vol VII: Notes
2019
Notes
Sunday 24 February 2019 - Saturday 2 March 2019
[Notebook: DB 83: Physical Theology]
[page 114]
Sunday 24 February 2019
[page 115]
Chapter 7: General Relativity: the path from initial singularity to current large scale structure via quantum mechanics. General relativity provides a framework within which quantum mechanics works. This framework serves to establish the conditions for the effectiveness of fixed point theory, ie a convex, compact space. This is today's bright idea and makes the day worthwhile for me even if nothing else is forthcoming, one day, one step at a time for 40 years = 15 000 steps and maybe I am getting closer.
The coexistence of energy, consistency and complexity requires the existence of spacetime, because the general theory [or maybe just the initial singularity] establishes the prerequisites for the operation of fixed point theorems. This would appear to be a bootstrapping situation which is OK as long as the bootstrapping becomes self sustaining as soon as it is implemented, which is consistent wth the evolutionary paradigm [which] says that fit variations survive. We can see this happening if the variation fits an ecological niche. The ecological niche for the primordial bootstrap in an absolutely simple world is simply [local] consistency [which requires two things in communication to be consistent with one another]. Energy can consistently exist if the imaginary phase annihilates the real phase and vice versa [in the circle group that we use to model 'energy waves']. There is no control on the frequency of this process, so all frequencies are possible and will be represented with some real probability.
Monday 25 February 2019
Two interesting features of quantum mechanics are entanglement, which is the source of 'spooky action at a distance' and the cosmological constant problem, where conclusions reached by the action of quantum field theory differ by a factor of the order of 10100
[page 116]
from observation. Both these problems lie at the very root of quantum mechanics, and so we think they might be amenable to solution by applying the heuristic simplicity, the idea that at the very beginning of the universe when it was exceedingly simple, structures were laid down that remain as symmetries of the universe but are misunderstood in modern physics. Quantum field theory assumes the existence of space-time and does not see it as an evolved emergent property. The heuristic of simplicity suggests that time and energy and the quantum mechanics of the energy operator predate space, so explaining how entanglement can embrace the whole universe and travel instantaneously. The solution of the cosmological constant problem seems to require a new understanding of the uncertainty principle that it too antedates space and is in fact a measure of a change in phase connected to entanglement and not necessarily an ontological principle that demands the zero point energy of a quantum harmonic oscillator. In other words we might see the cosmological constant problem as an error in the interpretation of the uncertainty principle, seeing it as an ontological rather than a measurement principle or a fixed point rather like the digits in the integral line.
Another use of the heuristic of simplicity is a digital interpretation of Feynman's many paths interpretation of quantum mechanics and the application of Feynman diagrams to the atom of the quantum network, two fermions bound by a boson in an environment where only these particles exist, ie an analogue of the Trinity.
[page 117]
Photos are distinguished by frequency alone, since they are bosons, meaning that any number of photons of one energy are effectively one photon. We imagine that photons predate space by frequency division multiplexing and that in the absence of any spatial harmonies their frequency division is random and each frequency is distinguished by a quantum of action, ie the frequencies are distributed as random integers / positive natural numbers, since we are assuming that Shannon's theory already holds here.
We might say that spooky action at a distance exists in a pre-spatial world where the only language has no grammar or syntax, just symbols whose energy is distinguished by integral frequencies.
A photon is a symbol (particle) distinguished by frequency. All the photons with a given frequency are entangled with one another and produce gravitation?? Since photons have integral spin, they have no zero point energy [??]
So how do photons create electrons and positrons [quantum field theory says they just do, but only in space where they have also acquired momentum]? Ie what does the heuristic of simplicity have to say about quantum electrodynamics?
We may guess that general relativity in some way establishes the [compact] complex space . . . which obliges the existence of the fixed points of quantum mechanics, in other words it places the boundary conditions on the energy equation that generates photons and the quantum harmonic oscillator. Bring in the ladder operators which deal with the abstract quantum harmonic oscillator. Quantum harmonic oscillator - Wikipedia
As we have said before a computer is a logically connected sequence of fixed or stationary points which wait for the next clock
[page 118]
pulse to interact to form the next set of fixed points and so on. In the real world the 'clock pulses' are the quanta of action that move the universe along step by step from one fixed point to the next. So in the computer network we see quantum systems emitting fixed points that serve as messages carrying messages to the next step analogous to a computer. Particles are fixed points with lifetimes. The primordial particles are photons, some of which have travelled from the beginning of the network to here and now [somewhere here we introduce Einstein's A and B coefficients, or the Dirac version].
