natural theology

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Notes

Sunday 14 March 2021 - Saturday 20 March 2021

[Notebook: DB 86: Hilbert / Minkowski]

[page 132]

Sunday 14 March 2021

Hilbert space is a symmetry of inertial space which is closed into a universe by gravitational particle interactions, ie the interaction of energy with itself [or is this the other way around: in general the symmetry has more degrees of freedom than the broken (instantiated) state, eg algorithm has more degrees of freedom than an application of the algorithm; Hilbert space exhibits vectors of states one only of which appears when the 'wave function' collapses.].

Misner, Thorne & Wheeler: The starting point for physics is events, that is something happening which we can interpret in network terms as an act of communication between two sources. We may address events with Gaussian coordinates which do not measure distances but relative positions in our universe relative to three spatial dimensions and one time dimension. Our first step toward dynamics is taken in inertial space where relativity is expressed in terms of velocity which is a relationship between space and time which is to some extent arbitrary but which has a fixed maximum point, the velocity of light which gives a fixed quantitative relationship between space and time which we understand as establishing a symmetry. We approach curved space [which deals with acceleration] by seeing it as an assembly of flat (inertial) spaces which can be coupled by differentials to create inertial paths through space which map out through their relative curvature ("geodesic deviation") the structure of spacetime. This structure is fixed by the fact that the "distances" between two events is a fixed quantity which is unchanged by our choice of reference points to measure it. From this point of view, the quantum mechanical approach to spacetime must begin with a study of events, that is quantum event. Misner, Thorne & Wheeler: Gravitation

[page 133]

I can take a hylomorphic view of life where I am the matter and my mode of life is the form. My forms of life have all come to an end, first the monastery, and then a series of jobs, marriages and relationships with my children but my life's energy has been consistent through all this and is slowly becoming invested in the theological project which has remained relatively constant through the last sixty or so years and often seems to be making some progress. now in its most recent incarnation as quantum theology. The reconciliation of divinity and physicality most clearly represented for me by images of women making energetic love. At this level of resolution all events in the universe are equivalent, quanta of action. Hylomorphism - Wikipedia, Jeffrey Nicholls (2021): Quantum theology: Scientific revolution = paradigm change, Room in Rome - Wikipedia

On the whole quantum operators must be represented by complex matrices; only the Hermitian ones with real diagonals being able to represent observations. Self-adjoint operator

Roger Penrose Nobel Lecture. Closed trapped surface → Hawking & Ellis. Big bang singularity very different from black holes. Roger Penrose (2020): Nobel Lecture: Black Holes, Cosmology, and Space-Time Singularities, Hawking & Ellis: The Large Scale Structure of Space-Time

Inflation, Thermodynamics, Mass = frequency.

Maxwell's equations are conformally invariant.

Penrose: Uncertainty: Roger Penrose (2011): Uncertainty in quantum mechanics: faith or fantasy?

'This article raises the question of whether [uncertainty] might be applied to the theory itself. . . . There are, indeed, seeming internal contradictions in the theory that lead us to infer that total faith in it at all levels of scale lead to almost fantastical implications.

[page 134]

Penrose page 4874: Riemann sphere: "I have always found it to be a very striking and beautiful fact that the geometry or ordinary three dimensional space can be related so graphically to the seemingly mysterious complex numbers that feature in such a fundamental way at the basis of quantum mechanics [geometrical connection via the complex plane].

page 4876: 'Linearty means that each part of a superposition evolves independently of the evolution of the other parts [and nevertheless maintains unitarity].

Unitary evolution is smooth and deterministic, while observation is discrete and random

Quantum evolution is linear. Chaos occurs in non-linear systems. So where does quantum chaos come from [vacuum = {quantum action} [= energy]].

page 4877: 'I would regard it as likely that the linear quantum mechanics that we now use is merely an approximation to some more refined non-linear evolution that we will someday discover . . .

"Measurement paradox". Since measuring system is also a quantum system, why is measurement not continuous and deterministic as unobserved quantum systems [because Shannon says communication requires discrete signals to prevent confusion and error]?

page 4881: 'The essential puzzle, [raised by the cat] would appear to be the issue of how the quantum state of a system relates to what is actually happening in the world of physical reality [ie the coupling between Hilbert and Minkowski space, which is my current favourite subject]?

