Notes
Sunday 18 October 2020 - Saturday 24 October 2020
[Notebook: DB 85 Science]
[page 238]
Sunday 18 October 2020
[page 238]
We see each particle as an embodied turing machine. We see particles as interacting by forming a composite turing machine which halts by producing child particles with the turing machines corresponding to the output of the interaction. Eg Shapiro lecture 17: γ + γ ⇄ p + p̅ [what is the mechanism for this interaction, given that a photon is much simpler than a proton?]. Why matter and antimatter? assymetry of universe? We need an explanation. Vertices in Feynman diagrams are interactions of embodied computers [and maybe their logical expressions are simpler than path integrals and solutions to the Dirac equation??]. Marjorie Shapiro: Particle Physics: Lecture 17 CP Violation (I)
Insofar as turing computable covers all computable functions we will presume that the notion of seeing particles as turing computer networks embodied in quanta of action seems capable of covering all the possibilities. The only thing we need to prove is that turing computable covers all the functions necessary for quantum mechanics. This is the program for milennium 7. Carlson, Jaffe & Wiles: The Millennium Prize Problems
What we are saying is that particles have "works" inside them that can be described by [networks of] digital computers [eg us].
The mass of a particle measures its energy, the rate of its internal process, and so we can imagine that massless photon are eternal but not necessarily immutable due to gravitational redshift, which is related to gravitational potential.
Monday 19 October 2020
How do we apply ideas like particles, fields, gauges and gauge
[page 240]
symmetry to entities like the mathematical community where particles are human individuals and the fields are the networks of communication between them?
Writing is like navigating through an enormous space guided only by an idea, an observation which may be formed in a large space of symmetrical expressions, some more felicitous than others.
Linear systems like the real line have no real size or measure, so we can see unlimited possibilities in the superposition of basis states in Hilbert space eg |ψ> = a|0> + b|1>. However when we have some sort of meeting or crossing a point is defined, giving us something like the eigenvalue equation where we have a relationship between a vector and a matrix that yields a fixed point so given operator A and vector x we find Ax = ax where a is scalar and the direction of x is unchanged.
Silence is golden and we might be able to say the same about inertial motion.
The equivalence of mass and energy is a consequence of the space and time. It is a special case of the energy-momentum relation. Wigner Francisco Fernflores (Stanford Encyclopedia of Philosophy): The Equivalence of Mass and Energy, Eugene Wigner: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Tuesday 20 October 2020
So long digging around in ancient theology and modern physics to the
[page 241]
detriment of the human side of the operation, drawing the lines from a divine universe to a potential human universe. The last four chapters of scientific theology need to lead more tightly to the beatific vision.
Entropy and statistics; fermion, boson, classical.
What I am looking for are the dramatic consequences of a divine world. Gildersleeve Jessica Gildersleeve: Guide to the classics: Rebecca by Daphne du Maurier — gender, gothic haunting and gaslighting
Wednesday 21 October 2020
The evolution of the wave funcrion in a photon is stationary and since the velocity of light is the ratio between space and time perhaps we can say that space travels through time at the velocity of light, or that time travels through space at −c (the velocity of light) or vice versa. This has got to have something to do with the creation of space, if only I could crack it.
How are we going to make spacetime out of quantum mechanics – it must come from fermions and bosons, two ways to permute wave functions? We want the answer by tomorrow. The velocity of light is the conversion factor between space and time. Space-time and energy-momentum vectors transform in the same way. Spacetime is a fixed point in the universe. Somewhere in there we must find potential and kinetic energy. All these bits and pieces can be used to make the operating system of the universe – communication and memory management.
[page 242]
We are trying to put together a universe that looks like a gigantic computer network starting, nevertheless, with the basic functions of Boolean algebra. The foundation of any computer system is its operating system. . . ..
Thursday 22 October 2020
Streater & Wightman page 147: The . . . spin statistics theorem, is an assertion, that in quantum field theory, a non-trivial integer spin field cannot have an anti-commutator vanishing for space-like separations, and a non-trivial half-odd integer spin field cannot have a commutator vanishing for space-like separations. If one puts aside the possibilities of laws other that Bose-Einstein or Fermi-Dirac, the spin statistics theorem then accounts for the experimental results. Streater & Wightman: PCT, Spin, Statistics and All That
von Neumann Chapter 6 measuring process
pure state: state vector or wave function - a ray in Hilbert space
mixed state: density matrix.
