Natural Theology

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Notes

Sunday 22 October 2023 - Saturday 28 October 2023

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Sunday 22 October 2023

Another thing I think I should have noticed years ago. I have been wondering how time turns into space, ie how changing phase turns into a measure of distance and all along I have known that the quantum mechanical implementation of momentum is in fact a matter of phase, so the natural approach to space is through momentum whose classical dimension ins MLT-1 which is related to wavelength p = -i h ∂/∂x = h/λ

Time / energy is a frequency, Space / momentum also is the

[page 326]

complex conjugate of time, ie time ≡ i, space ≡ x.

Monday 23 October 2023

Quantum phase (in Hilbert space) and the relationship between energy and frequency (in Minkowski space) are two different things, as is demonstrated by the absurdity of Everett's many worlds hypothesis which uses the notion of creating new universes all over the place in a Hilbert space way without making any concession to the principle of conservation of energy which would be infinitely broken by every quantum of action in every one of the new universes that he creates, so the dfemand for energy would increase as ∞ . . . .

As long as there is tension between large groups there will always be a fringe in each that would be inclined to violence. Israel repressing the Palestinians will never get rid of the violence toward its repression, Hamas or equivalent will reappear as long as [the repression] is not eliminated.

Tuesday 24 October 2023

So far we have got the initial singularity to create one photon which we might imagine to be orbiting inside the singularity constrained by the gravitational field there but we want to decide if this is possible in one dimension of

[page 327]

Minkowski space. So let us create a mob of photons which might start transforming into gluons, quarks and other elementary particles which begin to populate the Universe and cause the Minkowski space to become 4D and create a little universe of the sort that we expect from the big bang.

Now all of these particles interact with eachother through Hilbert space carried inside each one which can be brought into contact by bosons travelling on null geodesics, very short in the case of W and Z, longer for photons. The bosons, quarks and gluons automatically coalesce to form hadrons.

The key to all this is that every elementary particle has a Hilbert space and quantum states associated with it which it can share with other particles by duplication and communication through bosons because they are kinematic in Hilbert space, maybe off the mass shell, that is virtual as the standard story goes, or in fact the mass shell has nothing to do with them because their associated Hilbert spaces are outside the Minkowski space where the on shell version of the particle exists and is subject to Lorentz transformations.

All this business is drawing energy from the gravitational potential making that potential well deeper. This must be the story with hadrons which are somewhat analogous to black holes in that their potential wells are so deep that their bosons and fermions cannot get out.

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Wednesday 25 October 2023

We have devised a quantum mechanical tale of mind and matter which has grafted modern theology and physics onto ancient physics and theology and provided something of a back story to the Big Bang theory. So far we have extracted one photon from our quantum mechanical singularity and come to the interface between mind and spacetime which is in effect a version of the old quantum mechanical problem of measurement which has been the subject of furious debate running from the calm reasoning of Zurek to the quasi madness of Everett III. Now we are ready to expand this little scenario to match the size and complexity of the Universe we see. our first step in this direction was taken with a picture of the Internet and real physical networks using the dynamics of computers to imitate the kinematics of mind. Now we turn to look at this picture, using the kinematics of mind described with Hilbert space and virtual particles to expand from one photon to the whole world, beginning with the creation of Minkowski spacetime and gravitation. The dream goes on, although this morning I thought I was waking from a nightmare. Now I am for a moment happy again because my work of fiction gains substance by tracking the real data of history. Wojciech Hubert Zurek (2008): Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical, Hugh Everett III (1973): The Many Worlds Interpretation of Quantum Mechanics

[page 329]

Question: Although the electron has no size it can still contain and operate Hilbert space as a kinetic entity inside the dynamic electron just as Hilbert space and quantum mechanics operate inside the initial singularity. This is just like the containment of thought in my brain which represent a large volume of information in a relatively large space, although the information density is effectively zero in terms of eg a hadron. This little paragraph is an insight worth a day's work answering the fundamental question I was trying to formulate in cc22_trans_hilbert. Write it into the page after lunch and a snooze.

Andrew Lok Hang Chan: The imperialists have wiped out thousands of lanuages and cultures. Andrew Lok Hang Chan: Opinion: Hong Kong authorities don’t want you to read this story. Here’s why.