[page 135]

Penrose page 4884: 'the rules of quantum field theory forbid us from taking superpositions of states from different vacua [does this mean super-selection rules [Streater and Wightman]. Streater & Wightman: PCT, Spin, Statistics and All That

blah blah. Does not seem to get anywhere trying to hook quantum mechanics to gravitation to explain 'collapse of wave function'. Prefer the idea that an observation is an interaction between two envirnements (like an animal and a forest) which perform a 'natural selection' for the state observed out of the spectrum of available possibilities [embodied in the measurement operator]. This does not get much closer to my quest for a way to create Minkowski space out of Hilbert space. Very disappointing article. And I feel that I am promoting far out ideas!

Monday 15 March 2021

We imagine that each orthonormal vector in Hilbert space represents a [distinctly different] quantum of action and they are differentiated in the first instance by the energy associated with them [which is a function of the period between each act] on a spectrum running from 0 [eternity between acts] to 0, ie equinumerous with the natural numbers [maximum discrete frequency]. The next step is the introduction of time and the bifurcation of energy into potential and kinetic, the potential energy associated with each basis vector being equal to the energy associated with its frequency, the inverse of time. These particles sound a bit like photons, 1 unit of spin + energy. Why don't photons have mass even though they have momentum [because all their energy is kinetic at c?]

[page 137]

Fundamental particles, like all particles, carry code inside, so we are looking for the [very powerful logical] mechanism that connects electrons to photons.

Tuesday 16 March 2021

I have a lot of quantum field theoretical scepticism in my blood.

So Zee page 3 (first edition) 'It is in the peculiar confluence of special relativity and quantum mechanics that a new set of phenomena arises. Particles can be born and particles can die [because mass and energy are equivalent, but what about photons? And what has mass got to do with it. Mass is not (specifically) what makes a particle a particle, there must be a cause of which mass is a consequence,]' Not so new. This goes back to Aristotle's hylomorphism. He said matter takes different forms. we say energy takes different forms, and energy is conserved at all scales. Eugene Wigner: On Unitary Representations of the Inhomogeneous Lorentz Group

Zee page 3: 'Let me give a heuristic discussion. In quantum mechanics the uncertainty principle tells us that energy can fluctuate widely over a small interval of time. According to special relativity, energy can be converted into mass and vice versa. With quantum mechanics and special relativity the widely fluctuating energy can metamorphose into mass, that is into particles not previously present.' But why does uncertainty become a dynamic principle driving wild fluctuation [since energy is not a direct consequence of action, it (like momentum) is a consequence of the rate of action]? It is simply a minimum unit of angular momentum in 4-space. There is evidence [for fluctuation] in the Casimir effect and the Lamb shift, but on the other hand the cosmological constant problem seems to suggest that the quantum fluctuations are vastly overrated. Maybe (from my point of view) they [the fluctuations] reflect random connections between sources in the quantum network rather than the dynamic consequences of uncertainty.

[page 137]

Zee page 5: 'since the theory is linear, two wave packets pass right through each other (as in linear superposition in Hilbert space). But once we include non-linear terms . . . the theory becomes anharmonic. Eigenmodes now couple to eachother. A wave packet may decay into two wave packets . . . '

Perhaps the non-linear nature of general relativity is an indication that the word is becoming creative, copying itself to make new particles whose relationships are new states.

page 7: Path Integral Formulation of Quantum Mechanics [or quantum field theory, since Feynman was working in spacetime].

'. . . it offers a peculiarly convenient way of going from quantum mechanics to quantum field theory.' Two slit / superposition principle. Paths defined by unitarity (page 10).

page 10: 'the momentum eigenstate is a plane wave in the coordinate representation.'

page 11: '. . . to obtain < qF | e-iHt | qI > we simply integrate over all possible paths [in the whole universe?] such that q0 = qI and qT = qF.'

