Notes
Sunday 11 October 2020 - Saturday 3 October 2020
[Notebook: DB 85 Science]
[page 223]
Sunday 11 October 2020
Braindead Sunday. Waiting for the spark. Deadly bored. The price I pay for having a good idea yesterday? Once again proving that trying hard to have ideas is not much more productive than trying hard to win a lottery. Maybe my mind thinks I know all I need to know and I should get on with a bit of writing, but I am too lazy to force myself to do things.
Monday 12 October 2020
Back to st06_constructing_world and continuing to search for the physical meaning of quantum mechanics, much of which I imagine to be incorporated in the space-time / momentum energy statement of the so called uncertainty principle which I prefer to call the principle
[page 224]
of limited resolution. Δx.Δp ≈ ΔE.Δt ≈ h The fact that this appears in two forms in space-time points (to me) to a bifurcation whose underlying symmetry is the distinction between kinetic and potential energy which seem to be the first or second break after actus purus. In space time act comes through as ML2T-1 and energy as ML2T-2 in which we might replace M by E/c2 . . . which is just action again, so did this little circle reveal anything?
Copenhagen Wikipedia: ' The Copenhagen interpretation denies that the wave function provides any directly apprehensible image of an ordinary material body or a discernible component of some such, or anything more than a theoretical concept.' Copenhagen interpretation - Wikipedia
Carl Friedrich von Weizächer: 'while participating in a colloquium at Cambridge denied that the Copenhagen interpretation asserted "What cannot be observed does not exist". Instead he suggested that the Copenhagen interpretation followed the principle "what is observed certainly exists; about what is not observed we are still free to make suitable assumptions; We use that freedom to avoid paradoxes.
" The domain of the wave function is configuration space [Hilbert space] an abstract object quite different from ordinary physical spacetime. At a single "point'" of [infinite dimensional] configuration space the wave function collects probabilistic information about several distinct particles that respectively have space-like separation. So the wave
[page 225]
function is said to supply a non-seperable representation".'
Heisenberg: 'Of course the introduction of the observer must not be understood to imply some kind of subjective features are to be brought into the description of nature. The observer has rather, only the function of registering decisions, ie processes in space and time, and it does nit matter whether the observer is an apparatus or a human being; but the registration, ie the transition from the "possible to the actual" is absolutely necessary here and cannot be omitted from the quantum theory.' Werner Heisenberg: Physics and Philosophy: The Revolution in Modern Science, p 137
Weinberg 'The Copenhagen interpretation describes what happens when an observer makes a measurement but the observer and the act of measurement are treated classically. This is surely wrong: Physicists and the apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wave function (or more precisely a state vector) that evolves in a perfectly deterministic way [lossless codec, ie turing machine]. So where do the probabilistic rules of the Copenhagen interpretation come from? . . . It is enough to say that neither Bohr nor Einstein had focussed on the real problem of quantum mechanics. The Copenhagen rules clearly work, so they must be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wave function., the Schrödinger equation, to observers and their apparatus.' Steven Weinberg: Einstein's Mistakes
The obvious answer (to me) is a combination of fixed point
[page 226]
theory, halting computation and the random interruptions of machines in a network, putting them on a new trajectory whose point of halt in one of the eigenfunctions embedded in the nature of the interacting particles. The image of the spinning die being interrupted and observed by the table [upon which is falls] seems appropriate.
Tuesday 13 October 2020
Energy has two roles, gravitation and quantum mechanics. Quantum mechanics looks at the fine structure of energy built round the quantum of action. Gravitation looks at the broad structure, treating the flow of energy as a power network wired in 4D without crossing, the most complex flows being described by the Riemann tensor [understood as we understand quantum hamiltonians] in which differentials between components measure the orthogonal / linear / independent flow rates. How does energy connect to a) the shape of space? - by orthogonality; how does it connect to quantum mechanics? by computation and by tuning / superposition. So we distinguish superposition from orthogonality. Lanczos tensor - Wikipedia
Having identifed the initial singularity, actus purus and the classical god, the next step is to see how closely we can
[page 227]
attribute the classical properties of god with the quantum of action, following step by step through the prima pars of the summa. This is the task for section 6.2, treating briefly of existence, simplicity, perfection, goodness, infinity, de existentia in rebus, immutability, eternity, unity, knowledge, ideas, truth, life, love, justice and mercy, providence, power, beatitude, and then to the trinity as the archetype of the creation of the universe within god by procession and communication, generating the transfinite network. Here we study how the quanta of action learn from each other, generating the language of love like the spirit by their own interaction. Thomas Aquinas, Summa, I, 2, 3: Does God exist? et sqq.
Wednesday 14 October 2020
Next step: how does the baby universe grow the shape of general relativity? Is quantum mechanics a prerequisite? Is it a web of rapidly reproducing quanta of action? Do we need fermions and bosons? The graviton is a boson. What is the corresponding fermion? What is the smallest sample of differentiable manifold that we can make [Riemann?]?
When we apply group theory to particle physics we assume that the group is in some way embodied in the particles as, for instance, the group SU(3) is embodied in the quarks. What we are wanting to say is that this embodiment is the representation of a certain turing machine (piece of software) in a quantum of action that acts as commanded by the software, thus playing its role in the group. So what is the gravitational group, and how is it shared among a swarm of quanta?
[page 228]
Thursday 15 October 2020
Looking for a logical foundation of the universe. 1. copying of quanta of action. 2. Time division multiplexing = energy. 3. bosons. 4. space division multiplexing - fermions. 5. Independent existence means independent form = {intrinsic, environmental}. 6. multiplication of quanta opens the way to potential energy → variation / selection. 7. logical processing by contact, not, and, or, so we are thinking in terms of logical pieces fitting together as we fit them in our minds. In mathematics the mathematical mind is the representation of the logic; in reality the logical structure embedded in the particle is the representation and a process occurs when two quanta communicate just as a mathematical argument proceeds by the meeting of the elements in an abstract turing machine played out in a human mind. So we base the whole universe on the axioms of set theory + the axioms of logic.
