Notes
Sunday 22 March 2020 - Saturday 28 March 2020
[Notebook: DB 84 Pam's Book]
[page 229]
Sunday 22 March 2020
In general people seem to have a greater propensity to believe in invisible things like God and the Demiurge than to believe in the physical realities that they can sense by sight and touch. This, if true, is probably an evolved tendency which underlines the power of imagination to create the rather invisible bonds necessary for social binding which is a very powerful source of evolutionary success, more powerful, in many instances, than death.
The meaning of life is built up from the meaningless initial singularity / absolutely simple God. Lust for life = lust for meaning.
We begin by emphasizing the nature of meaning which relates to relationship and communication, real, not an accident, and emphasize the meaninglessness of god/initial singularity which is not even a point. It has no magntude, for sure, but no position and then we go on to explain why this lonely not-being is filled with lust and begins to build a universe inside itself just as a baby builds a culture within itself.
Fame is a relationship to other people
Begin at the beginning: "In the beginning . . . "
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Three beginnings: Aristotle; Aquinas; Newton, Einstein and Hawking and Ellis: all tell us God was alone, the unmoved mover, dispassionate, logical, formal, platonic, mathematical, not inherently dynamic [??].
1600 Orlando: Do not grow old. Elizabeth I R 17/11/1558 - 24/3/1603. Virginia Woolf 11/October/1928. Virginia Woolf: Orlando: A Biography, Orlando (film) - Wikipedia
Monday 23 March 2020
Lust-4-Life Preface, running through the history of formalism and dynamics to the point where Newton gave a dynamic meaning to formalism, particularly through the second law and the notion of force. The next step forward was to interpret force as the gradient of a potential, so that gravitational potential causes things to move unless they are prevented by an equal and opposite force. Then we turn to Einstein and the notion of geometrodynamics and the potential that accelerates inertial frames toward one another. Then we turn to the initial singularity and summarize the three Gods, Aristotle, Thomas and Einstein. This is as far as the classics can take us.
Lust-4-life Introduction. Classical physics tells us what the world looks like. Now we turn to logical, causality and quantum mechanics to see behind the scenes how it actually works., the difference between the formal representation in [say] a movie and the real dynamic representation in reality. An outline.
Then we go into the details, not necessarily in this order:
Chapter 1: Continuity tells us nothing: all messages are quantized: why quantized [because every event is a copy of the initial singularity, implicit in fixed point theory?].
[page 231]
2. Logic, communication and computation
3. The transfinite network : Trinity to transfinity
4. Fixed point theory: extracting meaning from nothing [network implementation of mathematical theory]
5. Statistical mechanics: where does potential come from [count and entropy]?
6. Energy, waves and modulation - superposition and heterodyning [implemented by addition].
7. Communication, combination and binding [from point particles to spatial / geometrical structures].
8. What set the big bang off [entropic potential]?
9. The divine properties of the universe: infinity, omniscience, omnipotence.
Stone page 265: Vincent: 'When I see a blank canvas staring at me with a certain imbecility, I just dash something down. Irving Stone: Lust for Life: The Classic biographical Novel of Vincent van Gogh
Then repeat the preface and introduction in detail so:
Chapter 1: Relativity special and general
Chapter 2: Black holes and initial singularity - light snd geodesics
3. Matter and Radiation
4. Planck and quantization
5. Initial singularity and quantum of action . . .
Tuesday 24March 2020
There is very little difference between writing, sculpting in a plastic medium and evolution. All are a matter of trial and judgement, are we getting closer or further from some desirable / functional / survivable product.
What is the problem I am trying to solve with all this theology talk? The relative absence of a human physically and psychologically sustainable world view which will contribute to health, wealth and peace, particularly peace of mind and coherent global culture.
[page 231]
I am trying to write lust-4-life, actionrules and creationsaves without particular reference to the Catholic Church but just to theology religion, culture and science in general. I have done enough whinging about the Catholic Church and have summarized it all on the home page of scientific-the0logy and that will do for the time being. I started at the beginning of 2018 to package scientific-theology as a book but became involved in so many other things that I let it slide. This may be another reason for abandoning university this year to get more private jobs done, to get over the coronavirus and to get my cash balance up so I have an egg to hatch in my nest.
