natural theology

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Notes

Sunday 31 October 2021 - Saturday 6 November 2021

[Notebook: DB 87: Cognitive Cosmology]

[page 83]

Sunday 31 October 2021

Up to this point I have insisted that the world is driven by a quantum system built on integral orthogonal quanta of action whose interactions are executed by a ring of operators which do not admit division or fragmentation of quanta, and that this fundamental analogy with the integers suggests that the use of continuous mathematics in physics is moot. The only continuity allowed is in the complex numbers which are necessary for the algebraic completeness of the system of the world and serve to describe the periodic functions implicit in a computational world. Von Neumann algebra - Wikipedia

Now we come to deal with gravitation which appear to be a perfect classical system based on the infinitely differentiable ( C ) domain of real numbers and it seems that we have two ways to approach this. The first is to accept that gravitation is not quantized. An argument for this is that because gravitation is a universal interaction between energy and energy affecting every form of energy indifferently it cannot ever be in error, needs no special coding and is therefore not quantized. This argument is strongly supported as a solution to the cosmic constant problem, since the ludicrously large values of the cosmological constant proposed by the proponents of quantum field theory show that quantum calculations of the energy of the vacuum based on the zero or fixed point energy predicted by quantization must be false ruling out quantization or at least this interpretation of it. The second approach is to assume that the application of the continuous mathematical

[page 84]

differential manifold used by Einstein is simply a fictitious symmetry obtained by assuming that the quantum of action in the case of gravitation, when dealing with the whole of the universe, can be declared to be infinitesimal, thus arriving at the traditional classical result that follows when we take the quantum to zero. We can then treat a differentiable manifold as a network, assuming that all the differential coefficients in the manifold are coupling constants between imagined sources in this network. The problem here is that we are back in the world of action at a distance.

So what? The essential point, I feel, is that the universe exists inside the initial singularity and in its primordial state this interior is continuous since it needs to be so as to implement the hypotheses of fixed point theorems which create particle states (fixed points) by mapping the interior of the initial singularity onto itself. Looking at this recursively we can see that the interiors of these fixed points must also be continuous like the interior of the initial singularity and so on recursively ad infinitum as Cantor would like to see. Cantor's theorem - Wikipedia

In other words we think of every particle, including the initial singularity, as a continuous (Lie) group and so in effect see every one of them as a little universe with an Einstein type gravitational field [group struture] inside. Now fo for a walk and think about this, to the Botanic gardens for a coffee. Then come back and propose the hybrid network view of classical gravitation which is our explanation of 3D space. Lie Group - Wikipedia

My new ideas will not get much traction until they spawn a new and more efficient method of calculation which models the computation of protons as fast (in principle) as real life, ie uses the same algorithms as the proton.

The discussion above depends on the existence of massless particles of which the photon [and the gluons] may be the sole example[s]. We now turn to gravitation and Yang-Mils theory which deal with mass-energy and massive bosons. We start with a question: is gravitation quantized. A positive answer to this question is the current grail of physics and has led to the rather fantastic multidimensional speculation known as string theory which seems to be clearly ruled out by the application of the heuristic of simplicity to the initial singularity. Michio Kaku (1998): Introduction to Superstrings and M-Theory

So we back off here to Yang-Mills and massive bosons, but start with the relationship between gravitation, the initial singularity, quantum mechanics and fixed point theory.

We may think of string theory as untethered mathematics, lovely, but a but like the physicists (dubbed the Feldverein) who have tried to develop axiomatic field theory: "Cynical observers have compared them to the Shakers, a religious sect of New England who built solid barns, and led celibate lives, a non-scientific equivalent of proving rigorous theorem and calculating no cross sections." Streater & Wightman (2000): PCT, Spin, Statistics and All That, Shakers - Wikipedia

Monday 1 November 2021

A clue is the construction of massive protons from a number of massless ingredient (gluons) and low mass particles (up and down quarks) with a complex array of fields designated by colours. The key here seems to be that massless particles travelling at the speed of light inside massive particles, where we understand mass as a form of static or potential energy, which comes into existence with the emergence of the spatial layer which owes its existence to the fact that null geodesics can carry quantum stated unchanged through space, maintaining the contact essential to quantum communication and causality. We imagine that the first and simplest particles to form in the universe are the ingredients for quantum electrodynamics, photons, electrons and positrons. This suggests that space-time has an electrical dimension [as suggested by Maxwell's equations] and we see in the modern world that almost all our experience, including our own bodies, is shaped by electrodynamics. Nevertheless we see roles for all the other fundamental particles as forming a complete set of operators to construct a universe.

[page 86]

A fixed point is not necessarily a point in the Euclidean sense. I am a fixed point albeit a complex one and we can see quantum operators as fixed points with complexity measured by the number of basis vectors in their superposition and make an equation f ( |ψ > ) = f ( |ψ0 > ) where |ψ0 > is a fixed operator representing a fixed particle, say an electron. We identify operators with particles and see the complete set of fundamental particles as the complete set of operators necessary to create a universe at the fundamental level. We may see these operators as analogous to the routines corresponding to the opcodes we use to get a logical processor to do what we want. In the early days programmers had to work bit by bit and input their work with switches, punched paper tape or cards but now we have high level languages which make it possible to have something along the lines of a conversation with a machine to give it instructions. At a much higher level we have the same facility with each other, teaching someone to drive or fly or swim by world and gesture.

