Notes
Sunday 28 February 2021 - Saturday 6 March 2021
[Notebook: DB 86: Hilbert / Minkowski]
[page 91]
Sunday 28 February 2021
Reality check week. On the face of it the network model and the gauge theories of quantum field theory are compatible and I can go ahead with writing the quantum theology
[page 92]
website with some confidence. Whether I will achieve my aim of cleaning up physics while interfacing it with theology remains an open question, but well worth pursuing. In my poetic heart I feel the possibility of success. The source of this feeling is (for me) the network structure of my central nervous system which I see as analogous to the network structure of the universe which has created the universe we now inhabit from the initial singularity so, on the notion that we are created in the image of god, this project is guaranteed success although my own work may not be the path to this success. Creative imagination, however, resides in me as it resides in the world that created me, and this is the foundation of my hope.
Bertschinger: page 1; 'Symmetry transformations are changes in the coordinates or variables that leave the action invariant [so perhaps the whole universe is just one invariant quantum of action, like the old god. How can this be?]. Edmund Bertschinger: Symmetry Transformations, the Einstein-Hilbert Action,and Gauge Invariance
'. . . continuous symmetries generate conservation laws (Noether's theorem [ nothing happens in a continuum]), dynamic symmetries arising from nature; non-dynamic symmetries arising from formulation of action. Dynamic symmetries → equations of motion; non-dynamic symmetries → mathematical identities.
page 2: general relativity coordinate invariance is a non-dynamical symmetry: 'Although the values of fields are dependent on the coordinate system chosen, the action must be a scalar and therefore invariant under coordinate transformations. This is true whether or not the action is extremized and therefore it is a non-dynamical symmetry.
[page 93]
'. . . in the field theory formulation [of GR] the contracted Bianchi identities arise from a non-dynamical symmetry while stress-energy arises from a dynamical symmetry.'
'. . . continuous symmetries (gauge invariance and diffeomorphism invariance or general covariance) . . .. '
page 7: 'A combination of pushforward and coordinate transformation is a diffeomorphism. A diffeomorphism is a one-to-one mapping between a manifold and itself.'
page 24: 'For continuous fields the configuration space is a Hilbert space, an infinite dimensional space of functions. The single parameter t is replaced by the full set of spacetime coordinates. Variation of a configuration space trajectory qi(t) → qi(t) + δqi(t) is generalized to a variation of the field at all points in spacetime , eg gμν(x) → gμν(x) + δgμν(x) .
page 15: In general relativity the metric is the fundamental field characterizing the geometric and gravitational properties of spacetime so the action must be a function of gμν(x). The standard action for the metric is the Hilbert action:
G[gμν(x)] = ∫ 1 /16π G gμν Rμν√-1 d4x
Polonyi General relativity: Janos Polonyi: Introduction to General Relativity
Polonyi page 6: 'The equivalence of inertial and gravitational mass
[page 94]
means x) that the only characteristic quality of a point particle, its mass, drops out from the gravitational dynamics. But what determines the particle trajectory if not its mass? It has been suspected ever since the construction of the Riemann geometry that the gravitational force ought to be related to the curvature because it determines the geometry.'
Polonyi page 8: 'It was Einstein's radically new point of view that the trajectory ought to be viewed in space-time rather than in space only, where the curvature becomes independent of the initial conditions and can be assigned to the geometry alone.
Gravitational charge (mass) is always positive, to no screening. Charges are not static but accelerate and the resulting radiations are different.
Electrical interaction is vector potential Aμ(x). General relativity is characterized by invariant length gμν(x). The tensor field can be considered as the dynamical degrees of freedom responsible for the gravitational interaction in classical physics.
page 9: Vector potential describes particles of spin 1, metric tensor spin 2.
I have got to where I am by skimming along the surface because I have had such a long way to go [one bit from god ≠ world to god = world], but now I feel that I am over the treasure and it is time to dig in. I have
[page 95]
now got a hypothesis in which I have sufficient faith to make it worth some serious work. So I must invest this year in order to see how far I can take it towards the mainstream. It means I must learn and embrace the current state of physics well enough to reinterpret it in theological terms. That feels like a possibility now rather than just a dream.
In Hilbert space all vectors are normalized to 1 and they are added by superposition, whole vector to whole vector rather than head to tail as we add vectors in Cartesian space. Although vectors are all normalized, their inner products are amplitudes which are not elements of Hilbert space and probabilities of events are the absolute squares of the amplitudes arising from the inner products. I just have to keep nibbling at the edges until I get to the heart of the matter. The key, I feel, is that the Hilbert space is the domain of Minkowski space rather than the other way around so that it is not constrained by the geometry of Minkowski space but can contain logical processes that may not be realizable in Minkowski space, ie have degrees of freedom that cannot be represented completely in Minkowski space. This removes the infinities becusse all the vectors, that is all the quanta of action in Hilbert space, are normalized to one, in a sense (dating from long ago) "logically confined". ie they are logical events, not physical events. Physical events are the consequences of logical events, not vice versa, even though the construction of classical computing machines like the abacus, sheet metal logic and computer chips and other structures seem to indicate otherwise.
We might say that Hilbert space is the divine musical spiritual world underlying and driving the material world of general relativity and its contents.
[page 96]
My first need is to upgrade the product, which is really just to continue with the trajectory I have been on since I entered the Dominicans in 1963 [and became fascinated with the doctrine of the Trinity].
Monday 1 March 2021
How do we manage computation by superposition and linear transformation? Time to read Nielsen & Chuang. Nielsen & Chuang: Quantum Computation and Quantum Information
Now I have a starting point. The elements of Hilbert space are all mutually orthogonal and therefore independent even when the space is transfinite, the cardinal of the continuum. In Minkowski space the discreteness [of points] is artificial and leads to zero sized particles and other problems of infinity [like complicated definitions of subsets of the space]. Such problems need not arise if we confine the computations to Hilbert space instead of Minkowski space.
Black Book Black Book (film) - Wikipedia
Hilbert space like the universe, is constructed from quanta of action, the root of all symmetry.
' QED is formluated in terms of a 4 component spinor field ψa(x) that creates electrons and annihilates positrons and a 4-potential Aμ(x) that creates and annihilates photons.' Stetina, Ciavarella, Li & Wiebe: Simulating Effective QED on Quantum Computers
[page 97]
'The construction of lattices in QFT may be rendered nugatory by the fact that Hilbert space may be considered as a lattice of real (actual) orthogonal dynamic quanta of action. This is a sentence. What it means is open to further development.
Stetina page 7: '. . . quantum simulations necessarily require discretized wave dunctions . . .. ' Natural approaches to discretization are position and momentum [why not energy, time, action?]
Back to Polonyi:
page 12: II Gauge Theories
A. Global Symmetries
' . . ..The remarkable fact is that all four interactions are described by the same type of models, by gauge field theories. These theories express a central assumption of physics in a distinguished manner, namely that the fundamental laws are local in spacetime.' Which is to say that they involve the exchange of messages [across space, using time] to join actors at a distance.
Global symmetrie are transformations that leave the variational equations of motion unchanged, ie there is no (change of) action.
'It is advantageous to distinguish two different spaces in field theory/ A field component of an n-component real field φa(x) : E → I is a mapping of the external space into the internal space, the former denoting the space time E = R and the latter standing for the set of values of the field I = Rn.
