Armstrong (2001), Karen, Holy War: The Crusades and their impact on today's world, Anchor Books (Random House) 2001 Jacket: 'In 1095, with the tomb of Jesus still in the hands of infidels and the Byzantine empire overrun by Muslim Turks, Pope Urban II summoned Christian warriors to take up the cross and their swords against the Turks and then recover the holy city of Jerusalem from Islam. It was to be the first of the Crusades, a holy war that would focus the power of the European kingdoms against a common enemy. The Crusades became the stuff of romantic legend, but in reality were a series of rabidly savage battles carried out in the name of Christian piety to advance the power of the Western Church. Their legacy of religious violence is felt today as the age old conflict of Christians, Muslims and Jews persists.' 
Amazon   back

Bell (1987), John S, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press 1987 Jacket: JB ... is particularly famous for his discovery of a crucial difference between the predictions of conventional quantum mechanics and the implications of local causality . . . . This work has played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of classical ideas of space, time and locality. 
Amazon   back

Dirac (1983), P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)  
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

McGregor (2010), Richard, The Party: The Secret World of China's Communist Rulers, Harper 2010 Amazon editorial review: From Publishers Weekly 'McGregor, a journalist at the Financial Times, begins his revelatory and scrupulously reported book with a provocative comparison between China's Communist Party and the Vatican for their shared cultures of secrecy, pervasive influence, and impenetrability. The author pulls back the curtain on the Party to consider its influence over the industrial economy, military, and local governments. McGregor describes a system operating on a Leninist blueprint and deeply at odds with Western standards of management and transparency. Corruption and the tension between decentralization and national control are recurring themes--and are highlighted in the Party™s handling of the disturbing Sanlu case, in which thousands of babies were poisoned by contaminated milk powder. McGregor makes a clear and convincing case that the 1989 backlash against the Party, inexorable globalization, and technological innovations in communication have made it incumbent on the Party to evolve, and this smart, authoritative book provides valuable insight into how it has--and has not--met the challenge. ' Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved. 
Amazon   back

Pais (1982), Abraham, 'Subtle is the Lord...': The Science and Life of Albert Einstein, Oxford UP 1982 Jacket: In this . . . major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire ouvre. . . . Running through the book is a completely non-scientific biography . . . including many letters which appear in English for the first time, as well as other information not published before.' [Raffiniert ist der Herr Gott, aber boshaft is er nicht] 
Amazon   back

Pais (1986), Abraham, Inward Bound: Of Matter and Forces in the Physical World, Clarendon Press, Oxford University Press 1986 Preface: 'I will attempt to describe what has been discovered and understood about the constituents of matter, the laws to which they are subject and the forces that act on them [in the period 1895-1983]. . . . I will attempt to convey that these have been times of progress and stagnation, of order and chaos, of belief and incredulity, of the conventional and the bizarre; also of revolutionaries and conservatives, of science by individuals and by consortia, of little gadgets and big machines, and of modest funds and big moneys.' AP 
Amazon   back

Pais (1991), Abraham, Niels Bohr's Times, in Physics, Philosophy and Polity, Clarendon Press 1991 Jacket: 'T he life of Niels Bohr spanned times of revolutionary change in science itself as well as in its impact upon society. Along with Albert Einstein, Bohr can be considered to be this century's major driving force behind the new philosophical and mathematical descriptions of the structure of the atom and the nucleus. Abraham Pais, the acclaimed biographer of Albert Einstein, here traces Bohr's progress from his well-to-do origins in late nineteenth-century Denmark to his position at centre stage in the world political scene, particularly during the Second World War and the development of atomic weapons.' 
Amazon   back