Wednesday 25 March 2020
Newton had to accept (postulate) action at a distance to represent a mechanism for the behaviour of gravitation. Faraday postulated electric field as the agent for electrical interactions, but this was not really much of a change, since the action was still at a distance, although can use iron filings to demonstrate the existence of magnetic field in a convincing visual way. Since then the notion of field has become ubiquitous in physics and authors such as Auyang seems to believe that the field is the reality and the particles in some way just artefacts of the field. Nevertheless it is particles that actually move through space and time and interact with one another just as hammers move through space and time and interact with nails. My logical network approach tries to iron out the wrinkles in the particle field picture by seeing particles as snippets of code, logical operators that can move through
[page 233]
spacetime and interact logically with one another in a quantized manner which is on such a small scale that us macroscopic entities cannot perceive it. The specific requirement for logical operators, ie turing machines or communication channels (ie turing machines whose output is identical to their input) is that they have orthogonal non-interfering elements as we find in linear Hilbert spaces. From this point of view superposition is a specific logical implementation of the and operator between two discrete vectors [representing periodic functions]. We can imagine action being converted to energy by repeated operation of the not operator to create wave motion out of pure continuity, and the construction of signals in quantum mechanics through the superposition of different frequencies of energy by the and operator, all this happening in the [logical] world antecedent to [geometric] space-time. We then use the network model that applies computation and communication to create the combinations and permutations of different turing machines [ie snippets of code embodied in particles] strung together to create the world as we know it, taking advantage of the uncertainty created by asynchronous machines interrupting one another [by contact]. The demands of a consistent and stable network structure give rise to 4D space-time, and somehow we introduce photons, electrons . . . and other particles to create the world as we know it. Action at a distance - Wikipedia, Michael Faraday - Wikipedia, Magnetic field - Wikipedia, Sunny Y. Auyang; How is Quantum Field Theory Possible?.
Thursday 26 March 2020
The notion that particles of zero size are snippets of code existing prior to the emergence of space is slowly getting a stronger grip on me. The idea may be that the logical processes (and quantum mechanics) require only time, that is [ordered] sequence to exist independently and only begin to interact when they collide with one another [contact] when space comes into being.
[page 234]
So we imagine that the personalities (and associated codes) of all the fundamental particles are encoded as frequencies, ie masses or energies as observed in spacetime and at this local level the outcomes of iterations ae bounded by energy conservation. Maybe. How do we deal with the bifurcation of energy into kinetic and potential? Potential energy seems to require the existence of space so cannot come into existence before space, ie a system with a distance metric [which allows for the existence of different particles at different places and their motion from place to place], the defining feature of [the geometric approach to] gravitation. Energy as a frequency is measured by count. In the absence of standard count, all counts of frequency are relative [as are potential energies].
If there is no space everything is in contact. When judging a proof, for example, we assume that all of it exists at a point so that inconsistencies cannot formally exist. A very long proof [in the fully formed world] may have inconsistencies if it is written out at length, so line x contradicts line y, but this cannot happen at a point [the lines would annihilate one another]. All human thought and conversation takes place, in effect, outside space so if you contradict me it stands no matter how far apart we are.
We can bring fixed points in here, assuming that the initial singularity is 'continuous', 'complete' and 'convex' and assume that each quantum of action is a mapping of the singularity onto itself and maybe uncontrolled random variations in [the frequency of?] these mappings are the mechanism for the complexification of the universe.
Friday 27 March 2020
MSO [Melbourne Symphony Orchestra] MSO Live | Beethoven's Symphony No.7
A spaced out orchestra delivering sound that can be fed through one serial line and every player's role
[page 235]
extracted with sufficiently powerful signal processing machinery. The score for this piece can be written out in a number of parallel likes to be performed simultaneously. Symphony. Frequencies fixed by the spatial shape of the resonators.
Photon/phonon are the only particles that can have an effectively infinite range of frequencies / energies, 'masses'. We have to explain how the photon works, the source of electric charge (magnetism follows given charge and the special theory of relativity).
All this brings me back to my oldest question: what hardware does the universe run on?The only answer can be itself, starting with the hardest and least complex part, the act, the act: Im anfang war die Tat. Johan Wolfgang von Goethe: Faust: Eine Tragödie
An explanation only needs to make logical sense. Why did you steal the tart? Because I was hungry. This is sufficient, although in the complex world questions of morality and justice might arise, but in the beginning, which we take to be absolutely simple, such questions do not arise. The only question that an arise is how can a simple system become complex? And the answer would seem to be by replication and variation, duplication with minimal control, the transition from continuity to discontinuity, from silence to signal. So the fundamental [evolutionary algorithm is] try everything; keep what works [in fact what works ipso facto keeps itself]; entropy feeds on entropy via Cantor's theorem. Cantor's theorem - Wikipedia
Friday 27 March 2020
One of the greatest pleasures in life is to find what you are looking for, this morning my hairbrush [and then my debit card, in my pocket!]
[page 236]
Here I am locked away from the coronavirus looking for inspiration to make my days productive. I have many pieces of the jigsaw of creation, a selection of them presented in my thesis, but I am still working around the edges, Some ideas:
1. The quantum of action is an image of the initial singularity created according to the requirements of fixed point theory. Fixed point theorem - Wikipedia
2. Energy is created by repeated quanta of action, changing some p into some not-p, a process that can be represented by wave motion. This process is interpreted as the emergence of time.