Modern physics has got used to the idea that we can represent functions of the quantum action by real numbers as in the equation Δx.Δp = Δt.ΔE = h, so that we conclude if position is defined exactly we have no knowledge of momentum, since 0.Δp = h implies that Δp is infinite. Maybe this is an illegal conclusion, given the unbreakable integrity of the quantum of action.
What I am hoping to do in the [next] few years is make the transition from talking shots in the dark to actually taking aim at a clear target. It took Einstein seven years to work from the notion of free fall to the general theory. I am hoping that the fifty years that have elapsed since I decided that the universe is divine will soon yield a clear and distinct understanding of the irrefutable truth of this proposition.
[page 119]
Does every event require the interaction of two particles, one acting as the clock for another. No, some particles and nuclei decay spontaneously by tunnelling out of their skins, so to speak.
Tuesday 26 February 2019
This discussion leads us closer to the simple idea that the universe is digital to the core, and any continuity we see is a product of the law of large numbers, which is consistent with Cantor's notion of sets or points being sets of digital events. So we see heuristic simplicity pointing toward machine infinity.
Hawking and Ellis The Large Scale Structure of Space-Time
page 1: The Role of Gravity
Discussion of the universe divides into local laws described by differential equations, and boundary conditions for these equations and global nature of solutions which brings us to the edge of space-time.
Mach: global controls local. Edge of spacetime: source and sink. Mach's principle - Wikipedia
'we shall take the local physical laws that have been experimentally determined and shall see what these laws imply about the large scale structure of the universe.' Following Einstein.
H&E results based on 1: description of space-time by pseudo-Riemannian geometry; and 2: positive definite energy density.
[page 120]
page 2: Gravity weak but always attractive, and determines causal structure of universe because it affects everything including photons.
Laplace. Penrose closed trapped surface as an explanation of singularity. Hubblesite: What is a black hole?, Pierre-Simon Laplace Wikiedia
page 3: 'One can think of a singularity as a place where the present laws of physics break down.' Or they are not yet formed.'One does not know what will come out of a singularity', a problem of boundary conditions.'
Recent observations of the microwave background indicate that the universe contains enough matter to cause a time reversed closed trapped surface. This implies the existence of a singularity in the past at the beginning of the present epoch of expansion of the universe. This singularity is in principle visible to us; it might be interpreted as the beginning of the universe.
page 4: book requires a knowledge of simple calculus, algebra and point set topology.
General Relativity specified by three postulates about mathematical model for spacetime. Model is a manifold M with a metric g of Lorentz signature. Postulates 1. local causality (ie local consistency); 2. local conservation of energy-momentum; 3. field equations of metric g depending only on the fact that gravity is attractive for positive matter densities.
Chapter 4 on geodesics.
[page 121]
Hawking & Ellis page 6: Chapter 5 exact solutions of Einstein's equations; Chapter 6: Causal structure of space-time; chapter 7: Cauchy problem for general relativity: 'We show that initial data on a spacelike surface determines a unique solution on the Cauchy development of the surface . . . ' ie it is deterministic.
page 7: Chapter 8: definition of space-time singularities. 'This presents certain difficulties because one cannot regard the singular points as being part of the space-time manifold M'. Ie M is emergent, and possibly the result of the action of quantum mechanics which therefore establishes the boundary conditions for M. Then proofs for the existence of singularities under certain conditions.
page 8: Chapter 9: black hole. Chapter 10: singularity at the beginning of the universe.
page 10: Chapter 2 Differential geometry, ie manifold with Lorentz metric and associated affine connection. Connection defines the covariant derivative and the curvature tensor.
page 11: The only concepts defined by the manifold structure are those that are independent of the choice of coordinate system.
'locally Lipschitz' places an upper bound on functions in Euclidean space.
page 12: 'coordinate neighbourhoods connected by continuous and differentiable maps.'
page 13: Hausdorff: distinct points are to be found in distinct open sets. Ie effectively digital?