Now let us turn to the millennium prize for Quantum Yang Mils Theory and try to apply the ideas above. Can I trust myself when I get excited? The thoughts I am trying to capture logically point to the first couple of cycles of development in the evolution of the universe from the pure initial singularity. I am in effect coming in at the front (back) door when all the high energy physicist are coming in from the back (front) door. The first job is to make a couple of k on the market. Carlson, Jaffe & Wiles: The Millennium Prize Problems page 129 '1. The Physics of Gauge Theory.'
[page 229]
' classical notions, such as "the trajectory of a particle" do not apply. Because we are talking about logical events that are prior to spacetime.'
Fields: may simply be proxies for the interaction of particles in contact, eg Maxwell, Einstein. 'Since fields interact with particles, it became clear by the late 1920s that an internally coherent account of nature must incorporate quantum concepts for fields as well as particles.' Why? Fields are invisible, but this may be a consequence of the invisibility theorem and be explained by the logical operations of embodied software http://naturaltheology.net/Development/Dev02_Model/model06Invisibility.html
' The distinction between fields and particles breaks down since the Hilbert space of a quantum field is constructed of particle-like excitations. Conventional particles, such as electrons are reinterpreted as states of a quantized field.' ie (I would say) quanta of action [in which are embedded code corresponding to the nature of the particle we are talkng about].
Anti particles – open the way to creation and annihilation, and we see conservation of energy as the conservation of matter in the Aristotelian sense: nec quid, nec quale, nec quantum, nec aliquid eorum quibus ens determinatur [neither what, now what sort nor what amount, nor anything of the properties by which being is determined].
gauge theories Gauge theory - Wikipedia
page 130: Hodge duality operator. Hodge star operator - Wikipedia
'In fact QED improved the accuracy for certain earlier quantum predictions by several orders of magnitude, as well as predicting new splittings of energy levels.
[page 230]
Testing QED – measure electromagnetic fine structure constant α, dimensionless number pproximately 1/137, 1/4πε0 × e2/ℏc. The latest calculation involved 12 672 tenth order Feynman diagrams. Precision tests of QED - Wikipedia
In QED α is coupling constant between electrons and photons. Measured, the theory does not predict its value. Probability that electron will emit or absorb a photon.
First physical interpretation of α (Sommerfeld) was ratio of velocity of electron in first circular orbit of relativistic atom to velocity of light in vacuo.
' QED is the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.' Quantum electrodynamics - Wikipedia
Perturbation theory of electromagnetic quantum vacuum.
History: first Dirac [equation] then infinities at higher orders of perturbation theory [ie superpositions of more complex processes].
Nobel Prize: 'covariant and gauge invariant formulations of QED that allow computations of observables at any order of perturbation theory.' Feynman, renormalization, hocus pocus [inspired by Dirac: “It seems that some essentially new physical ideas are here needed.” 'At any rate, I believed that the difficulty arose somehow from a combination of the electron acting on itself and the infinite number of degrees of freedom of the field.']. Richard P. Feynman: Nobel Lecture: The Development of the Space-Time View of Quantum Electrodynamics
a) Feynman diagrams operate in spacetime
b) more complex diagrams make smaller contributions
In full QED ' There is a possibility that an electron at A or a photon at B, moving as a basic action to any place and time in the universe'.
[page 231]
That includes places that can only reached at speeds greater than than that of light and also earlier times (An electron moving backwards in time can be viewed as a positron moving forward in time.) [more hocus pocus?].
Propagators are essentially solutions to the Dirac equation (electron) and Maxwell's equation (photon).
Infinite probability amplitudes arise from self energy = not unitary.
Mathematical formulation. Peskin & Schroeder: An Introduction to Quantum Field Theory, p 78
Why is this so? Are these fictions real? It seems unlikely. They are a product of the two contradictory notions that on the one hand quantum processes exist prior to space and on the other hand that space-time is the domain of QED and so gives us an infinity of loops of possibly infinite energy. One way to deal with this is to replace continuous parameters with digital logic, a process slowly oozing ahead in the conceptual world.
From algorithmic information point of view Dirac and Maxwell's equations do not tell us much and then we have to add thousands of Feynman diagrams and propagators to get an accurate answer. What if we filled all the particles with turing machines and linked them into gigantic network, we could make a complex system out of simple pieces?
What, for instance, is the code f0r asymptotic freedom? Maybe
[page 234 (sic)]
it is very easy to build within the spacetime operating system. I seem to have the same block here trying to make computational physics as I faced when I began to try to write software.
Friday 16 October 2020
Writing is at a standstill while confidence is building in the creative approach I hypothesize for the universe to build itself, seeing parallels between the discoveries of high energy physics and the early days of the logical evolution of the universe. The parallel between creation and the development of the mathematical community seems to be growing clearer and the promise of a consistent logical approach to the complexification of action seems to be showing some daylight around the difficulties currently induced in quantum field theory by the historical burden of analytically continuous mathematics that became entrenched in the nineteenth century. [This] has yet to be fully exorcised by the logical and quantum development of the twentieth century, all played out against the background of overly simplistic and politically naive authoritarian religion, which is currently (I hope) enjoying its last gasp. Thinking about no 7 of the millennium prize problems, I feel more strongly the need to go back to logical continuity after we have been led into a lot of ad hocery to make the very narrow complexity of continuous mathematics do the job of modelling the pure intelligence of the universe. The US election is bringing this confrontation between fundamentalist religion and creative excitement into sharp focus, since of the big three authoritarian countries, China, Russia and the current US, [US] is the only one that can save itself.
Saturday 17 October 2020
Although I have been thinking my approach to particle physics (where 'particle' means any independent entity) is a long way from the current standard, the more I think about the two pictures the more they appear to converge and the more timid confidence I am beginning to feel in the logical quantum of action / turing machine model I have been on for years. So I hope that in the end I will congeal on something that looks credible in the eyes of both physicists and theologians, which is the aim. My present impasse in the relationship between quantum mechanics and gravitation may also have a germ of a solution in section 3.4.2 of my thesis. Jeffrey Nicholls: Prolegomenon to Scientific Theology, 3.4.2
. . .