3. Although from the point of view of logic, which works outside space, not-not-p = p, the role of space is to enable to simultaneous existence of p and not-p, spatially separated rather like fermions. This suggests the 'simultaneous' emergence of space and fermionic behaviour, perhaps captured by the spin-statistics theorem. Fermion - Wikipedia, Spin-statistics theorem - Wikipedia
4. Orthogonal vectors in Hilbert Space are discrete representations of the circle group corresponding to different energies and frequencies. In the beginning there is no control on the rate of action so all frequencies and energies are possible [and presumably equally probable], so be represented by a space of countably infinite dimension. Hilbert space - Wikipedia, Circle group - Wikipedia
5. We represent the circle group by a phase function ψ(t) (the wave function) whose value is given by the complex exponential eiω(t) where ω represents the frequency in time, the parameter that distinguishes
[page 237]
vectors in Hilbert space. ψ is called the probability amplitude, and the probability P of an event is given by the absolute square of ψ, |ψ|2, a real number 0 ≤ P ≤ 1. Wave function - Wikipedia, Probability amplitude - Wikipedia
6. The mechanism of quantum mechanics works by the addition of probability amplitudes, that is the linear superposition of frequencies which act to modulate one another to give a more complex signal. Quantum superposition - Wikipedia
7. Quantum mechanics describes the probability of communication between two states through the "Born Rule" which measure the distance between states by the "inner product" (von Neumann page 34). A quantum measurement confronts an unknown state |ψ> with a "measurement operator" A with a discrete spectrum of eigenstates. The result of the measurement will be one of the eigenvalues of A wth a probability corresponding to the inner product of the the eigenvector of A with an eigenvector of the state to be measured. Measurement in quantum mechanics - Wikipedia, Eigenfunction - Wikipedia, Born rule - Wikipedia, John von Neumann: Mathematical Foundations of Quantum Mechanics, Inner product space - Wikipedia,
8. The full theory of quantum mechanics embraces measurement operators and measured systems of countably infinite dimension which correspond in communication terms to sources with countably infinite alphabets. The linearity of quantum mechanics means that the sum of the possibilities of possible outcomes to an observation is 1, the same normalization as the mathematical theory of communication assumes on a communication source. This linearity is a consequence of a source only emitting one symbol at a time. Like throws of a die, these outcomes are considered to be completely uncorrelated. Claude E Shannon: A Mathematical Theory of Communication
9. The role of knowledge: if there are many indistinguishable
[page 238]
routes to a particular event the probability of the event is computed by adding individual probability amplitudes and then squaring the result. If the routes are distinguishable, one first squares the probability amplitudes and the overall probability of the event is the sum of the resulting probabilities. The Feynman Lectures on Physics, Volume III Chapter 1: Quantum Behaviour
10. We may imagine applying the methods of quantum mechanics to a normalized distribution of energies represented by a set of vectors in Hilbert space, the vectors representing a discrete spectrum of energies εn, such that 0 < εn ≤ 1, so that no energy is zero and all the energy may be contained in one line of the spectrum as an initial [condition]. We may then explore the notion of increasing the number of lines in the spectrum, taking advantage of the fact that different frequencies / energies are initially independent states so their probabilities are not correlated. With the subsequent development of, say, atomic structure, particular eigenfrequencies may emerge. [In the light of 3 above, we can imagine that if different frequencies are to exist simultaneously, they must be spatially separated.]
11. Logical functions can be represented by quantum mechanical operators which transform wave functions and are represented by matrices. The simplest operator is simply a (complex) number [a one dimensional matrix] which modifies a one dimensional probability amplitude. Operators on two state quantum systems [like the spin of an electron] require two dimensional operators like the Pauli matrices. All Boolean operators can be represented by two dimensional matrices. More complex operators in quantum mechanics may use countably infinite dimensional operators to manipulate states which are countably infinite superpositions of single vectors representing energies or frequencies. [Given the condition 3 at the end of 10 above, we imagine that the all these states are spatially separated by their orthogonality]. Nielsen & Chuang: Quantum Computation and Quantum Information
[page 239]
12. Quantum mechanics gives us a detailed account of the small scale structure of the universe. Relativity describes the large scale structure in which quantum mechanics works. The special theory of relativity describes the boundaries of causality in the universe through the axiom that no real casual influence can travel through space-time faster than the velocity of light. Quantum mechanics describes logical processes that occur prior to space [and therefore may be considered the source of space]. We are very familiar with this situation. Although we may be separated by large physical distance [as in the case of this document] our social distances are rendered almost absent by communication. We now have to turn to explaining the origin of space and its relationship to the velocity of light. The first step in this direction is the logical role of space described in 3 above.