Polanyi (1966, 2009), Michael, and Amaryta Sen (foreword), The Tacit Dimension, University Of Chicago Press 1966, 2009 ' “I shall reconsider human knowledge by starting from the fact that we can know more than we can tell,” writes Michael Polanyi, whose work paved the way for the likes of Thomas Kuhn and Karl Popper. The Tacit Dimension argues that tacit knowledge—tradition, inherited practices, implied values, and prejudgments—is a crucial part of scientific knowledge. Back in print for a new generation of students and scholars, this volume challenges the assumption that skepticism, rather than established belief, lies at the heart of scientific discovery.' 
Amazon   back

Albert Einstein (1905c), On a heuristic point of view concerning the production and transformation of light, ' The wave theory of light, which operates with continuous spatial functions, has proved itself splendidly in describing purely optical phenomena and will probably never be replaced by another theory. One should keep in mind, however, that optical observations apply to time averages and not to momentary values, and it is conceivable that despite the complete confirmation of the theories of diffraction, reflection, refraction, dispersion, etc., by experiment, the theory of light, which operates with continuous spatial functions, may lead to contradictions with experience when it is applied to the phenomena of production and transformation of light. Indeed, it seems to me that the observations regarding "black-body" light, and other groups of phenomena associated with the production or conversion of light can be understood better if one assumes that the energy of light is discontinuously distributed in space.' back

Albert Einstein (1919), Do gravitational fields play an essential role in the structure of the material universe., ' Neither the Netonian nor the relativistic theory of gravitation has so far led ro any advance in the theory of the constitution of matter. In view of thus fact it will be shown in the following pges that there re reasons for thinking thst the elementary formations which go to make up the atom are held together by gravitational force. back

Albert Einstein (1933), On the Method of Theoretical Physics: Herbert Spencer Lecture 1933, ' It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience. back

Albert Einstein (1951), The Advent of Quantum Theory, ' Thereafter, by way of an ingenious thermodynamic consideration, which also made use of Maxwell's theory, W. Wien found that the universal function p of the two variables v and T would have to be of the form p v3f(f ) whereby f(v/T) is a universal function of one variable v/T only. It was clear that the theoretical determination of this universal function f was of fundamental importance-this was precisely the task which confronted Planck. Careful measurements had led to a very precise empirical determination of the function f. Relying on those empirical measurements, he succeeded in the first place in finding a statement which rendered the measurements very well . . . back

Alex Lo, US proxy Anthony Albanese goes to Beijing, 'As for the protection of sea lanes, it is actively undermining its own national interest, as former prime minister Paul Keating has clearly and repeatedly spelled out. The problem? In a word: Aukus. The original, now scrapped, deal with the French involved 12 diesel-driven attack submarines at a cost of roughly US$66 billion that were expected to be ready by the early 2030s. They were well-designed to patrol Australia’s immediate maritime environment and to protect alternative sea lanes from the South to the North Pacific in the event of a hot war in the South China Sea. Daily Opinion Newsletter Thought-provoking commentary and Op-ed content, curated daily by our world-class editorial team. By submitting, you consent to receiving marketing emails from SCMP. If you don't want these, tick here By registering, you agree to ourT&CandPrivacy Policy Instead, under US pressure, Morrison committed his country to eight ultra-expensive nuclear-powered subs at a projected cost of between US$268 billion and US$368 billion, the first of which won’t be ready before the early 2040s. Albanese, his foreign minister, Penny Wong, and the entire Labor Party reportedly went completely along with it - with no prior consultation - less than a day after Morrison disclosed the secret deal. Imagine: the entire military establishment and posture of a major country took a U-turn with no public consultation and no objection from the then obsequious opposition within 24 hours! No wonder Washington considers Albanese and his Labor Party a safe pair of hands.' back

