vol VII: Notes
2015
Notes
[Sunday 13 September 2015 - Saturday 19 September 2015]
[Notebook: DB 79: Galileo Wins]
[page 75]
Sunday 13 September 2015
Elements of metaphysics = [root] symmetries:
1. The universe is divine, conservation of act, gauge symmetry
2. conservation of energy - time
3. Symmetry with respect to complexity
4. Definition = 1/Universality
5. Fixed point theory
6. Logical continuity vs geometric continuity
7. gravitation is tone deaf
Can I convince myself of the truth of my gravitation story? [it remains a suggestion]
Gravitation is tone deaf and therefore continuous (equiprobable, every point on the real line has an equal chance [of 1/ℵn where ℵn is the cardinal of a continuum].
Lets say that fixed points are logically bound. They come in pairs at each end of an invariant operator [codec], that is a bit of software in the network model. Networks open sets to mapping, so we can imagine every natural number correlated to every other natural numbers, one at a time, as the basic group of the world modelled as a network.
The constraint of quantum mechanics is that a message must be codable and decodable, ie reversible elements of a group. [orthogonal, Wojciech Hubert Zurek: Quantum origin of quantum jumps]
Groups of computations, logical group. Gravitation as the generator of the transfinite discrete (logical) group.
[page 76]
Gravitation is the protocol for sending an empty message from one point to another, The only constraints in Einsteins theory are continuity and the conservation of energy, a consequence of the conservation of action and the relationship ℏ = E / ω, E and ω are the same number, cardinal.
The group of the universe increases in order like the transfinite numbers. Order (group theory) - Wikipedia
What is fixed is the metric, relating ℏ, time and distance [space-time interval].
The space of computable numbers, computable transformations. The codec group, comptising all the pairs (a, b) = I, ie b = a-1. Quantum reversibility is the fundamental constraint.
We begin with the Lorentz transformation in 2D universe (the other two space dimensions are ignored). So we can say the group of Lorentz transformations is the group of codecs [isomorphic up to a cardinal with the circle group].
Quantum codec |ψ|2 = ψψ* = 1. Can write this but do I understand it. The network idea is leading me deeper into the woods.
ie to be real a quantum message must be a product of two components ψ and ψ* representing the forward and return phases of communication, send and check.
The software of spacetime underlies all observable action.
Spacetime is the smallest self-sustaining computation, in a consistent system of energy conservation, potential and kinetic.
[page 77]
Lonergan judgement: is this idea worth going on with?
Field theory is an example of space filling plumbing which we imagine as a network of discrete leakproof pipes whose cross section is proportional to flow [and volume to flow2 ?].
The desire to construct a logically consistent picture of a divine universe has taken me a long way away from both Christian and physical dogma.
Every act is consistent is guaranteed by the uncertainty principle.
MTW: page 305 '(5) Between every every event and every nearby event there exists a frame independent coordinate independent space-time interval ("Riemannnian geometry"). (6) Space-time is always and everywhere locally Lorentz in character. . . . " Misner, Thorne & Wheeler: Gravitation
Einstein's geometry is descriptive rather than explanatory. It does not actually tell us what makes things tick. This is true of all continuous theories. We need discrete computation to explain things.
The unit of space-time is the quantum of action. The unit of space-time is the velocity c [the unit of all events is the quantum of action].
Quantum mechanics describes the physical realization of a computer. Computation becomes universal in 4-space. Meaning? Tba. 'Not' is a logical tool, can be used to create both sequential and simultaneous dualities (boson, fermion).
Lorentz = 2D. Lorentz × Lorentz (geodesic deviation) = 4D.
Memory: fixed point
[page 78]
Lorentz × Lorentz = first order to second order. Gravitation binds to itself.
How do we express fixed points in terms of amplitudes and probabilities. The Born Rule. So a state of fixed (potential) energy is a stationary state: stationary / potential; dynamic / kinetic.