12a. Photons are the only particles which are both massless, have no rest state, and may have any energy, representing the whole spectrum of possible energies [4 above]. Photon energy is sensitive to gravitational potential, a consequence of the fact that gravitation arises, sees and acts upon energy alone, without being in any way influenced by the form in which the energy is embodied, ie in communication terms, energy is the source of gravitational potential, ie both transmitter and receiver. Photon - Wikipedia
13. We proceed from experience to understanding. Almost all our encounters with space on Earth involve potential, the only exceptions being which we are in free fall, which exceptions are terminated by landing under conditions of strong force. The forces we feel in our gravitation world are caused by potential differences. So the difference in potential between the top of a hill is the source of the force that accelerates a vehicle as it rolls down a hill. Where does the potential come from? The general theory of relativity tells us that the source of potential is the shape of space induced by the presence of energy. The source of energy is described in 2 above. How does this shape space?
14. The first step toward understanding shaped space, is to explore the nature of flat, shapeless space, called inertial space in which bodies feel no force due to potentials and Newton's first law of motion holds: the motion of a body does not change unless it is acted upon by a force. There are two sources of force that we frequently encounter
[page 240]
gravitational and electrical potential. Electrical potentials are enormously stronger than gravitational potential but because there are positive and negative sources of electrical potential it is usually neutralized over a short distance, whereas gravitation is always attractive so that every atom in Earth, for instance, contributes a tiny bit to the overall gravitational potential of our planet. How do these potentials (and two others that operate over imperceptibly short distances which are the sources of the strong and weak forces) arise? The generic answer is by communication. Our hypothesis is that flat space is space in which there is no communication and, paradoxically, that such space does not exist [in our physical universe]. Hawking & Ellis: The Large Scale Structure of Space-Time
15. Einstein, Podolsky and Roses realised that quantum mechanics predicted a rather remarkable phenomenon which they called 'spooky action at a distance, also known as entanglement.
Saturday 28 March 2020
My father would be 101 today.
Continuing 50 paragraphs of cosmology.
15. (cont) The authors argue that quantum mechanics does not meet the requirements of a classical physical theory:
In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false, One is thus led to conclude that the description of reality given by the wave function is not complete.
The idea is that quantum mechanics shows that if two systems than have been in contact are separated, a measurement [operation] performed on the first will affect the state of the second since the woo systems, as a result of their contact, share a joint state. This contention has been tested experimentally and found to be true. In addition the change in second system induced by the measurement of the first has been shown to propagate faster than the velocity of light. A theoretical examination of such a system by John Bell [and others] supports the contention that quantum mechanics implies non-classical correlations that are not localized, suggesting that we explore the notion that spooky action at a distance, aka entanglement is the source of gravitational potential [which is in turn the source of the large scale structure of the Universe.] Einstein, Podolsky and Rosen: Can the Quantum Mechanical Description of Physical Reality be Considered Complete?, Quantum entanglement - Wikipedia, Juan Yin et al: Bounding the speed of 'spooky action at a distance', John S. Bell: Speakable and Unspeakable in Quantum Mechanics, Faster-than-light - Wikipedia, No-communication theorem - Wikipedia
16. Although Yin, Bell and others show that entanglement produces non-classical correlations that travel faster than the velocity of light, it is generally agreed, as shown in the references to the paragraph above, that special relativity holds. Information carried by photons travels at the local velocity of light. Information carried by massive particles necessarily travels at less than the velocity of light. General relativity predicts that gravitational waves , which have now been detected, travel at the velocity of light. [The correlations arising from entanglement are nevertheless real, however, and serve as a foundation for the theory of quantum computation and communication, and since everything emerged from a single state in the initial singularity, we may be worth looking for quantum correlations in the universe which are equivalent to gravitation]. The title of the published version Yin et al's paper cited above is "Lower Bound on the Speed of Nonlocal Correlations without Locality and Measurement Choice Loopholes'. How does this relate to gravitational potential? One of the biggest problems facing modern physics is the development of a quantum theory
[242]
of gravitation to complete the Standard Model. Standard model - Wikipedia, Nielsen & Chuang: Quantum Computation and Quantum Information ref link above
17. We imagine that quantum theory and the theories of relativity are somehow embedded in the logical foundations of the universe and serve in effect as hardware, pipework or switching systems to control the flow of energy / action in the world to determine the shape of the universe and the probabilities of various events. Perhaps the most fundamental thing we seek after the implementation of the not function to bring energy out of action is the and function and the inner product to implement the Born rule. As in my thesis, I propose here to set this up as a computer network whose foundation is nand and whose structure is implemented in hardware that is in effect congealed or fixed software [which] gives us the world we observe. The next thing we want to build is inertial space, and then assemble that, as Einstein did, into gravitation.
18. We can build a computer network using the logical operators not and and to form the NAND gate, or Sheffer Stroke which is sufficient to construct the whole of Boolean algebra which is in turn sufficient to construct a computer, which is a network of logical operations [and memories]. We have already noted that the not operation can be used to create energy from action. And (boson) and nand (fermion) serve to create bosons and fermions from the superposition waves of the same frequencies. We see this for bosons in laster light and for fermions in the Pauli exclusion principle . We go on from here to create network interpretations of quantum physics and [relativity] thus unifying them. One advantage of logical approach may be that it is "flat" insofar as it is purely formal and has no potential, which appears to come with curvature. Sheffer stroke - Wikipedia
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Further readingBooks
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.'
