Notes
Sunday 25 April 2021 - Saturday 1 May 2021
[Notebook: DB 86: Hilbert / Minkowski]
[page 197]
Sunday 25 April 2021
We may see music as low resolution emotional communication
[page 198]
analogous to quantum amplitude, open to an infinite set of interpretations defined by the eigenfunctions of the observable [matrix] used by the listener.
What we are looking for is a version of quantum theory in spacetime as simple and transparent as special relativity itself. Much of the trouble arises from the effort to build quantum mechanics on classical mechanics, with its infinities, infinitesimals and continuity, which is all wrong.
We need to begin with a quantum special relativity which grows out of Hilbert space. What we need, to begin with, is a Hilbert explanation of the velocity of light. We cannot be far away from this if we direct the full power of logic and causality onto the job. What we want is the quantum syllogism put into action by the quantum of action. Action is in effect the middle term of every syllogism, establishing the Aristotelian conception of continuity where two systems have ends in common. In computer, two systems communicate by reading from and writing to the same location in memory. This is the foundation of all methods of communication which is a form of computation (we communicate in speech by writing on and reading from the air surrounding us). Aristotle: Physics V, iii: continuity
The eigenvalue equation defines states which are fixed points under the operation of the measurement operator. The Born rule is the propagator between eigenstates, telling us the probability of observing each of the eigenstates when an unknown system interacts with a known system, the measurement operator. Propagator - Wikipedia, Gilbert Strang: Eigenvalues and Eigenvectors, Born rule - Wikipedia
Actions are logical and local initiated when two systems become continuous by contact with one another. Two become one flesh / body, at least temporarily.
[page 199]
Continuity based on discrete points tells us nothing about causality since causality requires two system to become one. The gravitational structure of the universe implies causal unity and overlap as described by the differential operators in a differential manifolds. We see Aristotelian continuity in differential operators.
Quantum mechanics (pace Zee page 3) already creates and annihilates particles without the [explicit] help of relativity so in fact relativity may be a consequence of quantum mechanics rather than vice-versa. Already the atomic emission and absorption of a photon requires the creation or annihilation of a photon and the annihilation or creation of electron states facilitated by a precise energy overlap accompanied by the exchange of a quantum of action. Anthony Zee (2010): Quantum Field Theory in a Nutshell
We assume that the standard Hilbert space has ℵ0 dimensions which may be put into correspondence with both the [elements] of the set of natural numbers and the [elements] of the set of unique turing machines (computable functions) so that we can see that the number of possible quanta of action [each corresponding to a dimension of Hilbert space] matches the number of turing machines. This gives us a computational space for the deterministic evolution of amplitudes in the world and maybe we can map this onto the set of Feynman propagators if we can see a way to cut the path integral down from a point continuum to a logical continuum. Given that every propagator represents quantum of action, this may happen automatically.
How do we determine the frequency with which real propagators are actuated? This is a matter for the Born rule which seems implicit in the path integral. Zee builds his whole book on the path integral, so we have a
[page 200]
grip on the whole field theory story here.
Some of the higher order propagators have almost zero probability. Let us guess that their probability is the inverse exponential of their length (or the order the the symmetric group corresponding to their length) ie the probability of a random series of event 'pulling off' the propagation in question.
A good little job would be to code up a Feynman propagator and then put some values in to see what we get. This is the first time I have ever got a clue about a computation in quantum theory. In fact the path integral approach has the effect of coupling quantum mechanics to field theory. Why does it take me so long to see these connections. Because I am a bottom feeder. Not a Knabenphysik but Altenphysik. Carlo Rovelli (2021): Helgoland (page 18)
Monday 26 April 2021
Given that the elements of a linear superposition maintain their identity so that we can see (almost) linear waves arising from different sources on the surface of a pond passing through one another, we can see similar linearity in the strings of operations that represent algorithmic computations since the elements of the computation retain their identities and can be strung together unchanged in different ways to produce new processes.
. . .
The Courier The Courier (2020 film) - Wikipedia
[page 201]
Have I got enough clues somewhere in my mind to explain the emergence of spacetime out of Hilbert space? We can imagine that quanta of action act at random times (since they do not in the beginning have the variety to control themselves) creating a random spectrum of energy we call the vacuum. Now what? We can imagine that this spectrum fills a whole Hilbert space with a countably infinite set of energies. This structure exists in the time energy domain. How does spacetime emerge within this? Low energies correspond to long times, something like memory, and we may see spacetime as the operating system of the universe, managing memory and communication. On the basis of time, we see high energy processes contained in low energy processes as short wavelengths are contained as modulation in long wavelengths. Stable space corresponds to zero frequency and therefore zero energy. Some ideas here, but we have far to go. We may see the initial singularity as a permanent zero, eternal feature of the universe, containing the energetic vacuum within itself in the way that short times are contained in long times. Perhaps gravitation enters here, close to zero energy, where the universe may be seen as one particle, a zero dimensional Hilbert space.