Alex Lo, The real ‘no limits’ friendship is only found between US and Israel, ' What Israel wants, Israel gets; and does not even have to ask first when it comes to emergency financial aid and weapons. As Israel bombs its way across the Gaza Strip and Jewish settlers commit murder to seize Palestinian land in the West Bank, the weapons they are using are mostly supplied by Washington. Unfortunately, the current Israeli government knows no moderation. Unlike the more restrained Labor Party government of old, the current Israeli state is run by extremists. The goal of this coalition was in fact spelled out, at least for the Israeli public. When this most extreme of far-right coalitions was formed late last year, it called for not only continued occupation but also annexation of the West Bank. Its coalition deal states: “The Jewish people have an exclusive and unquestionable right to all areas of the Land of Israel. The government will promote and develop settlement in all parts of the Land of Israel – in the Galilee, the Negev, the Galan, Judea and Samaria. . . . But it strikes me that it’s the spiritual or moral equivalent of “penny-wise and pound-foolish”. According to one estimate, about 18,000 tonnes of bombs have been dropped on Gaza up to the start of this month. The death toll has hit more than 10,000 as a result. How did the Israelis deliver those bombs and who supplied them? There are the all-purpose Mk80 bombs, which are considered “dumb” but can be converted into “smart” bombs when fitted with GPS-targeting devices called JDAM. F-15, F-16 and the most advanced F-35 fighter jets have all been deployed. There are also CH-53 heavy-lift helicopters and KC-46 aerial refuelling tankers.” back

Alex Lo, Why Democratic US lawmaker Rashida Tlaib needs three cheers, ' In North America where I live, corporations and governments like to advertise their racial and gender-diversity profiles. Often, though, it’s a bit cosmetic. When the diversity hires start to take their jobs seriously beyond being photo-op props, and threaten to rock the boat, the fury unleashed on them can be quite swift and frightful. Take, for example, Democrat Rashida Tlaib, the only Palestinian-American in the US Congress. She took a stance with her own people against the war on Gaza. Sure enough, the White House condemned her and the House of Representatives voted to censure her. While their excuse was her use of allegedly antisemitic language, it’s clear her real crime was daring to step out of line, which in this case, is the United States’ bipartisan and unconditional support of Israel, however brutal the war in Gaza has become.' back

Aristotle (continuity), Physics V, iii, 'A thing that is in succession and touches is 'contiguous'. The 'continuous' is a subdivision of the contiguous: things are called continuous when the touching limits of each become one and the same and are, as the word implies, contained in each other: continuity is impossible if these extremities are two. This definition makes it plain that continuity belongs to things that naturally in virtue of their mutual contact form a unity. And in whatever way that which holds them together is one, so too will the whole be one, e.g. by a rivet or glue or contact or organic union. ' 227a10 sqq. back

Ben Cubby, Punishment and control: the secret handbook that rules a religion, 'Australian children in the Jehovah’s Witnesses religion are being trained to avoid life-saving blood transfusions and parents are being coached to thwart court processes that may prevent their children from dying, internal church documents reveal. An investigation following an inquest into the death of Jehovah’s Witness Heather Winchester, who died in Newcastle after refusing a blood transfusion, has uncovered disturbing practices within the Australian church, including the systems for discipline, punishment and control contained in the secret rule book for church “elders”. . . . The handbook Shepherd the Flock of God and other documents seen by The Sydney Morning Herald set out the lengths the church goes to prevent believers from receiving blood and details the secretive rules that govern the lives of its 70,000 members in Australia and 8.7 million around the world. . . . According to the handbook, a 290-page document issued to the church’s leaders earlier this year, elders must direct parents in the sect to read and follow the instructions in a church manual on blood issues before their child undergoes a hospital procedure. “Firm conviction is vital because a well-meaning doctor may adamantly claim that blood will improve a child’s condition,” the manual says. “Parents must be firmly resolved to ‘abstain from blood’ by refusing it for their children.” Parents are told to seek out a co-operative doctor and “train their children to defend their faith”.' back

Bucket argument - Wikipedia, Bucket argument - Wikipedia, the free encyclopedia, ' Isaac Newton's rotating bucket argument (also known as Newton's bucket) was designed to demonstrate that true rotational motion cannot be defined as the relative rotation of the body with respect to the immediately surrounding bodies. It is one of five arguments from the "properties, causes, and effects" of "true motion and rest" that support his contention that, in general, true motion and rest cannot be defined as special instances of motion or rest relative to other bodies, but instead can be defined only by reference to absolute space.' back