This little piece of text has cleared up my day of worry on how to take my essay forward opening a way for the discussion of evolution at the level of fundamental partices. So how do we couple a photon to an electron?

Oscar Wilde Happy Prince; 'there is no mystery as great as suffering.' The Happy Prince (2018 film) - Wikipedia

Gravitation can squeeze the life out of any structure like pushing the electrons into the nuclei of atoms in the process of cresting neutron stars on the way to a black hole. This is why Hawking and Elis's time reversed black hole makes [no] sense. Why should something squeezed down to nothing by its own enormous mass decide to expand again? This is why I began my universe with a a gentle quantum of action which quietly generates energy, quantum theory, photons, electrons, spacetime and then gradually winding up the energy to hadrons, baryons, atoms, molecules and our world. Hawking & Ellis (1975): The Large Scale Structure of Space-Time

Tuesday 2 November 2021

The next step is to work out how evolution works in the fundamental particle situation.

Feynman II_1: 'the deepest principle of electrodynamics . . . is the superposition principle.' Feynman Lectures on Phyics II: Chapter 1: Electrodynamics

'It is interesting that the correct equations for light were worked out by McCullagh in 1839. But people said to him: "Yes, but there is no material whose mechanical properties could possibly satisfy these equations, and since light is a vibration, they must vibrate in something, we cannot believe this abstract equation business. '

'Magnetic force is 10-25 of the "normal" forces between moving electrons. The near perfect cancellation of electrical effects allows relativity effects (that is magnetism) to be studied and correct equations of order v2 / c2 to be discovered, even though physicists did not know what was happening.'

[Feynman] 'From the long view of history . . . there can be no doubt that the most significant event of the nineteenth century will be Maxwell's discovery of the laws of electrodynamics.'

FLP II_2: 'A physical understanding is completely unmathematical, imprecise, an inexact thing but absolutely necessary to a physicist. Feynman Lectures on Physics II: Chapter 2: Differential Calculus of Vector Fields

We imagine the evolution of particles from low to high energy, from simple to complex, from electron to proton. We start with electromagnetism and wonder about the electromagnetic properties of space and the machinery of Maxwell's equations beginning with electrons, positrons and photons, coupled by Dirac's equation. By going more abstract we get more symmetry since there are fewer ways to go wrong. With binary logical computation, for instance, we do not need all the nuance which comes with writing novels which are systems operating in the complexity of the space of human psychology.

[page 88]

Each new layer in the structure of the universe lays the foundations for the next and given the emergence of space-time built on the energy / quantum mechanics layer we now need to re-examine the role played by quantum electrodynamics in this step as the title of Einsteins paper on the special theory of relativity suggests. Maxwell drew out some of the lessons that have arisen from the original quantum theoretical attempts to synthesize quantum mechanics and relativity, so now we need to look deeper into this step given the hypothesis that Hilbert space and quantum mechanics are the independent source of the electro-magnetic spacetime in which classical electrodynamics is played out. Albert Einstein (1905): On the Electrodynamics of Moving Bodies

The "fortuitous" point is that Maxwell's equations are relativistically invariant and so have served as a bridge between quantum theory and the classical spacetime as Einstein has demonstrated. MTW page 73 em field Tensor Faraday. Misner, Thorne & Wheeler (1973): Gravitation

dpα / = eFαβ νβ

Where eFαβ νβ =

  
0ExEyEz
Ex  0Bz-By
Ey-Bz 0-Bx
EzBy-Bx  0

The velocity of light is a property of spacetime, connected to the permeability μ and permittivity ε of space where the phase velocity of light is 1 / √με. Electromagnetic wave equation - Wikpedia

Given the source and success of the special theory it is not surprising that Einstein and Weyl sought to unite general relativity and electrodynamics. Can we show how this can be done under the assumption that spacetime is a quantum mechanical product based on the requirement for contact causality and the existence of null geodesics in Minkowski space as I propose. I wish,

[page 89]

but I am stupidly optimistic enough to think that I can do this. A clear success would consolidate my position by providing a better understanding of the role of light in the creation of spacetime and more generally feed (as quantum electrodynamics has done) into the further development of quantum field theory and the evolution of specific particle roles as the universe complexifies, hopefully leading to the proton, neutron and atom from which the progress of molecules, cells and biology in general is pretty well understood. The first step is to find the physical understanding which Feynman mentions above and slot it into the network interface between the quantum and classical worlds in the context of evolutionary variation and selection at the very simple and abstract level, quantum variation, classical selection. Now 7 am, snooze until 9 then into the market to make the money to finance my project. Hermann Weyl (1985): Space Time Matter

Wednesday 3 November 2021

First question: where does the electron come from? And why is it charged, ie why does it receive and transmit photons? We can imagine a long and detailed essay about this, but we are working in a tiny universe whose principal ingredients are structureless quanta of action and superpositions of these quanta.