Still not happy with cc22_trans_hilbert. Latest plan is to start from cc19_network in Minkowski space and attach Hilbert space to each functioning system in the network and subnetworks, ie network of networks working down to the elementary particles and up to planets and galaxies. How does this work? Each elementary particle is a dynamic entity driving an internal Hilbert space and the shared Hilbert spaces of the interacting particles work like Zurek measurement systems which can be deployed to explain bonding.

Thursday 26 October 2023
Friday 27 October 2023

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cc22_from gravitation to quantum electrodynamics. Astronomers are creatures of the night. In daytime the intense light of the Sun blinds us to the immense world that surrounds us.

Final link cc22_network_QED, a bit of humility. Follow Feynman but adapt to my story somewhat and claim that uniting physics and theology does help to explain why the world works as it does, emphasizing that QED is the physics of conversation between particles / sources controlled by quantum mechanics in Hilbert space underlying Minkowski space. Can I make this work while sticking to the facts. So work through Feynman's QED. Richard Feynman (1988): QED: The Strange Story of Light and Matter

Feynman page 6: Dirac electron magnetic moment adjusted from 1 to 1.00118 in 1948.

page 9: 'Will you understand what I am going to tell you? . . . No, you are not going to be able to understand it . . . It is my task to convince you not to turn away because you don't understand it. . . . That is because I don't understand it. Nobody does.' Very theological!

page 10: ' The theory of quantum electrodynamics describes nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept nature as she is—absurd.

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Feynman page 12: 'So again, we are not going to deal with why Nature behaves in the particular way She does: there are no good theories to explain that [except the variation introduced by Hilbert space?]'

Now I am on a new tack and have to see it through. Yesterday, after Auntie, I went to the hospital for the eye injection, had a haircut, collected my mail and went to the Reading and Writing Dangerously do at the Hawke centre UNISA where guests were Peter Greste, Geraldine Brookes, Kylie Moore-Gilbert and Behroug Bouchani talking about their experiences as journalists, academics and political prisoners, the role of writing in maintaining their stability and making their experiences while I wondered about my own very private work. Does anybody read my stuff? According to my web stats natural theology despatched a bit over a GB or material in the last 12 months. This is supposed to exclude crawlers etc, but what proportion is actually read? Maybe 10 000 visitors per year, so a bit might be seeping out, with no promotion. I now have a database of a few megabytes of text available for exploitation, but do not feel ready yet.

A photon has its energy in one box, ie frequency. Its phase in another box, its polarization Propagation requires a 2D space (Hilbert?)

I suppose I feel that I have got to save my soul by doing something significant, but that is not available on demand. I am

[page 332]

coming to the crunch with cognitive cosmology. I have been following some ideas for 21 pages, and now on pages 22, 23, and 24 I have to put these ideas to work to produce a critique of QED, QFT and QCD and I do not have a clear idea about how to do it and I would love to get it done by the end of the month (impossible) or at least by the end of November so that I can write the simple summary in time for a marketing effort next year.

The more I think about my life the dumber I think I have been, but I am still alive, so I can start again by counting my blessings and looking forward to doing better, a perennial Christian trait. No doubt a consequence of reading Le Carré Our Game. David Cornwell (1995): Our Game

Saturday 28 October 2023

Still stuck. My real problem is that I do not understand quantum theory. Feynman emphasizes (QED page 12 above) that we do not understand quantum mechanics, we just have to deal with it, and his book explains how he did that, and I see it as a very theological approach: God is beyond our ken so we just have to deal with them and the result is the hodge podge of self contradictory doctrine that has made the Catholic Church an outstanding success, helped along with judicious applications of military violence. As Geraldine

[page 333]

Brooks commented on Thursday night, there is one word behind the corruption of the press around the world, populism and capitalism. We are all prepared to pay big money for the stories we want to hear and the Murdoch press delivers it, supported by populist politicians like Trump. In the face of this I am trying to claim that a proper understanding of the nature of the world obtained by combining physics and theology is the answer, but physics also contains a lot of mythology, so that although things like the cosmological constant problem are easy to criticize, the real answer is hard to find. My promises induce in me a sort of imposter syndrome because I do not know the answer. My feeling about trying to be a member of the Order of Preachers in my youth was that I would be an imposter if I preached the stuff they were telling me then. So the answer appeared to be in science, and so I made the world divine and was expelled.