Casimir effect - Wikipedia, Casimir effect - Wikipedia, the free encyclopedia, ' In physics, the Casimir effect or Casimir-Polder force is a physical force arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, placed a few micrometers apart, without any external electromagnetic field. In a classical description, the lack of an external field also means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using quantum mechanics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. This force has been measured, and is a striking example of an effect purely due to second quantization.' back

Christopher Pollard, Is capitalism dead? Yanis Varoufakis thinks it is – and he knows who killed it, Review: Technofeudalism: What Killed Capitalism – Yanis Varoufakis (Bodley Head) ' Traditional capitalists are people who can use capital – defined as “anything that can be used to produce saleable goods” (such as factories, machinery, raw materials, money) – to coerce workers and generate income in the form of profits. Such capitalists are clearly still flourishing, but Varoufakis argues they are not driving the economy in the way they used to. . . . Even though most of us are regularly interacting with capitalists and earning wages via our labour, now, for the first time in history, all of us contribute to “the wealth and power of the new ruling class” through our “unpaid labour”. Every time we use our cloud-linked devices – smartphones, laptops, Alexa, Google Assistant, Siri – we replenish the capital of the Big Tech cloudalists. This in turn increases their capacity to generate more wealth. How? We train their algorithms, which train us, to train them, and so on, in a feedback loop whose goal is to shape our desires and behaviour. They are “selling things to us while selling our attention to others”.' back

Donald McRae, Stuart Broad: ‘I’m still not 100% sure what “the spirit of cricket” means’, ' Was Broad surprised Australia did not try to avoid such controversy after their image had been so tarnished by the ball-tampering scandal in 2018? “That irked my frustration. Don’t get me wrong. I’ve played cricket for a long time and I’m still not 100% sure what ‘the spirit of cricket’ means. Pat quite rightly said: ‘You’re hardly a custodian of the spirit of cricket.’ I felt like saying: ‘You’re dead right. But that doesn’t mean you made the right decision.’ I thought it was a good opportunity for Australian cricket to make a statement that it had moved forward. back

Feynman, Leighton & Sands: FLP I:22, The Feynman Lectures on Physics: I:22 Algebra , ' In our study of oscillating systems we shall have occasion to use one of the most remarkable, almost astounding, formulas in all of mathematics. From the physicist’s point of view we could bring forth this formula in two minutes or so, and be done with it. But science is as much for intellectual enjoyment as for practical utility, so instead of just spending a few minutes on this amazing jewel, we shall surround the jewel by its proper setting in the grand design of that branch of mathematics which is called elementary algebra.' back

Fourier transform - Wikipedia, Fourier transform - Wikipedia, the free encyclopedia, 'The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.' back

Hallam Stevens, A new Silicon Valley manifesto reveals the bleak, dangerous philosophy driving the tech industry, ' In 1993, Marc Andreessen was an undergraduate at the University of Illinois Urbana-Champaign, where he also worked at the US-government funded National Center for Supercomputing Applications. With a colleague, the young software engineer authored the Mosaic web browser, which set the standard for cruising the information superhighway in the 1990s. Andreessen went on to cofound Netscape Communications, making a fortune in 1999 when the company was acquired by AOL for US$4.3 billion. Since then, through his venture capital firm Andreessen Horowitz, the outspoken billionaire has become one of the most influential wallets in Silicon Valley. His investments – in companies including Facebook, Foursquare, Github, Lyft, Oculus and Twitter – have definitively shaped tech over the past 15 years. (He once described his approach as “funding imperial, will-to-power people”.) . . . Andreessen’s essay shows what these ideals have become in 2023. The political and economic worldview beneath its ideas about technology is most visible towards the end of the manifesto, in a list of “enemies”. Remarkably, these include “sustainability”, “trust and safety”, “tech ethics” and “social responsibility”. According to Andreessen, who describes himself as an “accelerationist”, such ideas are holding back the advance of technology and therefore human progress.. . . Andreessen describes his mission in explicitly colonial terms: “mapping uncharted territory, conquering dragons, and bringing home the spoils for our community”. This is a worldview in which territories must be constantly expanded (“our descendants will live in the stars”) in a perpetual war for supremacy.' back