Introduction of gauge theory: ' In field theories, different configurations of the unobservable fields can result in identical observable quantities. A transformation from one such field configuration to another is called a gauge transformation. The lack of change in the measurable quantities is called a gauge invariance. . . . Since any kind of invariance under a field transformation is considered a symmetry, gauge invariance is sometimes called gauge symmetry. . . .. Over the course of the 20th century physicists gradually realized that all forces (fundamental interactions) arise from the constraints imposed by local gauge symmetries, in which case the transformations vary from point to point in space and time. . . . Gauge theories constrain the laws of physics because all the changes introduced by gauge transformations have to cancel each other out when written in terms of observable quantities. Introduction to gauge theory - Wikipedia
[page 236]
Gauge theory assumes that there is a lot going on that is not really happening, that is that it is not really represented in a physically observable way. This plethora of events is caused by the use of continuous mathematics on the assumption that it represents an infinite amount of information when in fact it represents [almost] nothing at all [really just the information content of the written equations and their tacit mathematical background].
This all comes from the decision to use artificial frames of reference that have no natural connection to the systems being studied, which go about their business through their internal relationships without reference to any external system. The tensor calculus that we use to honour the fact that reference frames are useless adds a lot of useless discussion of transformation which are more talk about the artificial reference frames than reality. This in turn is the result of trying, like Newton, to achieve a god's eye view of reality rather than the natural subjective view.
Invisibility is not caused by the absence of representation but by the invisibility theorem (see above). Everything real is physically represented. Even spiritual and metaphysical notion are represented by human brain states. Representation means that all physical states are locally finite and not [geometrically] continuous.
A Night at the Louvre: Leonardo da Vinci Louvre
The "mathematical field" in the mathematical community exists in the minds of the mathematicians and their communications. The mathematicians are the fermions and the communications are the bosons. How do we model these as a local gauge symmetry? One point to note
[page 237]
is that given all the human languages that may be involved each core mathematical idea may have a large space of expressions which can be translated [transformed] into each other by the usual process of human communication. The advantage of the turing machine approach coupled with the idea of lagrangian, stationarity and invariance means that at least in simple cases we can arrive at a canonical proof which we might find reflected in nature.
We may think of mathematicians as particles and sources and use symmetry with respect to complexity to "intrapolate" down to fundamental particles.
Obtaining numerical precision (by renormalization and other hocus pocus) at the cost of logical consistency might be a mistake.
How do quanta of action evolve / learn from each other so becoming more complex? Evolution requires some sort of memory which means states that have longer lives than others which is a consequence of reducing energy / frequency [so that higher slower layers (like genes) control the states of lower faster layers (individuals)] so this reducing energy /increasing complexity [are self consistent]. So how do quanta of action exploit this process to create language like children learn. Potential is the final cause, attracting creation out of nothing [by arranging pre-existing parts / quanta like a jigsaw]. We take the foundation of all this from the trinity. The spirit is the language [boson] that father and son share as a consequence of their common descent [so maybe the son is slower than the father and so controls them].
Jaffe & Witten page 130: 'The massless nature of classic Yang-Mills waves was a serious obstacle to applying the Yang-Mills to other forces, for the weak and nuclear forces are short range and many of the particles are massive.' ie massive bosons, W, Z.
Jaffe & Witten page 131: Problem (somewhat) solved by Glashow-Salam-Weinberg electroweak theory with Higgs to give mass. One day I might understand this. Have a look at Shapiro/ Marjorie Shapiro: Physics 226: Particle Physics: Lectures 1 - 28
For strong force masslessness solved by "asymptotic freedom".
Quarks are SU(3) electrons.
'For QCD to describe the strong force we need:
.
'(1) "Mass gap", ie every excitation of vacuum needs energy Δ > 0
'(2) "quark confinement" means individual SU(3) quarks form an SU(3) invariant unit like proton and pion.' Ie quarks form a closed system so they are not independently represented.
page 132: '(3)"chiral symmetry breaking" which means 'the vacuum is potentially invariant (in the limit that the quark masses vanish) only under a certain subgroup of the full symmetry group that acts on the quark fields. ' (?) Vacuum state, QCD vacuum. Sounds a bit like rubbish, see cosmological constant problem: Wilczek, expectation value. Vacuum state - Wikipedia, QCD vacuum - Wikipedia, Expectation value (quantum mechanics) - Wikipedia, Frank Wilczek: The Lightness of Being: Mass, Ether, and the Unification of Forces page 109
1. explains why nuclear force is strong.
2. explains no free quarks.
3. current algebra theory of soft pions. Current algebra - Wikipedia
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Further readingBooks
Carlson, James, and Arthur Jaffe & Andrew Wiles, The Millennium Prize Problems, ClayMathematics Institute and American Mathematical Society 2006 1: The Birch and Swinnerton-Dyer Conjecture: Andrew Wiles
2: The Hodge Conjecture: Pierre Deligne
3: The Existence and Smoothness of the Navier-Stokes Equation: Charles L Fefferman
4: The Poincare Conjecture: John Milnor
5: The P versus NP Problem: Stephen Cook
6: The Riemann Hypothesis: Enrico Bombieri
7: Quantum Yang-Mills Theory: Arthur Jaffe and Edward Whitten
Amazon
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Heisenberg, Werner, Physics and Philosophy: The Revolution in Modern Science, Harper Perennial Modern Classics 2007 ' The seminal work by one of the most important thinkers of the twentieth century, Physics and Philosophy is Werner Heisenberg's concise and accessible narrative of the revolution in modern physics, in which he played a towering role. The outgrowth of a celebrated lecture series, this book remains as relevant, provocative, and fascinating as when it was first published in 1958. A brilliant scientist whose ideas altered our perception of the universe, Heisenberg is considered the father of quantum physics; he is most famous for the Uncertainty Principle, which states that quantum particles do not occupy a fixed, measurable position. His contributions remain a cornerstone of contemporary physics theory and application.'