My immediate problem with cc22_network_QED is explaining the quantum mechanical foundations of standard classical computation, which comes down to the quantum explanation of transistors which seems to be a bit technical for my purposes. A parallel task is to explain the hopes of quantum computation which also seems a bit mythological to me. My principal understanding is that there is no way to beat the measurement problem except by applying Shannon's theory

[page 334]

of error prevention to quantum mechanics to show how, despite the measurement problem, quantum devices can be made sufficiently deterministic to be useful for computation. The root of my imposture here is that I feel too lazy and incompetent to carry this through. Like an old time theologian following Jesus of Nazareth I am praying for a miracle. I have the pleasant feeling that my story on the cognitive cosmology site has been rather miraculous so far, given my general state of ignorance, but now I have come to a dead end and am looking for a way to worm my way out of it by cooking up a new hypothesis as Planck and Einstein did so well. So what is this hypothesis? As usual I want it by sundown today. Meanwhile I will finish reading my current bit of escapist trash, Le Carré Our Game, an old Public schoolboy thing. The basic idea of isolating the children into authoritarian schools is to corrupt them sufficiently to fit into the current political management paradigm which is basically that we rich and powerful should ride on the backs of the rest. Long live, Popes, Kings and celebrities. I want to be one, but have little hope, hence the need for a miracle. So far my best idea is that despite the uncertainty introduced by the Diophantine quantum, the world can be manipulated to give quite definite answers at a particular scale, so that we can get a lot of information out of a few photons captured in deep space.

[page 335]

The way forward that appeals to me is to go back to the beginning when there was nothing but an omnipotent agent who could try anything that did not involve explicit contradictions. This being is isomorphic to Hilbert's proposal for formal mathematics: any set of axioms and algorithms that does not lead to contradiction qualifies as mathematics even though it may be trivial and boring, like counting sheep by establishing correspondences with bags of beans. As it evolves, the world discovers mathematics. As it evolves, science discovers the mathematics that the Universe has discovered. This is my explanation of Wigner's observation. Eugene Wigner (1960): The Unreasonable Effectiveness of Mathematics in the Natural Sciences

The big question is how does this process lead to quantum mechanics, and specifically to quantum mechanics as described by Feynman's QED?

Le Carré enjoys emphasizing the ambivalence and misery of those who play at the violent end of politics, like his mate Ian Fleming. Their subjects may have reason to hate what they have to do. James Bond seems to revel in it, Le Carré's protagonists suffer, which is why he is seen as a novelist. I am my own protagonist and while I have committed a few sins of the flesh and taken a stand against the Catholic church, my only regret is that I am not gifted enough to realize my dream of rewriting theology, even though I do feel that I have done well so far and generated some preachable material that goes some distance to erasing my imposter feeling.

I would like a lover

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and some funds but I am comfortable and have a lot of time ahead of me so I live in hope. I suppose it is ultimately very hard not to write or talk about oneself. I am addicted to it because I see myself as a conscious particle trying to understand my place in the Universe like all the other particles that are described by quantum mechanics because we have Hilbert space kinematic interiors inside our physical dynamic shells. Kinematics need not be on the mass shell, but dynamics must. Here we are looking for a way to understand Lagrangians and Feynman diagrams and wee their attachment to momentum and spacetime as the problem identified by Dirac when he set out to apply Hamiltonian methods to quantum mechanics. These remain both orthodox and the source of many problems which seem to be avoided by Feynman's path integrals which are purely kinematic. P. A. M. Dirac (1933): The Lagrangian in Quantum Mechanics

My fundamental theological problem has been that sex was both the best and the worst thing in my life, emphasizing the barrier between reality and Christianity,

Back to Feynman QED page 40: How so we know that light also reflects off the the ends of the mirror? Diffraction grating.

page 41: All arrows have the same length because all paths are equally probable [but between them their probabilities must all add up to 1, since only one is actually followed].