[page 122]
Hawking and Ellis page 14: paracompact: 'A function on a ck manifold M is a map from M tp R1.
page 15: 'Every longest vector at a point p can be expressed as a linear combination of the coordinate derivatives ∂/∂xi |p . . .. At every p is a tangent vector space.
page 16: One form (covariant vector) is a real valued linear function on the Tangent space. If X is a vector at p, the number into which the one form ω maps X is written <ω, X>
Given a basis {Ea} there is a a basis of one forms {Ea} such that <Ea, Ea> = δab. The basis {Ea} of one forms is the dual basis to the basis {Ea} of vectors. This duality maintains the invariance of tensors as the bases change.
page 24: Differentiation on a manifold
1. Exterior dfferentiation: 'The exterior differentiation operator d maps r-form fields to (r+1)-form fields. Actiong on a zero-form field (ie a function f) it fives the one form field df
page 27: Lie differentiation.
page 30: Covariant differentiation.
[age 56: General relativity: The mathematical description of
[page 123]
differential geometry in chapter 2 is already quite detailed and complex. Did all this exist in the universe before gravitation and general relativity came along? A lot of the complexity arises from the dual system required to enable the system to deal with any system of coordinates in order to render the system in effect coordinate free.
space-time = collection of all events.
Models are equivalent if their metrics g = g'
Hawking and Ellis page 57: 'A manifold corresponds naturally to our intuitive ideas of the continuity of spacetime. So far this continuity has been established for distances down to about 10-15 cm . . . ' They are talking about distance, but an event, quantized by h, is an action, not a distance.
Vectors at p are timelike, spacelike or null. We would like to think that the first "vectors" to arise would be null, ie before the bifurcation into space and time and the advent of the velocity c which enables the existence of null vectors in spacetime.
page 59: There will be various fields on M such as the electromagnetic field . . . which describe the matter content of spacetime. These field will obey equations which can be expressed as relations between tensors on M in which all derivatives with respect to position are covariant derivatives with respect to the symmetric connection defined by the metric g. This is so because the only connections defined by a manifold structure are tensor relations, and the only connection defined so far is given by the metric. [which is to assume that everything is to be understood in terms of geometric continuity. What if the world works by logical continuity? How do we think about this?].
[page 124]
'the theory one obtains depends on what matter fields are incorporated in it.'
Hawking and Ellis page 60: Postulates obeyed by matter fields; Postulate a) local causality, ie we ignore entanglement. Points must be connected by non-spacelike curves, ie no signal faster than c.
page 61: '. . . light must travel on null geodesics. This, however, is a consequence of the particular equations that the electromagnetic field obeys, not of the theory of relativity itself.' Ie c may have any value and the theory holds? What about Lorentz transformations, which seem to be an intrinsic property of spacetime so that we might say that light travels at c not because of Maxwell's equations, but because it is determined by relativity and the values of the permeability μ0 and permittivity ε0 of space are defined by relativity, ie the properties of space are relativistic properties. The question: does c define Lorentz, or does Lorentz define c?
. . . all elements of the theory will be physically observable.
page 61: Postulate b) local conservation of energy and momentum. By local we mean within (say) 10-15 cm, ie the conservation laws do not depend on the long distance transport of energy and momentum, and we may assume that they are precisely local, ie conserved within the minimum event measured by h.
Energy momentum tensor Tab with properties
[page 125]
(1) Tab vanishes on an open set U if and only if all matter fields vanish on U.
(ii) Tab obeys the equation Tab;b = 0.
Hawking and Ellis page 62: Inhomogeneous Lorentz group is a ten parameter group. p4 is energy, p1, 2, 3 momentum and the other six the flow of angular momentum (which involves quantum mechanics).
page 64: ' . . . there is a definite and unique formula for the energy momentum tensor in the case that the equations of the field can be derived from a Lagrangian.'
page 78: 'In general space-time . . . one will not have any special frame against which to measure acceleration. The best one can do is to take two bodies close together and measure their relative acceleration. This will enable one to measure the gradient of the gravitational field.
page 88: '. . . one has little idea of the behaviour of matter under extreme conditions of density and pressure. Thus it might seem that one has little hope of predicting the occurrence of singularities in the universe from the Einstein equation as one does not know the right hand side of these equations. However, there are certain inequalities which it is physically reasonable to assume for the energy momentum tensor . . . It turns out that in many circumstances these are sufficient to prove the existence of singularities.
. . .
page 117: Exact solutions. 'Any space-time metric can in
[page 126]
a sense be regarded as satisfying Einstein's field equations . . . The matter tensor so defined will in general have unreasonable physical properties; the solution will be reasonable only if the matter content is reasonable.