Ilan Pappe, Why Israel wants to erase context and history in the war on Gaza, ' On October 24, a statement by United Nations Secretary-General Antonio Guterres caused a sharp reaction by Israel. While addressing the UN Security Council, the UN chief said that while he condemned in the strongest terms the massacre committed by Hamas on October 7, he wished to remind the world that it did not take place in a vacuum. He explained that one cannot dissociate 56 years of occupation from our engagement with the tragedy that unfolded on that day. The Israeli government was quick to condemn the statement. Israeli officials demanded Guterres’s resignation, claiming that he supported Hamas and justified the massacre it carried out. The Israeli media also jumped on the bandwagon, asserting among other things that the UN chief “has demonstrated a stunning degree of moral bankruptcy”. This reaction suggests that a new type of allegation of anti-Semitism may now be on the table. Until October 7, Israel had pushed for the definition of anti-Semitism to be expanded to include criticism of the Israeli state and questioning the moral basis of Zionism. Now, contextualising and historicising what is going on could also trigger an accusation of anti-Semitism. Thus, the October 7 attack is used by Israel as a pretext to pursue genocidal policies in the Gaza Strip. It is also a pretext for the United States to try and reassert its presence in the Middle East. And it is a pretext for some European countries to violate and limit democratic freedoms in the name of a new “war on terror”. But there are several historical contexts for what is going on now in Israel-Palestine that cannot be ignored. The wider historical context goes back to the mid-19th century, when evangelical Christianity in the West turned the idea of the “return of the Jews” into a religious millennial imperative and advocated the establishment of a Jewish state in Palestine as part of the steps that would lead to the resurrection of the dead, the return of the Messiah, and the end of time. . . . 'srael will continue to be an apartheid state – as declared by a number of human rights organisations – however the situation in Gaza unfolds. The Palestinians will not disappear and will continue their struggle for liberation, with many civil societies siding with them and their governments backing Israel and providing it with an exceptional immunity. The way out remains the same: a change of regime in Israel that brings equal rights for everyone from the river to the sea and allows for the return of Palestinian refugees. Otherwise, the cycle of bloodshed will not end.' back

Kenan Malik, In the Middle East, as in Greek tragedy, justice must prevail over moral absolutism, ' Watching the tragedy unfold in Israel and Palestine has sometimes felt like reading the Oresteia backwards. A trilogy of plays by Aeschylus, written in the fifth century BC, the Oresteia tells of the transformation of ancient Greece from a society rooted in blood and revenge into one shaped by justice. The Oresteia begins with the return home from the Trojan war of Agamemnon, the leader of the triumphant Greeks. He is brutally murdered by his wife, Clytemnestra, in furious revenge for his having ritually sacrificed their daughter Iphigenia on the eve of conflict to placate the gods. To avenge his father, Agamemnon’s son, Orestes, kills Clytemnestra. Pursued by the Furies, ancient deities whose role is to exact vengeance for major sins, he seeks refuge in Athens. The goddess of wisdom, Athena, convenes a jury to try Orestes. With the jury split, Athena votes in favour of acquittal, and in so doing opens up the possibilities of a world beyond that governed by the Furies. . . . There is more here than simply hypocrisy about free speech. It is an attempt to reframe the Gazan conflict as a moral, rather than political, issue, and to delegitimise Palestinian perspectives, an approach that can only make political engagement on a difficult terrain even more intractible. “Where will it end? Where will it sink to sleep and rest, this murderous hate, this Fury?”, the Chorus asks at the end of The Choephori, the second play in the Oresteia trilogy, after Orestes kills Clytemnestra. Today, the answer depends on whether we, and political leaders in Israel, Palestine and the west, wish to listen to the Furies or to Athena.' The Oresteia is a complex work engaging in issues from patriarchy to democracy. The human condition, for Aeschylus, was tragic, with Agamemnon, Clytemnestra and Orestes all facing impossible choices. Part of the process by which humans civilise themselves and learn to live with the tragedy of their condition is, he suggests, in forging the distinction between vengeance and justice. Justice brings us into the sphere of politics and allows for the possibility of reasoned change and redemption. back