Amazon
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Kapuscinski, Ryszard, The Emporer: Downfall of an Autocrat, Vintage 1989 Jacket: The Emporer is a brilliant portrait of the last days of Haile Selassie and his maniacal, medieval court. Kapuscinski's writing, always concrete and observant, conjures marvels of meaning out of minutiae. And his book transcends reportage, becoming a nightmare of power, power depicted as a refusal of hstory, that reads as if Italo Calvino had rewritten Machiavelli. This Ethiopia is a murderous Ruritania in which real people are starving by the thousand. An unforgettable, fiercely comic and finally compassionate book.' Salman Rushdie.
Amazon
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Kotzwinkle, William, Queen of Swords, Abacus 1985 'This is a challenging book by a writer who knows how to create suspense and multi-dimensional characters. The author grabs the reader on the first page and doesn't let go until the last line. His dialogue is unbeatable. I recommend this book to every serious reader who enjoys fantastic literary experiences.' Susan Schubert
Amazon
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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. . . . '
Amazon
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Peskin, Michael E, and Dan V Schroeder, An Introduction to Quantum Field Theory, Westview Press 1995 Amazon Product Description
'This book is a clear and comprehensive introduction to quantum field theory, one that develops the subject systematically from its beginnings. The book builds on calculation techniques toward an explanation of the physics of renormalization.'
Amazon
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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
Amazon
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Papers
Toney, Jeffrey H, et al, "Purposeful Leearning with Drug Repurposing", Science, 325, 5946, 11 September 2009, page 1339-1340. 'High-throughput screening (HTS) of comprehensive approved drug libraries has revealed new uses for old drugs . Although repurposing of drugs has been used for decades at the discretion of physicians (3), the Policy Forum "Repurposing with a difference" by M. S. Boguski et al. (12 June, p. 1394) describes a revolutionary approach to research and development in the drug industry that uses "repurposing pharmacovigilance" to find novel beneficial effects of drugs rather than adverse effects. This is a systematic approach that integrates new business models, patient-as-consumer activism through online social networking, information technology, and genomics as powerful tools.'. back |
Links
2001: A Space Odyssey (film) Wikipedia, 2001: A Space Odyssey (film) Wikipedia, the free encyclopedia, ' 2001: A Space Odyssey is a 1968 epic science fiction film produced and directed by Stanley Kubrick. The screenplay was written by Kubrick and Arthur C. Clarke, and was inspired by Clarke's 1951 short story "The Sentinel" and other short stories by Clarke. A novel released after the film's premiere was in part written concurrently with the screenplay. The film, which follows a voyage to Jupiter with the sentient computer HAL after the discovery of an alien monolith affecting human evolution, deals with themes of existentialism, human evolution, technology, artificial intelligence, and the possibility of extraterrestrial life.' back |
Adam Behr, Two of Us: inside John Lennon's incredible songwriting partnership with Paul McCartney, ' Sean Lennon also wonders about his father’s insecurities as a musician and a feeling that: “Somehow he wasn’t officially a true musician, and everyone else was.”
McCartney’s response is telling: “I don’t think any of us were, tell you the truth. And I think that was a very good, strong thing about us, actually.”
Part of the significance of The Beatles as a phenomenon, and the Lennon-McCartney partnership within that, was that its overwhelming industrial and creative success helped to ingrain the “band” as a modus operandi for making popular music into common cultural currency.' back |
Anthropic principle - Wikipedia, Anthropic principle - Wikipedia, the free encyclopedia, 'The anthropic principle (from Greek anthropos, meaning "human") is the philosophical consideration that observations of the universe must be compatible with the conscious and sapient life that observes it. Some proponents of the anthropic principle reason that it explains why the universe has the age and the fundamental physical constants necessary to accommodate conscious life. As a result, they believe it is unremarkable that the universe's fundamental constants happen to fall within the narrow range thought to be compatible with life.' back |
BBC Earth, Cost the Earth Sources, 'It is widely acknowledged that the natural world should not just be reduced to a series of financial values, which are necessarily estimates.
However, in a world that often focuses on money, it can be a useful tool to help remind us that nature does have a value, and what might be lost if aspects of it disappear.' back |
Ben Doherty and Paul Farrell, Medial bodies call for all places of detention to be opened up to scrutiny, 'Eighteen of Australia’s peak health bodies issued the statement urging the Australian government to ratify the UN’s optional protocol to the convention against torture and other cruel, inhuman or degrading treatment or punishment, known as Opcat.
The Opcat was passed by the UN’s general assembly in 2002 and came into force globally in 2006. Australia is in the unusual position of having signed the treaty in 2009 – an indication of support for the purposes of the treaty – but not ratified it, which would make the country legally bound to adhere to it.
The Opcat requires countries to set up an independent and sufficiently-resourced monitoring body that has unrestricted access to all places of detention, including prisons, police lock-ups, juvenile detention centres, immigration detention facilities, locked psychiatric facilities, and secure disability and aged care facilities.' back |
Binyamin Appelbaum, Nobel in Economics Given to Angus Deaton for Studies in Consumption, 'The economist Angus Deaton has devoted his career to improving the data that shape public policy, including measures of wealth and poverty, savings and consumption, health and happiness.
Taking advantage of faster computers and an explosion of newly accessible information, he assembled the details of many individual lives to better understand the sweep of economic trends.' back |
Bruce Alberts, Redefining Cancer Research, 'Senator Ted Kennedy's recent death from malignant glioma, an incurable brain tumor, reminds us of the terrible toll that cancer takes on humanity. The United States alone experiences nearly 1.5 million new cases of cancer each year, resulting in more than 500,000 annual deaths, and about one-fourth of us will die in this way. Jim Watson, of DNA double-helix fame, argues that because of our new profound understandings of the molecular mechanisms underlying the disease, it's finally time to launch a real war on cancer.* I agree. But for success in such a project, we will need to expand the scope of “cancer research” funding, so as to include far more than work with cancer cells themselves.' back |
Christopher Ingraham, New research explores authoritarian mind-set of Trump's core supporters, ' They found a striking linear relationship between support for Trump and an authoritarian mind-set: The stronger a person supported Trump, the higher he or she scored on the RWA scale. People saying they strongly disapproved of Trump, for instance, had an average RWA score of 54. Those indicating complete support of the president, on the other hand, had an average score of 119, more than twice as authoritarian as Trump opponents.