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Further reading

Books

Cornwell (1995), David, and (aka John le Carré), Our Game, Hodder and Stoughton 1995 Jacket: 'At forty-eight, Tim Cranmer is a secret servant in premature retirement in deepest Somerset. His Cold War is fought and won, and he is free to devote himself to his stately manor hoiuse, his vineyard and his beau tiful young mistress Emma. But no man can escape his past, and Tim's past lies twenty miles way, in the chaotic person of Larry Pettifer, bored rsadical, don, philanderer and for twenty years Tim's mercurial double agent against the now vanquished Communist threat. And between the two men stands Emma, an unresolved rivalry thar dates all the way to their shared boyhood at public school.' 
Amazon
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Everett III (1973), Hugh, and Bryce S Dewitt, Neill Graham (editors), The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press 1973 Jacket: 'A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book has developed. The volume contains Dr Everett's short paper from 1957, "'Relative State' formulation of quantum mechanics" and a far longer exposition of his interpretation entitled "The Theory of the Universal Wave Function" never before published. In addition other papers by Wheeler, DeWitt, Graham, Cooper and van Vechten provide further discussion of the same theme. Together they constitute virtually the entire world output of scholarly commentary on the Everett interpretation.' 
Amazon
  back

Feynman (1988), Richard, QED: The Strange Story of Light and Matter, Princeton UP 1988 Jacket: 'Quantum electrodynamics - or QED for short - is the 'strange theory' that explains how light and electrons interact. Thanks to Richard Feynmann and his colleagues, it is also one of the rare parts of physics that is known for sure, a theory that has stood the test of time. . . . In this beautifully lucid set of lectures he provides a definitive introduction to QED.' 
Amazon
  back

Links

Alex Lo (2023_10_24), America is ‘the danger’ and will end up getting us all killed, ' What he actually said in the Oval Office was: “America is a beacon to the world, still, still. We are, as my friend Madeleine Albright said, the indispensable nation … American leadership is what holds the world together.” He said something even more boastful in an earlier interview on CBS’ 60 Minutes. “We’re the United States of America for God’s sake, the most powerful nation in the history – not in the world, in the history of the world,” he said. “The history of the world. We can take care of both of these and still maintain our overall international defence.” . . .. While it may be easy to dismiss Biden’s remarks as the bombast of an ageing leader no longer in full command of his mental faculties, such a belief is actually common “inside the Beltway”, among the US governing elites. . . .. Effectively, America is telling everyone in the Middle East and beyond to stay still and shut the hell up until Israel finishes whatever it wants to do to the Palestinians. That’s not just about repeating America’s mistakes, but adding a few extras with exclusively Israeli features.. . . .. America is the danger. Its self-styled indispensability will end up getting us all killed.' back

Andrew Lok Hang Chan, Opinion: Hong Kong authorities don’t want you to read this story. Here’s why. , ' Every day, I am inundated with news about Hong Kong’s national security law — but I never imagined becoming ensnared in its grasp. That changed when the police arrived at our front door and told my father they would search our apartment without a warrant. Until then, I had naively believed that their focus was on politicians and protesters, never nerds like me. The police’s concern was stranger than fiction: They had taken umbrage at 11 essays submitted to a Cantonese writing competition that I had organized in 2020. The national security law is intended to promote “social harmony” — in large part by stamping out Cantonese, the mother tongue of most Hongkongers, in favor of forcing the widespread use of Mandarin, China’s national language. The essays had violated that “social harmony,” a government official told me, pointing out their “problematic content,” ranging from Cantonese profanities to narratives of emigration, all deemed unlawful.' Andrew Lok Hang Chan is the former president of Societas Linguistica Hongkongensis. back

Ari Chand, Scarygirl: the richly built world of this new Aussie film tells a story of human-nature connection, ' With growing streaming demand for original content, Australia has been going through an animation and VFX industry boom. Scarygirl marks a 3D animated feature film release that incorporates Australian accents, colloquialisms and sensibilities for a global audience. Animation and visual ways of expressing ideas about the world have long been used to share messages with a new generation. Filled with fantastical world-building, character and creature design, the Scarygirl universe mimics our concern for the natural world and the need for human-nature connection. With some darker themes in the story around biodiversity loss, the film introduces a healthy level of cynicism concerning capitalism, technological innovation and progress.' back