A symmetry transformation can be external, internal or both. Internal
[page 98]
symmetry transformations act in the internal space only. Examples are charge conjugation, rotation in flavour or colour space in quarks and gluons. External symmetry transformations change the space-time coordinates only φa(x) → φa(x'), eg the Poincare group consisting of space-time translation and Lorentz transformations [but Veltmann, for instance, does a Lorentz transformation on Hilbert space, which looks like an internal transformation: "Thus corresponding to a Lorentz transformation there is a complicated big transformation in Hilbert space (page 20)]. Martinus Veltman (1994): Diagrammatica: The Path to the Feynman Rules, page
'Continuous symmetries generate currents in classical field theories which satisfy the continuity equation according to Noether's theorem. The conserved quantity, the space integral of the time component (?) of the Noether current is usually called charge in the case of an internal symmetry. The conserved quantities of external symmetry define energy-momentum (translation), angular momentum (space rotation) and a further vector (Lorentz boosts). Note that these symmetry transformations are global, meaning that they are charcterized by the same parameters everywhere in spacetime.
Global symmetries conflict with relativity because signals cannot travel faster than c.
Quantized action is a dimensionless scalar, a simple count like entropy. Classical physics gives action the dimension of angular momentum m.v.r = ML2T-1. The time integral of action in this system is energy, ML2T-2. If action is a dimensionless scalar, ML2T-1 = 1, so energy has the dimension T-1, ie E = ℏω, ω = T-1.
Global symmetries and action exist prior to space-time so they are not constrained by special relativity by create it by symmetry breaking (application)
[page 99]
(realization). Special relativity, embodied in the Lorentz algorithm, is in itself a global symmetry like the algorithms of arithmetic because it deals, like arithmetic, with scalar items, beans, dollars, quanta of action, rods and clocks considered as actions not yet differentiated into space and time. When this differention arises, the transformation parameter c arises to preserve their primordial identity. What primordial identity does ℏ preserve?
page 13: Polonyi: B. Local Symmetries
' The symmetry transformations that appear to be in harmony with special relativity should concern change of basis in locations equipped with the possibility of exchange of physical signals.'
page 14: '. . . covariant or 'absolute' equations are valid in any convention, in other words in any gauge. We are interested in laws of physics in as simple a form as possible. Thus we seek absolute equations. Invariant quantities are called scalars and a set of numbers or fields transforming in a homogeneous manner are called vectors or tensors. The rules for generating absolute equations consist of prescriptions of constructing scalars, vectors and tensors from scalars, vectors and tensors.'
Because of their all pervading orthogonality vectors in transfinite Hilbert spaces may easily be separated into local orthogonal subspaces like me and trees which can be studied as individuals within the overall structure [and exchange signals with the overall structure].
It is a long time since I have felt too excited to write
[page 100]
but I have been feeling a lot of little indicia that make me feel that quantum theology is a fruitful path to the union of physics and theology and may do them both good.
A vector in Hilbert space models a physical state, that it is a representation of a state which has a certain complexity or entropy which must be reflected in the entropy of the representation, which we may take to be a count of the number of dimensions which must be superposed to give a Fourier representation of the state vector we take to be the algorithm (set of actions) corresponding to the state.
In gravitation mass is both the charge and the substance affected by charge and we see it as a symmetry underlying all other charges so electrons have electric charge but also electric "mass" that controls how they respond to electric charge.
Gauge theory is a theory of communication and underlies the overall network structure of the universe, starting at very short range in the baryons and expressing itself on an "infinite" scale in photons snd gravitons.
We understand the velocity of light c to be the transformation that connects space and time back to their primordial unity somehow reflected in the Minkowski metric. Somewhere here, we feel, is the clue that explains how quantum behaviour in Hilbert space becomes the source of space-time and the gigantic universe whose creation has been in some way facilitated by the tiny but massive baryons.
[page 101]
Implicit in this notion is the idea that QCD and the baryons are in some way the precursors of spacetime in that their complex internal structure enables them to exist as self sustaining entities independently of facilities they have developed in spacetime to multiply themselves and build a universe of a huge number of atoms from an initial structureless quantum of action. Here sits the heart of the mystery of being, the true subject of theology. Although many would like to see it have a finite lifetime, it seems that the proton is the closest thing we have to the ancient idea of a necessary being. Frank Wilczek: The Lightness of Being: Mass, Ether, and the Unification of Forces
Tuesday 2 March 2021
Wednesday 3 March 2021
This baryons → space concept receives some support from the number 3 insofar as space has three dimensions and the gluons and quarks have three orthogonal dimensions of communication. As we have noted many times before, 3D is necessary if we are to connect any number of points in space without crossed wires. Our first mathematical ansatz into this idea might be the Gell-Mann matrices. Gell-Mann matrices - Wikipedia
Polonyi: page 22: III Gravity
It seems to be an essential feature of nature that all known interactions belong to the class of gauge theories For the electrodynamic, weak and strong interactions, the internal space is independent of space-time. The special feature of gravitation is that it influences the geometry of the space-time and therefore its internal space is not independent of external space.'
[page 102]
Polonyi page 23: 'The internal space, a linear space consisting of possible field values, is called tangent space in the case of gravity . . . the space of possible space-time directions at the given space-time point.
page 25:
B. Geometry - 'three important properties of the space-time geometry which appears in gravitational interactions:
1. The metric property; 2. affine property controls parallelism; 3 torsion: 'this property seems to be important in describing the interaction of quantum mechanical spin with the gravitational field only.
page 26: Gauge group
'. . . the choice of the coordinate system in the space-time is mere convention, the role of the coordinates is to identify space-time points only and the actual numerical value of the coordinates hav no physical meaning.'
'We are interested here the fundamental laws therefore we assume that the equations of motion are expressed for each spacetime location independently. This assumption leads to a rich gauge theory in an obvious manner [?] and gravity can be founded on a gauge theory with either external or internal symmetries.'
Not much help here, so we go to Charles Francis: Charles Francis: A construction of full QED using finite dimensional Hilbert space
page 3: 'In standard approaches to quantum field theory one starts with a classical field and then quantises it. Space is thus a fundamental physical
[page 103]
concept on which the theory is built. Covariance requires that space must be a continuum and hence that if a lattice is used the limit of small lattice spacing must be taken. In the present treatment quantum properties are understood to arise precisely because space does not appear as a fundamental physical concept [I like this, of course].
'The interpretation here follows Dirac and Von Neumann, but goes further than either. . . . It is found that this formulation of quantum mechanics allows a complete construction of qed in which Maxwell's equations and the Lorentz force law are derived in the classical correspondence.
Francis page 6: Space-time coordinate lattice.
page 8: Quantum logic: Birkoff and Von Neumann. Quantum logic - Wikipedia, Garrett Birkoff & John Von Neumann: The Logic of Quantum Mechanics
'Kets are interpreted as formal conditional clauses. The dual space [bras] consists of corresponding consequent causes. The inner product combines clauses to generate formal propositions in the subjunctive mood, showing that the language is a consistent and intuitive extension of two-valued logic and classical probability theory. The principle of superposition is simply logical disjunction in formal language. There is no suggestion of an ontological magnitude |<x|<f>| associated with a particular particle.' [tbc, 7 March]
Thursday 4 March 2021
It is only now, rather late in my life, that I fully realize the weirdness of the religious regime of my youth as I try to develop a realistic alternative. What I see looking back
[page 104]
are the political consequences of our evolutionary origin where the practical survival of the fit has evolved into a military thing where religions have fundamentally served as justifications for killing the competition so as to generate more for us in the zero sum struggle for existence. In this context we have glorified military struggle and placed great emphasis on being prepared to die for our fatherlands, a theme which is deeply interwoven into the Jewish-Christian story built around the crucifixion of Jesus as in some way winning salvation for the universe and its people by placating the invisible divine creator of it all. Nowhere is this weirdness more manifest than in those parts of fundamentalist America where people are prepared to reject palpable facts in order to endow their saviour, Donald Trump with some sort of supreme power. In may ways he is akin to the pope, god's vicar on earth, although through its long political and military history the papacy, like British royalty, has had some of its sharper ideological edges rounded off so that dreams of imperial world domination are tempered by the growing scientific and democratic realization that power comes from below rather than above and that we owe our existence to the creative nature of the universe which depends more on communication and cooperation than murder and conquest, although we cannot deny that the creative process involves much cosmic violence. We are living in a period of precarious balance between political arbitrary power and science based rational management epitomized by the covid plague and the spectrum of responses it has elicited
[page 105]
from different segments of the community. Sarah Repucci & Amy Slipowitz: Freedom House: Democracy under Siege
The childlike desires of our hearts seek instant satisfaction and the developmental phase we call the terrible twos is the point in our lives where we have to learn to wait. The old god created the world in six days; the new god has taken 14 billion years and counting. Newton initiated scientific cosmology with instantaneous action at a distance. Einstein showed that we have to wait. Nothing can be done faster than the velocity of light. Newton invented calculus for his work and mathematics became a study fo differentiable functions. Einstein worked in this tradition to give us the general theory of relativity, but smoothness did not conquer all. Planck found that we must see the world as quantized, acting in discontinuous steps if we are to overcome the ultraviolet catastophe in the interface between matter and communication reprsented by black body radiation. Planck expressed his idea mathematically with the hypothesis that radiation came in packets of energy represented by the equation E = hf, where h is a new constant of nature repressing the proportionality between energy and frequency, that is inverse time. Five years later Einstein took this further and invented what we now call photons, particle of light which give concrete reality to Planck's mathematical model. Since that time physics has been embroiled in the old debate that began among the scientifically inclined philosophers of Ancient Greece: is the universe continuous or discrete? The modern solution is that it is made of waves, continuous processes which embody discrete ups and down, so the most common version of fundamental physics is wave mechanics.