Because of the complexity of the field equations one cannot find exact solutions except in spaces of rather high symmetry.' One would think that the fundamental solution would be the one which sees all 'matter' identically as energy. At this point all matter is the same. This energy, if not a single boson state ( = God), will have some frequency distribution and therefore different states and entropy. We would like to start with a zero energy God, absolutely simple.
Hawking and Ellis page 118: 'In §5.7 we describe the Gödel universe and in §5.8 the Taub-NUT solutions. These probably do not represent the actual universe, but they are of interest because of their pathological global properties.
Einstein's field equation is a second order differential equation which needs to be constrained by the boundary conditions of the actual universe to model the actual universe. At a guess these boundary conditions are provided by naked quantum theory, ie the energy equation alone [a differential equation is itself a boundary condition on some dynamics, but what? The big difficulty is trying to discover what the mathematics means, since all the answers are simply numbers boiled down from complex situations. The layered network, like the manifold, gives meaning to these numbers by providing a story about where they came from. In the end we are just counting quantum events in the structures of interest.].
page 119: Note written in 2006: 'There must be a theory of space that describes all spaces from Einsteins universe to the human collective mind [noosphere] SYMMETRIC UNIVERSE [in the sense of symmetric group]. Symmetric group - Wikipedia
[page 127]
Hawking and Ellis page 119: In Minkowski space-time 'any two points of M can be joined by a unique geodesic curve. . . . (M, η) is geodesically complete [in relativity can one follow a geodesic in the negative time direction?].
Wednesday 27 February 2019
page 134: 'The Copernican Principle' - we occupy no special position in the universe.page 135: So the universe is approximately spherically symmetrical about every point, as it is spherically symmetrical about us [the initial singularity is everywhere present and we are inside it, since there is no outside].
so Robertson-Walker or Friedman space.
A Robertson-Walker metric: ds2 = -dt2 + S2(t) dσ2 where dσ2 is the metric of a three space of constant curvature that is independent of time.
page 136: 'The symmetry of th RobertsonWalker solutions requires that the energy-momentum tensor has the form of a perfect fluid whose density μ and pressure p are functions of t only. . . This fluid may be thought of as a smoothed our approximation to the matter in the universe. Then the function S(t) represents the separation of neighbouring flowlines, that is of nearby galaxies.'
page 137: '. . . the density decreases as the universe expands, and conversely that the density was higher in the past, increasing without bound as S → 0. . . . the fact that the density is infinite [at S = 0] shows that some scalar defined by the curvature tensor is also infinite . . . the world lines of all the particles intersect in a point and the density becomes infinite, but here
[page 128]
space-time itself becomes singular at the point S = 0. We must therefore exclude that point from the space-time manifold, as no known physical laws could be valid there.' Conversely, all partial world lines must begin near S = 0 and become the mass-energy of the expanding universe.
Hawking and Ellis page 138: . . . whether physically realistic solutions with homogeneities would contain singularities is s central question of cosmology and constitutes the principal problem dealt with in this book; it will turn out that there are good evidence to believe that the physical universe does in fact become singular in the past.
page 142: '. . . the singularity is universal in the following sense: all timelike and null geodesics through any part of space approach it for some finite value of their affine parameter.' S all go back to one beginning.
page 149: 'While spatially homogeneous solutions may be good models for the large scale distribution of matter in the universe, they are inadequate for describing, for example, the local geometry of space-time in the solar system One can describe this geometry to a good approximation by the Schwartzchild solution which represents the spherically symmetric empty space-time outside a spherically symmetric massive body.
161: 'Kerr solutions are the only known family of exact solutions which could represent the stationary axisymmetric asymptotically flat field around a rotating massive object.
[page 129]
Thursday 28 February 2019
I am going for the biggest paradigm change ever. Making the universe divine has deep implications for all the other sciences and requires a complete revision o how we see ourselves in the world.
The identification of the initial singularity with God is the first product of the use of simplicity as a heuristic approach. Thinking of Lonergan's definition of metaphysics: '. . . let us say that explicit metaphysics is the conception, affirmation and implementation of the integral heuristic structure of proportionate being (page 426). Lonergan: Insight: A Study of Human Understanding
Lonergan page 417: '. . . what is meant by heuristic structure?