Many fervent Trump supporters, Altemeyer and Dean write, “are submissive, fearful, and longing for a mighty leader who will protect them from life’s threats. They divide the world into friend and foe, with the latter greatly outnumbering the former.” ' back |
Copenhagen interpretation - Wikipedia, Copenhagen interpretation - Wikipedia, the free encyclopedia, ' According to the Copenhagen interpretation, physical systems generally do not have definite properties prior to being measured, and quantum mechanics can only predict the probability distribution of a given measurement's possible results. The act of measurement affects the system, causing the set of probabilities to reduce to only one of the possible values immediately after the measurement. This feature is known as wave function collapse.' back |
Current algebra - Wikipedia, Current algebra - Wikipedia, the free encyclopedia, ' Certain commutation relations among the current density operators in quantum field theories define an infinite-dimensional Lie algebra called a current algebra.[1] Mathematically these are Lie algebras consisting of smooth maps from a manifold into a finite dimensional Lie algebra.' back |
Cybernetics - Wikipedia, Cybernetics - Wikipedia, the free encyclopedia, 'Cybernetics is a transdisciplinary approach for exploring regulatory systems, their structures, constraints, and possibilities. Cybernetics is relevant to the study of systems, such as mechanical, physical, biological, cognitive, and social systems. Cybernetics is applicable when a system being analyzed is involved in a closed signaling loop; that is, where action by the system generates some change in its environment and that change is reflected in that system in some manner (feedback) that triggers a system change, originally referred to as a "circular causal" relationship.' back |
David Brooks, The Republican's Incompetent Caucus, '. . . this new Republican faction regards the messy business of politics as soiled and impure. Compromise is corruption. Inconvenient facts are ignored. Countrymen with different views are regarded as aliens. Political identity became a sort of ethnic identity, and any compromise was regarded as a blood betrayal. . . .
This anti-political political ethos produced elected leaders of jaw-dropping incompetence. Running a government is a craft, like carpentry. But the new Republican officials did not believe in government and so did not respect its traditions, its disciplines and its craftsmanship. They do not accept the hierarchical structures of authority inherent in political activity.' back |
Dirac equation - Wikipedia, Dirac equation - Wikipedia, the free encyclopedia, 'In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1⁄2 massive particles such as electrons and quarks, for which parity is a symmetry, and is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It accounted for the fine details of the hydrogen spectrum in a completely rigorous way.' back |
Einstein, Podolsky and Rosen, Can the Quantum Mechanical Description of Physical Reality be Considered Complete?, A PDF of the classic paper. 'In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false, One is thus led to conclude that the description of reality given by the wave function is not complete.' back |
Eliza Borello & Karen Michelmore, Juukan Gorge traditional owners given 'gag order
warnng by ;awyers for Rio Tinto, inquiry hears, 'Lawyers for mining company Rio Tinto warned traditional owners trying desperately to save the 46,000-year-old Juukan Gorge rock shelters that they could not speak publicly about the issue, an inquiry has heard.
They were also told they could not apply for a federal emergency halt to works without first asking Rio Tinto's permission and giving 30 days' notice, according to Puutu Kunti Kurrama and Pinikura (PKKP) Aboriginal Corporation chief executive Carol Meredith.' back |
Expectation value (quantum mechanics) - Wikipedia, Expectation value (quantum mechanics) - Wikipedia, the free encyclopedia, ' In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which can only yield integer values may have a non-integer mean). It is a fundamental concept in all areas of quantum physics. . . . Operational definition: Consider an operator A. The expectation value is then ⟨ A ⟩ = ⟨ ψ | A | ψ ⟩ in Dirac notation with | ψ ⟩ a normalized state vector. ' back |
Feynman, Leighton & Sands FLP I:52, Symmetry in Physical Laws, 'First, what is symmetry? How can a physical law be “symmetrical”? The problem of defining symmetry is an interesting one and we have already noted that Weyl gave a good definition, the substance of which is that a thing is symmetrical if there is something we can do to it so that after we have done it, it looks the same as it did before. For example, a symmetrical vase is of such a kind that if we reflect or turn it, it will look the same as it did before. The question we wish to consider here is what we can do to physical phenomena, or to a physical situation in an experiment, and yet leave the result the same.' back |
Feynman, Leighton & Sands FLP III:05, Chapter 5: Spin One, 'In this chapter we really begin the quantum mechanics proper—in the sense that we are going to describe a quantum mechanical phenomenon in a completely quantum mechanical way. We will make no apologies and no attempt to find connections to classical mechanics. We want to talk about something new in a new language. The particular situation which we are going to describe is the behavior of the so-called quantization of the angular momentum, for a particle of spin one.' back |
Feynman, Leighton & Sands FLP III:06, Chapter 6: Spin One-Half, 'We will show you in this chapter how the transformation coefficients can be derived for spin one-half particles. We pick this case, rather than spin one, because it is somewhat easier. Our problem is to determine the coefficients Rji for a particle—an atomic system—which is split into two beams in a Stern-Gerlach apparatus. We are going to derive all the coefficients for the transformation from one representation to another by pure reasoning—plus a few assumptions. Some assumptions are always necessary in order to use “pure” reasoning!' back |
Feynman, Leighton & Sands FLP III:07, Chapter 7: The Dependence of Amplitudes on Time, 'We want now to talk a little bit about the behavior of probability amplitudes in time. We say a “little bit,” because the actual behavior in time necessarily involves the behavior in space as well. Thus, we get immediately into the most complicated possible situation if we are to do it correctly and in detail. We are always in the difficulty that we can either treat something in a logically rigorous but quite abstract way, or we can do something which is not at all rigorous but which gives us some idea of a real situation—postponing until later a more careful treatment. With regard to energy dependence, we are going to take the second course. We will make a number of statements. We will not try to be rigorous—but will just be telling you things that have been found out, to give you some feeling for the behavior of amplitudes as a function of time.' back |
Feynman, Leighton & Sands FLP III:08, Chapter 8: The Hamiltonian Matrix, 'One problem then in describing nature is to find a suitable representation for the base states. But that’s only the beginning. We still want to be able to say what “happens.” If we know the “condition” of the world at one moment, we would like to know the condition at a later moment. So we also have to find the laws that determine how things change with time. We now address ourselves to this second part of the framework of quantum mechanics—how states change with time.' 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 |
Geraint Lewis, We are lucky to live in a universe made for us, 'We are not the only universe, but just one in a semi-infinite sea of universes, each with their own peculiar set of physical properties, laws and particles, lifetimes and ultimately mathematical frameworks. As we have seen, the vast majority of these other universes in the overall multiverse are dead and sterile.