There are two ways to look at this. First many of the paths will be outside the light cone of the interaction of interest and therefore possibly entangled with this interaction; or the path integral method works because the interaction of the wave functions happens prior to the emergence of interaction in spacetime accounting for quantum non-location. Is this an issue? Feynman's original aim was to produce a space-time version of quantum mechanics which avoided the postulation of fields but he eventually came to accept vacuum fluctuations in the formulation of QED but remained sceptical about renormalization [and he does not appear to have thought of discrete Hilbert space, (with many more degrees of freedom) as the foundation of continuous Minkowski space (which is strongly constrained because of its alleged continuity, see Ashby page 133).] W Ross Ashby: An Introduction to Cybernetics

[page 138]

Zee (page 5) sees that we may go beyond the harmonic paradigm. Von Neumann sees that observations in quantum mechanics obey Bayesian statistics rather than Boolean algebra (page 131 above, these notes). Insofar as Boolean algebra is irreversible (and therefore non-linear) we may see it as providing an irreversible basis for quantum mechanics. This irreversibility arises from the destruction of unitarity by replacing a complete system of events in the quantum formalism by a chosen eigenvalue in observation. At the heart of the path integral method are the ideas of unitarity and complete sets of states [and no observation along the paths, which might be seen as traversed by particles travelling at c.

Quantum ⇆ classical theology hinges on the measurement [communication] problem [and quantum field theory hides the measurements (interactions, communications) in the complex Hilbert domain].

I am in the Bertrand Russell mode of consciousness, staring into blank space all day getting nowhere (Russell's paradox). Quantum field theory is to me a forest of paradoxes, but it seems to work and for the moment I see no other way than by getting some more degrees of freedom by divorcing Hilbert space from Minkowski space [in order to find a role for evolution]. Will this gap (wound) ever heal?

Another degree of freedom: we separate the field (massless bosons) from the particles (fermions) which create and absorb the bosons, so we see the fermions as the structures where the information is stored and the bosons as the messengers, existing outside space-time, which carry information between the fermions and in effect creates them as the spirit creates the father and the son.

Isolated systems are unitary, going their own way. Insofar

[page 139]

as the path integral method depends entirely on unitarity, it is linear and can only deal with particles in inertial motion, so it does not tell us anything. Indeed it may only be appropriate for massless particles travelling at c which are, from the point of view of their sources (= sinks) frozen in space and time. A problem with gauge theory is that it seems to require massless bosons so it was difficult to apply to massive messengers like W and Z. So space need not be a continuous medium but a network of orthogonal tracks, point to point like connecting wires, no common origin like the basis vectors of Euclidean space, strings with two ends, complete quanta of action, not half actions lik fermions, ie it takes two fermions to make a boson, eg a photon is made of e + e+, e and e+ made from a photon.

Path integral is reversible and preserves entropy (unitarity) like a codec, complete set of states.

Wednesday 17 March 2021

Quantum theology seems to be moving toward a critique of quantum field theory. I find that very little of it makes sense to me and from this point of view feels rather like the catholic doctrine that I encountered in the monastery which was largely nonsense which has nevertheless a large body of adherents who treat it as gospel and who discuss it as if it were true. In a way it is for them. Quantum field theory has a closer coupling to reality but nevertheless may be a rather contrived fit considering the large number of tricks it uses to get around the many mathematical difficulties that arise. The bottom line for me is the so called vacuum which is considered to be the practical zero

[page 140]

energy while we have the cosmological constant problem and similar problems listed by Wilczek which differ from the measured reality by factors in the range of 1040 to 10100. It is now critical for me to give myself an intensive course on quantum field theory based on Zee's second edition and note all my objections and possible fixes as I go along. This notebook will be reserved for the broad picture and I will record the more detailed critique in another. I am working on intuition here but I only have myself to trust snd my project of uniting theology and quantum theory is too exciting to abandon and seems t offer an endless source of excitement for the last 25 years of my life. Frank Wilczek: The Lightness of Being: Mass, Ether, and the Unification of Forces, page 109

Thursday 18 March 2021

The path integral approach to quantum mechanics [multiply consequences, add alternatives]:

1. Multiply an infinite sequence of infinitesimal steps along each path using a Hamiltonian and the unitarity of complete sets of states.

2. Establish a superposition of the resulting amplitudes to give an amplitude for the transition from an initial to a final state.

3. Develop the exploration of the trajectory of a single particle by introducing more complex Hamiltonians for more multiple particles and multiple potentials.

4. Go to the limit from particle to field by treating every point

[page 142]

in a continuous field as a particle. Imagine that the integrals will converge even though the particle trajectories in any case are imagined to traverse the whole universe because the phenomena are expected to approach zero at large distances [because of oscillating amplitudes?].