'A heuristic structure . . . is a notion of unknown content, and is determined by anticipating the type of act through which the unknown would become known. A heuristic structure is an ordered set of heuristic notions. Finally, an integral heuristic structure is the ordered set of all heuristic notions.' Nice words, but . . . [The heuristic of simplicity deletes the need for Lonergan's distinction between proportionate and transcendent being, since God, the transcendent being, is absolutely simple and therefore very easy to understand, since all that we can say is "the essence of God is to be".]
'In illustration, one may point to the definition of proportionate being. It is whatever is to be known by human experience, intelligent grasp and reasonable affirmation.' [ie the universe in which we evolved and lived, which is identical to god, so also transcendent being.
Lonergan page 662: 'Man's unrestricted desire to know is mated to a limited capacity to attain knowledge.'
page 663: 'Being is proportionate or transcendent according as it lies within or without the domain of man's inner and outer experience. The possibiity
[page 130]
of transcendent knowledge is then the possibility of grasping intelligently and affirming reasonably ta transcendent being. And the proof of the possibility lis in the fact that such intelligent grasp and reasonable affirmation occur.' But only to unintelligent and unreasonable ones like the Catholic Lonergan [wrong, and silly comment, since the universe is divine so we all live in the midst of a transcendent being].
So back to Einstein and the 'real' world: Hawking and Ellis page 168 § Gödel's universe.
page 180: Chapter 6 Causal Structure
'A signal can be sent between two points of M if they can be joined by a non-spacelike curve,' ie by photons. Here we ignore entanglement
'Geodesic completeness will be discussed further in chapter 8 where it forms the basis of a definition of singularity.'
page 182: '. . . if one assumes that space-time is time orientable then it must also be space-orientable. (This fact follows on using the experimental evidence without appealing to the CPT theorem)' Streater and Wightman: PCT, Spin, Statistics and All That
'Geroch (1968c) has also shown that if it is possible to define two component spinor fields at every point then space-time must be parallelizable, that is it must be possible to introduce a continuous system of bases of the tangent space at every point.'
page 189: 'the chronology condition', ie there are no closed timelike curve which one could follow in a certain direction and arrive before one left.
[page 131]
Hawking and Ellis page 201: Cauchy developments. 'in Newtonian theory there is instantaneous action at a distance and so in order to predict future events in space-time one has to know the state of the entire universe and also to assume some boundary conditions at infinity, such that the potential goes to zero.'
'In relativity, on the other hand, events can only influence one another if they can be joined by a non-spacelike curve. Thus the knowledge of appropriate data on a closed set S . . . would determine events in a region D+(S) to the future of S called the future Cauchy development or domain of dependence of S . . .
page 206: Global hyperbolicity: Quality of a region not containing point at infinity or singularities - closely related to Cauchy development.
page 213: The existence of geodesics: If p and q lie in a globally hyperbolic set then there is a non-spacelike geodesic whose length is greater than or equal to any other non-spacelike curve from p to q.
page 217: The casual boundary of space-time: (M, g) satisfies the strong causality condition if any point p in (M, g) is uniquely determined by its chronological past or future.
page 221: Asymptotically simple spaces - 'to study bounded physical systems such as stars one wants to investigate spaces that are asymptotically flat, ie whose metrics approach Minkowski space at large distances from the system.
page 226; Chapter 7: The Cauchy problem in general relativity.
[page 132]
Hawking and Ellis page 227: 'The Cauchy problem for the gravitational field differs in important respects from that for other physical fields:
(1) The Einstein equations are non-linear. The distinctive feature of the gravitational field is that it is self interacting: It is non-linear even on the absence of other fields.
(2) Two metrics g1 and g2 on M are physically equivalent if there is a diffeomorphism M → M which takes g1 into g2, so solutions to field equations are unique only up to a diffeomorphism which introduces 4 degrees of freedom which must be controlled to give s unique metric.
(3) 'Since the metric determines the space-time structure one does not know in advance what the domain of dependence of the initial surface is and hence what the region is on which the solution is to be determined [because metric is local?].
page 256: Space-time singularities .
How did God create the world? He just said let it be. How did the big bang create the world? Same [the initial singularity said let there be space-time filled with fundamental particles], there is no mechanism, no explanation, no algorithm. But we know there is an algorithm expressed by copying, variation and selection, and we intend to implement this algorithm using the heuristic of simplicity to be more explicit to be more explicit tomorrow afternoon when I complete cybernetics / cyber09Evolution.