FLP II_04 'Electricity and magnetism are distinct phenomena as long as the charges and currents are static.' Feynman Lectures on Physics II Chapter 4: Electrostatics

Thursday 4 November 2021

Nothing coming through. We are looking for a simple quantum explanation of electrodynamics, which is then sculpted into electromagnetism in Minkowski space by the interactions between moving frames of reference.. How does this work in terms of the relationship between Hilbert and Minkowski spaces? Is this idea a dead end? Can anything be derived from it? We need the physical understanding (Feynman page 87 above)

[page 89]

We say shape pf spacetime determined by the need for quantum contact which is implicit in entanglement. Entanglement transmits 'undefined' information from a classical point of view since Alice does not know until after she makes her observation what she is transmitting to Bob. How does she transmit information in classical space. Needs to be able to prepare photons with known and fixed characteristics like polarization and frequency [using eg a laser]. Photons are also the means of realizing electric and magnetic fields.

What is the theological import of electrodynamics? Feynman on QED and phase - communication and interaction. All communication is determined by 'change' ie rate of emission and reception of symbols.

All signalling in the quantum regime is by phase and rate of change of phase [for each category of boson] and the value of null geodesics is that they carry phase through space unchanged. The creative break in symmetry which carries us from energy-time to momentum-space is the representation of phase not just as a function of time but as a function of velocity [momentum] in space. Here we find gauge invariance. Space introduces a new degree of freedom not present in time-frequency which is position - relative motion which provides a new classical way of storing information. In the section on the evolution of particles we confine our explanation to physical understanding without any mathematics so that it is appropriate to theology [the important point being, from the medieval point of view, that God is a body].

In the quantum mechanical regime changes in phase take us through time. In the classical regime changes in phase carry us through space.

Veltmann page 33: 'A vector in Hilbert space represents a physical state. What is a physical state? A physical state is simply a possible physical situation, with particles moving here and there, with dogs chasing cats, with people living and dying, with all

[page 91]

kinds of things happening. Often people make the mistake of identifying a physical state with a situation at a given moment, one picture from a movie, but that is not what we call a physical state. The situation at some moment may be seen as a boundary condition: if one knows the whole situation at some moment, and one knows the laws of nature, then in principle we can deduce the rest [this is the deterministic view of quantum evolution which may be seen as cycling through the eigenfunctions of the relevant operator, to be broken by an observation which stops the process at one eigenfunction / eigenvalue]. Matinus Veltman (1994): Diagrammatica: The Path to the Feynman Rules

Veltmann page 36: 'The S-matrix contains all the physical information for any scattering process = interaction between particles = intertaction between states' (?) [but an interaction is an observation, so the outcome is at best statistically predictable].

The true story of the creation of the universe has got to be better than all the Marvel comics put together. Marvel Comics - Wikipedia

Attraction does not make sense in a world without space? in Euclidean space the inverse square law is explained by the geometry of the sphere. In Hilbert space and the space of human attraction connection depends on frequency or harmony which is a function of phase locking (bosons) or anti-locking (fermions), a phenomenon related to attraction and repulsion like like and opposite charges. Like charges repel, whereas like phases (bosons) attract. Julia Naughtan: Love at first sniff: What’s the science of attraction?

Attraction between [static] charges is independent of the frequency of the photons involved so coding does not seem to be an issue, same as for gravitation which is universal. Nevertheless gravitation, strong, weak and electromagnetic are different languages [species of attraction].

What I am looking for is a clear physical understanding of how the simple initial physical world works, trying to take advantage of the simple principles learnt in fifty years of construction work.

Positive and negative charges cancel or balance, so that we can guess that they are created by 'zero sum bifurcation' This makes algebraic sense, but how do we imagine a mechanism for it. Maybe there is no mechanism but confinement is a consequence of limited possibilities

[page 92]

like a fluid confined to a pipe or a logical space where not-not-p = p so in the primitive quantum world things may be confined by their low cardinal, binary constraints, and then the ternary system of constraints we find in baryons. A proton is a group and anything that tries to escape feels the boundaries. Quantum chromodynamics - Wikipedia

The most general source of particles would seem to operate by fixed point theory driven by the closed aspect of an open universe. Is local three dimensional space the source of the openness through the mechanism of a curved manifold closed in 4 dimensions. Going round and round in speculation is in effect a demonstration of closure in thought processes and closure is a source of stability, whereas creative openness tends to disrupt comfortable closed (numb?) systems. M L Garcia de la Rocha: Sir John C. Eccles: from synapses to consciousness

Friday 5 November 2021

Creation is to open into a wider closure, finding new fixed points [as in quantum observation, which increases entropy]. John von Neumann (2014): Mathematical Foundations of Quantum Mechanics

How do we overcome dead ends? By a jump made possible by momentum (which some say is measured by uncertainty). Maybe most of the problems in quantum fields theory (such as the cosmological constant problem) arise from misunderstanding of uncertainty. Where is the uncertainty in entanglement? Not in the phenomenon itself, just there is no uncertainty in an actual die. The uncertainty arises in the use. Alice does not know what she is going to to observe in her half of the entangled state, but as soon as she sees it she knows for certain what Bob is going to see. This is consistent with the idea that the quantum world is deterministic, a notion based on the idea that real and complex arithmetic is deterministic because uncertainly is allegedly eliminated by taking the 'quantum' to the zero limit.