Then ask:

Does fragmentation of the paths of an infinity of particles into infinitesimal steps connected by unitarity and complete sets of state make sense in reality even though it may work in that region of mathematics that accepts the logical consistency of continuity and the addition of infinite numbers of infinitesimals to obtain finite quantities even though empirical evidence suggests that the minimum size of real "infinitesimals" is ℏ. In addition, does the notion of taking integrals over the whole universe make any sense in the light of the special and general theories of relativity. An alternative view is that Hilbert space, whose metric is amplitude, exists prior to [coordinate] space and so issues of distance are irrelevant and the only variables are the one time/frequency/energy coupled by the fundamental equation E = hf

Friday 19 March 2021

Let us say that the vacuum is made of quanta of action, that is events, and we define an event as something that replaces a particular state with another different state, ie Z (let us call an event) is {p → not-p}.

Saturday 20 March 2020

I regularly remind myself that I am engaged in a hopeless task

[page 142]

but this seems to have no effect on my ambition to exploit the advantages of mapping quantum mechanics onto theology, and so following in the steps of Aristotle from matter and form to potency and act to the first mover and through Thomas Aquinas to the theoretical foundation of theology. Sometimes I think I should step back and concentrate on the beauty of god reflected in the beauty of nature, since I have no doubt at all that the universe is divine, but the quantum mechanical flame draws me like a moth and I can't resist identifying the divine characterization of actus purus with the quantum of action. It may seem a long shot to identify the nature of the whole universe with the smallest event within it but this seems inevitable and by defining action in logical terms as the creation of something eww, a not-p out of a p, I avoid any preoccupation with the actual size of god and give a foundation to the notion that the universe is full of gods and every event, no matter how small, is divine. God becomes the fundamental symmetry of the universe.

The divinity of action is the wormhole between physics and theology and my task in quantum-theology.net is to explore this idea in exhaustive detail, beginning perhaps by exploiting the physicists' 'vacuum' as the source of variation that lies at the foundation of the evolution of the universe from the absolute simplicity predicted by Penrose as the source of everything and so the beginning of the theory of everything.

My best ancient clues are the divine initial singularity and the emergence of the trinity from the one god and the slogan 'from trinity to transfinity'. My strength will be in plausibly capturing the essence

[page 143]

of quantum field theory for theological purposes. The vacuum provides us with variation, the location of stable potential wells represented by eigenvalues provides us with a selective mechanism and the network model shows how complex systems can be built on the stable features of simple systems like fundamental particles, atoms, molecules, cells and so on which provide us with a path via the layered construction of complexity from initial simplicity to cosmic complexity.

We can ask, in the beginning, why would a quantum of action want to do anything? Why would god not just sit there being happily eternal? Because, as the word says, action is action, its nature is inherently dynamic rather than the static eternal god that Parmenides and Plato imagined. To act is to create, q.e.d. (quod erat demonstrandum, quantum electro dynamics).

Michelle Pfeiffer French Exit (2020 film) - Wikipedia

The fact that we can act proves that we are divine [since we may see the quantum of action as the modern equivalent of the divine unmoved mover].

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Further reading

Books

Abbott, Walter M, and Joseph Gallagher (translation editor), The Documents of Vatican II: in a new and definitive translation, with notes and commentaries by Catholic, Protestant and Orthodox authorities, Geoffrey Chapman 1972 Jacket: 'All 16 Documents of Vatican II are here presented in a new and readable translation. Informed comments and appraisals by Catholics and non-Catholics make this book essential reading for anyone, of whatever shade of belief, who is interested in the changing climate of today's world.' 
Amazon
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Ashby, 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.' 
Amazon
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Dawkins, Richard, Climbing Mount Improbable, W. W. Norton & Company 1997 Amazon editorial review: 'How do species evolve? Richard Dawkins, one of the world's most eminent zoologists, likens the process to scaling a huge, Himalaya-size peak, the Mount Improbable of his title. An alpinist does not leap from sea level to the summit; neither does a species utterly change forms overnight, but instead follows a course of "slow, cumulative, one-step-at-a-time, non-random survival of random variants" -- a course that Charles Darwin, Dawkins's great hero, called natural selection. Illustrating his arguments with case studies from the natural world, such as the evolution of the eye and the lung, and the coevolution of certain kinds of figs and wasps, Dawkins provides a vigorous, entertaining defense of key Darwinian ideas.' 
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Hawking, 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.' 
Amazon
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Keynes, John Maynard, The General Theory of Employment, Interest and Money, Macmillan 1936-1964 The classic twentieth century economics text that revealed that there are more ways to get an economy to grow than simply balancing the books.back