Friday 1 March 2019
'We adopt the view that timelike and null geodesic completeness are minimum conditions for space-time to be considered singularity free.
[page 133]
This idea seems to overlook the creation and annihilation of particles and entanglement.
Hawking and Ellis page 261: 'It was therefore suggested by a number of authors that singularities were simply the result of symmetries and that they would not occur n general solutions.
One may imagine that a singularity is completely symmetrical insofar as no matter how one transforms it it looks the same because, like god, it has no structure [this property of the initial singularity is preserved as the universe expands and is the symmetry that is built into the general theory of relativity]. Auyang: How is Quantum Field Theory Possible?
'singularities involve infinite curvature.' Infinite curvature indicates total change in properties over finite distance which is like annihilation and creation, ie digitization.
page 276: 'The preceding theorems prove the occurrence of singularities in large class of solutions but give little information as to their nature.
page 287: One can regard a singularity as a point where the Einstein equation (and presumably other presently known laws of physics) break down.
page 299: Gravitational collapse and black holes.
page 302: 'To see why a burnt out star of more than a certain mass cannot support itself against gravity we will give a qualitative discussion . . . of the zero temperature equation of state for matter.
page 303: 'In hot matter these is pressure produced by the thermal motions of the atom and by the radiation present. However in cold matter at densities lower than that of nuclear matter (~1014 gm cm-3) the only significant pressure will arise from the quantum mechanical exclusion principle.
[page 134]
Hawking and Ellis page 303; Consider a number density of n fermions of ass m so each occupies a volume of n-1. The uncertainty principle means that each has a spatial component of motion of the order of hn½. If hn½ is greater than m, the velocity of the particles wil be c and the prssure will be of the order of (momentum) × (velocity) × (number density). At high densities when particles become relativistic pressure is independent of mass of particles and depends only on number density, proportional to hn1.333.
Using the Newtonian approximation to gravitational pressure we see that cold stars of greater than ML = 1.5 MSun cannot be supported by the degeneracy pressure of electrons. At this point beta decay sets in and the star becomes supported by the degeneracy pressure of neutrons. Above a certain mass this no longer suffices, so collapse will continue (page 305).
page 307; '. . . a star containing more than ML/ mn nucleons will not reach nuclear densities until it is inside its Schwartschild radius. . . . Of its mass is more than slightly greater than ML, there is no low temperature equilibrium state. Therefore the stsr must pass within is Schwartzchild radius or eject sufficient matter that its mass is reduced to less thsn ML . . .
page 308: 'and so give rise to closed trapped surfaces.'
Black holes: 'What would a collapsed body look like to n observer O who remained a large distance from it?
page 309: A second observer passing r = 2m will not notice anything special, but the distant observer will see the close observer's watch slow down and the light from the collapsing
[page 135]
star will be redshifted until it eventually becomes invisible. The collapsing star will still have its original mass and gravitational field.
Hawking and Ellis page 310: The singularity occurs within the Schwartzchild radius and is not visible to an outside observer.
page 311: 'If future asymptotic predictability does not hold around a singularity one cannot say anything definite about the evolution of any region of space containing a collapsing star as new information might come out of the singularity.
page 323; The final state of black holes.
page 348: The initial singularity of the universe.
'. . . one can view the expansion of the universe as the time reversal of a collapse.
Cosmic background is a black body at 2.7 K and quite close to isotropic.
page 350 Most likely '(1) the radiation is black body radiation left over from a hot early stage of the universe [and redshifted by expansion].
From the Copernican principle it follows that most of the microwave background has propagated toward us from a long distance: (~3 ×1027 cm).
page 351: From the fact that the [CBR] remains isotropic after travelling such a long distance we can conclude that on a large scale the metric of the universe is close to one of the Rbertson-Walker metrics (first argument).
[page 136]
Hawking and Ellis page 354 (second argument) 'The approximately black body nature of the spectrum and the high degree of small scale anisotropy of the radiation indicate that it has been at least partially thermalised by repeated scattering. In other words there must be enough matter in each past directed null geodesic to cause the opacity to be high in that direction. We shall now show that this matter will be sufficient to make our past light cone converge.'
page 356; 'We shall give an argument that indicates that the universe contains a singularity in the past.'
page 358: '. . . if the usual energy conditions and causality conditions hold, we can conclude that there should be a singularity in our past (ie that there should be a past directed non-spacelike geodesic from us which is incomplete.'