[page 106]
The birth of quantum mechanics reflected this ancient debate, coming in two forms, matrix mechanics which tends towards the discrete and wave mechanics that emphasizes continuity. They were found to both give the same answers which results from the fact that when you confine waves in some way they form 'standing waves' which have a fixed quantized frequency like the waves of air confined in a flute or organ pipe and the waves in the strings we find in pianos and guitars. So far so good. By the thirties we had two major theoretical foundations for our understanding of the physical world and it seemed obvious that in reality they were mutually consistent. In theory, however, things were not so good. Starting in the 30s and continuing to the present the attempt to unite relativity and quantum mechanics known as quantum field theory has thrown up very reassuring successes at modelling the world surrounded by a cloud of what we might call philosophical difficulties. We have identified four communication channels in nature, known as the four forces or interactions, gravitation, electromagnetism, the weak force and the strong force. The first two have potentially infinite range and account for most of the visible structure of the universe, The second pair are confined to nuclear interactions whose range is approximately the size of a proton whose diameter is about 10-15 metres, one million billionth of a metre. It is generally conceded that all four forces are described by gauge theories, that is communication theories, and that all the fundamental particles in the universe fall into two classes, bosons which are messenger particles and fermions which are structural particles. Atoms and molecules, for instance are made of electrons and nucleons which are fermions, bound
[page 107]
by photons which are bosons. Inside the nucleons we find quarks, which are fermions and gluons, which are bosons. This theory provides us with a sound foundation for engineering, chemistry biology and most technologies [including nuclear weapons] but problems remain. Gravitation does not fit into the quantum mechanical scheme of things, although it is a gauge theory, and it is agreed that the standard model that describes the other three forces may be an interim version of something deeper. We do not know a lot about how things got this way and so we do not really know why they are this way. The general theory of relativity tells us that it all began as a structureless initial singularity and we must presume that some evolutionary process brought the system from that point to its current condition., but how did that work? Current cosmology sees it all starting with a 'big bang', which was not an explosion of some powerful explosive expanding into an existing space, but the rapid creation of space-time itself and all its fundamental contents within the initial singularity.
Here we try to conceptualize this event in a metaphysical and theological context and take it back to the history of ancient ideas recorded in the 5000 or so years of extant literature. First we face the fact that we have no idea how the initial singularity, like the ancient gods, came to be, so we assume as Aristotle and many of the ancients assumed, that they are eternal and still with us in the heart of the evolving world.
An ancient beginning to the notion that a god could multiply itself and become more complex is the Christian doctrine of the Trinity. A modern analogue of this process may be found in the quantum
[page 108]
harmonic oscillator, an explanation of the processing of the world in terms of the creation and annihilation of fundamental particles. One may see this as a reconciliation of eternity and change. Particles are eternal as long as they last [but in a way many have half lives, so their clocks are ticking]; change comes when one particle is annihilated and replaces by another. From this point of view change is a stepwise rather than a continuous process and we see it at all scales: people are born and die; governments come and go. Molecules are created and destroyed.
Aristotle was among the first to put this idea on a firm footing with his theory of matter and form hylomorphism. Plato proposed a heaven of eternal forms as the source of patterns and structures in the world. Aristotle brought these forms down to earth, proposing that change occurred when a material substrate like bronze took on different forms like a sword or a ploughshare. He imagined a hierarchy of forms, so bronze itself comprises some combination of the elements fire, air, water and earth. Philosophers taking this idea to the extreme, proposed the existence of prime matter which is not something, not a quality, not a quantity, nor any of the things which make a being determinate. In modern physics energy often serves as an analogue of prime matter and the big bang theory assumes that the initial singularity comprised all the energy of the universe which has fashioned itself into the world we see. The equation derived from the special theory of relativity, E = mc2 suggests that we can make anything out of energy, or almost anything. Hylomorphism - Wikipedia
E = mc2 is a consequence of the metric structure of Minkowski space which tells us in effect that time is the inverse of space, making
[page 109]
possible the existence of null geodesics. From the point of view of any observer in inertial space an entity going past at the velocity of light would appear to be of zero length and any clocks on it would appear to be stopped. Photons travel at the velocity of light, but we cannot observe them without annihilating them. Massive particles in cosmic rays and high energy accelerators travel at very close to the velocity of light and exhibit the predicted time dilation and foreshortening, so we might surmise that photons exist in a regime that predates space and time. This is not surprising since the initial singularity itself id imagined to be without any space-time structure. Minkowski space - Wikipedia, Geodesics in general relativity - Wikipedia
Here we find ourselves back with Aristotle who, via the medieval theologian Thomas Aquinas, provided us with a model of god which is still current in Christian theology. Thomas Aquinas, Summa, I, 2, 3: Does God exist?
Friday 5 March 2021
Aristotle developed his hylomorphism into a more abstract theory of potential and action and defined motion or change as the change from potential to actual. He also assumed, as an axiom, that no potential can actualize itself and used this idea to propose the existence of an unmoved mover of pure actuality which is the cause of all motion in the world. Thomas Aquinas took Aristotle's argument as a proof for the existence of god and, following Aristotle, defined god as pure actuality, the realization of all potential. Unmoved mover - Wikipedia
[page 110]
As science evolves old terms take on new meanings. One of the most important ideas to emerge over the last few centuries is the conservation of energy. This principle became possible when it was realized that energy comes in two forms, potential and kinetic. Potential is stored energy [static]; kinetic is the energy of motion [dynamic]. In modern physics, unlike Aristotle's view, potential and kinetic energy are completely interchangeable, and it may be that, taken across the universe, their sum is zero, meaning that the initial singularity, outside space and time, may be pure action, carrying zero energy, and that the first step in the emergence of the universe from the initial singularity may be the origin of time and the differentiation of action into [timeless] potential and [timeful] kinetic energy, laying a foundation for the creation of the harmonic oscillator and the creation and annihilation of particles, bosons being messenger particles and fermions being stable structures storing potential energy. Zero-energy universe - Wikipedia
Is this fantasy true? We can only find out by developing and testing it. Act (actus, energeia, entelecheia) has been a central concept in philosophy, theology [and physics] since Aristotle's time. The quantum of action is central to quantum mechanics. The dream here is to renew the connection between physics and theology through the medium of quantum theory, which is as mysterious as it is marvellous. Can our imagination match the imagination of the divine universe that creates us?