In the theory of evolution genes are duplicated and exist over a long period compared to the lives of the organisms that have temporary custody of the genes corresponding to each species. Is there a clue here that can be carried from the complexities of biology to the simple state that began the formation of the universe within itself? We might see the structureless initial singularity as implementing the hypotheses of fixed point theory creating fixed points within itself which reflects its own logical closure. All these little bits and pieces may be arranged to give a consistent story of particles within particles all derived from the initial divine particle.
[page 202]
What we are seeking to do here is to map periods in time into periods in space, ie explain the transformation of energy into momentum, via the quantum of action ΔE.Δt ≡ ΔxΔp ≡ ℏ/2.
[quantum theology] page 1: What is not?
Tuesday 27 April 2021
How do we apply evolution to the initial singularity? We need both memory from generation to generation and variation from generation [to generation]. The longest memory in the system is eternity which we attribute to the initial singularity which we identify with the whole universe described by general relativity. The differentiable manifolds attributed to gravitation have no inherent metric, so the initial universe may be as small as we like and the expansion has nothing to do with the differentiable manifold but with the energy within it. We like to think that this remains at zero because the negative gravitational potential compensates for the positive kinetic energy revealed as the mass of particles [but maybe it is possible that gravitation sees and accounts for both by addition rather than subtraction]. We imagine the evolution of particles being a consequence of fixed point theory occurring within smaller and smaller local closed spaces. The difficult point here might be to explain the bifurcation of energy into potential (which seems spacelike, related to fermions) [and kinetic] timelike related to bosons. The clue here must lie in the difference between integral and odd half integral spin, and we are still keen to get the velocity of light involved here. This stuff is a species of metaphysical scat, all based on the notion that the quantum of action is act but due to cybernetic constraints its actions are random and we understand the gaps between actions as analogous to time. Scat singing - Wikipedia
[page 203]
Whatever explanation we seek, we seem to learn from accelerator experiments that bubbles of pure energy can create complex clouds of standard particles and we assume, on cybernetic grounds, that this requires the rapid production of entropy to determines the structure [and number] of the particles we see formed and must involve some sort of evolutionary process. Martinus Veltman (2003): Facts and Mysteries in Elementary Particle Physics: 6.1, Ashby (1964): An Introduction to Cybernetics, Part II
Dear Prof Rovelli, I feel that your book is on the right track, and it is a very old track, dating back at least to the dawn of Christianity [and perhaps other theologies] when the doctrine of the trinity was invented. The Father, reflecting on itself, generates the Son who, while identically god, is differentiated from the father by the reciprocal relationship of paternity and sonship. We might think of Father, Son and Spirit as fermions differentiated by bosons. More abstractly, the father is pure action which we might call a quantum of action. Logically an action is what turns some p into not-p, but the not-p is also an action, fertile and capable of creating more actions each differentiated by its decent from its predecessor. So we have a clue about how to turn a threesome of actions into an infinity of actions, all orthogonal to one another, elements of a transfinite Hilbert space, each dimension of which is a quantum of action. Aquinas, Summa, I, 27, 1: Is there procession in God?
Wednesday 28 April 2021
Things are getting more weird and exciting as I push on into new
[page 204]
country into a world full of gods all divine quanta of action identical to . . . the initial singularity as the Christian [divinity] multiples into the trinity and moves on into a transfinity of gods, all multiplying as the traditional god multiplied, differentiating as we go by their relationships with one another as Rovelli would have it, to form complex entities like myself and forests, animals planets and the universe as we now see it. [All this] is based on the idea that action is an implementation of the not operator, forming a Hilbert space of discrete identical and yet differentiated actions whose fundamental properties are that one is not the other and so they are all orthogonal to one another. We now have to trace the differentiation in detail, tracing the emergence of gravitation and the other three categories of relationship that we describe with our current version of quantum field theory, seeking to rebuild this theory on the basic backbone of reproduction and differentiation, a concrete process that provides us with the layers of symmetry that provide us with the universals that make both knowledge and knowers emerge. Sleeping and dreaming my way into a dazzling new world, the madness of creation.
Quantum field theory seems very much like a movie alleged to be based on a true story which nevertheless often deviates from truth to beat the boredom of real live as the heroes make their way through trackless wastes, introducing moments of confected drama to produce an artistic product carefully shaped to attract viewers and revenue. The producers of field theory have to feed the defence industry above all because that is where the money mostly comes from, so a quick and dirty route to a
[page 205]
weapon that satisfies their clients is much favoured. So now I go to the movies to collect evidence for this paragraph.
Thursday 29 April 2021
The entropy of a click is equal to the number of [discrete] clickable points on a screen.