Amazon
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Bell, 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
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Cercignani, Carlo, Ludwig Boltzmann: The Man Who Trusted Atoms, Oxford University Press, USA 2006 'Cercignani provides a stimulating biography of a great scientist. Boltzmann's greatness is difficult to state, but the fact that the author is still actively engaged in research into some of the finer, as yet unresolved issues provoked by Boltzmann's work is a measure of just how far ahead of his time Boltzmann was. It is also tragic to read of Boltzmann's persecution by his contemporaries, the energeticists, who regarded atoms as a convenient hypothesis, but not as having a definite existence. Boltzmann felt that atoms were real and this motivated much of his research. How Boltzmann would have laughed if he could have seen present-day scanning tunnelling microscopy images, which resolve the atomic structure at surfaces! If only all scientists would learn from Boltzmann's life story that it is bad for science to persecute someone whose views you do not share but cannot disprove. One surprising fact I learned from this book was how research into thermodynamics and statistical mechanics led to the beginnings of quantum theory (such as Planck's distribution law, and Einstein's theory of specific heat). Lecture notes by Boltzmann also seem to have influenced Einstein's construction of special relativity. Cercignani's familiarity with Boltzmann's work at the research level will probably set this above other biographies of Boltzmann for a very long time to come.' Dr David J Bottomley
Amazon
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Descartes, Rene, and John Cottingham (editor), Bernard Wiliams (Introduction), Descartes: Meditations on First Philosophy: With Selections from the Objections and Replies, Cambridge University Press 1996 Amazon Product Description
'This authoritative translation by John Cottingham of the Meditations is taken from the much acclaimed three-volume Cambridge edition of the Philosophical Writings of Descartes. It is based on the best available texts and presents Descartes' central metaphysical writings in clear, readable modern English.'
Amazon
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Diamond, Jared, Guns, Germs and Steel: The Fates of Human Societies, W W Norton and Co 1997 'Diamond's book is complex and a bit overwhelming. But the thesis he methodically puts forth—examining the "positive feedback loop" of farming, then domestication, then population density, then innovation, and on and on—makes sense. Written without favor, Guns, Germs, and Steel is good global history.' Amazon.com
Amazon
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Hawking, Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.'
Amazon
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Nielsen, Michael A, and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2000 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002.
Amazon
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Stone, Irving, Lust for Life: The Classic biographical Novel of Vincent van Gogh, Plume 1984 Amazon book desciption: 'LUST FOR LIFE is a fictionalized biography of the Dutch painter, Vincent Van Gogh and is based primarily on Van Gogh's three volumes of letters to his brother, Theo. Van Gogh was a violent, clumsy and passionate man who was driven to the extremity of exhaustion by his fervor to get life -- the essence of it -- into paint. Irving Stone treats the artist with great compassion and gives us a portrait that is sympathetic but fair.'
Amazon
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Streater, Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2005 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.'
Amazon
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von Neumann, John, and Robert T Beyer (translator), Mathematical Foundations of Quantum Mechanics, Princeton University Press 1983 Jacket: '. . . a revolutionary book that caused a sea change in theoretical physics. . . . JvN begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which JvN regards as the definitive form of quantum mechanics. . . . Regarded as a tour de force at the time of its publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.'
Amazon
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Woolf, Virginia, and Mark Hussey (editor) Maria de Battista (annotation), Orlando: A Biography, Harvest Books; Annotated edition 2006 Amazon editorial review:
Book Description
'Begun as a "joke," Orlando is Virginia Woolf's fantastical biography of a poet who first appears as a sixteen-year-old boy at the court of Elizabeth I, and is left at the novel's end a married woman in the year 1928. Part love letter to Vita Sackville-West, part exploration of the art of biography, Orlando is one of Woolf's most popular and entertaining works. This new annotated edition will deepen readers' understanding of Woolf's brilliant creation.'
Amazon
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Links
Action at a distance - Wikipedia, Action at a distance - Wikipedia, the free encyclopedia, ' In physics, action at a distance is the concept that an object can be moved, changed, or otherwise affected without being physically touched (as in mechanical contact) by another object. That is, it is the nonlocal interaction of objects that are separated in space.
This term was used most often in the context of early theories of gravity and electromagnetism to describe how an object responds to the influence of distant objects. For example, Coulomb's law and Newton's law of universal gravitation are such early theories.