They only way we can exist to ask the question “why are we here?” is that we happen to find ourselves in a universe conducive to our very existence. In any other universe, we simply wouldn’t be around to wonder why we didn’t exist.' back |
Gerard 't Hooft, Dimensional Reduction in Quantum Gravity, 'The requirement that physical phenomena associated with gr
avitational collapse
should be duly reconciled with the postulates of quantum mec
hanics implies that at a
Planckian scale our world is not 3+1 dimensional. Rather, th
e observable degrees of free-
dom can best be described as if they were Boolean variables de
fined on a two-dimensional
lattice, evolving with time. This observation, deduced fro
m not much more than unitarity,
entropy and counting arguments, implies severe restrictio
ns on possible models of quantum
gravity. Using cellular automata as an example it is argued t
hat this dimensional reduction
implies more constraints than the freedom we have in constru
cting models. This is the
main reason why so-far no completely consistent mathematic
al models of quantum black
holes have been found.' back |
Haile Selassie - Wikipedia, Haile Selassie - Wikipedia, the free encyclopedia, 'Haile Selassie I . . . (23 July 1892 – 27 August 1975), born Tafari Makonnen Woldemikael, was Ethiopia's regent from 1916 to 1930 and Emperor of Ethiopia from 1930 to 1974. He also served as Chairperson of the Organisation of African Unity from 25 May 1963 to 17 July 1964 and 5 November 1966 to 11 September 1967. He was a member of the Solomonic Dynasty.' back |
Higgs boson - Wikipedia, Higgs boson - Wikipedia, the free encyclopedia, ' The Higgs boson is an elementary particle in the Standard Model of particle physics, produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory] It is named after physicist Peter Higgs, who in 1964, along with five other scientists, proposed the Higgs mechanism to explain why particles have mass. This mechanism implies the existence of the Higgs boson. The boson's existence was confirmed in 2012 by the ATLAS and CMS collaborations based on collisions in the LHC at CERN.
On December 10, 2013, two of the physicists, Peter Higgs and François Englert, were awarded the Nobel Prize in Physics for their theoretical predictions. Although Higgs's name has come to be associated with this theory (the Higgs mechanism), several researchers between about 1960 and 1972 independently developed different parts of it. ' back |
Hodge star operator - Wikipedia, Hodge star operator - Wikipedia, the free encyclopedia, ' In mathematics, the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element. This map was introduced by W. V. D. Hodge.
For example, in an oriented 3-dimensional Euclidean space, an oriented plane can be represented by the exterior product of two basis vectors, and its Hodge dual is the normal vector given by their cross product; conversely, any vector is dual to the oriented plane perpendicular to it, endowed with a suitable bivector. back |
Introduction to gauge theory - Wikipedia, Introduction to gauge theory - Wikipedia, the free encyclopedia, 'A gauge theory is a type of theory in physics. Modern theories describe physical forces in terms of fields, e.g., the electromagnetic field, the gravitational field, and fields that describe forces between the elementary particles. A general feature of these field theories is that the fundamental fields cannot be directly measured; however, some associated quantities can be measured, such as charges, energies, and velocities. In field theories, different configurations of the unobservable fields can result in identical observable quantities. A transformation from one such field configuration to another is called a gauge transformation;[ the lack of change in the measurable quantities, despite the field being transformed, is a property called gauge invariance.' back |
Jeff Sparrow, Flying a refugee to Nauru in secret" is this any different from extraordinary rendition", 'Today, the institution tasked with responding to desperate people fleeing persecution has been thoroughly militarised. Its personnel are uniformed; its key leaders comes from the army and navy, and treat the most basic information about refugees and their conditions as a state secrets.
But recent events – particularly the government chartering a RAAF jet to secretly fly a pregnant refugee out of Australia to escape a court injunction on Friday – remind us of another, less obvious, intersection between the treatment of asylum seekers and the treatment of terrorists, one that relates to the American policy known as “extraordinary rendition”.' back |
Jeffrey Nicholls, Prolegomenon to Scientific Theology, 3.4.2, ' This thesis is an attempt to carry speculative theology beyond the apogee it reached in the medieval work of Thomas Aquinas into the world of empirical science (Aquinas 2019). Since the time of Aquinas, our understanding of the Universe has increased enormously. The ancient theologians not only conceived a perfect
God, but they also saw the world as a very imperfect place. Their reaction was to place God outside the world.
I will argue that we live in a Universe which approaches infinity in size and complexity, is as perfect as can be, and fulfils all the roles traditionally attributed to God, creator, lawmaker and judge.' back |
Jim Branson, Eigenvalue Equations, 'The time independent Schrödinger Equation is an example of an Eigenvalue equation. ' back |
Jo McDonald, Can a mining state be pro-heritage? Vital steps to avoid another Juukan Gorge, ' The destruction of 46,000-year-old Juukan Gorge sites in the Pilbara has created great distress for their traditional owners, seismic shockwaves for heritage professionals and appalled the general public.
