proposed it must be impossible. Then . . . nobody could figure out a way to measure the position and momentum of anything . . . with any greater accuracy. Quantum mechanics maintains its perilous but still correct existence.' Werner Heisenberg: Über den anschauclichen Inhalt der quantentheoretischen Kinematik und Mechanik
So we try to measure the diagonal of a unit square with a tape graduated in units. The best we can do is say that it is between 1 and 2, so let us guess [one and a] half. When the unit is ℏ the best we can do with the accuracy of ΔxΔp is half a Planck. This is a measure of the product of errors. People say that if we know the momentum exactly we have no idea of the position, but perhaps this is taking it a bit too far. On the whole all we can say is that our calculations are accurate to ±ℏ.
A Schrödinger [moving] eigenvector is a computer in action
Quantum jump (from orbit a to orbit b is logical, not continuous.
[page 133]
Farmelo: Dirac page 87: xp - px = iℏ/2π
page 88: Eddington: ' "The fascinating point is that as the development of the process proceeds, actual numbers are exuded from the symbols.
page 89: Dirac: The fundamental equations of quantum mechanics Paul Dirac
page 94: 'Stoppard: "A door like this has cracked open five or six times since we gt up on our hind legs. It is the best possible time to be alive, when almost everything you know is wrong." '
page 109: The interpretation problem is classical quantum mechanics was solved by Born. How do we solve the parallel problem in logical mechanics? Psychological mechanics is based on [abstract, transfinite] computer networks.
Saturday 2 September 2017
Logical tunnelling annihilate the input, create the [output]. Instead of a continuous field, we have a logical field implemented by a network [a channel is not a continuous 'wire' but a computation].We see the interface between logic and arithmetic in the binary digital computer, first revealed in Russell and Whitehead's Principia. The simplest process we have is the 'half adder'. How does this idea manifest itself in quantum mechanics? Mapping, eg 0 = false, 1 = true. Whitehead & Russell: Principia Mathematica, Adder (elecronics) - Wikipedia
Farmelo page 129: 'The great majority of [physicists] still thought like engineers and were mathematically weak by the standards of Dirac and his peers. So most physicists were still trying to visualise the atom as if it were a mechanical device.' Rather than a logical device, a network exchanging quanta of information as understood by Shannon.
My ideas need a matrix, and are given context by the[page 134]
theory of everything we call theology.
Dirac (Farmelo 130) ' "[Projective geometry] was most useful for research but I did not mention it in my published work . . . because I felt most physicists were unfamiliar with it. When I had obtained a particular result, I translated it into analytic form ad put down the argument in terms of equations.
In a 'full' unverse, all motion is permutation. I go north the air I occupy goes south. Wave motion is rather like this, swapping one thing for another and back again At the bottom level of the universe, permutation of bosons produces on new phenomena but permutation of fermions produces structure through the exclusion principle.
Fixed point theory picks structure out of completely simple divine dnamic continuum, which is functionally identical to the initial singularity or the vacuum. How many times hae I said this? Each time slightly coloured by a new context, feeling a sort of Lamb shift.
page 181: [Dirac] was convinced that [his equation] was correct—what was needed was a correct interpretation of the mathematics.
page 204: ' "No progress without paradox." '
Cosmological constant problem: the lowest energy states of the vacuum harmonic oscillatorsare ½ℏω, and there are so many of them, and theor frequencies o high that their energy appears t be 10
[page 135]
to deal with this problem.
Vacuum - fundamental information free energy network from which all else is built, quantum mechanics, relativity . . . Vacuum is the region where pure action bifurcates into kinetic and potential energy, whose total is zero . . .
From a logical point of view an electron is not a pint of zero size and infinite self energy but a symbol with two spin states and mass which means a 'private' process and momentum which is relative to an observer in a certain reference frame (as is the direction of spin)). Make sen of this. A photon has spin 1, but the frequency of the quanta in its process is proportional to its momentum which is fixed by its energy, since its velocity is fixed, so its time frequency and spatial frequency are deterministically related.
pag 330: J S Mill: "What are the first general propositions from which all the uniformities existing in nature could be derived?' We say computer network theory, NAND.