Knox, Ronald, Let Dons Delight: Being Variations on a Theme in an Oxford Common Room, Sheed and Ward 1958 Jacket: When Mgr. Knox died, many of his panegyrists singled this book out as the best of its kind he ever wrote - which in this case is saying much. Certainy, he alone could have done it. To create eight sets of Simon Magus dons, from 1588 to 1938, conversing and arguing with eachother each in the very voice of his age and in terms of the topics of his day - for that you really have to know your Oxford, your dons, your history, classics and English literature.'back

Lodge, David, The Art of Fiction, Illustrated from Classic and Modern texts., Penguin Books 1992 Jacket: 'Brings to criticism the verve and humour of his own novels. DL has provided essential reading for students of literature, aspirant writers, and anyone who wishes to understand how literature works.'  
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Misner, 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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Stiglitz, Joseph E, Freefall: America, Free Markets and the Sinking of the World Economy, W. W. Norton & Company 2010 Amazon Product Description ' . . . The Great Recession, as it has come to be called, has impacted more people worldwide than any crisis since the Great Depression.

Few are more qualified to comment during this turbulent time than Joseph E. Stiglitz. Winner of the 2001 Nobel Prize in Economics, Stiglitz is “an insanely great economist, in ways you can’t really appreciate unless you’re deep into the field” (Paul Krugman, New York Times). In Freefall, Stiglitz traces the origins of the Great Recession, eschewing easy answers and demolishing the contention that America needs more billion-dollar bailouts and free passes to those “too big to fail,” while also outlining the alternatives and revealing that even now there are choices ahead that can make a difference. The system is broken, and we can only fix it by examining the underlying theories that have led us into this new “bubble capitalism.” ' 
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Streater, 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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Wilczek, Frank, The Lightness of Being: Mass, Ether, and the Unification of Forces, Basic Books 2008 ' In this excursion to the outer limits of particle physics, Wilczek explores what quarks and gluons, which compose protons and neutrons, reveal about the manifestation of mass and gravity. A corecipient of the 2004 Nobel Prize in Physics, Wilczek knows what he’s writing about; the question is, will general science readers? Happily, they know what the strong interaction is (the forces that bind the nucleus), and in Wilczek, they have a jovial guide who adheres to trade publishing’s belief that a successful physics title will not include too many equations. Despite this injunction (against which he lightly protests), Wilczek delivers an approachable verbal picture of what quarks and gluons are doing inside a proton that gives rise to mass and, hence, gravity. Casting the light-speed lives of quarks against “the Grid,” Wilczek’s term for the vacuum that theoretically seethes with quantum activity, Wilczek exudes a contagious excitement for discovery. A near-obligatory acquisition for circulating physics collections.' --Gilbert Taylor  
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Papers

Marton-Lefevre, Julia, "Biodiversity Is Our Life", Science, 327, 5970, 5 March 2010, page 1179. 'Julia Marton-Lefèvre is the director general of the International Union for Conservation of Nature, Gland, Switzerland.
2010 is the International Year of Biodiversity, in recognition of life on Earth. Eight years ago, more than 190 countries agreed, through the United Nations Convention on Biological Diversity, to reduce biodiversity loss by 2010. This October, the Convention will meet in Nagoya, Japan, to evaluate progress and agree on new biodiversity targets for the world. Shortly before that, the UN General Assembly will address the biodiversity crisis for the first time.'
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Links

Angel investor - Wikipedia, Angel investor - Wikipedia, the free encyclopedia, 'An angel investor or angel (also known as a business angel or informal investor) is an affluent individual who provides capital for a business start-up, usually in exchange for convertible debt or ownership equity. A small but increasing number of angel investors organize themselves into angel groups or angel networks to share research and pool their investment capital.' back

Bansari Kandar & Sheyasee Das, Women grow as much as 80% of India’s food – but its new farm laws overlook their struggles, ' Indian women are left behind on farms to make ends meet as more men in India migrate from rural areas to cities, seeking higher incomes and better jobs. Nearly 75% of the full-time workers on Indian farms are women, according to the international humanitarian group OXFAM. Female farmers produce 60% to 80% of the South Asian country’s food. So it’s little surprise women are playing a visible role in the monthslong nationwide protests against agricultural reforms passed last September by the Indian government.' back