Friday 23 October 2020
Problem with quantum field theory is that there is very little connection between Hilbert space and Minkowski space. Hilbert space is a representation of abstract computation whose connection to Minkowski space is through the input and output of information, as is made clear by the roles of fermions and bosons. So what is the connection between Hilbert and Minkowski?
It has been generally assumed (eg Veltman) that Minkowski space is the domain of Hilbert space [so that Lorentz tranformations must be applied to Hilbert spaces as well as to particles], but this does not seem to be the case and my feeling [is] that they are distinct entities with a loose connection established by the Born rule and the eigenvalue equation. In fact the coupling between the two spaces [Minkowski] and Hilbert space describes the inner life of particles, ie it is the story of consciousness in the same way as my conscious awareness is related to my physical actions. So we imagine the Hilbert spaces described by computation are to be found inside particles as my consciousness is to be found inside me. This is pretty much what I have been thinking for the last few months, but it has become clearer today. What has become clear is that there are clear distinctions between Hilbert and Minkowski and a lot of the difficulties in quantum field theory arise from blurring this distinction. So we think that every particle is a computer and the relationships between particles are networks. Martinus Veltman: Diagrammatica: The Path to the Feynman Rules, page 20
In a nutshell, quantum mechanics happens inside the particles, and, insofar as the universe is a big particle, gravitation is inside the universe and is therefore not observable and there are no gravitational particles but waves. This does not quite work out, but the capture of quantum theory within particles imbues it with fixed points that do the processing. Quantum mechanical bonding between two particles establishes them to that degree as one particle.
[page 244]
Saturday 24 October 2020
The simplicity with respect to complexity mantra suggests that there is nothing new under the Sun, but all that really matters is that the universe is one descended from a single point of action to which all possibilities are open, meaning local consistency rules which is what the physicists are saying with local gauge theory. Everything is contained in a cocoon of consistency which, via fixed point theory, induces structure into the Universe. This structure has many layers and consistency in the lower layers does not necessarily mean consistency in the higher layers so we have a problem of evil. High explosive is just doing its thing while shattering lives and communities so the moral principle must be that the higher layers have to maintain control of the lower layers in order to maintain their own existence and the principle of requisite variety guarantees them that this is at least theoretically possible. W. Ross Ashby: An Introduction to Cybernetics pp 206 sqq.
From our essay on the mathematical community [ref] we my conclude that the real action occurs inside the mathematicians and we are inclined to narrow this down to the minds of the mathematicians, ie their brains, which work by superposition and so may be modelled in Hilbert space. We may say the mathematicians are fermions. All their words, questions, papers, books, speeches and videos fall under the heading of bosons. Using our mantra, we may attribute the same picture to fundamental particles. The action goes on inside the fermions and they communicate with one another via the bosons, which is pretty standard. The principal property of fermions is that they stand aloof and protect their integrity while bosons are happy to share their space. We may see this as a function of 4D spacetime and the root of gravitation.
[page 245]
Strogatz: p 98: algebra + geometry → theology + physics Steven Strogatz: Infinite Powers: How Calculus Reveals the Secrets of the Universe
Every fermion is Cartesian in that it says cogito ergo sum
Although fundamental particles have zero size they are nevertheless capable of representing computations by logical confinement which is a consequence of fixed point theory because a particle is an image of the universe, closed, logically continuous, convex and animated by a quantum of action.
How does a positron differ from an electron? On the direction of processing in time. Given a unitary quantum process is identical to a lossless codec, we see time reversal as the decoding of the encoding and when a particle and an antiparticle meet they effectively delete one another's software so that in many cases only photons are left. A photon is its own antiparticle because it has no interior dynamics [?].
An electron may have a lot of logical processing inside whose halted output may be charge, spin and photons.
We are oozing toward the conclusion that quantum mechanics is a pure energy/time enterprise and the introduction of spacetime is a whole new layer in the cosmic network related to gravitation whose charge is simply energy so the 'particles' of gravitation are undifferentiated quanta of action [images of the universe] that combine the roles of fermions and bosons and whose uninterrupted internal flow requires three dimensions of orthogonal geodesics and one dimension of energy/time. Photons move along geodesics outside time. Somehow this will all fit together one day.