As Veltman points out, any particle or energy bubble in spacetime that is moving at less than the velocity of light is not pure [energy]. There is always a reference frame wth respect to which it is in effect at rest and it already carries the constraints that it has inherited from the [colliding] particles from which it is formed, so it carries their inherited properties, conservation of energy, charge, momentum, spin and so on. The task of quantum field theory is to map the path from the input constraints to the potential [outputs]. These constraints are conserved in spacetime no matter how high the momentum of the inputs may be and so we are led to guess that these constraints arise not from processes in spacetime but from deeper structure encoded in the underlying Hilbert space. We are thus led to seek explanations of these symmetries in Hilbert space and they add urgency to the quest for logical explanations which are enforced in the rest frames of these massive particles. The deepest source of understanding must therefore be built into the massless particle that carry these messages, that is in the massless gauge particles that carry these messages from the massive inputs to the massive outputs [since the limited entropy of these particles places constraints on the messages they can carry]. When electrons and positron annihilate one another to produce photons we must assume that the photons or other massless bosons carry all the information that was transferred from the massive inputs to the massive outputs. What goes on behind the velocity of light? Once again I feel that
[page 206]
that it is something to do with the interface between Hilbert and Minkowski spaces. S-matrix - Wikipedia, Gauge theory - Wikipedia
When everything is online it can be hacked from anywhere. The basic security of the universe is spacetime separation. Space division multiplexing (overpasses, separate lanes) is much more efficient that time division multiplexing (traffic lights, roundabouts). Space has an enormous selective advantage over time, and time is all that [pure] quantum mechanics has. The basic power of evolution comes from orthogonality, the power of not. Mathematics creates orthogonal spaces by fiat. The world does it concretely with independent degrees of freedom in spacetime. Freedom means separation, the opposite of communication, fermion vs boson.
The pure quantum world is FM, frequency/energy modulated ie quantized ≡ quantum module.
Friday 30 April 2021
Streater and Wightman page 5: Super-selection rules.
'Does every ray in [a Hilbert space] H describe a possible state of the system? The answer is, in general, no. . . . Any statement that singles out certain rays as not physically realizable is called a super-selection rule [ie a constraint on Hilbert space]. If there are super-selection rules in a theory, then not all hermitian operators are observables and the superposition principle does not hold in H. Streater & Wightman (2000): PCT, Spin, Statistics and All That
Super-selection rules are a consequence of observations and split Hilbert space into orthogonal subspaces, ie there is physics here that is not in the mathematics of Hilbert space.
[page 207]
Streater & Wightman page 7: 'A symmetry operation of a physical system is a correspondence which yields for each physically realizable state another state such that all transition probabilities are preserved [ie the mathematical model has degrees of freedom which do not have observable consequences]:
|(Φ' , Ψ')|2 = |(Φ , Ψ)|2
Energy travelling at the velocity of light [in effect outside spacetime] has no mass. Energy at rest (in some frame) has mass. Why? Massive particles carry their rest frame with them. Photons have no rest frame. Massive particles exist in spacetime; photons travelling at c are outside it, they have no size and their clocks are stopped. In the photon world velocity has no meaning because there is no space and no time. Velocity only comes into existence with space and time, as do massive particles with rest frames. The interface is observation, the meeting of two particles in spacetime that enables their associated amplitudes to interfere. The properties of the interaction that are conserved exist in the orthogonal subspaces that do not superpose and so do not change one another. Super-selection is in effect the foundation of structure and differentiation, of independence, orthogonality. Within each orthogonal subspace, quantum mechanics goes on as usual [so we might see the origin of space connected to the differentiation of Hilbert space into orthogonal subspaces].
page 5: 'The super-selection rules associated [with] charge (Q), baryon number (B) and bosons/fermion distinction are known as charge, baryon and univalence super-selection rules respectively.'
We may imagine that the two first orthogonal subspaces in the universal Hilbert space are the boson space and the fermion space and we
[page 208]
would like to imagine that they are closely related to the bifurcation of the initial singularity into positive (kinetic) and negative (potential) energy, kinetic associated with massless bosons outside space and potential associated with massive fermions and space.
Saturday 1 May 2020
My efforts to revise physics to be more compatible with theology are on bumpy ground. My thesis 'Prolegomenon' made what I see to be a good start covering all the necessary ground, but it took a classical view of physics, coupling with quantum mechanics [through] the general conception that every elementary event in the universe is discrete measured by the quantum of action with a nature that can be captured by a turing machine and so a foundation for a logical conception of the universe as the mind of god and therefore divine. The current task is to take this classical conception deeper, into the quantum world, based on the idea that we can say all we need to say about the foundations of the world, including space-time, gravitation and quantum field theory by a careful application and exploration of Hilbert space. After skimming through Zee and taking on the difficulties of QFT catalogued by Kuhlman, I can see little chinks of light here and there and have a certain confidence that I can cook up a coherent story on quantum-theology.net by the end of the year which will serve as a companion to physicaltheology.com and scientific-theology.com. Meinard Kuhlmann (Stanford Encyclopedia of Philosophy): Quantum Field Theory, Jeffrey Nicholls (2021): Quantum theology: Scientific revolution = paradigm change
One way to encode logical operations, taking a page out of Gödel's book, is to associate them with frequencies so a serial string of
[page 209]
frequencies can represent a serial string of operations and given that we have ℵ0 different frequencies available in a Hilbert space there is room to represent all possible turing machines. At the top (or bottom) of the heap is 0, eternity, the frequency of the universe and we go to higher and higher frequencies as we go to finer and finer detail. Given my mass of 80 kg, my aggregate operating frequency [measured as a serial process] in quanta per second is 80 c2/ℏ. Most of my systems work at about 0.1 Volt, so this energy is multiplexed over a vast number of [parallel] systems. Kurt Gödel I: On formally undecidable propositions of Principia Mathematica and related systems, I
We would like to think of the world in terms of music as a big band made of lots of little bands, each band working as a unit of individual players working together, listening to each other and putting their contribution in.