Inertial space is symmetric with respect to momentum, ie momentum conservation. How does motion in space-time look from the quantum mechanical poit of view - a wave equation in space.

[page 93]

We have seen that quantum mechanics maps onto sound and particularly music. We have next seen how memory created by null geodesics translates the music into space and momentum.

Saturday 6 November 2021

I think my theological ideas are a big deal, but I do not yet think they are bankable, but feel that the next week and the last four section 15-19 of e35_path_2_toe_Oct2021 may make the difference if they come out looking plausible enough for a preliminary hypothesis.

Religions justify war and murder. Moses, Exodus. Exodus 32: Moses slaughters the worshippers of the Golden Calf

Mass = internal energy = spin. Charge = zero sum bifurcation into +, -. Antiparticle = zero sum bifurcation. Why so few antiparticles? Antimatter - Wikipedia

Two primary issues: boson / fermion and PCT and all that which seem to appear with the advent of spacetime. However C (antiparticles) and T (time reversal) may be purely quantum mechanical effects arising from the reversibility and constant entropy of quantum mechanics. On the other had, parity reversal may only be possible in space. Check Lorentz transformation is Streater and Wightman. Streater & Wightman (2000): PCT, Spin, Statistics and All That

Another point: Time becomes unidirectional when we enter spacetime so it is linked to P. The overall claim is that as a whole P, C, and T are not individually conserved but PCT as a whole is.

Waiting for a new writeable idea to cross my mind. Following Eccles, this may be due to the closure of a neural loop analogous to the establishment of a fixed point in a quantum operator. The fixed point may not be just a Euclidean point but an idea encoded in a broad spectrum eigenfunctions and corresponding eigenvalues which may be read as a serial sequence like these sentences.

[page 94]

Old question: do ideas come faster if I try hard? If I read more? I have read a lot in my time and some of it is probably in me somewhere being superposed here and there to produce new correlations.

I write 'near enough' by covering all the points I want to make. There is too much variety available to ever make it perfect. This can only happen in very low entropy situations like binary logic which I am trying to identify near the beginning. In the modern world a qubit is assumed to have infinite entropy, but is this real? Probably not at the initial levels because no cloning limits the number of basis vectors which can be included in a superposition. Qubit - Wikipedia

We begin with a photon as the individual particle and then see it as a generator of electrons and positrons by zero sum bifurcation. Photons, or more particularly massless bosons are understood to be the causes of spacetime and potential (ie non kinetic) energy, ie energy locked in null geodesics.

Minkowski space therefore makes potential energy possible and so spacetime is necessary for the zero energy universe.

Things take time, which introduces uncertainty because processes can fork before completion.

We can apply Darwinian evolution at the fundamental level by considering the quantumd realm as the source of variation by superposition and the classical realm as the selector, using the requirement for real transmission of information and increase in entropy (von Neumann, Zurek) as the reason for the existence [emergence] of a particle. Wojciech Hubert Zurek (2008): Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical

The only way I can go is to follow my own instincts about the world leavened by religiously reading physics, chemistry and biology since an early age and some training in theology and philosophy. So I am writing a work of informed fiction trying to steer my way through the masses of contradictions I find in philosophy, theology and physics. This view relaxes

[page 95]

me greatly since I do not feel that I shall be judged as a scientists [although] I use the term freely, but as a prolegomenative scientist, looking for a consistent and presentable hypothesis, a fiction, but a fiction seeking the salvation of justification.