[page 246]
An intuition to chew over in the morning. Time measured by the velocity of light, is the fundamental count of progress in the universe. At the velocity of light time stops and we have space. This is how space a created out of time by the Minkowski metric. Somewhere is here lies the coupling between energy and massive particles that can exist at rest in space, which in order to be at rest travels at the velocity of light. So we find the coupling between E = mc2 and space and time.
Let us say that the boundary of the particle is the spacetime representation of the function it contains just as the boundary of a jigsaw piece or a piece of lego represents its function in the overall picture. In the time domain this boundary is a superposition of energies or frequencies as we see in quantum mechanical state vectors.
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Further readingBooks
Ashby, W Ross, An Introduction to Cybernetics, Methuen 1956, 1964 'This book is intended to provide [an introduction to cybernetics]. It starts from common-place and well understood concepts, and proceeds step by step to show how these concepts can be made exact, and how they can be developed until they lead into such subjects as feedback, stability, regulation, ultrastability, information, coding, noise and other cybernetic topics.'
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Auyang, Sunny Y., How is Quantum Field Theory Possible?, Oxford University Press 1995 Jacket: 'Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena and particle interactions are encompassed in a unified framework.'
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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
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Christie, Agatha, The Cat Among the Pigeons, Putnam Publishing Group 1986 Amazon Book Description: 'Welcome to Meadowbank, an exclusive school for privileged young ladies. A fine lot. A dangerous one, too. Two teachers have already bitten the dust. It's obvious to Hercule Poirot that someone is out to scratch Meadowbank's respectable veneer.'
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Lakatos, Imre, Proofs and Refutations: The Logic of Mathematical Discovery, Cambridge University Press 1976 Amazon Editorial Review
'For anyone interested in mathematics who has not encountered the work of the late Imre Lakatos before, this book is a treasure; and those who know well the famous dialogue, first published in 1963-64 in the British Journal for the Philosophy of Science, that forms the greater part of this book, will be eager to read the supplementary material ... the book, as it stands, is rich and stimulating, and, unlike most writings on the philosophy of mathematics, succeeds in making excellent use of detailed observations about mathematics as it is actually practised.' Michael Dummett, Nature
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Polanyi, Michael, and Amaryta Sen (foreword), The Tacit Dimension, University Of Chicago Press 1966, 2009 Amazon product description: '“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.'
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Streater, Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2000 Amazon product description: 'PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.'
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Strogatz, Steven, Infinite Powers: How Calculus Reveals the Secrets of the Universe, Haughton Mifflin Harcourt 2019 ' For reasons nobody understands, the universe is deeply mathematical. Maybe God made it that way, or maybe it is the only way a universe with us in it could be, because nonmathematical universes can't harbour life intelligent enough to ask the question. In any case it's a mysterious and marvellous fact that our universe obeys laws of nature that always turnout to be expressible in the language of calculus as sentenced called differential equations.' Introduction, vii
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Veltman, Martinus, Diagrammatica: The Path to the Feynman Rules, Cambridge University Press 1994 Jacket: 'This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. ... The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. ...'
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Papers
Balazs, Anna C, Irving R Ep[stein, "Emergent or Just Complex", Science, 325, 5948, 25 September 2009, page . 'Efforts toward creating artificial cells are shedding light on how live may have emerged. back |
Mann, C, R Crease, "Interview with John Bell", Omni Magazine, , 85, May 1988, page 84-121. back |
Zhang, Ying, et al, "Three Dimensional Structural View of the Central Metabolic Network of Thermotoga mritima", Science, 325, 5947, September 2009, page 1544-49. Abstract: 'Metabolic pathways have traditionally been described in terms of biochemical reactions and metabolites. With the use of structural genomics and systems biology, we generated a three-dimensional reconstruction of the central metabolic network of the bacterium Thermotoga maritima. The network encompassed 478 proteins, of which 120 were determined by experiment and 358 were modeled. Structural analysis revealed that proteins forming the network are dominated by a small number (only 182) of basic shapes (folds) performing diverse but mostly related functions. Most of these folds are already present in the essential core (~30%) of the network, and its expansion by nonessential proteins is achieved with relatively few additional folds. Thus, integration of structural data with networks analysis generates insight into the function, mechanism, and evolution of biological networks.'. back |
Links
Aquinas 20, Summa I, 3, 7: Whether God is altogether simple? , 'I answer that, The absolute simplicity of God may be shown in many ways.