The fallout for Rio Tinto has been profound as has the groundswell of criticism of Western Australia’s outdated heritage laws. A path forward must ensure a pivotal role for Indigenous communities and secure Keeping Places for heritage items. More broadly, we need more Indigenous places added to the National Heritage List, ensuring them the highest form of heritage protection.
In a state heavily dependent on mining, the model for this could follow the successful seven-year heritage collaboration I have been part of on-country with Murujuga Aboriginal Corporation (MAC) and Rio Tinto in the Dampier Archipelago (Murujuga).' back |
John Keane, A short history of the future of democracy, 'This is the global orthodoxy. Yet all’s not well in the house of elections; public fractiousness and political dissent are brewing. There are signs of rising citizen disaffection with mainstream ‘catch-all’ parties accused of failing to be all good things to all voters. Support for populist parties is rising. Experiments with ‘anti-political’, direct-action social networks are flourishing. In some quarters, voting is judged a worthless waste of time, money and energy. And more than a few democracies are shaped by what can be called the Philippines syndrome: a strangely contradictory trend marked by elections that come wrapped in intense media coverage and great public excitement mixed with bitter disappointment about the sidelining of elected governments by big banks, big money and the outsourcing of state functions to cross-border power chains. The feeling that elections are pointless manipulations by the rich and powerful finds its nadir in the whole phenomenon of ‘electoral despotism’ in Russia, China, central Asia and elsewhere: the use by oligarchs of periodic elections as an instrument for consolidating arbitrary power.' back |
Lanczos tensor - Wikipedia, Lanczos tensor - Wikipedia, the free encyclopedia, 'The Lanczos tensor or Lanczos potential is a rank 3 tensor in general relativity that generates the Weyl tensor. It was first introduced by Cornelius Lanczos in 1949. The theoretical importance of the Lanczos tensor is that it serves as the gauge field for the gravitational field in the same way that, by analogy, the electromagnetic four-potential generates the electromagnetic field.' back |
Louvre, A Night at the Louvre: Leonardo da Vinci, ' Filmed especially for the cinema, this visit is a unique opportunity to contemplate the most beautiful works of Leonardo da Vinci up close. It takes the viewer on a nocturnal stroll through the Louvre in the company of the exhibition’s curators, Vincent Delieuvin and Louis Frank, whose commentaries provide precious insight into Leonardo’s artistic practice and pictorial technique. This major and unprecedented retrospective devoted to the artist’s work in its totality demonstrates how Leonardo elevated painting above all other pursuits, and how his investigation of the world – the “science of painting” as he put it – was at the service of an art whose supreme ambition was to give life to his paintings.' back |
Marjorie Shapiro, Physics 226: Particle Physics: Lectures 1 - 28, ' I am an experimental particle physicist whose interests lie in probing the most basic interactions in nature. There now exists a theory of the Strong and Electroweak interactions (“the Standard Model”) that has been tested to high accuracy and that explains almost all existing experimental data. The great success of this theory provides a framework for asking even more basic questions: What is the physics that generates quark and lepton masses? What determines the size of the Fermi constant? What is the mechanism responsible for the CP noninvariance observed in nature? It is such questions that my collaborators and I hope to address.' back |
Maureen Dowd, James Murdoch, Rebellious Scion, back |
Michael Bradley, Anti-rerror laws: Control order plan takes us closer to a police state, '. . . politics trump process every time. All that careful and intricate consideration of what everyone agrees is an extraordinarily harsh instrument of law (we are talking, after all, about the forcible detention of people who have not been charged with any crime) has been casually tossed out the window in the excitement of optimising the opportunity to bite down just a little harder on our freedom of movement, association and expression. That we are now happily contemplating locking up 14-year-olds on suspicion (not proof) of what they may otherwise do is just a fascinating reflection of how far we've come.
For another, sadly, it establishes that Turnbull is apparently every bit as willing to play politics with national security as his predecessor. The death cult is gone, but he is equally unprepared to make out his case using actual facts. As Bret Walker commented this week:
There's simply no experience from which one could sensibly say, "This is going to make us safer".' back |
Neuron - Wikipedia, Neuron - Wikipedia, the free encyclopedia, 'A neuron . . . is an electrically excitable cell that processes and transmits information through electrical and chemical signals. These signals between neurons occur via synapses, specialized connections with other cells. Neurons can connect to each other to form neural networks. Neurons are the core components of the brain and spinal cord of the central nervous system (CNS), and of the ganglia of the peripheral nervous system (PNS).' back |
Oxford Journals, Mathematics and Physical Sciences, Journal of Logic and Computation, Infor for authors: http://www.oxfordjournals.org/our_journals/logcom/for_authors/index.html back |
Pauli matrices - Wikipedia, Pauli matrices - Wikipedia, the free encyclopedia, 'In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian and unitary.' back |
Pax Romana - Wikipedia, Pax Romana - Wikipedia, the free encyclopedia, 'Pax Romana (Latin for "Roman Peace") was the long period of relative peace and minimal expansion by the Roman military force experienced by the Roman Empire after the end of the Final War of the Roman Republic and before the beginning of the Crisis of the Third Century.' back |
Peter C. Doherty, Meeting Bill Campbell, the Nobel Prize winner for medicine, 'What I recall most clearly from that evening in 2012 was Bill’s story of his involvement in the discovery and development of Ivermectin. At the time he was as a senior scientist with the Merck drug company. . . . River blindness, a horrible disease that was prevalent in the developing world, is caused by the worm Onchocerca volvulus. When Merk realised it could be treated or prevented with Ivermectin, he and then-Merck President Roy Vagelos arranged for the company to provide the drug free to all who need it, for as long as it’s needed. . . . Now, giving just three inexpensive pills a year prevents people from developing river blindness, with as many as 60 million people treated in any given year.' back |
Pion - Wikipedia, Pion - Wikipedia, the free encyclopedia, ' In particle physics, a pion (or a pi meson, denoted with the Greek letter π) is any of three subatomic particles: π0,π+, and π−. Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more generally, the lightest hadrons. They are unstable, with the charged pions π+ and π decaying after a mean lifetime of 2.6033 x 10-8 sconds , and the neutral pion π 0 decaying after a much shorter lifetime of 8.4×10−17 seconds. Charged pions most often decay into muons and muon neutrinos, while neutral pions generally decay into gamma rays.' back |
Precision tests of QED - Wikipedia, Precision tests of QED - Wikipedia, the free encyclopedia, 'Quantum electrodynamics (QED), a relativistic quantum field theory of electrodynamics, is among the most stringently tested theories in physics. . . .