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Further reading

Books

Baigent, Michael, and Richard Leigh, Henry Lincoln, Holy Blood, Holy Grail: The Secret History of Christ and the Shocking Legacy of the Grail, Dell Trade Paperbacks 2004 Amazon.com review: 'Michael Baigent, Henry Lincoln, and Richard Leigh, authors of The Messianic Legacy, spent over 10 years on their own kind of quest for the Holy Grail, into the secretive history of early France. What they found, researched with the tenacity and attention to detail that befits any great quest, is a tangled and intricate story of politics and faith that reads like a mystery novel. It is the story of the Knights Templar, and a behind-the-scenes society called the Prieure de Sion, and its involvement in reinstating descendants of the Merovingian bloodline into political power. Why? The authors of Holy Blood, Holy Grail assert that their explorations into early history ultimately reveal that Jesus may not have died on the cross, but lived to marry and father children whose bloodline continues today.. . .' 
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Betancourt, Ingrid, Even Silence Has An End: My Six Years of Captivity in the Colombian Jungle, Penguin Press HC 2010 Amazon editorial review: 'Born in Bogotá, raised in France, Ingrid Betancourt at the age of thirty-two gave up a life of comfort and safety to return to Colombia to become a political leader in a country that was being slowly destroyed by terrorism, violence, fear, and a pervasive sense of hopelessness. In 2002, while campaigning as a candidate in the Colombian presidential elections, she was abducted by the FARC. Nothing could have prepared her for what came next. She would spend the next six and a half years in the depths of the jungle as a prisoner of the FARC. Even Silence Has an End is her deeply personal and moving account of that time. Chained day and night for much of her captivity, she never stopped dreaming of escape and, in fact, succeeded in getting away several times, always to be recaptured. In her most successful effort she and a fellow captive survived a week away, but were caught when her companion became desperately ill; she learned later that they had been mere miles from freedom. The facts of her story are astounding, but it is Betancourt's indomitable spirit that drives this very special account, bringing life, nuance, and profundity to the narrative. Attending as intimately to the landscape of her mind as she does to the events of her capture and captivity, Even Silence Has an End is a meditation on the very stuff of life-fear and freedom, hope and what inspires it. Betancourt tracks her metamorphosis, sharing how in the routines she established for herself-listening to her mother and two children broadcast to her over the radio, daily prayer-she was able to do the unthinkable: to move through the pain of the moment and find a place of serenity. Freed in 2008 by the Colombian army, today Betancourt is determined to draw attention to the plight of hostages and victims of terrorism throughout the world and it is that passion that motivates Even Silence Has an End. The lessons she offers here-in courage, resilience, and humanity-are gifts to treasure.' 
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Fredriksen, Paula, From Jesus to Christ: The Origins of the New Testament Images of Jesus, Yale University Press 1988 Jacket: 'How did Jesus of Nazareth become the Christs of the Christian tradition? And why did the early Christian communities develop different theological images of Jesus? In this exciting book, PF answers these questions by placing he various canonical images of Jesus within their historical context.' 
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Hawking (1975), Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.' 
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Kaku (1998), Michio, Introduction to Superstrings and M-Theory (Graduate Texts in Contemporary Physics), Springer 1998 ' Called by some "the theory of everything," superstrings may solve a problem which has eluded physicists for the past 50 years -- the final unification of the two great theories of the twentieth century, general relativity and quantum field theory. This is a course-tested comprehensive introductory graduate text on superstrings which stresses the most current areas of interest, not covered in other presentation, including: string field theory, multi loops, Teichmueller spaces, conformal field theory, and four-dimensional strings. The book begins with a simple discussion of point particle theory, and uses the Feynman path integral technique to unify the presentation of superstrings. Prerequisites are an aquaintance with quantum mechanics and relativity. This second edition has been revised and updated throughout.' 
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Kimura, Motoo, The Neutral Theory of Molecular Evolution, Cambridge University Press 1985  
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Misner (1973), Charles W, and Kip S Thorne, John Archibald Wheeler, Gravitation, Freeman 1973 Jacket: 'Einstein's description of gravitation as curvature of spacetime led directly to that greatest of all predictions of his theory, that the universe itself is dynamic. Physics still has far to go to come to terms with this amazing fact and what it means for man and his relation to the universe. John Archibald Wheeler. . . . this is a book on Einstein's theory of gravity. . . . ' 
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Streater (2000), Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2000 Amazon product description: 'PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.' 
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Veltman (1994), Martinus, Diagrammatica: The Path to the Feynman Rules, Cambridge University Press 1994 Jacket: 'This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. ... The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. ...' 
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Weyl (1985), Hermann, Space Time Matter (translated by Henry L Brose), Dover 1985 Amazon customer review: ' The birth of gauge theory by its author: This book bewitched several generations of physicists and students. Hermann Weyl was one of the very great mathematicians of this century. He was also a great physicist and an artist with ideas and words. In this book you will find, at a deep level, the philosophy, mathematics and physics of space-time. It appeared soon after Einstein's famous paper on General Relativity, and is, in fact, a magnificent exposition of it, or, rather, of a tentative generalization of it. The mathematical part is of the highest class, striving to put geometry to the forefront. Actually, the book introduced a far-reaching generalization of the theory of connections, with respect to the Levi-Civita theory. It was not a generalization for itself, but motivated by the dream (Einstein's) of including gravitation and electromagnetism in the same (geometrical) theory. The result was gauge theory, which, slightly modified and applied to quantum mechanics resulted in the theory which dominates present particle physics. Weyl's unified theory was proved wrong by Einstein, and his criticism alone, accepted by Weyl and included in the book, would justify the reading. Though wrong, Weyl's theory is so beautiful that Paul Dirac stated that nature could not afford neglecting such perfection, and that the theory was probably only misplaced. Prophetic words! . . . ' Henrique Fleming 
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Links

Al Jazeera and Agencies, US military jurors decry Guantanamo detainee torture, ' Seven United States military officers have written a letter urging clemency for Guantanamo Bay detainee Majid Khan, calling his account of torture at so-called CIA black sites a “stain on the moral fiber of America”. The seven officers were part of an eight-member military jury that on Friday issued a sentence of 26 years in prison to Khan for his support of al-Qaeda in the wake of the September 11 attacks. Khan had previously pleaded guilty in 2012 to serving as a courier for the group and helping to plan attacks. back

Albert Einstein (1905), On the Electrodynamics of Moving Bodies, An english translation of the paper that founded Special relativity. 'Examples of this sort, [in the contemporary application of Maxwell's electrodynamics to moving bodies] together with the unsuccessful attempts to discover any motion of the earth relatively to the ``light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.' back