Clay Lucas, Power failure: Homes hit by solar limits as distributors protect network, and profits, ' Thousands of Victorian homeowners having solar power installed are being told by the state’s distributors they will not be able to feed electricity into the network, as a rising tide of sustainable power hits the energy grid. The block on new solar power feeding into Victoria’s grid comes despite a decade of warnings by regulators to the state’s power distributors they need to spend money on upgrading their networks.' back

Eugene Wigner, On Unitary Representations of the Inhomogeneous Lorentz Group, ' 1. 0RIGlN AND CHARACTERIZATION OF THE PROBLEM: It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold, in which a unitary scalar product is defined. The states are generally represented by wave functions in such a way that ψ and constant multiples of ψ represent the same physical state. It is possible, therefore, to nornalize the wave function, i.e., to multiply it by a constant factor such that its scalar product with itself becomes 1. Then, only a constant factor of modulus 1, the so-called phase, will be left undetermined in the wave function. The linear character of the wave function is called the superposition principle. The square of the modulus of the unitary scalar product (φ , ψ) of two normalized wave functions φ and ψ is called the transition probability from the state φ into ψ or conversely. back

French Exit (2020 film) - Wikipedia, French Exit (2020 film) - Wikipedia, the free encyclopedia, ' French Exit is a 2020 surreal comedy film directed by Azazel Jacobs, based on the novel of the same name by Patrick deWitt, who also wrote the screenplay. It tells the story of a Manhattan heiress (Michelle Pfeiffer) who moves to Paris with her son (Lucas Hedges) with the little money they have left. The film had its world premiere at the New York Film Festival on October 10, 2020, and was theatrically released in the United States and Canada on February 12, 2021. It received mixed reviews from critics, although Pfeiffer's performance was praised. For her role, she was nominated for Golden Globe Award for Best Actress – Motion Picture Comedy or Musical. back

Geoff Brumfiel, Quantum uncertainty not all in the measurement, ' The researchers made a ‘weak’ measurement of the photon’s polarization in one plane — not enough to disturb it, but enough to produce a rough sense of its orientation. Next, they measured the polarization in the second plane. Then they made an exact, or 'strong', measurement of the first polarization to see whether it had been disturbed by the second measurement. When the researchers did the experiment multiple times, they found that measurement of one polarization did not always disturb the other state as much as the uncertainty principle predicted. In the strongest case, the induced fuzziness was as little as half of what would be predicted by the uncertainty principle.' back

Hylomorphism - Wikipedia, Hylomorphism - Wikipedia, the free encyclopedia, 'Hylomorphism (Greek ὑλο- hylo-, "wood, matter" + -morphism < Greek μορφή, morphē, "form") is a philosophical theory developed by Aristotle, which analyzes substance into matter and form. Substances are conceived of as compounds of form and matter.' 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

Katerina Malofieieva, ‘Pure terror’: COVID-19 on the front lines of Ukraine’s war, ' Koryak, who has lived in Stanytsia Luhanska since 2000, was one of the few doctors who remained during the fighting. The others were mostly surgeons who had to work 48-hour shifts treating soldiers and civilians caught up in the war. Doctors like Koryak were on hand to carry stretchers and care for the wounded and frostbitten – for nine months the town had no electricity and, during that first winter of the war, temperatures dropped as low as -24C (-11.4F) – as well as psychological disorders triggered by the conflict. According to the UNHCR, approximately 13,200 people have been killed in the conflict in Ukraine, about a quarter of them civilians.' back

Kenneth Chang, 2 Win Abel Prize for Work That Bridged Math and Computer Science, ' Two mathematicians will share this year’s Abel Prize — regarded as the field’s equivalent of the Nobel — for advances in understanding the foundations of what can and cannot be solved with computers. The work of the winners — László Lovász, 73, of Eötvös Loránd University in Budapest, and Avi Wigderson, 64, of the Institute for Advanced Study in Princeton, N.J. — involves proving theorems and developing methods in pure mathematics, but the research has found practical use in computer science, particularly in cryptography. The Norwegian Academy of Science and Letters, which administers the prize, cited Dr. Lovász and Dr. Wigderson “for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics.” ' back

Luke Buchmaster, My Name Is Gulpilil review – sublime, humane, elegant traversal of Indigenous actor's life in film, ' Nobody in the world has ever had “it” quite like the great Yolŋu actor David Gulpilil, a titanic force in Australian cinema and now the subject of director Molly Reynolds’ superb, sad, yet in its own way wonder-filled documentary, which achieves the intimidating task of doing justice to the life and career of this extraordinary artist. Reynolds understands that Gulpilil isn’t just a great actor but a portal to a different way of thinking, a different way of being, even a different state of consciousness. If you think that sounds like hyperbole, you have not seen a David Gulpilil movie.'˜ back