Tests of a theory are normally carried out by comparing experimental results to theoretical predictions. . . . The agreement found this way is to within ten parts in a billion . . . . This makes QED one of the most accurate physical theories constructed thus far.' back |
QCD vacuum - Wikipedia, QCD vacuum - Wikipedia, the free encyclopedia, ' The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by non-vanishing condensates such as the gluon condensate and the quark condensate in the complete theory which includes quarks. The presence of these condensates characterizes the confined phase of quark matter.' back |
Quantum electrodynamics - Wikipedia, Quantum electrodynamics - Wikipedia, the free encyclopedia, 'In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.'
back |
Quantum superposition - Wikipedia, Quantum superposition - Wikipedia, the free encyclopedia, 'Quantum superposition is the application of the superposition principle to quantum mechanics. The superposition principle is the addition of the amplitudes of waves from interference. In quantum mechanics it is the sum of wavefunction amplitudes, or state vectors. It occurs when an object simultaneously "possesses" two or more possible values for an observable quantity (e.g. the position or energy of a particle)' back |
Regina Munch, Baptizing White Supremacy, ' Robert P. Jones is the CEO and founder of Public Religion Research Institute (PRRI) and writes regularly on politics, culture, and religion for the Atlantic, NBC Think, and other outlets. . . . Assistant editor Regina Munch spoke with him about his new book, White Too Long: The Legacy of White Supremacy in American Christianity, and current attitudes among white Christians on issues of racial justice. . . . A transcript of the interview follows, edited for length and clarity.' back |
Richard P. Feynman, Nobel Lecture: The Development of the Space-Time View of Quantum Electrodynamics, Nobel Lecture, December 11, 1965: 'We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover all the tracks, to not worry about the blind alleys or to describe how you had the wrong idea first, and so on. So there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work, although, there has been in these days, some interest in this kind of thing. Since winning the prize is a personal thing, I thought I could be excused in this particular situation, if I were to talk personally about my relationship to quantum electrodynamics, rather than to discuss the subject itself in a refined and finished fashion. Furthermore, since there are three people who have won the prize in physics, if they are all going to be talking about quantum electrodynamics itself, one might become bored with the subject. So, what I would like to tell you about today are the sequence of events, really the sequence of ideas, which occurred, and by which I finally came out the other end with an unsolved problem for which I ultimately received a prize.' back |
Richard P. Feynman, Simulating Physics with Computers, 'I want to talk about the possibiity that there is to be an exact simulation, that the computer will do exactly the same as nature. If this is to be proved and the type of computer is as I've already explained, then it's going to be necessary that everything that happens in a finite volume of space and time would have to be exactly analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore if this proposition is right, physical law is wrong.' back |
Ross Gittins, Competition does have its drawbacks, 'In the real world – including the media – competitor-oriented competition is rife. This robs customers of genuine choice. It's a form of risk aversion: if I do the same as my competitor, I minimise the risk of him beating me.
It's what, in Harold Hotelling's classic example, prompts two ice-cream sellers to be back-to-back in the middle of the beach, regardless of whether some other positioning would serve customers better. It explains why business economists' forecasts tend to cluster, usually around the official forecast.' back |
Schrödinger equation - Wikipedia, Schrödinger equation - Wikipedia, the free encyclopedia, 'IIn quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a quantum system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger. . . .
In classical mechanics Newton's second law, (F = ma), is used to mathematically predict what a given system will do at any time after a known initial condition. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). It is not a simple algebraic equation, but in general a linear partial differential equation, describing the time-evolution of the system's wave function (also called a "state function").' back |
Stephen Koukoulas, Dear Scott Morrison: stop waffling anf learn to master your brief, quickly, 'A new slogan, “work, save, invest”, and an analysis of the government’s budget deficit issue as one which is “a spending problem, not revenue” suggests Morrison is either putting politics ahead of economic policy or doesn’t yet understand the linkages in the economy.' back |
Steven Weinberg, Einstein's Mistakes , ' The difficulty is not that quantum mechanics is probabilistic—that is something we apparently just have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.' back |
Thomas Aquinas, 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. . . . ' back |
United Nations, Official UN Universal Declaration of Human Rights Home Page, 'The Universal Declaration of Human Rights (UDHR) is a milestone document in the history of human rights. Drafted by representatives with different legal and cultural backgrounds from all regions of the world, the Declaration was proclaimed by the United Nations General Assembly in Paris on 10 December 1948 General Assembly resolution 217 A (III) (French) (Spanish) as a common standard of achievements for all peoples and all nations. It sets out, for the first time, fundamental human rights to be universally protected.'' back |
Vacuum state - Wikipedia, Vacuum state - Wikipedia, the free encyclopedia, 'In quantum field theory, the vacuum state (also called the vacuum) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. Zero-point field is sometimes used as a synonym for the vacuum state of an individual quantized field.' back |
Wave function collapse - Wikipedia, Wave function collapse - Wikipedia, the free encyclopedia, 'In quantum mechanics, wave function collapse is said to occur when a wave function—initially in a superposition of several eigenstates—appears to reduce to a single eigenstate (by "observation"). It is the essence of measurement in quantum mechanics and connects the wave function with classical observables like position and momentum. Collapse is one of two processes by which quantum systems evolve in time; the other is continuous evolution via the Schrödinger equation.' back |
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