Bain Munro Attwood, History and myth: why the Treaty of Waitangi remains such a ‘bloody difficult subject’, ' By seeking to tell more truthful histories, historians might provoke New Zealanders to consider whether there are not intellectually sounder bases than the Treaty/te Tiriti for the political project it stands for. Such histories could also provide – and indeed have provided – accounts that show how differently te Tiriti/the Treaty has been interpreted and understood over time, changing as the present has changed. In performing such a task, historians can demonstrate, in the words of an American historian, “how the horizon of the present is not the horizon of all that is in the world”. In other words, the discipline of history’s primary intellectual justification probably lies in it being able to reveal that, once upon a time, there were ways of seeing things that are different to those that dominate in contemporary society. Works of history should surprise, even astound readers, by retrieving those ways of seeing and acting that are no longer known by most people. In this sense, good history is a comparative exercise, drawing attention to differences and similarities between the past and the present. This could enable us to ask whether, in seeking to redress Māori loss and suffering, something is to be gained by broadening our horizons to include some of those that have largely disappeared from sight. back

Brendan M. Lake & Marco Baroni, Human-like systematic generalization through a meta-learning neural network, ' The power of human language and thought arises from systematic compositionality— the algebraic ability to understand and produce novel combinations from known components. Fodor and Pylyshyn1 famously argued that artificial neural networks lack this capacity and are therefore not viable models of the mind. Neural networks have advanced considerably in the years since, yet the systematicity challenge persists. Here we successfully address Fodor and Pylyshyn’s challenge by providing evidence that neural networks can achieve human-like systematicity when optimized for their compositional skills. To do so, we introduce the meta-learning for compositionality (MLC) approach for guiding training through a dynamic stream of compositional tasks. To compare humans and machines, we conducted human behavioural experiments using an instruction learning paradigm. After considering seven different models, we found that, in contrast to perfectly systematic but rigid probabilistic symbolic models, and perfectly flexible but unsystematic neural networks, only MLC achieves both the systematicity and flexibility needed for human-like generalization. MLC also advances the compositional skills of machine learning systems in several systematic generalization benchmarks. Our results show how a standard neural network architecture, optimized for its compositional skills, can mimic human systematic generalization in a head-to-head comparison. back

David Rothkopf, Opinion | This Was Netanyahu's Most Catastrophic Error, ' Of all the mistakes made by Netanyahu before Hamas' despicable assault, from attacking Israeli democracy to personal corruption, from embracing Putin to promoting extremists, his strategy of shunting the Palestinians aside has been a catastrophe – and has undermined the popular global support Israel might have expected.' back

Debanji Ganguli, ‘Now I am become Death, the Destroyer of Worlds’ – the Bhagavad Gita explained, ' The Bhagavad Gita dramatises a meditative exchange between Arjuna and Lord Krishna, who appears as his charioteer during the momentous battle between two clans, the Pandavas and the Kauravas. The battlefield is located in Kurukshetra, a town close to New Delhi. Each clan stakes its claim to be the mightiest ruling dynasty of erstwhile Bharat (present day India). Poets, philosophers, scientists, public intellectuals and political leaders have been enthralled by the Bhagavad Gita since its first English translation appeared in 1785. Wherein lies Gita’s popular appeal across oral and performative cultures? The Gita is more than just a sacred text of the Hindus. It distils insights from several schools of philosophy in classical India. Wilhelm von Humboldt, the renowned 19th century German scholar and philologist, called the Bhagavad Gita “the most beautiful, presumably the only real philosophical poem of all known literatures.”. . .. The Oxford philosopher and president of India from 1962-1967, Sarvapalli Radhakrishnan, once remarked the trauma of the two world wars spurred thinkers to turn to Gita for “its dramatization of a perpetually recurring predicament.” Radhakrishnan’s treatise on the Bhagavad Gita continues to be a revered scholarly source. The “recurring predicament” at the heart of the Bhagavad Gita is this: what constitutes righteous action in the face of moral ambiguity and the inevitability of violence?' back

Eamonn Wooster & Erick Liundgren, From meerkat school to whale-tail slapping and oyster smashing, how clever predators shape their world, ' In the 1980s a single humpback whale in the Gulf of Maine developed the “lobtail feeding method”. This unique hunting method of slapping the water’s surface appears to drive fish into dense schools, making it easier to consume them. Lobtail feeding caught on. Now many humpback whales are doing it. Ecologists have long thought animals acted on instinct alone. But a growing body of evidence shows many animals, much like us, have complex brains and social lives. In our new research, we argue the science of ecology can learn a great deal from the study of animal cognition and culture. Cognition is what goes on in the mind, which determines how animals perceive and respond to the world around them. Culture is the development and spread of socially learned behaviours. These are important – but generally overlooked – mechanisms influencing ecosystems.' back