Like the Catholic Church, cosmologists want us to believe some impossible things such as that the point like initial singularity which has no space and time structure nevertheless contains all the energy of the universe. Here, we like to think, consistent with ancient theology, that the singularity is a quantum of action which acts at random times to create energy. In order [to implement the conservation of energy and] maintain the energy of the universe at zero each act must produce as much negative potential energy as it creates kinetic energy, the frequency of the kinetic energy f = E/ℏ being determined by the depth of the corresponding potential well. Aquinas, Summa, I, 2, 3: Does God exist?
We imagine that three early steps in the emergence of the universe [within the eternal initial singularity]: [the] first we might call logical or boolean, beginning with the notion that the quantum of action is equivalent to the not operator; second time based quantum
[page 210]
mechanics executed in Hilbert space; and then some form of field theory executed in spacetime with the introduction of momentum, gravitation and a spectrum of particles divided into fermions and bosons. We might see the bosons as more primitive, corresponding to energy/time and the fermions being built on the bosons giving space-time motivated by the fact that space-time allows for the existence of many more degrees of freedom (ie more entropy) than pure time and we can imagine the transition from time to spacetime as modelled by Cantor's transformation of sets of cardinal ℵ0 into sets with cardinal ℵ1. All quite pretty if true. I say this stuff again and again, but it is a bit like polishing a [telescope] mirror, increasing precision with every round. George G. Jones: How a Telescope Mirror is Ground, Polished and Figured, Georg Cantor: Contributions to the Founding of the Theory of Transfinite Numbers
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Further readingBooks
Ashby (1964), W Ross, An Introduction to Cybernetics, Methuen 1956, 1964 'This book is intended to provide [an introduction to cybernetics]. It starts from common-place and well understood concepts, and proceeds step by step to show how these concepts can be made exact, and how they can be developed until they lead into such subjects as feedback, stability, regulation, ultrastability, information, coding, noise and other cybernetic topics.'
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Cantor, Georg, Contributions to the Founding of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain), Dover 1895, 1897, 1955 Jacket: 'One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc, as well as the entire field of modern logic.'
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Carter, Graydon, and Mark Summers (Illustrator), Todd S Purdum (Foreword), Vanity Fair's Presidential Profiles: Defining Portraits, Deeds and Misdeed of 43 Notable Americans -- And What Each One Really Thought About His Predecessor, Abrams Amazon product description:
'Forty-three men have held the highest office in the United States, making up an exclusive club of statesmen and sinners, grinds and slackers, winners and losers, Boy Scouts and rogues. They are profiled in incisive and entertaining commentaries written by Vanity Fair contributors Judy Bachrach, David Friend, David Kamp, Todd S. Purdum, and Jim Windolf that tell of their deeds, plumb their characters, and dispense the essential dish about their personal lives. Portraits newly drawn by the acclaimed artist Mark Summers illuminate each of them as vivid individuals. Also included: revealing remarks-in the presidents' own words-showing what each really thought about the man who had preceded him in the Oval Office, an introduction by Graydon Carter, and a foreword by Washington insider Todd S. Purdum.'
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Christie, Agatha, Murder in the Mews:Four Cases of Hercule Poirot, PAN 1954 Jacket: 'Murder in the Mews comprises the exciting stories of four of Hercule Poirot's cases; . . . [Murder in the Mews], . . . The Incredible Theft, . . . Dead Man's Mirror [and] . . . Triangle at Rhodes.'back |
Domb, Cyril, The Critical Point: An historical introduction to the modern theory of Critical Phenomena, CRC Press
1996 Jacket: 'The relationship between liquids and gases engaged the attention of a number of distinguished scientists in the nineteenth century. In a paper published in 1869, Thomas Andrews described experiments that he had performed on carbon dioxide. From this he concluded that a critical temperature exists below which liquids are gases are distinct phases of matter. but above which they merge into a single phase. Other natural phenomena were subsequently discovered to which the same critical point description can be applied. These included ferromagnetism, solutions and various types of lambda point transition.
This book provides a historical account of theoretical explanations of critical phenomena which ultimately led to a major triumph of statistical mechanics in the twenteth century.
Contents include Historical survey; classical theories of fluids, magnets and light scattering; the Onsager revolution; Reconciliation; renormalisation group.'
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Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. . . . In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands
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Lewis, Michael, The Big Short: Inside the Doomsday Machine, W. W. Norton & Company; Reprint edition 2011 Review from Bookmarks Magazine
'Michael Lewis has written from the perspective of a financial insider for more than 20 years. His first book, Liar's Poker, was a warts-and-all account of Wall Street culture in the 1980s, when Lewis worked at the investment bank Salomon Brothers. Everything Lewis has touched since has turned to gold, and The Big Short seems to be another of those books, combining an incendiary, timely topic with the author's solid, insightful, and witty investigative reporting. Only the Pittsburgh Post-Gazette criticized what it felt was a rush job of writing and a failure to integrate the individual stories. Few readers will care for the message here (despite laugh-out-loud moments of absurdity), but Lewis is a capable guide into the world of CDOs, subprime mortgages, head-in-the-sand investments, inflated egos--and the big short. However, as Entertainment Weekly points at, if you're only going to read one book on the topic, perhaps this should not be the one.'