Antimatter - Wikipedia, Antimatter - Wikipedia, the free encyclopedia, ' In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter. Minuscule numbers of antiparticles are generated daily at particle accelerators—total artificial production has been only a few nanograms[1]—and in natural processes like cosmic ray collisions and some types of radioactive decay, but only a tiny fraction of these have successfully been bound together in experiments to form antiatoms. No macroscopic amount of antimatter has ever been assembled due to the extreme cost and difficulty of production and handling.' back

Benny Morris & Dror Ze'evi, Then Came the Chance the Turks Have Been Waiting For: To Get Rid of Christians Once and for All , ' Many aspects of the Turkish Christian tragedy have yet to be studied in depth. We hope that our research has contributed something to an understanding of its scope. “The Thirty-Year Genocide,” by Dror Ze’evi and Benny Morris, was published in English by Harvard University Press in 2019. A Hebrew edition was published last month by Am Oved/Sifriyat Ofakim.' back

Brian Devlin, Minding the Church: How should the hierarchy respond to whistleblowers?, ' The Catholic Church in Scotland—and later in the United States with the Cardinal McCarrick case—felt the power of whistleblowing in action. But what, exactly, is whistleblowing? How does it help the Church? And what can the Church do to make sure it has the proper effect? As a whistleblower, I can attest that the act itself can occasion a terrible case of imposter syndrome. You’re constantly asking yourself—because you know you are likely to be asked by others—“Who do you think you are?” There is a passage in the Book of Amos where Amaziah, the priest of Bethel, tells Amos to back off. We’ll not be having any of that stuff going on here in the royal sanctuary. Amos replies, “I was no prophet, neither did I belong to any of the brotherhoods of prophets…. I was a shepherd and looked after sycamores: but it was Yahweh who took me from herding the flock.” God Himself asked this of Amos.' back

Cantor's theorem - Wikipedia, Cantor's theorem - Wikipedia, the free encyclopedia, ' In elementary set theory, Cantor's theorem is a fundamental result which states that, for any set A, the set of all subsets of A (the power set of A, denoted by P(A) ) has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with n members has a total of 2n subsets, so that if card (A) = n, then card (P(A)) = 2n, and the theorem holds because 2n > n for all non-negative integers.' back

Constantine the Great and Christianity - Wikipedia, Constantine the Great and Christianity - Wikipedia, the free encyclopedia, ' During the reign of the Roman Emperor Constantine the Great (AD 306–337), Christianity began to transition to the dominant religion of the Roman Empire. Historians remain uncertain about Constantine's reasons for favoring Christianity, and theologians and historians have often argued about which form of early Christianity he subscribed to. . . . Constantine's decision to cease the persecution of Christians in the Roman Empire was a turning point for early Christianity, sometimes referred to as the Triumph of the Church, the Peace of the Church or the Constantinian shift. In 313, Constantine and Licinius issued the Edict of Milan decriminalizing Christian worship. The emperor became a great patron of the Church and set a precedent for the position of the Christian emperor within the Church and raised the notions of orthodoxy, Christendom, ecumenical councils, and the state church of the Roman Empire declared by edict in 380. He is revered as a saint and is apostolos in the Eastern Orthodox Church, Oriental Orthodox Church, and various Eastern Catholic Churches for his example as a "Christian monarch”.' back

Electromagnetic wave equation - Wikpedia, Electromagnetic wave equation - Wikpedia, the free encyclopedia, 'The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. . . . the speed of light (ie phase velocity) in a medium with permeability μ and permittivity ε is 1/√με. back

Erin Harrington, Is a world without men a dystopia or a utopia? Creamerie and Y: The Last Man explore loss at a time of mass grief, ' It is a remarkable coincidence that both New Zealand black comedy Creamerie and American post-apocalyptic drama Y: The Last Man have arrived on our screens in the middle of a global pandemic. Both are shows about the aftermath of plagues that kill off the male population. Both were well into production by the time COVID-19 hit, the latter adapting a critically acclaimed DC Comics series by Brian K. Vaughn and Pia Guerra. Both are led and entirely directed by women – a strong statement in a significantly male-dominated industry. And as dystopian narratives, they also tap into some significant areas of current social and political interest. These include anxieties about gender roles, and how we deal with loss and grief at a global scale.' back

Exodus 32, Moses slaughters the worshippers of the Golden Calf, '27 Then he said to them, “This is what the Lord, the God of Israel, says: ‘Each man strap a sword to his side. Go back and forth through the camp from one end to the other, each killing his brother and friend and neighbour'.” 28 The Levites did as Moses commanded, and that day about three thousand of the people died. 29 Then Moses said, “You have been set apart to the Lord today, for you were against your own sons and brothers, and he has blessed you this day”.' back

Feynman, Leighton & Sands FLP II_01, Chapter 1: Electromagnetism, 'We now discuss the application of the special theory of relativity to electrodynamics.' back

Feynman, Leighton & Sands FLP: II_04, Chapter 4: Electrostatics, ' Now if you look at the equations of statics you will see that the study of the two subjects we call electrostatics and magnetostatics is ideal from the point of view of learning about the mathematical properties of vector fields. Electrostatics is a neat example of a vector field with zero curl and a given divergence. Magnetostatics is a neat example of a field with zero divergence and a given curl. The more conventional—and you may be thinking, more satisfactory—way of presenting the theory of electromagnetism is to start first with electrostatics and thus to learn about the divergence. Magnetostatics and the curl are taken up later. Finally, electricity and magnetism are put together. We have chosen to start with the complete theory of vector calculus. Now we shall apply it to the special case of electrostatics, the field of E\FLPE given by the first pair of equations. back