Eugene Wigner (1960), The Unreasonable Effectiveness of Mathematics in the Natural Sciences, 'The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories.' back

Geoffrey Robinson, There is a path to peace in the Middle East, but neither side is taking it, ' There must be an independent and expert inquiry into the bombing of Al Ahli Arab Hospital, which killed so many children. Whether it came from an incompetently fired Hamas rocket or a malign Israeli attack is not of immediate concern because it was indubitably a crime against humanity in a war that will continue to kill children unless and until there is a ceasefire. Yet in the immediate aftermath of the hospital bombing, the United Nations Security Council, the body entrusted to keep world peace, refused to pass a resolution calling for a cease-fire. It was vetoed by the US and France, in deference to Israel’s desire to keep bombing Gaza to “eliminate Hamas”. . .. Nonetheless, and for all the crimes of Hamas, it is necessary to protest against the cruel destruction of Palestinian lives and homes. An eye for an eye is a brutal philosophy. The Israeli version, two eyes for an eye, leads only to moral blindness in Gaza. The international law solution remains clear, namely that Israel is entitled to exist, to be recognised, and to security, and the Palestinian people are entitled to their territory, to the right of self-determination, and to their own state. Both sides are under a duty to negotiate to achieve this position but neither has been prepared to give peace this chance. It would be over optimistic to predict an international law solution, or any solution at all.' back

Jess Davis & Tyne Logan, Gagged and grief stricken, but not without hope, ' For the past 40 years, Antarctic ecologist Dana Bergstrom has studied one of the wildest places on the planet. “Antarctica gets into your blood,” she says. “For somewhere so cold, it really makes your heart warm.” A woman wearing a yellow and black jacket and red beanie stands in front of a clear blue lake snow behind. Dana Bergstrom visited Antarctica and sub-Antarctica more than 20 times over her career. Supplied: Patti Virtue As a public servant with the Australian Antarctic Division, she operated inside a system where any outside communication about her scientific work was carefully calibrated, crafted and monitored. But eventually that calibration went beyond what Bergstrom thinks can be justified. “I was gagged,” she says. Recently retired, Bergstrom is now speaking out about being silenced. “I went with it, I was a good public servant. “But it was disheartening to not be able to tell the whole story.” And she’s not alone. Ecologists and climate scientists have told the ABC of a widespread culture of suppression and self-censorship. Sometimes it’s insidious, driven by the fear of losing funding or contracts. Sometimes it’s overt, through active gagging or academic careers being threatened. All of that for attempting to “speak the truth” about environmental damage, ecosystem collapse and climate change. And it’s taking a toll, with scientists suffering mental anguish at their research being suppressed instead of being used to help save species on the brink of extinction, to help arrest the rapidly deteriorating state of the natural world. As one says: “It really impacts you, because how can it not? “You can’t look away.” back

Katherine Harry & Emma Rettner, New class of recyclable polymer materials could one day help reduce single-use plastic waste, ' But say you can recycle one of these plastics by a different method, so it doesn’t end up contaminating the recycling stream. When we mixed samples of polypropylene with a polymer we made, we were still able to depolymerize – or break down the material – and regain our building blocks without chemically affecting the polypropylene. This indicated that a contaminated waste stream could still recover its value, and the material in it could go on to be recycled, either mechanically or chemically. . . . .. Connecting two different polymers together multiple times until they form a single, long molecule creates what’s called a multiblock polymer. Just by adjusting how much of each polymer type goes into the multiblock polymer, our team created a wide range of materials with properties that spanned across polyolefin types. But creating these multiblock polymers is easier said than done. . . . .. In our method, the reactive groups are now the same as each other, meaning we didn’t have to worry about pairing the ends of each building block to make polymers that can compete with the polyolefins we already use. Using the same strategy, applied in reverse by adding hydrogen, we could disconnect the polymers back into their building blocks and easily separate them to use again. back

P. A. M. Dirac (1933), The Lagrangian in Quantum Mechanics, ' . . . there is an alternative formulation [to the Hamiltonian] in classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulation are closely related but there are reasons for believing that the Lagrangian one is more fundamental. . . . Secondly the lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; . . .. ' [This article was first published in Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933), pp. 64–72.] back

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

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