An impasse.
points to make
: gravitation may be continuous / carries no information
: it is a subroutine in every process because it affects them all
: coterminous with Lorentz transformation, the symmetry that couples inertial frames
: second order, created by interacting with itself
: second order metaphysics, after first order, in which essence and existence are indistinguishable
: gravitation is the unifying symmetry of space-time
; gravitation = metaphysics (again)
: potential
Have we come to a dead end? What is it? How are quantum states propagated? Encoded in particles. Gravitation and entanglement. Quantum computation operators used to make a Lorentzian 4-space. Quantum circuit for Minkowski space. Particle - fixed point - memory - potential.
Monday 14 September 2015
Developing a fork of Christianity. Fork (software development) - Wikipedia
A coupling based on differentiation is a flow coupling. What flows in general relativity? Energy. The disposition of
[page 79]
the energy that we see in the current universe depends forst of all om gravitation, and then on particle physics when gravitational collapse heats things to fusion temperatures, and, in the inverse sense, the universe expands toward zero temperature and energy is conserved and recycled through the network of pipes described by quantum theory, ie mappings of the natural numbers to themselves.
I think I am gradually making my way from timid interloper into a confident player on the science / theology scene. A slashy.
Fixed points are surrounded by potentials. Curvature = potential
Trying to bring the principles to bear. The Einstein equation embodies the idea that all continuous second order transformations with an invariant metric are possible in spacetime. What is the digital version of this, starting from 2D Lonentz - 2 basis states, 1 fixed, the other continually advancing in phase, perpetual motion. So we consider the Pauli matrices. Particles 1D, 2D, 3D. So we have a basis vector |space, time>, |momentum, energy>, |4-momentum>. The basis of the universe is the energized qubit.
Now we consider digital transformation beginning with not and we imagine a structure <not-p|operator|p>, where the operator may be considered to be any invertable transformation whatever, [the computer group].
We are avoiding detail by being abstract, broadening the focus by reducing the resolution until we come to zero resolution, we see a big formless nothing which then, like a developing egg, begins to divide in the sequence 2, 4, 8, 16 etc. How do we see this happening in a network? How many divisions
[page 80]
until we have dynamic 4-space? Construct space as one constructs an embryo. What we need to do is construct a pre-geometry to explain the space of the universe.
At the pointy (simple) end, God and gravitation.
Tuesday 15 September 2015
Einstein's general transformation is co complex in 4D that the elucidation of gravitational physics did not really get going until computers were invented. What we wish to do here is examine the transform in smaller spaces, starting with the single dimension of local (proper) time which predates the Lorentz transformation and then working up to 4D and beyond into particle physics, biology, psychology and theology.the basic question for relativity is how do the dimensions interact [how are their measures related]. In Euclidean and Minkowski space metrics between dimensions are transformed by pythgoras' theorem: r2 = x2 + y2 + z2. At high velocities we introduce time into the equation, transforming it to distance with the constant c and prefixing it with the operator i. The basic dimension is represented by the recurrent phase of the circle group [which we might imagine as running forward and backward in time, a superposition of opposing complex phases].
How would you build a computer given no constraints, [that is no hardware?]. In other words how do we introduce constraints into an unconstrained system, and in particular how do we introduce constraints that introduce no constraint, ie they leave the unconstrained system unconstrained and simply exist as fixed points in the unconstrained dynamics. God = dicttor = captain = etc, unconstrained constraint.
[page 81]
The beauty of the monastery was that it was all time to think. This was enforced by the rule of silence (except in recreation periods). I remember sitting at recreation reading Park's book on quantum mechanics: antisocial in the quest for knowledge? Maybe a lifetime characteristic - come home from the party early and read. I feel that id have come a long way not becasue I am particularly intellgicne but becasue I have kept my nose to one gridstone for about fifty years and have followed a fairly straight trajectory from How universal until now, where I am trying to see the relation between God and spacetime, the interface where we meet God [God's face].