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O'Murchu, Diarmuid, Quantum Theology : Spiritual Implications of the New Physics, Crossroad Publishing Company 1997 Jacket: 'For quantum theorists, the fact that the whole is greater than the sum of its parts underpins all reality. "This is not merely a scientific principle of immense significance for our times" writes DO'M, "it is also a theological norm, known to mystics for centuries and now maturing into the supreme wisdom of our age."'
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Orwell, George, George Orwell Omnibus: The Complete Novels: Animal Farm, Burmese Days, A Clergyman's Daughter, Coming up for Air, Keep the Aspidistra Flying, and 1984, Secker and Warburg : Octopus Books 1976
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Riesz, Frigyes, and Bela Sz-Nagy, Functional Analysis, Dover Publications 1990 Jacket: 'This noted text, highly regarded in its field, discusses modern theories of differentiation and integration and the principal problems and methods of handling integral equations and linear functional and transformations. ..."
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Rovelli (2021), Carlo, and Erica Segre & Simon Carnell (translators), Helgoland, Allen Lane / Penguin 2021 ' In June 1925, twenty-three-year-old Werner Heisenberg, suffering from hay fever, retreated to a small, treeless island in the North Sea called Helgoland. It was there that he came up with one of the most transformative scientific concepts- quantum theory.
Almost a century later, quantum physics has given us many startling ideas - ghost waves, distant objects that seem magically connected to each other, cats that are both dead and alive. At the same time, countless experiments have led to practical applications that shape our daily lives. Today our understanding of the world around us is based on this theory. And yet it is still profoundly mysterious.
In this enchanting book, Carlo Rovelli, one of our most celebrated scientists, tells the extraordinary story of quantum physics and reveals its deep meaning- a world made of substances is replaced by a world made of relations, each particle responding to another in a never ending game of mirrors.
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Schiff, Leonard I, Quantum Mechanics, McGraw-Hill 1968 Preface: 'This volme has a threefold purpose: to explain the physical concepts of quantum mechanics, to describe the mathematical formalism, and to provide illustrative examples of both the ideas and the methods.'
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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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Tymoczko, Thomas, New Directions in the Philosophy of Mathematics: An Anthology, Princeton University Press 1998 Jacket: 'The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. ... By bringing together essays of leading philosophers, mathematicians, logicians and computer scientists, TT reveals an evolving effort to account for the nature of mathematics in relation to other human activities.'
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Veltman (2003), Martinus, Facts and Mysteries in Elementary Particle Physics, World Scientific 2003 'Introduction: The twentieth century has seen an enormous progress in physics. The fundamental physics of the first half of the century was dominated by the theory of relativity, Einstein's theory of gravitation and the theory of quantum mechanics. The second half of the century saw the rise of elementary particle physics. . . . Through this development there has been a subtle change in point of view. In Einstein's theory space and time play an overwhelming dominant role. . . . The view that we would like to defend can perhaps best be explaned by an analogy. To us, space-time and the laws of quantum mechanics are like the decor, the setting of a play. The elementary articles are the actors, and physics is what they do. . . . Thus in this book the elementary particles are the central objects.'
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Wain (1980), John, Samuel Johnson: A Biography, Macmillan 1980 Jacket: 'This universally acclaimed book, first published in 1974, is about every aspect of Samuel Johnson: a discussion of his ideas, a criticism of his writings, an historical placing of the man within the social and intellectual landscape of the day, and a personal story—above all a personal story. ... '
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Wigner, Eugene, Symmetries and Reflections: Scientific Essays , MIT Press 1970 Jacket: 'This volume contains some of Professor Wigner's more popular papers which, in their diversity of subject and clarity of style, reflect the author's deep analytical powers and the remarkable scope of his interests. Included are articles on the nature of physical symmetry, invariance and conservation principles, the structure of solid bodies and of the compound nucleus, the theory of nuclear fission, the effects of radiation on solids, and the epistemological problems of quantum mechanics. Other articles deal with the story of the first man-made nuclear chain reaction, the long term prospects of nuclear energy, the problems of Big Science, and the role of mathematics in the natural sciences. In addition, the book contains statements of Wigner's convictions and beliefs as well as memoirs of his friends Enrico Fermi and John von Neumann.
Eugene P. Wigner is one of the architects of the atomic age. He worked with Enrco Fermi at the Metallurgical Laboratory of the University of Chicago at the beginning of the Manhattan Project, and he has gone on to receive the highest honours that science and his country can bestow, including the Nobel Prize for physics, the Max Planck Medal, the Enrico Fermi Award and the Atoms for Peace Award. '.
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Zee (2010), Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2010 ' Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading.'