Mridula Nath Chakraborty, Friday essay: is this the end of translation?, ' The act and the art of translation requires the permission to transcend borders, the permission to make mistakes, and the permission to be repeated, by anyone who feels the tempestuous tug, and the clarion call, of the unfamiliar. To rein in such liberty through categories and compartments that imprison our creativity is a disservice to the human imagination. So let a thousand translations bloom: that would be a start and not an end to translation as we know it now.' back

Ofer Aderet, Dozens of Zionist Pioneers Committed Suicide When Their Dreams Shattered in Palestine. This Is One of Them, ' A short item in the newspaper Hapoel Hatza’ir (The Young Worker) in early November 1911 reported a “sad case” that had occurred in the Jewish village of Kinneret. “The shepherd Alexander took his life with a pistol shot. Two days earlier he didn’t go to work, claiming he was sick. The incident noted above happened in the morning, and he died in the evening.” . . . Stories of pioneers who took their lives are not new. What makes Brekner’s case exceptional, even from a remove of 110 years, is that he left behind a detailed diary in Hebrew. “His diary is so rich that it encapsulates the whole period of the Second Aliyah through the prism of one pioneer,” says Gur Alroey, a professor of history in the Israel Studies department at the University of Haifa.' back

Rentier state - Wikipedia, Rentier state - Wikipedia, the free encyclopedia, 'A rentier. . . is an individual who depends on income derived from rents, which, in turn, are defined as “a reward for ownership of all natural resources”, or the “income derived from the gift of nature.” A rentier state is a term in political science and international relations theory used to classify those states which derive all or a substantial portion of their national revenues from the rent of indigenous resources to external clients.' back

Roger Penrose (2011), Uncertainty in quantum mechanics: faith or fantasy?, ' The word ‘uncertainty’, in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very ‘truth’ into question. This article addresses the issue of quantum ‘uncertainty’ from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications. back

Roger Penrose (2020), Nobel Lecture: Black Holes, Cosmology, and Space-Time Singularities, ' Roger Penrose The Nobel Prize in Physics 2020 Born: 8 August 1931, Colchester, United Kingdom Affiliation at the time of the award: University of Oxford, Oxford, United Kingdom Prize motivation: "for the discovery that black hole formation is a robust prediction of the general theory of relativity." ' back

Room in Rome - Wikipedia, Room in Rome - Wikipedia, the free encylopedia, ' Room in Rome (Spanish: Habitación en Roma) is a 2010 Spanish erotic romantic comedy-drama film, depicting the emotional and sexual relations of two women (Alba and Natasha) throughout a single night in a hotel room in Rome. . . . Over the next 10 hours, Alba and Natasha grow closer to each other as Natasha becomes more relaxed and comfortable around Alba with their lovemaking. Alba and Natasha share stories, periodically stopping to illustrate their points with pictures on the Internet, talk about the artwork in the hotel room, and explore each other's nude bodies through sex. . . . . Eventually, the two women tell each other the truth.' back

Self-adjoint operator, Self-adjoint operator, ' In mathematics, a self-adjoint operator on a complex vector space V with inner product ⟨ ⋅ , ⋅ ⟩ . . . is a linear map A (from V to itself) that is its own adjoint: ⟨ A v , w ⟩ = ⟨ v , A w ⟩ . . . If V is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of A is Hermitian, i.e., equal to its conjugate transpose A*. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this basis is a diagonal matrix with entries in the real numbers. In this article, we consider generalizations of this concept to operators on Hilbert spaces of arbitrary dimension.' back

Von Neumann universal constructor - Wikipedia, Von Neumann universal constructor - Wikipedia, the free encyclopedia, ' John von Neumann's universal constructor is a self-replicating machine in a cellular automata (CA) environment. It was designed in the 1940s, without the use of a computer. The fundamental details of the machine were published in von Neumann's book Theory of Self-Reproducing Automata, completed in 1966 by Arthur W. Burks after von Neumann's death. . . . Von Neumann's goal, as specified in his lectures at the University of Illinois in 1949,[2] was to design a machine whose complexity could grow automatically akin to biological organisms under natural selection.' back

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