[page 111]
The story without which there is nothing. The story that sustains the universe. The Imaginarium of Doctor Parnassus - Wikipedia
Saturday 6 March 2020
Now back to Charles Francis [from page 102-3]
Francis page 3: This paper reviews the Fock space formulation of quantum electrodynamics in the context of an axiomatic formulation of quantum theory using a finite Hilbert space based on the principle described by, eg Rovelli, that all measured quantities are relational, not just velocity as in relativity. Fock space - Wikipedia
Sidetracked to Rovelli Carlo Rovelli: Relational Quantum Mechanics
Rovelli page 1: 'This paper is based on a critique of a notion generally assumed uncritically. . . . The notion rejected here is the notion of absolute or observer independent state of a system; equivalently the notion of observer-independent values of physical quantities.
' This conclusion derives from the observation that the experimental evidence at the basis of quantum mechanics forces us to accept that distinct observers get different descriptions of the same events.'
My point of view in this regard is that quantum mechanics synthesizes most of what we have learned about the physical world: the issue is not to replace or fix it but to understand what precisely it says about the world; '
[page 112]
Rovelli page 2: ' . . . quantum mechanics will cease to look puzzling only when we are able to derive the formalism of the theory from a set of simple physical assertions.'
What was Einstein's contribution to spacial relativity: 'It was to understand the physical meaning of the Lorntz transformations.' ie 'simultaneity as observer independent is physically untenable.'
' The aim of this paper is to hunt for [the incorrect notion leading to a forest of paradoxical interpretations of quantum mechanics] with the hope that by exposing it to public contempt we could free ourselves from unease with our best present theory of motion and fully understand what the theory does assent about the world.'
So: find the set of physical facts [as Einstein did with SR] from which the quantum mechanics formalism can be derived.
Information is prominent among the concepts which make sense of the quantum mechanical description of the world.
page 3: 'Quantum mechanics is a theory about information', ie information observed when the universe observes itself. Wojciech Hubert Zurek: Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
page 4: 'Main observation: In quantum mechanics different observers may give different accounts of the same sequence of events.'
Contra Wigner: ' Hypothesis 1: All systems are equivalent. Nothing
[page 113]
distinguishes a priori macroscopic systems from quantum systems.'
Rovelli page 6: Main Discussion.
'In quantum mechanics all physical variables are relational, as is velocity.
page 7: 'As is well known, there are no indications on physical grounds that quantum mechanics in incomplete.
' Hypothesis 2 (Completeness) Quantum mechanics provides a complete and self-consistent scheme of description of all of the physical world, appropriate to our present level of experimental observations.'
'Quantum mechanics is a theory about the physical description of physical systems relative to other systems, and this is a complete description of the world.' Ie it is the complete hardware foundation for the universal network.
If this is true, the source of our unease is uncovered: 'it is the notion of true, universal, observer independent description of the state of the world.'
page 8: 'It is possible to compare different views, but the process of comparison is always a physical interaction, and all physical interactions are quantum mechanical in nature.' ie all knowledge is quantum-mechanical.
'There is no half-a-measurement; there is a probability one-half that the measurement has been made.'
[page 114]
Rovelli page 9: E. Information
page 10: 'in the technical sense of information theory, the amount of information is the number of the elements of a set of alternatives out of which the configuration is chosen. . . . any physical system may contain information about another physical system.'
[Wheeler 988, 1989, 1992] John Archibald Wheeler: Information, Physics, Quantum: The Search for Links
' "we have information that spin is up" leaves the possibility that somebody other has different information.'
III: On the Reconstruction of Quantum Mechanics.
Basic concepts
'Information is a discrete quantity, minimum unit 1 bit', discriminating between p and not-p
page 11: Answers to Qi give binary string ei, the initial section of which already constrains subsequent sections.
A question is a version of measurement: yes/no measurement is represented by projection operator. Projection (linear algebra) - Wikipedia
'In place of the notion of state, which refers solely to the system, the notion of the information that a system has about another system has been introduced.'
[page 115]
B. The two main postulates
'Postulate 1 (Limited information). There is a maximum amount of relevant information that can be extracted from a system' ie N bits of information is all we can say about S.
So at most one bit in initial singularity [does it exist? yes].
Rovelli page 12: 'Postulate 2 (Unlimited information) It is always possible to acquire new information about a system . . . so what we know cannot be fully deterministic.'
'Rather surprisingly, these two potulates are (almost) sufficient to reconstruct the full formalism of quantum mechanics.
C. Reconstruction of the formalism and the third postulate.
'. . . the reconstruction attempt is not fully successful. I will be forced to introduce a third postulate.'
Orthogonality Q1 → ¬ Q1, then Q1, Q2 orthogonal.
Every pair of questions Qi, Qj + logical operators give 'orthomodular lattice".
page 13: Unitary operators are reversible and entropy preserving.
page 14: Postulate 3 (Superposition principle) If c and b define two
[page 116]
complete families of questions, then the unitary matrix Ucb in p(Q(i)c, Q(j)b) = |Uijcb|2 [eq (18)]
can be chosen in such a way that for every c, b and d, we have Ucd = UcbUbd and the effect
of composite questions is given by [eq.(17)]:
pi(jk)i = |U ijU ji + U ikU ki |2.
Rovelli page 14: D. The observer observed
'two observers can compare their information (their measured outcomes) only by physically interacting with eachother.'
page 15: 'there is no way two observers, P and O can get information about a system S independently of eachother: one of the two (say O) will have to obtain the information first. In doing so he will interct with S at a certain time t. The interaction means that there is a non-vanishing interaction Hamiltonian between S and O. If P asks a question to O at a later time t' she will either have to consider the interacting correlated S - O system or realize that the unitary evolution of the O dynamics has broken down, due to the physical interaction, she was not taken into account.'
IV Critique of the Concept of State
'If different observers give different descriptions of the state of the same system, this means that the notion of state is observer dependent.' After an observation has been made' (Einstein did not like this). The unitary evolution of an unobserved system described by the Schrödinger equation still seems good. The critical point in all this seems to be the moment when the observing particle meets the observed particle and they make a mutual accommodation over some coincident eigenvalue.
[page 117]
Rovelli page 14: 'A physical system is characterized by the structure of the set W(S) of questions that can be asked about the system. This set has the structure of a non-Boolean algebra of a family of linear subspaces of a complex k dimensional Hilbert space. The Information about S that one observer O can possess can be represented by a string S containing an amount of information N [the length of the binary string S].
' There is no way to "exit" from the observer-observed global system" "Any observation requires an observer".' The universe observes itself [and that's how it creates itself, as the ancient theologians realised]. Aquinas, Summa, I, 27, 1: Is there procession in God?
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Further readingBooks
Abelard, Peter, and Translated with an introduction by Betty Radice, Letters of Abelard and Heloise, Penguin (USA) 1998 Jacket: The grim tale of Abelard and Heloise has echoed down from the twelfth century as one of the world's great love stories. These staunch Christians, as their letters reveal, found a path through self-pity into acceptance of a changed but lasting relationship. Whilst Heloise attained fame for her learning and administrative genius as an abbess, Abelard became an inspired teacher in Paris and the foremost logician of his day. This new translation includes Abelard's account of his misfortunes (Historia Calamitatum); four of their personal letters; the 'letters of direction', in which he advises her how to adapt for women the rule of Benedict; correspondence between Heloise and Peter the Venerable; and two of Abelard's hymns.'