More generally "action at a distance" describes the failure of early atomistic and mechanistic theories which sought to reduce all physical interaction to collision. The exploration and resolution of this problematic phenomenon led to significant developments in physics, from the concept of a field, to descriptions of quantum entanglement and the mediator particles of the Standard Model.' back |
Assaf Shomer, A pedagogical explanation for the non-renormalizability of gravity, ' We present a short and intuitive argument explaining why gravity is non-renormalizable. The argument is based on black-hole domination of the high energy spectrum of gravity and not on the standard perturbative irrelevance of the gravitational coupling. This is a pedagogical note, containing textbook material that is widely appreciated by experts and is by no means original. . . . The crux of the argument . . . is one line long and here it is: The very-high energy spectrum of any d-dimensional quantum field
theory is that of a d-dimensional conformal fieldtheory. This is not true for gravity. back |
Big O notation - Wikipedia, Big O notation - Wikipedia, the free encyclopdia, 'In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation (after Edmund Landau and Paul Bachmann), or asymptotic notation.' back |
Born rule - Wikipedia, Born rule - Wikipedia, the free encyclopedia, 'The Born rule (also called the Born law, Born's rule, or Born's law) is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of the Copenhagen interpretation of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results. . . . The Born rule states that if an observable corresponding to a Hermitian operator A with discrete spectrum is measured in a system with normalized wave function (see bra-ket notation), then
the measured result will be one of the eigenvalues λ of A, and
the probability of measuring a given eigenvalue λi will equal <ψ|Pi|ψ> where Pi is the projection onto the eigenspace of A corresponding to λi'. back |
Cantor's theorem - Wikipedia, Cantor's theorem - Wikipedia, the free encyclopedia, ' In elementary set theory, Cantor's theorem is a fundamental result which states that, for any set A, the set of all subsets of A (the power set of A, denoted by P(A) ) has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with n members has a total of 2n subsets, so that if card (A) = n, then card (P(A)) = 2 n , and the theorem holds because 2n > n for all non-negative integers. ' back |
Christopher Knaus, Magistrate condemns 'pernicious evil' of domestic violence while sentencing drunk wife-basher, '"That is, to classify the root cause of the defendant's aberrant behaviour towards the victim as being because of alcohol or drug misuse, or because of an issue with anger management, is simply wrong," she said.
"He may in fact have those problems, but family violence is a pernicious evil – unfortunately prevalent in our society – that stems directly from the perpetrator's attitude to women, and from his attempt and desire to exert power and control over his partner.' back |
Circle group - Wikipedia, Circle group - Wikipedia, the free encyclopedia, ' In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, i.e., the unit circle in the complex plane or simply the unit complex numbers.' back |
Claude E Shannon, A Mathematical Theory of Communication, 'The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages.' back |
Daniel Lippman, DHS wound down pandemic models before coronavirus struck, ' The Department of Homeland Security stopped updating its annual models of the havoc that pandemics would wreak on America’s critical infrastructure in 2017, according to current and former DHS officials with direct knowledge of the matter.
From at least 2005 to 2017, an office inside DHS, in tandem with analysts and supercomputers at several national laboratories, produced detailed analyses of what would happen to everything from transportation systems to hospitals if a pandemic hit the United States. back |
David Ignatius, Powell's success at the Fed is a reminder of the importance of expertise, ' Powell’s message is that the Fed’s support for U.S. business is unlimited, “in the amounts needed to support smooth market functioning,” as a Fed statement Monday put it. His basic rationale is simple: Nobody caused this crisis, and nobody is to blame. The government-ordered lockdown affects every company and worker, and the government should protect people until the crisis eases. Any other concern is secondary.
For the rest of the world, Powell offers “swap lines” to provide the dollars needed to keep trade and finance going. . . .
One measure of success for Powell will be if people decide in retrospect that his crisis moves were unnecessary. They’ll have the luxury of not understanding how much worse things could have been if the central bank hadn’t taken strong action.' back |
Eigenfunction - Wikipedia, Eigenfunction - Wikipedia, the free encyclopedia, ' In mathematics, an eigenfunction of a linear operator, A, defined on some function space is any non-zero function f in that space that returns from the operator exactly as is, except for a multiplicative scaling factor. More precisely, one has Af = λf for some scalar, λ, the corresponding eigenvalue.' back |
Einstein, Podolsky and Rosen, Can the Quantum Mechanical Description of Physical Reality be Considered Complete?, A PDF of the classic paper. 'In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false, One is thus led to conclude that the description of reality given by the wave function is not complete.' back |
Faster-than-light - Wikipedia, Faster-than-light - Wikipedia, the free encyclopedia, ' Faster-than-light (also superluminal or FTL) communications and travel are the conjectural propagation of information or matter faster than the speed of light.
The special theory of relativity implies that only particles with zero rest mass may travel at the speed of light. Tachyons, particles whose speed exceeds that of light, have been hypothesized, but their existence would violate causality, and the consensus of physicists is that they cannot exist.' back |
Fermion - Wikipedia, Fermion - Wikipedia, the free encyclopedia, 'In particle physics, fermions are particles with a half-integer spin, such as protons and electrons. They obey the Fermi-Dirac statistics and are named after Enrico Fermi. In the Standard Model there are two types of elementary fermions: quarks and leptons. . . .