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Links
Alan Crawford, The Greens Once Took On Germany, But Now They’re Taking It Over, ' The Greens, with their youthful image and impeccable environmental credentials that capture the Zeitgeist of climate summits and Fridays for Future demonstrations, are the clear beneficiaries. Their rise to become contenders represents an extraordinary journey from protest movement to mainstream respectability over the course of two generations.' back |
Andrew J. Bacevitch, Biden’s Foreign Policy: Delaying the inevitable, ' Biden’s tribute to the “world’s most powerful military” qualifies as accurate. As measured by their capacity for delivering lethal target effects, whether on land, sea, air, or in outer space (and probably in cyberspace), U.S. forces are in a league of their own. But the following statements are also true:
A penchant for armed intervention abroad finds the United States using force more frequently than any other nation on the planet; while promising peace, U.S. presidents have delivered something akin to perpetual war. . . .
Particularly revealing on this point is the fact that Biden’s interim strategic guidance omits any mention of Iraq or Libya, and includes just a single glancing reference to Afghanistan, which apparently will see the last U.S. troops withdraw a tidy twenty years after 9/11. The defining U.S. military campaigns of the past two decades, not one of them—least of all Afghanistan—has yielded anything remotely like success. A fair judgment would be that all three produced catastrophic results.' back |
Aquinas, Summa, I, 2, 3, Summa: I 2 3: Does God exist?, I answer that the existence of God can be proved in five ways. The first and more manifest way is the argument from motion. . . . The second way is from the nature of the efficient cause. . . . The third way is taken from possibility and necessity . . . The fourth way is taken from the gradation to be found in things. . . . The fifth way is taken from the governance of the world. back |
Aquinas, Summa, I, 27, 1, Is there procession in God?, 'As God is above all things, we should understand what is said of God, not according to the mode of the lowest creatures, namely bodies, but from the similitude of the highest creatures, the intellectual substances; while even the similitudes derived from these fall short in the representation of divine objects. Procession, therefore, is not to be understood from what it is in bodies, either according to local movement or by way of a cause proceeding forth to its exterior effect, as, for instance, like heat from the agent to the thing made hot. Rather it is to be understood by way of an intelligible emanation, for example, of the intelligible word which proceeds from the speaker, yet remains in him. In that sense the Catholic Faith understands procession as existing in God.' back |
Aristotle, Physics V, iii, , ' A thing that is in succession and touches is 'contiguous'. The 'continuous' is a subdivision of the contiguous: things are called continuous when the touching limits of each become one and the same and are, as the word implies, contained in each other: continuity is impossible if these extremities are two. This definition makes it plain that continuity belongs to things that naturally in virtue of their mutual contact form a unity. And in whatever way that which holds them together is one, so too will the whole be one, e.g. by a rivet or glue or contact or organic union. ' 227a10 sqq back |
Ashley Parker, Fresh off election falsehoods, Republicans serve up a whopper about Biden, ' Daniel A. Effron, a professor of organizational behavior at London Business School who studies the psychology of lies, said that even if people don’t believe a specific falsehood, its mere existence can still help perpetuate a damaging narrative.
“One of the things misinformation can do is signal to people that there’s a deeper truth to what’s being claimed, even if people know it’s not literally true,” Effron said. “So you see a bunch of people sharing this thing about the burger and you may not think, ‘Biden is going to literally take away the burgers,’ but you may start to believe the broader point this misinformation is making — the broader point in this case being Biden is super liberal, he’s going to infringe on our liberties, he can’t be trusted.” ' back |
Barry Gittins, Is the word ruled by ideas or by interests?, '. . . John Maynard Keynes . . . claimed that "the ideas of economists and political philosophers, both when they are right and when they are wrong, are more powerful than is commonly understood.
"Indeed, the world is ruled by little else. Practical men, who believe themselves to be quite exempt from any intellectual influence, are usually the slaves of some defunct economist.
"Madmen in authority, who hear voices in the air, are distilling their frenzy from some academic scribbler of a few years back." ' back |
Born rule - Wikipedia, Born rule - Wikipedia, the free encyclopedia, 'The Born rule (also called the Born law, Born's rule, or Born's law) is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of the Copenhagen interpretation of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results. . . . The Born rule states that if an observable corresponding to a Hermitian operator A with discrete spectrum is measured in a system with normalized wave function (see bra-ket notation), then
the measured result will be one of the eigenvalues λ of A, and
the probability of measuring a given eigenvalue λi will equal <ψ|Pi|ψ> where Pi is the projection onto the eigenspace of A corresponding to λi'. back |
Bradshaw , The First Australians grew to a population of millions, much more than previous estimates, ' We know it is more than 60,000 years since the first people entered the continent of Sahul — the giant landmass that connected New Guinea, Australia and Tasmania when sea levels were lower than today.
But where the earliest people moved across the landscape, how fast they moved, and how many were involved, have been shrouded in mystery.
Our latest research, published today shows the establishment of populations in every part of this giant continent could have occurred in as little as 5,000 years. And the entire population of Sahul could have been as high as 6.4 million people.' back |
Crabtree et al, We mapped the ‘super-highways’ the First Australians used to cross the ancient land, ' Several of the super-highways our models identified echo well-documented Aboriginal trade routes criss-crossing the country. This includes Cape York to South Australia via Birdsville in the trade of pituri native tobacco, and the trade of Kimberley baler shell into central Australia.