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Archer, Jeffrey, The Fourth Estate, Harpercollins Uk 1996 Amazon customer review: 'We hear much of how the media of the world is controlled by the hands of a few men. THis fictionalized account of Rupert Murdoch and Robert Maxwells fight over the worlds media empires will help all those interested in how the media operates in the world today(or more precisely in the 1990s). This book is also a superb read, it combines the flair of real life with the fictionlized account of the private affairs of two great men, both of whom a flawed. A great character study. By far it is Archers best work.' Seth J Frantzman
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Canon Law Society of America, Holy See, Code of Canon Law: Latin-English Edition, Canon Law Society of America 1984 Pope John Paul XXXIII announced his decision to reform the existing corpus of canonical legislation on 25 January 1959. Pope John Paul II ordered the promulgation of the revised Code of Canon law on the same day in 1983. The latin text is definitive. This English translation has been approved by the Canonical Affairs Committee of the [US] National Conference of Catholic Bishops in October 1983.
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Escher, Maurits Cornelius, and John E. Brigham (translator), The Graphic Work: Introduced and explained by the artist, Taco 1989 Introduction: '. . . then there came a moment when it seemed as though scales fell from my eyes. I discovered that technical mastery was no longer my sole aim, for I became gripped by another desire . . . Ideas came into my mind quite unrelated to graphic art, notions which so fascinated me that I longed to communicate them to other people. . . . The ideas that are basic to [my prints] often bear witness to my amazement and wonder at the laws of nature which operate in the world around us. . . . and here is yet another reason for my astonishment - no matter how objective or how impersonal the majority of my subjects appear to me, so far as I have been able to discover, few, if any, of my fellow-men seem to react in the same way to all that they see around them.' pp 5-6
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Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. . . . In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands
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Fleming, Ian, For Your Eyes Only, Thomas & Mercer 2012 'A departure from the full-length James Bond novels, For Your Eyes Only is a stunning collection of five stories that sends 007 to Bermuda, Berlin, and beyond, and places him in the dangerous company of adversaries of all varieties.'
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Griffel, D H, Applied Functional Analysis, Dover Publications 2002 Amazon customer review: '... The main strength of Griffel's book is its readability. It is one of the most accessible advanced math books I have encountered, comparable to Munkres' "Topology". Griffel explains the intuitions underlying the abstract concepts he presents. He is also careful to point out when he makes a simplification or omission to avoid a difficult or subtle point more suitable to a pure math treatment of the subject. Furthermore, Griffel explains the logic behind his notation, something that is rarely done in math texts. Each chapter concludes with a set of problems. The problems are challenging, but test and expand the reader's understanding of the material. Hints are given for many of the problems.
Overall, this is an excellent resource for the applied mathematician, engineer, or scientist who wants an accessible introduction to functional analysis. Besides, the price of the Dover Edition makes this book a real bargain. Reviewer:"elddm" (Boston, Ma United States)
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Lonergan, Bernard J F, Insight: A Study of Human Understanding, Harper and Row 1978
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Lonergan, Bernard J F, Insight: A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '. . . Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding'
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Merton, Robert C, Continuous Time Finance, Wiley-Blackwell 1992 Amazon Product Description
'Robert C. Merton's widely used text provides an overview and synthesis of finance theory from the perspective of continuous-time analysis. It covers individual financial choice, corporate finance, financial intermediation, capital markets, and selected topics on the interface between private and public finance. For this revised edition a new section on managing university endowments has been added. The book begins with a foreword by Paul Samuelson.'
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Miles, Jack, God: A Biography, Vintage Books 1996 Jacket: 'Jack Miles's remarkable work examines the hero of the Old Testament . . . from his first appearance as Creator to his last as Ancient of Days. . . . We see God torn by conflicting urges. To his own sorrow, he is by turns destructive and creative, vain and modest, subtle and naive, ruthless and tender, lawful and lawless, powerful yet powerless, omniscient and blind.'
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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.
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Nin, Anais, Incest: From a Journal of Love: The Unexpurgated Diary of Anais Nin 1932-1934, Houghton Mifflin Harcourt 1992 Amazon editorial review: From Library Journal
"This second volume of the unexpurgated version of Nin's diary spans the period from October 1932 to November 1934. It draws upon previously unpublished material from the period covered by the first volume of the diary as published in 1966. Incest follows Henry & June ( LJ 10/1/86), focusing not only on Nin's continued relationship with author Henry Miller but also on her physical and emotional attachments to four other men. Nin offers intimate details of disturbing events such as her intense incestuous affair with her father and her abortion during her sixth month of pregnancy. Her diary offers direct insight into a narcissistic, passionate, analytical, and complex mind, but the brief introduction does disappointingly little to explain the editorial process that created this version of Nin's diary, which differs dramatically in style and content from its expurgated counterpart. Nevertheless, this is an important supplement to the 1966 diary and is recommended for most literature collections.'
- Ellen Finnie Duranceau, MIT Lib.
Copyright 1992 Reed Business Information, Inc.
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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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Veltman (1994), 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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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.'
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Wilczek, Frank, The Lightness of Being: Mass, Ether, and the Unification of Forces, Basic Books 2008 ' In this excursion to the outer limits of particle physics, Wilczek explores what quarks and gluons, which compose protons and neutrons, reveal about the manifestation of mass and gravity. A corecipient of the 2004 Nobel Prize in Physics, Wilczek knows what he’s writing about; the question is, will general science readers? Happily, they know what the strong interaction is (the forces that bind the nucleus), and in Wilczek, they have a jovial guide who adheres to trade publishing’s belief that a successful physics title will not include too many equations. Despite this injunction (against which he lightly protests), Wilczek delivers an approachable verbal picture of what quarks and gluons are doing inside a proton that gives rise to mass and, hence, gravity. Casting the light-speed lives of quarks against “the Grid,” Wilczek’s term for the vacuum that theoretically seethes with quantum activity, Wilczek exudes a contagious excitement for discovery. A near-obligatory acquisition for circulating physics collections.' --Gilbert Taylor
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Wilmott, Paul, Derivatives: The Theory and Practice of Financial Engineering, John Wiley & Sons 1988 Amazon Product Description
'Derivatives by Paul Wilmott provides the most comprehensive and accessible analysis of the art of science in financial modeling available. Wilmott explains and challenges many of the tried and tested models while at the same time offering the reader many new and previously unpublished ideas and techniques. Paul Wilmott has produced a compelling and essential new work in this field.
The basics of the established theories - such as stochastic calculus, Black-Scholes, binomial trees and interest-rate models - are covered in clear and precise detail, but Derivatives goes much further. Complex models - such as path dependency, non-probabilistic models, static hedging and quasi-Monte Carlo methods - are introduced and explained to a highly sophisticated level. But theory in itself is not enough, an understanding of the role the techniques play in the daily world of finance is also examined through the use of spreadsheets, examples and the inclusion of Visual Basic programs.'
