vol VII: Notes
2016
Notes
Sunday 5 June 2016 - Saturday 11 June 2016
[Notebook: DB 80: Cosmic plumbing]
[page 95]
Sunday 5 June 2016
. . .
Monday 6 June 2016
Tuesday 7 June 2016
[page 96]
Back to phys10Space, exploring the notion of a zero-energy universe. This depends on a bifurcation of action into potential and kinetic energy, where potential = − kinetic, so potential + kinetic = 0. This eliminates the problem of an infinitely hot infinitely dense initial singularity which makes no sense, and fits the idea of a dynamic god with fixed points that are mathematically formal but physically endowed with [potential] energy. It also seems to fit the Lagrangian approach to mechanics which defines action S as the time integral of the difference between kinetic and potential energy
S = ∫ (T - V) dt
Still struggling to make space, but the step action to {potential energy, kinetic energy} looks like a good one. The kinetic energy is the rate of processing, the potential energy is in the fixed points at the beginning and end of the process, a particle annihilation creates the energy necessary to create the next particle. This may seem a bit too simple, but we know that one quantum of action is required to create or annihilate a particle, even if we use continuous lagrangian densities to compute the probabilities of these events.
The other idea that is good here is that higher layers need to curate lower layers in order to preserve their own existence, as my mind for instance, must give some thought to my food supply if it is to remain embodied.
And what about the spin-statistics theorem and the matter of entanglement, spooky action at a distance and the velocity of light?
[page 97]
Sacks, Anthropologist page 116: '[Virgil] would pick up on details incessantly — an angle, an edge, a colour, a movement — but he would not be able to synthesize them to form a complete perception at a glance. This was one reason the cat, usually, was so puzzling: he could see a paw, the nose, the tail, an ear, but he coud not see them all together, see the cat as a whole.' Aristotle's 'common sense', the tacit dimension. Oliver Sacks, Polanyi
page 117: 'We, with a full complement of senses, live in space and time. The blind live in time alone.' We measure distance by time, light years.
Wednesday 8 June 2016
Renormalization / quantum field theory. Want to think that all these things should be very simple if looked at from the right perspective (phys11QFT). The mathematics is very complex and riddled with infinities which mostly seem to arise from the assumption of continuity which requires dividing by zero or summing infinite sequences of finite values both of which yield infinities which need to be regularized and renormalized out. I wish I was intelligent enough to see through all this and use the computable network to get some accurate physical results, but really do not have a clue how to start. So will continue on my heuristic adventure until I get too mentally disabled to go on.
Thursday 9 June 2016
Mathematicians and physicists compute with numbers but I compute with words, trying sequences of words to see of they lead to the right result. What is a computation anyway? In the mathematical
[page 98]
sense it is akin to a proof, following a sequence of definite steps (an algorithm) to get from a starting point to somewhere. If the problem is computable, and one follows the right sequence of steps, one will get to the conclusion. This is a bit like driving around the city. The possible routes are endless but I have got to using the map apps in my phone to find an optimum route to my destination. I use the 'map' in the [lexical] / grammatical / syntactical part of my head to get a piece of writing (like this) to get me from a starting point (the nature of computation) to an end point. The end point here is that if one uses a deterministic algorithm like the multiplication algorithm, the answer one gets depends on the numbers you put in [which break the symmetry of the algorithm]. We find a similar feature in search algorithms — the question one asks (to some extent) determines the answer you get. My whole intellectual life revolves around the question is the universe divine and the answer I give is yes, but now I am trying to trace this out in detail and at the present moment am interested in knowing how quantum electro- and chromo-dynamics fit into this journey. I have a heuristic notion that the universe started as a perfectly simple god and gradually complexified to its present state and it is this perhaps that makes me revolt a little when I observe the baroque complexity of the mathematical descriptions of the simplest layers of the world. It seems to me that a lot of this complexity is injected by the physical assumption that the world is built on a continuous differentiable manifold, rather than, as it seems to me, very simple logical calculations, or
[page 99]
symmetries. One good idea I have, I think, is that a continuous symmetry is a nothing [no marks to represent information] and so if we get from A to Bvia a continuous symmetry nothing happens, ie A is identical to B, so we have a conservation law a la Noether. Physicists are inclined to express their conservation laws numerically, so a number corresponding to action does not change with rotation, to energy does not change with time, and momentum does not change with space. We can also turn to more complex group transformations, so we work through U(1), SU(2), SU(3) to get more complex but identical structure in QED and QCD and we can continue this complexification right up to the human group (the human layer) where it is expresses by a list of human rights which are dimensions of human symmetry, features of our nature in which we are all identical [in principle we are all formally identical before the law]. So how do we carry this back into physics using the idea of symmetry with respect to complexity? Neuenschwander
Symmetry, algorithm, equation. Dirac's equation, like Schrödinger's, Newton's and thousands of others is a fixed point in the dynamics and has potential energy to guide the kinetic energy of engineers and tradespeople. Such equations are numerical expressions of the probabilities of discrete events made continuous by the law of large numbers. So we should be able examine Dirac's equation and discern the sort of events it is representing as probabilities, as the normal distribution gives us a continuous function describing the outcome of tossing coins. The Born rule tells us the probability of execution of eigenfunction, giving us the rate of occurrence of a particular computation. Follow this line, perhaps through Planck's quantum harmonic oscillator. There may be hope yet to an answer to be teased out by painstakingly unravelling the knotted strings of partly understood processes. An intelligent universe needs encodes and decodes.