There are also striking similarities between our map of super-highways and the most common trading and stock routes used by early Europeans. They followed already well-known routes established by Aboriginal peoples.' back |
Ecclesiastes 3:1, There is a time, '1There is a time for everything,
and a season for every activity under the heavens:' back |
Ecstasy of Saint Theresa - Wikipedia, Ecstasy of Saint Theresa - Wikipedia, the free encyclopedia, 'The Ecstasy of Saint Theresa (alternatively Saint Teresa in Ecstasy or Transverberation of Saint Teresa) is the central sculptural group in white marble set in an elevated aedicule in the Cornaro Chapel, Santa Maria della Vittoria, Rome. It was designed and completed by Gian Lorenzo Bernini, the leading sculptor of his day, who also designed the setting of the Chapel in marble, stucco and paint. It is generally considered to be one of the sculptural masterpieces of the High Roman Baroque.' back |
Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, 'The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories.' back |
Gauge theory - Wikipedia, Gauge theory - Wikipedia, the free encyclopedia, ' In physics, a gauge theory is a type of field theory in which the Lagrangian does not change (is invariant) under local transformations from certain Lie groups.
The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called gauge invariance). When such a theory is quantized, the quanta of the gauge fields are called gauge bosons. If the symmetry group is non-commutative, then the gauge theory is referred to as non-abelian gauge theory, the usual example being the Yang–Mills theory. ' back |
George G. Jones, How a Telescope Mirror is Ground, Polished and Figured, ' The "silver-on-glass reflecting telescope has of late years been in high favor with amateur astronomers, particularly in England. Its mirrors of pure silver—the glasss being merely the mould or form on which the mirrors proper rest—reflect nearly as large a percentage of the light as finds it way through the four surfaces of an object glass; it is entirely free of the defect of "chromatism" which cannot be said of the best "achromatic" and with careful workmanship is may be corrected perfectly for spherical aberration, — points which render it for most urposes a formidable rival to the common refractor.' back |
Gilbert Strang, Chapter 6: Eigenvalues and Eigenvectors, 'Linear equations Ax = bcome from steady state problems. Eigenvalues have their greatest importance in dynamic problems. The solution of du/dt = Au changing with time—growing or decaying or oscillating. We can’t find it by elimination. This chapter enters anew part of linear algebra, based on Ax = λx. All matrices in this chapter are square.' back |
Gillian Brockell, The Armenian ‘genocide’: This is what happened in 1915, ' The Ottoman Empire killed an estimated 1.5 million Armenians during World War I. On Saturday, President Biden called it “genocide,” making him the first president to do so since Ronald Reagan. It’s a move that could further strain relations with U.S. ally Turkey. . . . On April 24, 1915, the [Ottoman}government arrested about 250 Armenian leaders and intellectuals. This is seen by many as the beginning of the massacre, and April 24 now marks Armenian Genocide Remembrance Day.' back |
Jeffrey Nicholls (2021), Quantum theology: Scientific revolution = paradigm change, ' A new idea does not, in the first instance, change physical reality, only the mental states of the people who conceive it and understand it. What it does change in society is our appreciation of the possibilities. Newton's laws opened the way for space travel and Bernoulli showed us how to fly. The idea behind this site is to totally change our vision of the world and ourselves. We are not aliens in an alien and damaged world, we are divine members of god. Quantum mechanics takes us deep into the heart of this divine world.' back |
Kurt Gödel I, On formally undecidable propositions of Principia Mathematica and related systems, I, The classic paper, part I. back |
Meinard Kuhlmann (Stanford Encyclopedia of Philosophy), Quantum Field Theory, ' Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. In a rather informal sense QFT is the extension of quantum mechanics (QM), dealing with particles, over to fields, i.e. systems with an infinite number of degrees of freedom. (See the entry on quantum mechanics.) In the last few years QFT has become a more widely discussed topic in philosophy of science, with questions ranging from methodology and semantics to ontology. QFT taken seriously in its metaphysical implications seems to give a picture of the world which is at variance with central classical conceptions of particles and fields, and even with some features of QM.' back |
Mohamed Zeeshan, Opinion | How Modi Led India Into a COVID Catastrophe , ' Meanwhile, the government stepped up its intimidation of those journalists who, vexatiously, still ask questions. After having thrown several journalists in jail for their reporting last year, it recently ordered Twitter to censor accounts critical of its mishandling of the pandemic. . . .
The pandemic has hit extremely close to home for an ever-increasing proportion of the population, and that includes those in the urban middle class who used to offer Modi uncritical, unconditional support.
India’s patience with centralized, strongman leadership is fast running out. COVID’s shattering toll may end up being the shock that re-awakens Indian democracy.' back |
Nagarjuna - Wikipedia, Nagarjuna - Wikipediam the free encyclopedia, ' Nāgārjuna (c. 150 – c. 250 CE) was an Indian Mahāyāna Buddhist thinker, scholar-saint and philosopher. He is widely considered as one of the most important Buddhist philosophers. Furthermore, according to Jan Westerhoff, he is also "one of the greatest thinkers in the history of Asian philosophy."