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Papers
Friedman, Matt, et al, "100-Million_Year Dynasty of Giant Planktivorous Bony Fish in the Mesozoic Seas", Science, 327, 5968, 19 February 2010, page 990-993. 'Large-bodied suspension feeders (planktivores), which include the most massive animals to have ever lived, are conspicuously absent from Mesozoic marine environments. The only clear representatives of this trophic guild in the Mesozoic have been an enigmatic and apparently short-lived Jurassic group of extinct pachycormid fishes. Here, we report several new examples of these giant bony fishes from Asia, Europe, and North America. These fossils provide the first detailed anatomical information on this poorly understood clade and extend its range from the lower Middle Jurassic to the end of the Cretaceous, showing that this group persisted for more than 100 million years. Modern large-bodied, planktivorous vertebrates diversified after the extinction of pachycormids at the Cretaceous-Paleogene boundary, which is consistent with an opportunistic refilling of vacated ecospace.'. back |
Godfray, H Charles J, et al, "Food Security: The Challenge of Feeding 9 Billion People", Science, 327, 5967, 12 February 2010, page 812-818. 'Continuing population and consumption growth will mean that the global demand for food will increase for at least another 40 years. Growing competition for land, water, and energy, in addition to the overexploitation of fisheries, will affect our ability to produce food, as will the urgent requirement to reduce the impact of the food system on the environment. The effects of climate change are a further threat. But the world can produce more food and can ensure that it is used more efficiently and equitably. A multifaceted and linked global strategy is needed to ensure sustainable and equitable food security, different components of which are explored here.'. back |
Newman, Dianne K, "Feasting on Minerals", Science, 327, 5967, 12 February 2010, page 793-794. 'Far up in the Chilean Andes, in remote arid regions seemingly inhospitable to life, intrepid microorganisms thrive on a diet of rocks and air. Unfazed by long periods of desiccation or high ultraviolet energy flux, they grow in baths of sulfuric acid replete with toxic metals. The microbes fix carbon dioxide into biomass by exploiting the energy to be gained by "eating" (oxidizing) minerals that contain reduced forms of iron and sulfur, such as chalcopyrite (CuFeS2). Through their metabolism, these microbes mobilize precious metals from ore deposits into solution, making them powerful catalysts for biomining. Recent research has begun to elucidate how they achieve this remarkable feat.. back |
Normile, Dennis, "Holding Back the Torrent of Rats", Science, 327, 5967, 12 February 2010, page 806-807. 'A "rat flood." That's what the tribes in Bangladesh's Chittagong Hill Tracts call it. Every 48 years, the bamboo forests that dominate the uplands of Bangladesh, Northeast India, and Myanmar (formerly known as Burma) simultaneously produce a feast of pear-sized fruit that allows rat populations to explode. After consuming the fruit, the rodents attack nearby fields, devouring 50% to 100% of the rice crop. Rat floods caused famine in 1863, 1911, and 1959, when the misery touched off a rebellion in what is now India's Mizoram State.'. back |
Science editorial, , "What it Takes to Make that Meal", Science, 327, 5967, 12 February 2010, page 809. 'Researchers have been taking a close look at just how much energy it takes to produce even seemingly similar foods. The conclusion: Food choices can have a significant impact on energy use in agriculture.'. back |
Stokstad, Erik, "Could Less Meat Mean More Food", Science, 327, 5967, 12 February 2010, page 810-811. 'If people in the developed world ate less meat, it would free up a lot of plants to feed billions of hungry people and gain a lot of good farmland. Some food-security researchers, however, are skeptical; they say the complexities of global markets and human food traditions could also produce some counterintuitive—and possibly counterproductive—results.'. back |
Links
Angela Mollard, All men need intimacy. Even priests, 'Denying intimacy and insisting on celibacy as a prerequisite for ministry is not a sacred act but a dark tunnel to a life of secrets, torment and hypocrisy. You only have to look at pictures of Pope Jean Paul II and Anna-Teresa camping and on a ski holiday to understand that human love nourishes.' back |
Antiparticle - Wikipedia, Antiparticle - Wikipedia, the free ecyclopdia, ' Feynman–Stueckelberg interpretation
By considering the propagation of the negative energy modes of the electron field backward in time, Ernst Stueckelberg reached a pictorial understanding of the fact that the particle and antiparticle have equal mass m and spin J but opposite charges q. This allowed him to rewrite perturbation theory precisely in the form of diagrams. Richard Feynman later gave an independent systematic derivation of these diagrams from a particle formalism, and they are now called Feynman diagrams. Each line of a diagram represents a particle propagating either backward or forward in time. This technique is the most widespread method of computing amplitudes in quantum field theory today.
Since this picture was first developed by Ernst Stueckelberg, and acquired its modern form in Feynman's work, it is called the Feynman-Stueckelberg interpretation of antiparticles to honor both scientists.' back |
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 |
Aquinas, Summa, I, 27, 1, Is there procession in God?, 'As God is above all things, we should understand what is said of God, not according to the mode of the lowest creatures, namely bodies, but from the similitude of the highest creatures, the intellectual substances; while even the similitudes derived from these fall short in the representation of divine objects. Procession, therefore, is not to be understood from what it is in bodies, either according to local movement or by way of a cause proceeding forth to its exterior effect, as, for instance, like heat from the agent to the thing made hot. Rather it is to be understood by way of an intelligible emanation, for example, of the intelligible word which proceeds from the speaker, yet remains in him. In that sense the Catholic Faith understands procession as existing in God.' back |
Barney Zwarz, The tragic legacy of George Pell, 'The penitential prayer with which Catholics begin their Mass, and which Cardinal George Pell would have recited thousands of times, asks God's forgiveness for what they have done and for what they have failed to do.
Few people could have failed to do what they should have done more devastatingly than the cardinal. That is perhaps the most shocking, and damaging, revelation of his four days of testimony to the Royal Commission into Institutional Responses to Child Sexual Abuse, given by video link from Rome this week.' back |
Black Book (film) - Wikipedia, Black Book (film) - Wikipedia, the free encyclopedia, 'Black Book (Dutch: Zwartboek) is a 2006 war drama thriller film co-written and directed by Paul Verhoeven and starring Carice van Houten, Sebastian Koch, Thom Hoffman, and Halina Reijn. The film, credited as based on several true events and characters, is about a young Jewish woman in the Netherlands who becomes a spy for the resistance during World War II after tragedy befalls her in an encounter with the Nazis.' back |
Bob Dylan, Murder Most Foul, ' Bob Dylan has released his first original music in eight years, a 17-minute long song about the JFK assassination.
Bob Dylan: Murder Most Foul review – a dark, dense ballad for the end times
4 out of 5 stars.