First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His "suppositum"; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple. . . . ' back |
Asian Metal Inc, Asian Metal - The World, 'Asian Metal has powerful and complete international trade access platform system, as well as independent and personalized trade information distribution and negotiation platform, which offers supports to tap potential business, search partners, expand consumer opportunity channel on the basis of Asian Metal's strong global client network.' back |
Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, 'The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories.' back |
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 |
Forbidden Planet - Wikipedia, Forbidden Planet - Wikipedia, the free encyclopedia, back |
Francisco Fernflores (Stanford Encyclopedia of Philosophy), The Equivalence of Mass and Energy, ' The equation E = mc2 is, arguably, the most famous equation in 20th century physics. . . . In this entry, we have presented the physics of mass-energy equivalence as widely understood by both physicists and philosophers. We have also canvassed a variety of philosophical interpretations of mass-energy equivalence. Along the way, we have presented the merits and demerits of each interpretation. We have also presented a brief history of derivations of mass-energy equivalence to emphasize that the equivalence of mass and energy is a direct result to changes to the structure of spacetime imposed by special relativity. Finally, we have briefly and rather selectively discussed the empirical confirmation of mass-energy equivalence.' back |
GHGSat, Global Emissions Monitoring, ' In June 2016, GHGSat launched the world’s first high-resolution satellite capable of measuring greenhouse gas (CO2 & CH4) emissions from any industrial facility in the world. GHGSat is using this unique satellite and its patented technology to provide greenhouse gas emissions monitoring data and services globally,with better accuracy and at at a fraction of the cost of comparable alternatives.' back |
Greenhalg, McKee and Kelly-Irving, The pursuiof herd immunity is a folly – so who's funding this bad science?, ' You may not have heard of the “Great Barrington declaration” but you’ll likely have seen the headlines that followed it. . . . Rightwing free-market foundations and institutions have long attempted to savage the public reputation of well-intentioned policies such as those aimed at curbing ecological threats and limiting smoking. Some of the tactics these organisations have used in the past are those we see at play in the Great Barrington declaration: discredit the scientific consensus, spread confusion about what the right response is and sow the seeds of doubt. It seems that lockdown restrictions aimed at bringing the virus under control are merely the latest target in this rightwing stealth campaign.' back |
Hamid Dabashi, Mohammad Reza Shajarian, ' Iran is in mourning. Mohammad Reza Shajarian has passed away.
How can I convey the depth of the pain of his loss to non-Iranians?
Think of Um Kalthum for Egyptians and the larger Arab world, think of Nusrat Fateh Ali Khan for Pakistan and the Indian subcontinent, think of Mercedes Sosa for Argentina and the Latin American world. Think of Edith Piaf, Charles Aznavour, Luciano Pavarotti, think of Ella Fitzgerald and Nina Simone, think of Demis Roussos, Nana Mouskouri, think of Mariem Hassan in Western Sahara and Mauritania. Now add to them anyone in their company you love and admire but I have missed and bring them all together in your imagination.' back |
Henry Giroux, Can America survive the re-relection of Donald Trump, ' There will be no real movement for real change in America without addressing a revolution in consciousness, one that makes education central to politics.
Americans can survive Trump — and even a second term of Trump — if they resurrect a language of critique and possibility, and develop a mass movement that draws from history and provides the economic, cultural and political conditions to lift the U.S. out of the present-day socio-political morass.
Americans need a vision they can fight for, not just a fear they can overcome.' back |
Jessica Gildersleeve, Guide to the classics: Rebecca by Daphne du Maurier — gender, gothic haunting and gaslighting, ' Rebecca’s capacity to haunt the second Mrs de Winter, Mrs Danvers’ maintenance of her place in Manderley, Maxim’s power over his new bride, and the narrator’s cowing acceptance of all of this, point to the gendered power structures of both the gothic and the marriage plot.' back |
Julian Burnside, Terror laws: Extreme laws an attack on what we hold dear, 'It's time for politicians to recognise that our anti-terror legislation is already more draconian than the scale of the problem justifies. It's time for them to think about devoting much-needed resources to a real problem, even if it does not promise them much political benefit.