Nāgārjuna is widely considered to be the founder of the madhyamaka (centrism, middle-way) school of Buddhist philosophy and a defender of the Mahāyāna movement. His Mūlamadhyamakakārikā (Root Verses on Madhyamaka, MMK) is the most important text on the madhyamaka philosophy of emptiness.' back |
Nicholas Perlroth, Daniel Kaminsky, Internet Security Savior, Dies at 42, 'In 2008, Mr. Kaminsky was widely hailed as a latter-day, digital Paul Revere after he found a serious flaw in the internet’s basic plumbing that could allow skilled coders to take over websites, siphon off bank credentials or even shut down the internet. Mr. Kaminsky alerted the Department of Homeland Security, executives at Microsoft and Cisco, and other internet security experts to the problem and helped spearhead a patch.' back |
Oliver Holmes, Israel is committing the crime of apartheid, rights watchdog says, ' Human Rights Watch has accused Israeli officials of committing the crimes of apartheid and persecution, claiming the government enforces an overarching policy to “maintain the domination by Jewish Israelis over Palestinians”.
In a report released on Tuesday, the New York-based advocacy group became the first major international rights body to level such allegations. It said that after decades of warnings that an entrenched hold over Palestinian life could lead to apartheid, it had found that the “threshold” had been crossed.
“This is the starkest finding Human Rights Watch has reached on Israeli conduct in the 30 years we’ve been documenting abuses on the ground there,” said Omar Shakir, the group’s Israel and Palestine director. Shakir said his organisation had never before directly accused Israeli officials of crimes against humanity.' back |
Patrick J. Connolly, Newton and God's Sensorium, 'Conclusion
In this paper, I have tried to provide an interpretation of Newton’s claim that God has a sensorium. I have disagreed with Leibniz that Newton’s claim is either unintelligible or entails somethingharmfultonaturalreligion. AnexaminationofmanyofNewton’sscientific, metaphysical, and theological views reveals that he had carefully considered ideas about sensoria, space, and God’s relation to the world. Specifically, I have argued that these passages show that Newton believed that God exercised His will in space.' back |
Propagator - Wikipedia, Propagator - Wikipedia, the free encyclopedia, 'In quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum. Propagators are used to represent the contribution of virtual particles on the internal lines of Feynman diagrams. They also can be viewed as the inverse of the wave operator appropriate to the particle, and are therefore often called Green's functions.' back |
Pushpalatha C. Bhat, Advanced Analysis Methods in Particle Physics (FERMILAB-PUB-10-054-E), ' Abstract: Each generation of high energy physics experiments is grander in scale than the previous – more powerful, more complex and more demanding in terms of data handling and analysis. The spectacular performance of the Tevatron and the beginning of operations of the Large Hadron Collider have placed us at the threshold of a new era in particle physics. The discovery of the Higgs boson or another agent of electroweak symmetry breaking and evidence of new physics may be just around the corner. The greatest challenge in these pursuits is to extract the extremely rare signals, if any, from huge backgrounds that arise from known physics processes. The use of advanced analysis techniques is crucial in achieving this goal. In this review, I discuss the concepts of optimal analysis, some important advanced analysis methods and a few examples. The judicious use of these advanced methods should enable new discoveries and produce results with better precision, robustness and clarity.' back |
S-matrix - Wikipedia, S-matrix - Wikipedia, the free encyclopedia, ' In physics, the S-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT).
More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the in-states and the out-states) in the Hilbert space of physical states. A multi-particle state is said to be free (non-interacting) if it transforms under Lorentz transformations as a tensor product, or direct product in physics parlance, of one-particle states as prescribed by equation (1) below. Asymptotically free then means that the state has this appearance in either the distant past or the distant future. ' back |
Scat singing - Wikipedia, Scat singing - Wikipedia, the free encyclopedia, ' In vocal jazz, scat singing is vocal improvisation with wordless vocables, nonsense syllables or without words at all In scat singing, the singer improvises melodies and rhythms using the voice as an instrument rather than a speaking medium.' back |
Six Minutes to Midnight - Wikipedia, Six Minutes to Midnight - Wikipedia, the free encyclopedia, ' Six Minutes to Midnight is a 2020 British war drama film directed by Andy Goddard from a screenplay by Goddard, Celyn Jones and Eddie Izzard, starring Izzard, Judi Dench, Carla Juri, James D'Arcy and Jim Broadbent. . . . back |
Stirling's approximation - Wikipedia, Stirling's approximation - Wikipedia, the free encyclopedia, 'In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for large factorials. It is named in honour of James Stirling.' back |
The Courier (2020 film) - Wikipedia, The Courier (2020 film) - Wikipedia, the free encyclopedia, ' The Courier is a 2020 historical drama film directed by Dominic Cooke. The film stars Benedict Cumberbatch as Greville Wynne, a British businessman who was recruited by the Secret Intelligence Service to deliver messages to secret agent Oleg Penkovsky (played by Merab Ninidze) in the 1960s. Rachel Brosnahan, Jessie Buckley, and Angus Wright also star. . . . The Courier tells the "true story of the British businessman who helped MI6 penetrate the Soviet nuclear programme during the Cold War. Wynne and his Russian source, Oleg Penkovsky (codenamed Ironbark), provided crucial intelligence that ended the Cuban Missile Crisis." ' back |
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