[page 100]
One would like to be a prodigy rather than a plodder. Born rule - Wikipedia, Normal distribution - Wikipedia
Insight = 'collapse of the wave function'.
Sacks, page 185: Nadia Selfe: Nadia Revisited
Friday 10 June 2016
Happy now writing abut the Dirac equation in terms of probability and probability currents, which allows us to think of the underlying process as digital (like the toss of a coin or the execution of an algorithm) while preserving the quantum mechanical formalism in terms of continuous complex numbers, ie cyclic processes like computation, smoothed by large numbers. Law of large numbers - Wikipedia
. . .
Saturday 11 June 2016
Planck eliminated the ultra-violet and infra-red catastrophes in black body theory by coupling the energy of photons to their frequency via E = hf. Maybe a similar strategy would enable us to eliminate all the infinity problems in QFT by reducing the available number of processes from ℵ1 and beyond to the countable set of computing machines.
[page 101]
S matrix - -∞ to +∞ in time and space.
Schwinger, Nobel Prize Lecture: 'Indeed, relativistic quantum mechanics—the union of the complementarity principle of Bohr with the relativity principle of Einstein— is quantum field theory.' Julian Schwinger, page 140
Improvements in the formal presentation of quantum mechanical principles, utilizing the concept of action, have been interesting by-products of work in quantum field theory.
Feynman vs Schwinger: Integral vs differential.
Classical mechanics sees the differential as the infinitesimal rate of change. Digital mechanics [computation] sees it as the execution of a local halting turing machines. Classical mechanics sees a trajectory as the integration of differential. Digital mechanics see it as a series of turing machines joined output to input.
A path that starts with a particle and ends with a particle must be one quantum of action, and since we take this to be the execution of a computation from one stationary point to the next, we associate a computation with a quantum of action. The quanta of actin have the dynamic property that they blend together seamlessly [invisibly], so quantum = {quantum}. see Chapter 2: Model, page 6: Invisibility
Schwinger page 9 (Nobel pdf) '. . . it is in the language of particles that observational material is presented.'
[page 102]
'The quantized field appears initially as a device for describing arbitrary numbers of indistinguishable particles. It was defined as the creator or annihilator of a particle at a specified point in space and time . . . It began to be appreciated that the properties of so-called elementary particles are partly determined by the effect of interactions.' Like us.
'The implication that physical charges are weaker than bare charges by a universal factor is the basis for charge renormalization.
Causality - locality - presence —> simultaneity.
Tanida: Higgs has a vacuum expectation value - a probability that there is a Higgs at every point in space-time. Higgs vev due to electroweak symmetry breaking. Flip Taneda
Handedness - helicity Helicity (particle physics) Wikipedia, Chirality (physics) - Wikipedia
'Mass is something which tells us whether or not helicity in an 'intrinsic property of the particle. If a particle is massless then its helicity has a fixed value in all reference frames. On the other hand, if a particle has mass then helicity is not an intrinsic property, since different observers . . . can measure different values of the helicity . . . '
Chirality
Spinor is a vector of group SL(2, C) which is the universal cover of the Lorentz group. Special linear group - Wikipedia
QFT etc are effective theories describing the statistical properties of the real theory which is an application of the transfinite computer network. (?)
Taneda 17: 'It turns out that even after removing the metaphysical 'faster than light' polarization of the photon, we still have too many degrees of freedom, A massless particles has only two polarizations . . . There is a redundancy in the 4-vector descrption of particles. . . . This redundancy is the cost of writing things in a way that manifestly represents spacetime symmetry. This redundancy is called gauge invariance [ie maybe the two extra dimensions are simply not there for photons at their level of network complexity].
Wiki: A transformation from one field configuration to another is called a gauge transformation; the lack of change in the measurable quantities, despite the field being transformed, is a property called gauge invariance. Gauge theory - Wikipedia
'. . . physicists gradually realized that all forces (fundamental interactions) arise from the constraints imposed by the local gauge symmetries, in which case the transformations vary from point to pont in space and time.'