Australia has some of the most extreme anti-terror legislation in the world. As it is brought to bear on 14-year-olds, we should reflect on the fact that our society – with its assumptions of freedom and justice – is less threatened by terrorism than it is by laws like these.' back |
Ken Wharton, The Ultimate Physics Experiment, Essay Abstract
'The ultimate limit of physics is not a theoretical limit, but rather an experimental one; without testable results (at least in principle), any purported theory could not be said to be physical, or even an application of the scientific method. Using a few basic tools from modern physics, this essay is an attempt to deduce those ultimate experimental limits.
This analysis ascribes a central importance to the very successful variational principles (VPs) used in both general relativity and quantum theory. Applying such VPs in some measureable 4D region of spacetime requires one to constrain partial-information boundary conditions on the 3D (hypersurface) boundary of that 4D region. Given the key premise that the constrained, mathematical boundary conditions in VPs directly correspond to values constrained by actual external measurements, one can build up a probabilistic block-universe framework that seems capable of encompassing future developments towards a general theory of measurement and quantum gravity. A general analysis of the ultimate experiments explainable by such a theory yields a reasonable estimation of the limits of physics.' back |
Kent A Peacock, The No-Signalling Theorems: A Nitpicking distinction, Essay Abstract
'The impossibility of using quantum nonlocality for controllable signalling is widely accepted in the literature. However, a critical examination of the proof strategies used to establish this claim shows that they are circular, in the sense that they depend upon locality assumptions that grant what needed to be proven in order to establish no-signalling, or which were embedded ad hoc in the formalism of quantum theory precisely in order to block predictions of signalling. We conclude that forty-five years after the publication of Bell's Theorem, the question of signalling remains open.' back |
Kinetic energy - Wikipedia, Kinetic energy - Wikipedia, the free encyclopedia, 'The kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest.' back |
Linear algebra - Wikipedia, Linear algebra - Wikipedia, the free encyclopedia, 'Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.
The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.' back |
Marjorie Shapiro (17), Physics 226: Particle Physics: Lecture 17 CP Violation (I), ' Matter-Antimatter Asymmetry of the Universe. The universe is made largely of matter with very little antimatter. Why is this the case? Matter dominance occurred during early evolution of the Universe. Assume Big Bang produces equal numbers of B and B̅ At high temperature, baryons in thermal equilibrium with photons. Temperature and mean energy of photons decrease as Universe expands. Forward reaction ceases. Baryon density becomes low and thus backward reaction rare. Need a mechanism to explain the observed matter-antimatter asymmetry. ' back |
Mass-energy equivalence - Wikipedia, Mass-energy equivalence - Wikipedia, the free encyclopedia, In physics, mass–energy equivalence is the concept that any mass has an associated energy and vice versa. In special relativity this relationship is expressed using the mass–energy equivalence formula E = mc2 where E is the energy of a physical system m is the mass of the system, and c = the speed of light in a vacuum . . . ' back |
Naureen S. Malik, Satellites Put the Worlds Biggest Methane Emitters on the Map, ' GHGSat Inc. released a new methane map on Wednesday that uses data from the company’s two satellites, which were launched earlier this year and can detect methane emitted by oil and gas wells, coal mines, power plants, farms and factories. It’s part of a wave of climate surveillance that will make it possible to hold countries and companies accountable for meeting targets to reduce and eventually eliminate planet-warming pollution. back |
Peter Lynd, What is ultimately possible in physics depends on foundations and philosophy, Essay Abstract
'I argue that what is ultimately possible in physics will ultimately depend on the willingness and ability of individual physicists to seriously concern themselves with the question of whether a theory's physical foundations and assumptions actually correspond to Nature or not. Several examples in modern physics related to the topics of time and space-time are discussed where I feel this issue to be especially pertinent, including the existence of spacetime, the theory of cosmic inflation, the standard interpretation of the 'block' view of time provided by relativity, the theory that time and space are quantized, and thermodynamic time reversal. I conclude with some comments about Albert Einstein, a physicist I believe physics can today still learn much from, not just for his theories and ideas, but also from his approach to physics.' back |
Potential energy - Wikipedia, Potential energy - Wikipedia, the free encyclopedia, 'In physics, potential energy is the energy of an object or a system due to the position of the body or the arrangement of the particles of the system. The SI unit for measuring work and energy is the joule (symbol J).