Feynman, Leighton and Sands FLP II_02, Chapter 2: Differential Calculus of Vector Fields, ' Ideas such as the field lines, capacitance, resistance, and inductance are, for such purposes, very useful. So we will spend much of our time analyzing them. In this way we will get a feel as to what should happen in different electromagnetic situations. On the other hand, none of the heuristic models, such as field lines, is really adequate and accurate for all situations. There is only one precise way of presenting the laws, and that is by means of differential equations. They have the advantage of being fundamental and, so far as we know, precise. If you have learned the differential equations you can always go back to them. There is nothing to unlearn.' back

Joanna Mendelssohn, Larger than life – sculptor Margel Hinder carved light and form and left a legacy, ' Many years ago my daily pleasure was to walk past a Margel Hinder masterpiece, the Civic Park Fountain in Newcastle. With water spraying in rhythmic patterns, it would bring a smile to my face for its beauty, the way the streams caught the light. Fountains can’t be moved for an exhibition, of course, but Hinder’s Civic Park Fountain and her sadly decommissioned Northpoint Fountain of 1975 have been digitally simulated by Andrew Yip for Margel Hinder: Modern in Motion, a joint project of Heide Museum of Modern Art and the Art Gallery of New South Wales.' back

John Cornwell, Pope Pius XII, Hitler's pawn?, Eugenio Pacelli, who took the name Pius XII, was elected Pope in 1939 and died in 1958, having steered the Catholic Church through the Second World War and the early deep freeze of the Cold War. The reasons for his failure to condemn the Nazi regime forthrightly have been debated for half a century. Was he afraid that more people would suffer if he spoke out? Or was he indifferent to the fate of the victims of Nazi atrocities, including the Holocaust itself? The motives, or excuses, for his anodyne statements (he avoided direct public mention of Jews, Nazis and Hitler) can only be surmised. Official papers relating to his pontificate are still under lock and key – though Pope Francis may allow them to be scrutinized soon. As far as we know, Pius left no private journal. He neither sought nor took advice. There was no intimate friend. He ate alone throughout his pontificate, and his daily walk in the Vatican gardens was ever solitary. After the war, he neither explained his omissions publicly, nor apologized.' back

John Palmer - Parmenides, Parmenides (Stanford Encyclopedia of Philosophy), First published Fri Feb 8, 2008 'Immediately after welcoming Parmenides to her abode, the goddess describes as follows the content of the revelation he is about to receive:
You must needs learn all things,/ both the unshaken heart of well-rounded reality/ and the notions of mortals, in which there is no genuine trustworthiness./ Nonetheless these things too will you learn, how what they resolved/ had actually to be, all through all pervading. (Fr. 1.28b-32) ' back

John Paul II: On Ecumenism, Ut unum sint, '3. At the Second Vatican Council, the Catholic Church committed herself irrevocably to following the path of the ecumenical venture, thus heeding the Spirit of the Lord, who teaches people to interpret carefully the "signs of the times" . The experiences of these years have made the Church even more profoundly aware of her identity and her mission in history. The Catholic Church acknowledges and confesses the weaknesses of her members, conscious that their sins are so many betrayals of and obstacles to the accomplishment of the Saviour's plan. Because she feels herself constantly called to be renewed in the spirit of the Gospel, she does not cease to do penance. At the same time, she acknowledges and exalts still more the power of the Lord, who fills her with the gift of holiness, leads her forward, and conforms her to his Passion and Resurrection.' back

John von Neumann (2014), Mathematical Foundations of Quantum Mechanics, ' Mathematical Foundations of Quantum Mechanics by John von Neumann translated from the German by Robert T. Beyer (New Edition) edited by Nicholas A. Wheeler. Princeton UP Princeton & Oxford. Preface: ' This book is the realization of my long-held intention to someday use the resources of TEX to produce a more easily read version of Robert T. Beyer’s authorized English translation (Princeton University Press, 1955) of John von Neumann’s classic Mathematische Grundlagen der Quantenmechanik (Springer, 1932).'This content downloaded from 129.127.145.240 on Sat, 30 May 2020 22:38:31 UTC back

Julia Naughtan, Love at first sniff: What’s the science of attraction?, ' Anthropologist Helen Fisher explored the process of communicating our attraction to another person via a copulative gaze in her book Anatomy of Love, first published in 1992. Advertisement “The gaze is probably the most striking human courting ploy,” Fisher writes. In cultures where eye contact between the sexes is permitted, “men and women often stare intently at potential mates for about two to three seconds during which their pupils may dilate – a sign of extreme interest. Then the starer drops his or her eyelids and looks away.” ' back

Lie Group - Wikipedia, Lie Group - Wikipedia, the free encyclopedia, 'In mathematics, a Lie group . . . is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Norwegian mathematician Sophus Lie, who laid the foundations of the theory of continuous transformation groups. Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. . . . One of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its "infinitesimal group" and which has since become known as its Lie algebra.' back