Lamb shift - Wikipedia, Lamb shift - Wikipedia, the free encyclopedia, 'In physics, the Lamb shift, named after Willis Lamb (1913–2008), is a difference in energy between two energy levels ²S_½ and ²P_½ (in term symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy. Interaction between vacuum energy fluctuations and the hydrogen electron in these different orbitals is the cause of the Lamb Shift, as was shown subsequent to its discovery.' back

Loveluck, George & Bimbaum, As Gaza death toll soars, secrecy shrouds Israel’s targeting process, ' In the Jabalya attack, which took out an entire residential block, the Israeli military suggested it was carefully planned to target a senior Hamas figure in the tunnels below the refugee camp. “And we struck it and it was taken out and dozens of Hamas operatives were killed with him,” Conricus said. “Of course, it’s sad and regrettable that civilians are killed, but it is a legitimate military target.” In calculating the risk to civilians, military planners could reasonably have assessed that the number of casualties would be in the hundreds, experts say. “The Jabalya strike, because it was a planned attack, shows that Israel must have a tolerance for civilian casualties which is orders of magnitude greater than that that was used by, say, the U.S. Air Force in the war against ISIS,” said Mark Lattimer, executive director of the Ceasefire Centre for Civilian Rights. Palestinians look at the aftermath of an airstrike on a house in Khan Younis, south of the Gaza Strip on Friday. (Loay Ayyoub for The Washington Post) On Oct. 14, just a week into the war, the Israeli air force said it had dropped 6,000 bombs on Hamas targets in Gaza. By contrast, a little more than 7,300 bombs were dropped on Afghanistan by the U.S.-led coalition in all of 2019, the heaviest year of aerial bombardment there.' back

Mark Blaskovich (2023), How do bacteria actually become resistant to antibiotics?, ' Antimicrobial resistance is one of the biggest global threats to health, food security and development. This month, The Conversation’s experts explore how we got here and the potential solutions. “What doesn’t kill me makes me stronger”, originally coined by Friedrich Nietzsche in 1888, is a perfect description of how bacteria develop antibiotic resistance. Contrary to a common belief, antibiotic resistance is not about your body becoming resistant to antibiotics. Resistance arises when bacteria are exposed to levels of antibiotics that don’t immediately kill them. They develop defences that prevent the same antibiotic from harming them in the future, even at higher doses. The ability for bacteria to adapt lies in part with their astonishing rate of reproduction. Some species, such as Escherichia coli, can replicate as quickly as every 20 minutes, depending on the environment. One bacterium can become more than 68 billion bacteria in 12 hours. While most changes are bad, sometimes they can help the bacteria grow in the presence of an antibiotic. This “new and improved” population quickly takes over.' back

Niels Bohr (1913), The Spectra of Helium and Hydrogen, ' RECENTLY Prof. Fowler (Month. Not. Roy. Astr. Soc, December, 1912) has observed a number of new lines by passing a condensed discharge through mixtures of hydrogen and helium. Some of these lines coincide closely with lines of the series observed by Pickering in the spectrum of the star ζ Puppis, and attributed to hydrogen in consequence of its simple numerical relation to the ordinary Balmer series. Other lines coincide closely with the series predicted by Rydberg and denoted as the principal series of the hydrogen spectrum. The rest of the new lines show a very simple relation to those of the latter series, but apparently have no place in Rydberg's theory. back