The term potential energy was coined by the 19th century Scottish engineer and physicist William Rankine although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with a set of forces that act on a body in a way that depends only on the body's position in space.' back |
Pretty Good Privacy - Wikipedia, Pretty Good Privacy - Wikipedia, the free encyclopdia, 'Pretty Good Privacy (PGP) is a data encryption and decryption computer program that provides cryptographic privacy and authentication for data communication. PGP is often used for signing, encrypting, and decrypting texts, e-mails, files, directories, and whole disk partitions and to increase the security of e-mail communications. It was created by Phil Zimmermann in 1991.
PGP and similar software follow the OpenPGP standard (RFC 4880) for encrypting and decrypting data.' back |
Quantum computing - Wikipedia, Quantum computing - Wikipedia, the free encyclopedia, 'Quantum computing studies theoretical computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data.' back |
Robert D Klauber, Mechanism for Vanishing Zero-Point Energy, 'IIn addition to the two standard solutions of the quantum field equations having the form e^{+/-(iwt-ikx)}, there exist two additional solutions of the form e^{+/-(iwt+ikx). By incorporating these latter solutions, deemed "supplemental solutions", into the development of quantum field theory, one finds a simple and natural cancellation of terms that results in an energy VEV, and a cosmological constant, of zero. This fundamental, and previously unrecognized, inherent symmetry in quantum field theory shows promise for providing a resolution of the large vacuum energy problem, simply and directly, with little modification or extension to the extant mathematics of the theory. In certain scenarios, slight asymmetries could give rise to dark energy.'
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Robert D. Klauber, Student Friendly Quantum Field Theory, 'Book/Website Aim
This book and this website aim to make learning, and teaching, quantum field theory (QFT) easier, and thus, more efficient and fulfilling.
Both the book and the website are products of extensive student input, incorporate innovative teaching methodologies, and avoid conciseness in favor of elaborate explanations. Every step-by-small-step is included in derivations, and big picture, conceptual overviews (called “wholeness charts”) are provided at every level.' back |
Robert Mickens, Letter from Rome: "Healthy Decentralization" Gone Awry, 'Whether the Roman Church can and should allow remarried Catholic divorcees (and others in “irregular” unions) to return to full sacramental life has been a hotly debated question these past few weeks, just as it was at last year’s extraordinary Synod assembly and during the twelve months in between.
Obviously, this is not the only issue the bishops were asked to address concerning marriage and family life (as it’s been said before, “there’s far too much meat on the fire”), but it has remained one of the most critical. And judging by the reports the thirteen discussion groups each issued this past Tuesday evening, the Synod Fathers are not of one mind on how to proceed on this question.'
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Rubik's Brand Ltd., The Home of Rubik's Cube, back |
Serge Schmemann, The Foreign Policy that Wasn't, ' But without Mr. Trump’s crude insults, erratic shifts and self-serving views, the United States will have a chance to reclaim at least some of its moral authority, and his coterie of wannabe dictators will feel less comfortable. Mr. Biden has already pledged to rejoin the Paris climate accord, and he is likely to re-enter other international forums and to take steps to repair relations with miffed allies.
If Mr. Trump is re-elected, he will conclude that he has a mandate to continue in his dysfunctional statesmanship, and the world will have no choice but to conclude that the past four years were not an aberration, but the United States they now have to deal with.' 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 |
Victor J Stenger, A Case Against the Fine-Tuning of the Cosmos, ' we need not invoke multiple universes to provide
plausible natural explanations for the anthropic coincidences. Published studies
show that some form of life should be possible over a
wide range of parameters.
However, a claim has been made that five parameters in physics and cosmology
are so exquisitely fine
-
tuned that even the tiniest change in any one of these
would have made any conceivable kind of life impossible. Here it is shown
that
these five parameters have exactly the values they should have or are within a
wide range allowed by known physics.' back |
William Chen, Lecture Notes: Linear Algebra, 'This set of notes has been compiled over a period of more than 30 years. Some chapters were used in various forms and on many occasions between 1981 and 1990 by the author at Imperial College, University of London. The remaining chapters were written in Sydney.
The material has been organized in such a way to create a single volume suitable to take the reader to a reasonable level of linear algebra. Chapters 1 - 4 cover very basic material. The concept of vector spaces is then introduced in Chapters 5 - 7. More advanced topics, including the concept of linear transformations from one vector space to another and the concept of inner products, are covered in Chapters 8 - 12.' back |
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