M L Garcia de la Rocha, Sir John C. Eccles: from synapses to consciousness, 'When at last he gave up laboratory activity, 50 years after having begun, he remained abreast of new developments in the field and continued publishing articles. Sherrington awakened his interest in the higher cerebral functions, an interest that would remain with Eccles for life. It was strengthened by his meeting with Popper, and then evolved to become the main focus of his intellectual activities after his retirement from experimental science.' back

Marvel Comics - Wikipedia, Marvel Comics - Wikipedia, the free encyclopedia, ' Marvel Comics is the brand name and primary imprint of Marvel Worldwide Inc., formerly Marvel Publishing, Inc. and Marvel Comics Group, a publisher of American comic books and related media. In 2009, The Walt Disney Company acquired Marvel Entertainment, Marvel Worldwide's parent company. . . . Marvel counts among its characters such well-known superheroes as Spider-Man, Iron Man, Captain America, the Hulk, Thor, Wolverine, . . . ' back

Michelle Cain, COP26: a global methane pledge is great – but only if it doesn’t distract us from CO₂ cuts , ' While these contrasting viewpoints may seem confusing, there is one simple fact that nobody can disagree with. Fossil fuels are the cause of about a third of all anthropogenic methane emissions. Therefore, if we stopped fossil extraction and use by 2030, the Global Methane Pledge would be achieved at the same time as eliminating most anthropogenic CO2 emissions. It’s that simple.' back

Quantum chromodynamics - Wikipedia, Quantum chromodynamics - Wikipedia, the free encyclopedia, ' In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics.' back

Qubit - Wikipedia, Qubit - Wikipedia, the free encyclopedia, 'A quantum bit, or qubit . . . is a unit of quantum information. That information is described by a state vector in a two-level quantum mechanical system which is formally equivalent to a two-dimensional vector space over the complex numbers. Benjamin Schumacher discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in a state, and storing the information on a smaller number of states. This is now known as Schumacher compression. In the acknowledgments of his paper (Phys. Rev. A 51, 2738), Schumacher states that the term qubit was invented in jest, during his conversations with Bill Wootters.' back

Richard Holden, Vital Signs: Borrowing from King Solomon, economists are getting closer to working out how good leaders can make good decisions , Here’s a story from the Bible. As far as I know, it’s the first reported instance of the branch of economics known as “implementation theory”. It’s from the First Book of Kings, Chapter 3, starting at Verse 16. Two women came before King Solomon with two babies, one dead and one alive. Each claimed the live boy was her son, and the dead boy belonged to the other. . . . ' back

Shakers - Wikipedia, Shakers - Wikipedia, the free encyclopedia, ' The United Society of Believers in Christ's Second Appearing, more commonly known as the Shakers, are a millenarian nontrinitarian restorationist Christian sect founded circa 1747 in England and then organized in the United States in the 1780s. . . . They practice a celibate and communal utopian lifestyle, pacifism, uniform charismatic worship, and their model of equality of the sexes, which they institutionalized in their society in the 1780s. They are also known for their simple living, architecture, technological innovation, music, and furniture.' back

The Happy Prince (2018 film) - Wikipedia, The Happy Prince (2018 film) - Wikipedia, the free encyclopedia, ' The Happy Prince is a 2018 biographical drama film about Oscar Wilde, written by, directed by, and starring Rupert Everett in his directorial debut The film stars Everett, Colin Firth, Colin Morgan, Emily Watson, Edwin Thomas and Tom Wilkinson. It premiered at the 2018 Sundance Film Festival, and was shown at the 2018 BFI Flare: London LGBT Film Festival. At the 9th Magritte Awards, it received a nomination in the category of Best Foreign Film.' back

Von Neumann algebra - Wikipedia, Von Neumann algebra - Wikipedia, the free encyclopedia, ' In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann algebras were originally introduced by John von Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. . . . Von Neumann algebras were first studied by von Neumann (1930) in 1929; he and Francis Murray developed the basic theory, under the original name of rings of operators, in a series of papers written in the 1930s and 1940s (F.J. Murray & J. von Neumann 1936, 1937, 1943; J. von Neumann 1938, 1940, 1943, 1949), reprinted in the collected works of von Neumann (1961).' back

Walter, Bourke, Bell, hunter & Atkinson, From dispossession to massacres, the Yoo-rrook Justice Commission sets a new standard for truth-telling, ' There can be no Treaty without truth. This simple but powerful statement is the reason for the Yoo-rrook Justice Commission’s mandate to reveal, record and analyse the systemic injustices experienced by Victorian First Peoples since colonisation. Named from a Wamba Wamba word meaning truth, the Yoo-rrook mandate will take three years from 2021-24. This is a significant step for truth-telling in Victoria. Truth-telling commissions are formal bodies tasked with discovering and revealing past wrongdoings in the hope of resolving conflict and repairing relationships. back

Wojciech Hubert Zurek (2008), Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical, 'Submitted on 17 Mar 2007 (v1), last revised 18 Mar 2008 (this version, v3)) Measurements transfer information about a system to the apparatus, and then further on – to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide framework for the “wavepacket collapse”, designating terminal points of quantum jumps, and defining the measured observable by specifying its eigenstates.' back

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