Nyquist-Shannon sampling theorem - Wikipedia, Nyquist-Shannon sampling theorem - Wikipedia, the free encyclopedia, ' In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called "analog signals") and discrete-time signals (often called "digital signals"). It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.' back

P A M Dirac (1927), The Quantum Theory of the Emission and Absorption of Radiation, ' Introduction and Summary. The new quantum theory, based on the assumption that the variables do not obey the commutative law of multiplication, has by now been developed sufficiently to form a fairly complete theory of dynamics. One can treat mathematically the problem of any dynamical system composed of a number of particles with instantaneous forces acting between them, provided it is describable by a Hamiltonian function, and one can interpret the mathematics physically by a quite definite general method. On the other hand, hardly anything has been done up to the present on quantum electrodynamics. . . .. ' back

P. A. M. Dirac (1926), On the Theory of Quantum Mechanics, ' The new mechanics of the atom introduced by Heisenberg may be based on the assumption that the variables that describe a dynamical system do not obey the commutative law of multiplication, but satisfy instead certain quantum conditions. One can build up a theory without knowing anything about the dynamical variables except the algebraic laws that they are subject to, and can show that they may be represented by matrices whenever a set of uniformising variables for the dynamical system exists. It may be shown, however (see 3), that there is no set of uniformising variables for a system containing more than one electron, so that the theory cannot progress very far on these lines. A new development of the theory has recently been given by Schrödinger. Starting from the idea that an atomic system cannot be represented by a trajectory, i. e., by a point moving through the co-ordinate space, but must be represented by a wave in this space, Schrödinger obtains from a variation prin­ciple a differential equation which the wave function ψ must satisty. This differential equation turns out to be very closely connected with the Hamiltonian equation which specifies the system, namely, if H (qr, Pr - W = 0 is the Hamiltonian equation of the system, where the qr, Pr are canonical variables, then the wave equation for ψ is {H(q r, ih ∂/∂q) - W} ψ = 0.' back

P. A. M. Dirac (1927), The Quantum Theory of Dispersion, ' The new quantum mechanics could at first be used to answer questions concerning radiation only through analogies with the classical theory. In Heisenberg’s original matrix theory, for instance, it is assumed that the matrix elementsf the polarisation of an atom determine the emission and absorption of radiation analogously to the Fourier components in the classical theory. In more recent theories* a certain expression for the electric density obtained from the quantum mechanics is used to determine the emitted radiation by the same formulae as in the classical theory. These methods give satisfactory results in manycases, but cannot even be applied to problems where the classical analogies are obscure or non-existent, such as resonance radiation and the breadths of spectral lines.' back

Richard P. Feynman (1981), 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.' International Journal of Theoretical Physics, VoL 21, Nos. 6/7, 1982 back

Rolf Landauer (1999), Information is a Physical Entity, 'Abstract: This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that on the ultimate nature of the laws of physics are included.' back

Unmoved mover - Wikipedia, Unmoved mover - Wikipedia, the free encyclopedia, ' The unmoved mover (Ancient Greek: ὃ οὐ κινούμενον κινεῖ, lit. 'that which moves without being moved' or prime mover (Latin: primum movens) is a concept advanced by Aristotle as a primary cause (or first uncaused cause) or "mover" of all the motion in the universe. As is implicit in the name, the unmoved mover moves other things, but is not itself moved by any prior action. In Book 12 (Greek: Λ) of his Metaphysics, Aristotle describes the unmoved mover as being perfectly beautiful, indivisible, and contemplating only the perfect contemplation: self-contemplation. He equates this concept also with the active intellect. This Aristotelian concept had its roots in cosmological speculations of the earliest Greek pre-Socratic philosophers and became highly influential and widely drawn upon in medieval philosophy and theology. St. Thomas Aquinas, for example, elaborated on the unmoved mover in the Quinque viae. ' back