Communication relies on orthogonality but also breaks it when rotating vectors into new codes, The maximum entropy form of a vector has all components equal.
Sets: containerization and packing my car.
Complexity increases with dimension because the computation of each dimension in a transformation concerns not only its pythogorean relation to other dimensions, but also their first and second derivative with respect to it So in 4-space we need an array of 64 connection coefficients, culled by symmetries. [connection coefficient = probability of traffic]
Space-time provides 'powered lego blocks' for the construction of systems.
MTW: the pregeometry of gravitation is quantum mechanics.We need the coordinates and their first and second derivatives to design a consistent flow of ? [probability?] in the universal system.
Dirac, on transformation. Gravity introduces Goedel, self reference and creation [the Word of God]. Gravitation introduces incomputability?
page 82]
Why is this? Because the gravitational mapping is the complete mapping of the natural numbers onto themselves, most of the elements of which are incomputable.
Geometric gravitation is computable because the local code is finite, but the curvature introduces uncertainty (through the second derivative) through recursion.
Wednesday 16 September 2015
Transformations operate at different 'depths', leaving some things the same and changing others. The hierarchical layered network models this behaviour. The 'width' of a transformation is the set of events that it effects. The deepest and widest transformation is gravitation which couples every event on the universe to every other by being in effect the basic hardware of the universe. In mathematical terms let us consider gravitation as the mapping of the natural nubmers onto themselves. An infinitesimal fragment of these mapping are computable, the rest incomputable, but the computable mappings have the advantage that they can reproduce themselves and so increase their probability of occurrent. Incomputable transformations occur at random, computable transformations on the other hand can take control of the transformation process by establishing memory and fixed points, Is this not a beautiful insight, which opens the way to completing phys09.
Einstein: In 1907 when I was working on a review of the consequences of special relativity . . . I realized that all the natural phenomena could be discussed in terms of general relativity except the law of gravitation. I felt a deep desire to understand theTransformation from seed to plant [what is conserved?].[page 83]
reason behind this . . . It was most unsatisfactory to me that although the relation between inertial and energy is so beautifully derived [in special relativity], there is no relation between inertial and weight. I suspected that this relationship was inexplicable by means of special relativity. Pais, page 179
General relativity deals only with computable transformations [?].
Pais page 213:
Einstein: 'The decisive step of the transition to generally covariant equations would certainly not have taken place [had it not been for the following consideration]. Because of the Lorentz contraction in a reference frame that rotates relative to an inertial frame, the laws that govern rigid bodies do not correspond to the rules of Euclidean geometry. Thus Euclidean geometry must be abandoned if noninertial frames are to be admitted on an equal footing.
Particle (like me, {hardware, software}, {layer}.
Thursday 17 September 2015
Einstein: local to global. General relativity is 'local' to the whole universe, ie a symmetry present everywhere: global metric.Principle of equivalence couples weight and inertia. How do we couple logic and distance? [action, uncertainty, size of atom]
The Towers of Hanoi: on rearranging a layered software system. Tower of Hanoi - Wikipedia
General linear group: matrices represent groups of operators.
De Jonge: phasing out the old guard: Evolution. Alice De Jonge
[page 84]
Evolution is made possible by feedback, that is the 'reality field' couples to itself. We have randomization and selection.
Pais page 201: 'In 1907 and 1911 Einstein had stretched the kinematic approach to gravitation to it limits. This time [1912] he embarked on one of the hardest problems of the century: to fins the new gravitational dynamics. His first steps were taken gingerly,"
It is difficult or impossible to build a useful computer on 2 space becasue of the crossed wire problem So the advantage of 3 spce over 2 space more than payys for the added complexity. We think of a processor moving around a memory, coupled to each location, two inputs and an output by connection coefficients, ie mappings.
What we need is the whole of mathematics, ie all consistent transformations. This is the space of quantum mechanics.
Catholic evil: Humanae Vitae 1968. Steinfels.