Read more
A ballad set to piano, strings and light drums, Murder Most Foul retells the 1963 killing in stark terms, imagining Kennedy “being led to the slaughter like a sacrificial lamb … they blew off his head while he was still in the car / shot down like a dog in broad daylight.” He paints an epic portrait of an America in decline ever since, but offered salvation of a sort in pop music: the Beatles, Woodstock festival, Charlie Parker, the Eagles and Stevie Nicks are all referenced in its lyrics.' back |
Carlo Rovelli, Relational Quantum Mechanics, ' I suggest that the common unease with taking quantum mechanics as a fundamental description ofnature (the measurement problem) could derive from the use of an incorrect notion, as the uneasewith the Lorentz transformations before Einstein derived from the notion of observer-independenttime. I suggest that this incorrect notion that generates the unease with quantum mechanics isthe notion of observer-independent state of a system, or observer-independent values of physicalquantities. I reformulate the problem of the interpretation of quantum mechanics as the problemof deriving the formalism from a set of simple physical postulates. I consider a reformulation ofquantum mechanics in terms of information theory. All systems are assumed to be equivalent, thereis no observer-observed distinction, and the theory describes only the information that systems haveabout each other; nevertheless, the theory is complete.' back |
Charles Francis, A construction of full QED using finite dimensional Hilbert space, ' Background: The first calculations giving finite results at any order in perturbative qed were carried out in the late 1940s, largely by Tomonaga, Schwinger and Feynman. Although these calculations have successfully been built into rigidly defined renormalisation schemes, a constructive approach to qed, showing that it is a mathematically consistent application of quantum mechanics, has been lacking. Among the problems such an approach must address are the requirement of a positive definite norm for valid probabilities, the indefinability of the equal point multiplication between field operators, loop divergences, the Lan-dau pole, the Dyson instability, and classical electromagnetism in the appropriate correspondence. back |
Christian Thiemann and Daniel Grady, Follow the Money: Human Mobility and Effective Communities, 'Ever wonder where your dollar bills travel after you plop them down for a cup of coffee? The Web site Where's George? allows you to do just that: Record your bill's serial number and then track its journeys as other people spend it across the country. But it's more than just a game. Because every time a dollar is spent in a new place, it means someone moved it there. Christian Thiemann and Daniel Grady of Northwestern University in Evanston, Illinois, have been using the Web site's data to study how people move within the United States.' Science, vol 327 page 951. back |
Edmund Bertschinger, Symmetry Transformations, the Einstein-Hilbert Action,and Gauge Invariance, ' Introduction Action principles are widely used to express the laws of physics, including those of general relativity. For example,freely falling particles move along geodesics, or curves of extremal path length. Symmetry transformations are changes in the coordinates or variables that leave the action invariant. It is well known that continuous symmetries generate conservation laws(Noether’sTheorem). Conservation laws are of fundamental importance in physics and so it is valuable to investigate symmetries of the action. It is useful to distinguish between two types of symmetries: dynamical symmetries corresponding to some inherent property of the matter or spacetime evolution (e.g.the metric components being independent of a coordinate,leading to a conserved momentum one-form component) and non dynamical symmetries arising because of the way in which we formulate the action. Dynamical symmetries constraint he solutions of the equations of motion while non dynamical symmetries give rise to mathematical identities. These notes will consider both.' back |
Entropy (arrow of time) - Wikipedia, Entropy (arrow of time) - Wikipedia, the fre encyclopedia, 'Entropy is the only quantity in the physical sciences that "picks" a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system will increase when no extra energy is consumed.' back |
Feynman diagram - Wikipedia, Feynman diagram - Wikipedia, the free encyclopedia, ' In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior of subatomic particles. The scheme is named after its inventor, American physicist Richard Feynman, and was first introduced in 1948. The interaction of sub-atomic particles can be complex and difficult to understand intuitively. Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. As David Kaiser writes, "since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations", and so "Feynman diagrams have revolutionized nearly every aspect of theoretical physics".' back |
Fock space - Wikipedia, Fock space - Wikipedia, the free encyclopedia, 'Informally, a Fock space is the sum of a set of Hilbert spaces representing zero particle states, one particle states, two particle states, and so on. If the identical particles are bosons, the n-particle states are vectors in a symmetrized tensor product of n single-particle Hilbert spaces H. If the identical particles are fermions, the n-particle states are vectors in an antisymmetrized tensor product of n single-particle Hilbert spaces H. A general state in Fock space is a linear combination of n-particle states, one for each n.' back |
Garrett Birkoff & John Von Neumann, The Logic of Quantum Mechanics, ' The object of the present paper is to discover what logical structure one may hope to find in physical theories which, like quantum mechanics, do not con- form to classical logic. Our main conclusion, based on admittedly heuristic arguments, is that one can reasonably expect to find a calculus of propositions which is formally indistinguishable from the calculus of linear subspaces with respect to set products, linear sums, and orthogonal complements-and resembles the usual calculus of propositions with respect to and, or, and not. back |
Gell-Mann matrices - Wikipedia, Gell-Mann matrices - Wikipedia, the free encyclopedia, ' The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics. They span the Lie algebra of the SU(3) group in the defining representation. . . . These matrices are traceless, Hermitian (so they can generate unitary matrix group elements through exponentiation), and obey the extra trace orthonormality relation. These properties were chosen by Gell-Mann because they then naturally generalize the Pauli matrices for SU(2) to SU(3), which formed the basis for Gell-Mann's quark model. Gell-Mann's generalization further extends to general SU(n). For their connection to the standard basis of Lie algebras, see the Weyl–Cartan basis. ' back |
Geodesics in general relativity - Wikipedia, Geodesics in general relativity - Wikipedia, the free encyclopedia, ' In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational force, is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.' back |
Gospel of Luke, Luke 12:22-31: NIV, ' 22 Then Jesus said to his disciples: "Therefore I tell you, do not worry about your life, what you will eat; or about your body, what you will wear. 23 Life is more than food, and the body more than clothes. 24 Consider the ravens: They do not sow or reap, they have no storeroom or barn; yet God feeds them. And how much more valuable you are than birds! 25 Who of you by worrying can add a single hour to his life[? 26 Since you cannot do this very little thing, why do you worry about the rest?' back |
Gospel of Luke, Luke 18:22-26: NIV, ' 22 When Jesus heard this, he said to him, "You still lack one thing. Sell everything you have and give to the poor, and you will have treasure in heaven. Then come, follow me."
23 When he heard this, he became very sad, because he was a man of great wealth. 24 Jesus looked at him and said, "How hard it is for the rich to enter the kingdom of God! 25 Indeed, it is easier for a camel to go through the eye of a needle than for a rich man to enter the kingdom of God."
26 Those who heard this asked, "Who then can be saved?" back |
Hylomorphism - Wikipedia, Hylomorphism - Wikipedia, the free encyclopedia, 'Hylomorphism (Greek ὑλο- hylo-, "wood, matter" + -morphism < Greek μορφή, morphē, "form") is a philosophical theory developed by Aristotle, which analyzes substance into matter and form. Substances are conceived of as compounds of form and matter.' back |
Jenna McLaughin, Eight Memorable Passages From Apple's Fiery Response fo the FBI, back |
John Archibald Wheeler, Information, Physics, Quantum: The Search for Links, ' Abstract
:This report reviews what quantum physics and information theory have to tell us about the age-old question, How come existence? No escape is evident from four conclusions: (1) The world cannot be a giant machine, ruled by any preestablished continuum physical law. (2) There is no such thing at the microscopic level as space or time or spacetime continuum. (3) The familiar probability function or functional, and wave equation or functional wave equation, of standard quantum theory provide mere continuum idealizations and by reason of this circumstance conceal the information-theoretic source from which they derive. (4) No element in the description of physics shows itself as closer to primordial than the elementary quantum phenomenon, that is, the elementary device-intermediated act of posing ayes-no physical question and eliciting an answer or, in brief, the elementary act of observer-participancy. Otherwise stated, every physical quantity, every it, derives AbstractThis report reviews what quantum physics and information theory have to tell usabout the age-old question, How come existence? No escape is evident from four conclusions: (1) The world cannot be a giant machine, ruled by any preestablished continuum physical law. (2) There is no such thing at the microscopic level as space or time or spacetime continuum. (3) The familiar probability function or functional, and wave equation or functional wave equation, of standard quantum theory provide mere continuum idealizations and by reason of this circumstance conceal the information-theoretic source from which they derive. (4) No element in the description of physics shows itself as closer to primordial than the elementary quantum phenomenon, that is, the elementary device-intermediated act of posing a yes-no physical question and eliciting an answer or, in brief, the elementary act of observer-participancy. Otherwise stated, every physical quantity, every it, derives its ultimate significance from bits, binary yes-or-no indications, a conclusion which we epitomize in the phrase, it from bit.' back |
John D Norton, Einstein for Everyone: Spacetime, 'We build a spacetime by taking instantaneous snapshots of space at successive instants of time and stacking them up. It is easiest to imagine this if we start with a two dimensional space. The snapshots taken at different times are then stacked up to give us a three dimensional spacetime.' back |
John Markoff, Cryptography Pioneers Win Turing Award, 'SAN FRANCISCO — In 1970, a Stanford artificial intelligence researcher named John McCarthy returned from a conference in Bordeaux, France, where he had presented a paper on the possibility of a “Home Information Terminal.” . . .
Whitfield Diffie, then a young programmer at the Stanford Artificial Intelligence Laboratory, read Mr. McCarthy’s paper and began to think about the question of what would take the place of an individual signature in a paperless world. Mr. Diffie would spend the next several years pursuing that challenge and in 1976, with Martin E. Hellman, an electrical engineer at Stanford, invented “public-key cryptography,” a technique that would two decades later make possible the commercial World Wide Web. back |
Kimberley Stephens & Joanne Ruthsatz, What Prodigies Could Teach Us About Autism, 'No link has yet been proved between autism and prodigy. Prodigies aren’t typically autistic (unlike savants, in whom extraordinary abilities and autism often coincide), and they don’t have the social or communication challenges that characterize autism. But some aspects of prodigy and autism do overlap.