In contrast to bosons, only one fermion can occupy a quantum state at a given time (they obey the Pauli Exclusion Principle). Thus, if more than one fermion occupies the same place in space, the properties of each fermion (e.g. its spin) must be different from the rest. Therefore fermions are usually related with matter while bosons are related with radiation, though the separation between the two is not clear in quantum physics. back |
Feynman, Leighton & Sands FLP III:01, Chapter 1: Quantum Behaviour, 'The gradual accumulation of information about atomic and small-scale behavior during the first quarter of the 20th century, which gave some indications about how small things do behave, produced an increasing confusion which was finally resolved in 1926 and 1927 by Schrödinger, Heisenberg, and Born. They finally obtained a consistent description of the behavior of matter on a small scale. We take up the main features of that description in this chapter.' back |
Fixed point theorem - Wikipedia, Fixed point theorem - Wikipedia, the free encyclopedia, 'In mathematics, a fixed point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. Results of this kind are amongst the most generally useful in mathematics.
The Banach fixed point theorem gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point.
By contrast, the Brouwer fixed point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point (See also Sperner's lemma).' back |
Hilbert space - Wikipedia, Hilbert space - Wikipedia, the free encyclopedia, 'The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used.' back |
Inner product space - Wikipedia, Inner product space - Wikipedia, the free encyclopedia, 'In mathematics, an inner product space is a vector space of arbitrary (possibly infinite) dimension with additional structure, which, among other things, enables generalization of concepts from two or three-dimensional Euclidean geometry. The additional structure associates to each pair of vectors in the space a number which is called the inner product (also called a scalar product) of the vectors. Inner products allow the rigorous introduction of intuitive geometrical notions such as the angle between vectors or length of vectors in spaces of all dimensions. It also allows introduction of the concept of orthogonality between vectors. Inner product spaces generalize Euclidean spaces (with the dot product as the inner product) and are studied in functional analysis.
An inner product space is sometimes also called a pre-Hilbert space, since its completion with respect to the metric induced by its inner product is a Hilbert space.' back |
Johan Wolfgang von Goethe, Faust: Eine Tragödie, 'Geschrieben steht: »Im Anfang war das Wort«
Hier stock ich schon! Wer hilft mir weiter fort?
Ich kann das Wort so hoch unmöglich schätzen,
Ich muß es anders übersetzen,
Wenn ich vom Geiste recht erleuchtet bin.
Geschrieben steht: Im Anfang war der Sinn.
Bedenke wohl die erste Zeile,
Daß deine Feder sich nicht übereile!
Ist es der Sinn, der alles wirkt und schafft?
Es sollte stehn: Im Anfang war die Kraft!
Doch, auch indem ich dieses niederschreibe,
Schon warnt mich was, daß ich dabei nicht bleibe.
Mir hilft der Geist! Auf einmal seh ich Rat
Und schreibe getrost: Im Anfang war die Tat!' back |
John, The Gospel of John, back |
Juan Yin et al, Bounding the speed of 'spooky action at a distance', ' In their well-known paper, Einstein, Podolsky, and Rosen called the nonlocal correlation in quantum entanglement a “spooky action at a distance.” If the spooky action does exist, what is its speed? All previous experiments along this direction have locality and freedom-of-choice loopholes. Here, we strictly closed the loopholes by observing a 12 h continuous violation of the Bell inequality and concluded that the lower bound speed of spooky action was 4 orders of magnitude of the speed of light if Earth’s speed in any inertial reference frame was less than 10-3 time the speed of light. ' back |
Magnetic field - Wikipedia, Magnetic field - Wikipedia, the free encyclopedia, ' A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials (such as iron) and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges (electric currents) such as those used in electromagnets.' back |
Measurement in quantum mechanics - Wikipedia, Measurement in quantum mechanics - Wikipedia, the free encyclopedia, 'The framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus.' back |
Michael Faraday - Wikipedia, Michael Faraday - Wikipedia, the free encyclopedia, ' Michael Faraday FRS (22 September 1791 – 25 August 1867) was a British scientist who contributed to the study of electromagnetism and electrochemistry. . . .
Although Faraday received little formal education, he was one of the most influential scientists in history. It was by his research on the magnetic field around a conductor carrying a direct current that Faraday established the basis for the concept of the electromagnetic field in physics.' back |
MSO Live | Beethoven's Symphony No.7, MSO Live | Beethoven's Symphony No.7, 'Thank you so much MSO for the delightful performance!