First break in the symmetry gravitation/energy is fermion/boson. Photon and electron early examples.
The main reason I do not understand things is that I do not take the trouble and the reason I do not take the trouble is that i am still flying around at high altitude trying to get together a general picture of logically constrained world and only occasionally trying to bring this into line with the arithmetically constrained world in which we find the bulk of physics.
Friday 18 September 2015
A bit of morning despair helped along by the news of
[page 85]
continuing destruction of the world by fundamentalists of various stripes. It seems in a way that my literary fight against fundamentalism is doomed to struggle — making reality your God is very hard in the face of the public relations stories of heaven and hell that the fundamentalists have dreamt up over the years. In the case of Christianity it is the false promise that we never die.
There is a sense of urgency to get things done and this suggests shortcuts, but this may lead to poor work. Einstein sought a transformation in space-time that left real (and physically operative) distances invariant. These are the distances that govern the interactions of events, that is of particles. Events are essentially the creation and annihilation of forms of energy. Aristotle and Thomas made the dual of form passive matter. The view here is that the dual of form is [active energy].
My biggest target and most clearly defined in the fairy tale world of Catholic belief.
Physics has always confined itself to space and time, energy and momentum and left questions of information and meaning to metaphysics. Following Lonergan, it is time to turn things upside down and explain physics not as some fixed structure set in place by the creator but the mind of God at work projected on the screen of spacetime. Einstein explored the space of all spacetime transformations that preserve distances. Quantum mechanics explores the space (we think) of all possible computable functions. We begin our metaphysics by considering all possible mappings of a st onto itself, ie the permutation group, and we believe that evolution selects efficient computable transformations out of all the possibilities.
Saturday 19 September 2015
[page 86]
Quantum mechanics operates in a system that predates space - there is no need to take account of distance, only energy, frequency, [phase] or time. The advent of spacetime honours this symmetry by making null geodesics possible by introducing the metric signature 1, -1.
The history of fundamentalism suggests that it is basically a set of opinion espoused by warlords to justify their supremacy. The role of violence in maintaing peace is the ability of the violent to kill alternative opinions, ie to maintain ancient symmetries built around the opinions of the rulers. The answer to fundamentalism of the source of evolution is the fact that complex systems can have better survival value than simpler ones because they can reproduce themselves more efficiently and thus claim a larger share of the available energy. In government this means spending more of the tax take on improving social awareness and communication ie extending the perks of the king to everyone.
Landauer tells us that meaning is not an imaterial thing. It is embodied in the structures of the world I am my own meaning, and I gain further meaning from my mappings to my environment.
Einstein's last few problems with gravitation revolved around the fact that the reference systems used by physicists are largely arbitrary and not part of reality. To simplify our work we choose the reference systems that make things appear simple, like making space and time symmetrical. The beauty of the network is that it is self referencing, My place in the network is represented by my address, which is effectively me and all my interactions with the environment is mediated by addresses - I go there to do that. A meeting is a bosonic device where a number of entities share an address, ie are simultaneously in the same place. Pais page 252: 'One may choose a coordinate
[page 87]
system at one's convenience simply because coordinate systems have no objetive meaning.'
We are becoming more aware of the effects of the social stresses experiences by people who are different. Jane Cadzow: Magda unmasked
phys10BosonFermion: What is the moral here: we are exploring a universe where all consistent possibilities are allowed, but their frequencies vary by 'survivability'.
Covariance emphasizes the fact that frames of reference are not part of physical reality.
How does the metric signature 1, -1 relate to the boson fermion distinction? Metric signature - Wikipedia, Boson - Wikipedia, Boson - Wikipedia, Fermion - Wikipedia
Defeating fundamentalism in physics is analogous to defeating fundamentalism in any other universe of discourse [ie taking a more comprehensive view].
Do photons cause Maxwell's equations or vice versa? How do we write a digital version of them? A photon can have any energy, but only spin 1. Photon - Wikipedia. Maxwell's equations - Wikipedia