Variety (cybernetics) - Wikipedia, Variety (cybernetics) - Wikipedia, the free encyclopedia, 'The term Variety was introduced by W. Ross Ashby to denote the count of the total number of states of a system. The condition for dynamic stability under perturbation (or input) was described by his Law of Requisite Variety. Ashby says: Thus, if the order of occurrence is ignored, the set {c, b, c, a, c, c, a, b, c, b, b, a} which contains twelve elements, contains only three distinct elements- a, b, c. Such a set will be said to have a variety of three elements. He adds The observer and his powers of discrimination may have to be specified if the variety is to be well defined. Variety can be stated as an integer, as above, or as the logarithm to the base 2 of the number i.e. in bits.' back

W. F. McGrew et al, Atomic clock performance enabling geodesy below the centimetre level, ' The passage of time is tracked by counting oscillations of a frequency reference, such as Earth’s revolutions or swings of a pendulum. By referencing atomic transitions, frequency (and thus time) can be measured more precisely than any other physical quantity, with the current generation of optical atomic clocks reporting fractional performance below the 10⁻¹⁷ level. However, the theory of relativity prescribes that the passage of time is not absolute, but is affected by an observer’s reference frame. Consequently, clock measurements exhibit sensitivity to relative velocity, acceleration and gravity potential. Here we demonstrate local optical clock measurements that surpass the current ability to account for the gravitational distortion of space-time across the surface of Earth. In two independent ytterbium optical lattice clocks, we demonstrate unprecedented values of three fundamental benchmarks of clock performance. In units of the clock frequency, we report systematic uncertainty of 1.4 × 10⁻¹⁸, measurement instability of 3.2 × 10⁻¹⁹ and reproducibility characterized by ten blinded frequency comparisons, yielding a frequency difference of [−7 ± (5)stat ± (8)sys] × 10⁻¹⁹, where ‘stat’ and ‘sys’ indicate statistical and systematic uncertainty, respectively. Although sensitivity to differences in gravity potential could degrade the performance of the clocks as terrestrial standards of time, this same sensitivity can be used as a very sensitive probe of geopotential. Near the surface of Earth, clock comparisons at the 1 × 10⁻¹⁸ level provide a resolution of one centimetre along the direction of gravity, so the performance of these clocks should enable geodesy beyond the state-of-the-art level. These optical clocks could further be used to explore geophysical phenomena, detect gravitational waves, test general relativity and search for dark matter.' back

William Bialek & Allan Schweitzer (1985), Quantum Noise and the Threshold of Hearing, ' We argue that the sensitivity of the ear reaches a limit imposed by the uncertainty principle. This is possible only of the receptor holds the detector elements in a special nonequilibirium state which has the same noise characteristics as a ground (T = 0 K) state. To accomplish this "active cooling" the molecular dynamics of the system must maintain quantum mechanical coherence over the time scale of the measurement.' back

Yui Yazaki (2017), How the Klein–Nishina formula was derived: Based on the Sangokan Nishina Source Materials, ' In 1928, Klein and Nishina investigated Compton scattering based on the Dirac equation just proposed in the same year, and derived the Klein–Nishina formula for the scattering cross section of a photon. At that time the Dirac equation had the following unsettled conceptual questions: the negative energy states, its four-component wave functions, and the spin states of an electron. Hence, during their investigation struggles, they encountered various difficulties. In this article, we describe their struggles to derive the formula using the “Sangokan Nishina Source Materials” retained in the Nishina Memorial Foundation.' back

Zero-energy universe - Wikipedia, Zero-energy universe - Wikipedia, the free encyclopedia, 'The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly cancelled out by its negative energy in the form of gravity. . . . The zero-energy universe theory originated in 1973, when Edward Tryon proposed in the journal Nature that the universe emerged from a large-scale quantum fluctuation of vacuum energy, resulting in its positive mass-energy being exactly balanced by its negative gravitational potential energy.' back