1st mvt 4:51
2nd mvt 20:13
3rd mvt 29:15
4th mvt 38:33 back |
No-communication theorem - Wikipedia, No-communication theorem - Wikipedia, the free encyclopedia, ' The basic assumption entering into the theorem is that a quantum-mechanical system is prepared in an initial state, and that this initial state is describable as a mixed or pure state in a Hilbert space H. The system then evolves over time in such a way that there are two spatially distinct parts, A and B, sent to two distinct observers, Alice and Bob, who are free to perform quantum mechanical measurements on their portion of the total system (viz, A and B). The question is: is there any action that Alice can perform on A that would be detectable by Bob making an observation of B? The theorem replies 'no'.' back |
Orlando (film) - Wikipedia, Orlando (film) - Wikipedia, the free encyclopedia, ' Orlando is a 1992 British period drama film loosely based on Virginia Woolf's 1928 novel Orlando: A Biography, starring Tilda Swinton as Orlando, Billy Zane as Marmaduke Bonthrop Shelmerdine, and Quentin Crisp as Queen Elizabeth I. It was written and directed by Sally Potter, who also co-wrote the music for the film (with David Motion).
Potter chose to film much of the Constantinople portion of the book in the isolated city of Khiva in Uzbekistan, and made use of the forest of carved columns in the city's 18th century Djuma Mosque. Critics praised the film, and particularly applauded its visual treatment of the settings of Woolf's novel.' back |
Photon - Wikipedia, Photon - Wikipedia, the free encyclopedia, 'A photon is an elementary particle, the quantum of all forms of electromagnetic radiation including light. It is the force carrier for electromagnetic force, even when static via virtual photons. The photon has zero rest mass and as a result, the interactions of this force with matter at long distance are observable at the microscopic and macroscopic levels.' back |
Probability amplitude - Wikipedia, Probability amplitude - Wikipedia, the free encyclopedia, 'In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.' back |
Quantum entanglement - Wikipedia, Quantum entanglement - Wikipedia, the free encyclopedia, 'Quantum entanglement is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole. . . . Entanglement is considered fundamental to quantum mechanics, even though it wasn't recognized in the beginning. Quantum entanglement has been demonstrated experimentally with photons, neutrinos, electrons, molecules as large as buckyballs, and even small diamonds. The utilization of entanglement in communication and computation is a very active area of research.' back |
Quantum superposition - Wikipedia, Quantum superposition - Wikipedia, the free encyclopedia, 'Quantum superposition is the application of the superposition principle to quantum mechanics. The superposition principle is the addition of the amplitudes of waves from interference. In quantum mechanics it is the sum of wavefunction amplitudes, or state vectors. It occurs when an object simultaneously "possesses" two or more possible values for an observable quantity (e.g. the position or energy of a particle)' back |
Sheffer stroke - Wikipedia, Sheffer stroke - Wikipedia, the free encyclopedia, 'In Boolean functions and propositional calculus, the Sheffer stroke, named after Henry M. Sheffer, written "|" . . . denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called nand ("not and") or the alternative denial, since it says in effect that at least one of its operands is false.' back |
Spin-statistics theorem - Wikipedia, Spin-statistics theorem - Wikipedia, the free encyclopedia, 'In quantum mechanics, the spin–statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin of a particle is its intrinsic angular momentum (that is, the contribution to the total angular momentum that is not due to the orbital motion of the particle). All particles have either integer spin or half-integer spin (in units of the reduced Planck constant ħ). The theorem states that:
The wave function of a system of identical integer-spin particles has the same value when the positions of any two particles are swapped. Particles with wave functions symmetric under exchange are called bosons.
The wave function of a system of identical half-integer spin particles changes sign when two particles are swapped. Particles with wave functions antisymmetric under exchange are called fermions.' back |
Standard model - Wikipedia, Standard model - Wikipedia, the free encyclopedia, 'The Standard Model of particle physics is a theory that describes three of the four known fundamental interactions between the elementary particles that make up all matter. It is a quantum field theory developed between 1970 and 1973 which is consistent with both quantum mechanics and special relativity. To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions. However, the Standard Model falls short of being a complete theory of fundamental interactions, primarily because of its lack of inclusion of gravity, the fourth known fundamental interaction, but also because of the large number of numerical parameters (such as masses and coupling constants) that must be put "by hand" into the theory (rather than being derived from first principles) . . . ' back |
Thomas B. Edsall, In God We Divide, back |
Tom Hawking, The Australian welfare system has always been needlessly cruel. Now it is punishing half the country, ' Over the last 30 years or so, successive governments have done their best to one-up each other in making benefits ever more difficult to access. Every passing year seems to bring a new requirement: the diaries that need to be filled out to “prove” you’re looking for work, with their implication that those claiming benefits are liars; the demerit point system, whereby applicants are punished unilaterally and without right of appeal – and, in many cases, unfairly – at the discretion of a private service provider; the “mutual obligation” system with its ever-moving goalposts, questionable courses and pointless make-work.' back |
Wave function - Wikipedia, Wave function - Wikipedia, the free encyclopedia, 'A wave function or wavefunction (also more appropriately named as statefunction) in quantum mechanics describes the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of space and time.' back |
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