Saturday 2 March 2019
Why are relativistic metrics quadratic? [for that matter why are Euclidean metrics quadratic?]. How did Pythagoras get in there? Is quadratic a consequence of spherical symmetry? A point is symmetrical in all dimensions. Pythagoras theorem carries is from one orthogonal dimension to another, like walking on the diagonal across a square [which we are all inclined to do].
Energy-momentum has the same shape as time-space, they are formally identical, transforming as identical 4-vectors [with the same metric signature which suggests that they have bifurcated from a source whose space-time measure is zero , null geodesic of photon].
False theology gives us a false idea of Newton's divine sensorium. General relativity makes space-time divine,
[page 137]
not merely a projection of god, but how do we map it to the traditional God? Relativity is quite complex, which means that there must be a number of emergent steps between the initial singularity and cosmic space-time, missing steps that Einstein managed to skip over by looking at the world as it is without asking too much about how it came to be. Isaac Newton: The General Scholium to the Principia Mathematica
The billion dollar question is how did the origin of the universe become a time reversed black hole when we know that black holes are one way street? Are we inside a black hole? There is a big issue hiding here along with the cosmological constant, the creation of energy and spacetime, antimatter and a few more conundrums built into the standard model that make it impossible to unite relativity and quantum mechanics. The answer, I feel, must lie in the network idea, building up the world in layers, in the beginning being a very different symmetry from a black hole.
War is a step on the way to peace, making the combatants realize that there has got to be a better way. We have sorted out biology and medicine. Now we have to sort out theology and politics.
The fact that God is constrained by Gödel and Turing gives a new angle on the problem of evil in that god is neither fully omnipotent of omniscient and so cannot outlaw evil even if it chose (in its "wisdom") to do so.
Monk: Wittgenstein: page 46: Russell on Wittgenstein: ". . . perhaps the most perfect example I have ever known of genius as traditionally conceived, passionate, profound, intense and dominating." Monk: Wittgenstein: The Duty of Genius
[page 138]
Monk page 92: 'In addition to his embryonic Theory of Symbolism, Notes on Logic contains a series of remarks on philosophy which state unequivocally Wittgenstein's conception of the subject, a conception that remained—in most respects at least—unchanged for the rest of his life:
In philosophy there are no deductions: it is purely descriptive. Philosophy gives no pictures of reality.
page 93: 'Philosophy can neither confirm nor confute scientific investigation.
Philosophy consists of logic and metaphysics: logic is its basis.
Epistemology is the philosophy of psychology
Distrust of grammar is the first requisite for philosophising.'
page 95: W: 'All the propositions of logic are generalizations of tautologies and all generalizations of tautologies are generalizations of logic. There are no other logical propositions (I regard this as definitive).'
page 96: W: I wish to God that I were more intelligent and everything would finally come clear to me — or else that I needn't live much longer.
I agree with the first part, but I have made a little progress over the last fifty years and hope to round things off in the next thirty.
page 118: 'Picture theory of language': 'Only in this way can the proposition be true of false. I can only agree or disagree with reality by being a picture of the situation.' Einstein and Riemann know this years
[page 139]
before Wittgenstein.
Monk page 129: W: 'The great problem round which everything I write turns is : Is there an order in the world a priori, and if so what does it consist in?
A: Layered network beginning at layer 0 ≡ God ≡ initial singularity.
fact = relationship of objects = communication = Trinity
The atomic fact is the atom of a network, two processes communicating, two fermions and a boson. Gravitation does not see this, only energy, pre-quantum communication, no particles, no quantization, Minkowski (Lorentz) metric.
'The demand for simple things is a demand for definiteness of sense.'
page 137: Schopenhauer: 'Undoubtedly it is the knowledge of death, and therewith the consideration of the suffering and misery of life, that gives impulse to philosophical reflection and metaphysical explanations of the world.' The World as Will and Representation
page 139: 'Only death gives life its meaning'.
Tractatus 6371, 6372: 'The whole modern conception of the world is founded on the illusion that the so-called laws of nature are the explanation of natural phenomena' . . .
[page 140]
Monk page 141: during heavy fighting the personal and the logical fused.
'To believe in God means to understand the meaning of life.'