Prodigies, like many autistic people, have a nearly insatiable passion for their area of interest. Lauren Voiers, an art prodigy from the Cleveland area, painted well into the night as a teenager; sometimes she didn’t sleep at all before school began. That sounds a lot like the “highly restricted, fixated interests” that are part of autism’s diagnostic criteria.' back |
Laura Secor, How Iran's Reformists Found Their Center, 'FOR decades, Iran’s politics have centered on a contest of visions that pitted democratic reformists against hard-line theocrats. Under President Hassan Rouhani, that binary has begun to give way. Last week’s elections showcased a coordinated movement toward the center of Iran’s political spectrum.
This reflects not only the ascendancy of Mr. Rouhani’s centrist faction, whose priorities are not civic empowerment or human rights so much as diplomatic and economic re-engagement with the world. It also reflects a transformation within the reformist camp. Today’s reformists are the left wing of a muted coalition. They navigate a world of lowered expectations and play by rules that demand ingenuity and patience.' back |
Light cone - Wikipedia, Light cone - Wikipedia, the free encyclopedia, 'A Light cone is the path that a flash of light, emanating from a single event E (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime. Imagine the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs—and when graphed the growing circle with the vertical axis of the graph representing time, the result is a cone, known as the future light cone (some animated diagrams depicting this concept can be seen here.) ' back |
Max Tegmark & John Archibald Wheeler, 100 Years of the Quantum, ' Abstract:As quantum theory celebrates its 100th birthday, spectacular successes are mixed withoutstanding puzzles and promises of new technologies. Thisarticle reviews both the successes ofquantum theory and the ongoing debate about its consequences for issues ranging from quantumcomputation to consciousness, parallel universes and the nature of physical reality. We argue thatmodern experiments and the discovery of decoherence have have shifted prevailing quantum inter-pretations away from wave function collapse towards unitary physics, and discuss quantum processesin the framework of a tripartite subject-object-environment decomposition. We conclude with somespeculations on the bigger picture and the search for a unified theory of quantum gravity.' back |
Michael West, The cat is out of the bag on corporate tax avoidance, back |
Michelle Boorstein and Julie Zauzmer, 'Payout chart' for molestation: Secret archive held chilling details of clergy abuse, 'A Catholic diocese in Pennsylvania announced Thursday that it will post the names online of priests credibly accused of sexually abusing children, a decision that came two days after a dramatic grand jury report alleged a decades-long cover-up. . . .
The report relied on a secret archive at the Altoona-Johnstown diocese, which dates back to the 1950s and was opened up this summer when authorities obtained a search warrant. The grand jury interviewed surviving priests and their alleged victims, and compiled a 147-page account detailing accusations against more than 50 religious leaders including priests and teachers. back |
Miguel Vatter, Have faith: civil religion can counter the lure of eternal ife for jihadists, 'Machiavelli’s solution was a new interpretation of the figure of the prophet. The prophet’s role was not to found a new church or empire, but to bring to his people a constitution that guarantees that power shall remain in the hands of the people, not their spiritual or worldly representatives. Hence, a civil religion is a philosophical idea of religion that allows us to interpret prophetic religions in a way that is supportive of republican constitutions.
The first person to have this idea may have been Al-Farabi, a 10th-century Muslim philosopher. His fundamental thought was that the prophet was both a legislator and a philosopher, rather than a theologian or a political leader.' back |
Minkowski space - Wikipedia, Minkowski space - Wikipedia, the free encyclopedia, ' In mathematical physics, Minkowski space or Minkowski spacetime is a combination of Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be an immediate consequence of the postulates of special relativity.' back |
Noel Debien, Five points to help you understand Pell's testimony, back |
PBS, Online NewsHour: The Mass Suicide near San Diego -- March 27 1997, 'Recent news reports have been filled with the troubling story of a mass suicide involving a computer-related cult. At a mansion outside San Diego, police found 39 bodies dressed in black and covered in purple shrouds. The members apparently killed themselves to prepare for the arrival of a alien spaceship they say is hiding behind the Hale-Bopp comet. After a background report by Charles Krause, Jim Lehrer leads a discussion of the suicides with a panel of cult experts.' back |
Projection (linear algebra) - Wikipedia, Projection (linear algebra) - Wikipedia, the free encyclopedia, ' In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that P2 = P. That is, whenever P is applied twice to any value, it gives the same result as if it were applied once (idempotent). It leaves its image unchanged. Though abstract, this definition of "projection" formalizes and generalizes the idea of graphical projection.' back |
Quantum logic - Wikipedia, Quantum logic - Wikipedia, the free encyclopedia, 'In quantum mechanics, quantum logic is a set of rules for reasoning about propositions that takes the principles of quantum theory into account. This research area and its name originated in a 1936 paper[1] by Garrett Birkhoff and John von Neumann, who were attempting to reconcile the apparent inconsistency of classical logic with the facts concerning the measurement of complementary variables in quantum mechanics, such as position and momentum.' back |
Relational quantum mechanics - Wikipedia, Relational quantum mechanics - Wikipedia, the free encyclopedia, ' Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint,[1] and has since been expanded upon by a number of theorists. It is inspired by the key idea behind special relativity, that the details of an observation depend on the reference frame of the observer, and uses some ideas from Wheeler on quantum information.' back |
Robyn Blewer, To believe or not to believe: child witnesses and the sex abuse royal commissiomn, 'Truth-telling is a base premise of Catholic religious instruction. Therefore, child witnesses who emerged from these institutions – through fear alone of the fiery depths of hell – had another dimension of witness reliability. In the right circumstances, with adult police and adult judges and adult juries ready to believe them, the impediments to these children being heard were significantly reduced.
That children from religious institutions were not listened to or protected, in circumstances where the law may well have done so, speaks volumes about the Catholic Church. While Pell claims these “muck-ups” were due to the personal failings of a few members of the church, the history of children in Australian courts suggests otherwise.
All the structures were in place, bolstered by Catholic dogma, to hear the testimonies of these children within the courts. That they were not heard points to an organisational structure that consistently and repugnantly failed the most vulnerable of its members.' back |
Sarah Repucci & Amy Slipowitz, Freedom House: Democracy Under Siege, ' The impact of the long-term democratic decline has become increasingly global in nature, broad enough to be felt by those living under the cruelest dictatorships, as well as by citizens of long-standing democracies. Nearly 75 percent of the world’s population lived in a country that faced deterioration last year. The ongoing decline has given rise to claims of democracy’s inherent inferiority. Proponents of this idea include official Chinese and Russian commentators seeking to strengthen their international influence while escaping accountability for abuses, as well as antidemocratic actors within democratic states who see an opportunity to consolidate power. They are both cheering the breakdown of democracy and exacerbating it, pitting themselves against the brave groups and individuals who have set out to reverse the damage.' 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 |
Stetina, Ciavarella, Li & Wiebe, Simulating Effective QED on Quantum Computers, ' Since its inception in the early 1980’s, quantum computers have been a highly anticipated technology forsimulating the laws of physics. Richard Feynman, known mainly for his work contributing to the development of quantum electrodynamics (QED), the quantum field theory of electromagnetism, was also a pioneer of the idea to use real quantum systems for computation. Bringing these two major scientific ideas together, we take a look at how an effective version of QED can be simulated on a universal quantum computer with applications to many body material and molecular systems, paving the way for analyses of full QED in 3+1 dimensions. A great body of literature exists that shows that quantum computers can provide exponential advantages for certain ab initio electronic structure calculations. The utility of quantum based devices stems from their ability to directly simulate the dynamics of the Coulomb Hamiltonian without making the approximations that are usually required to make their classical counterparts efficiently tractable. However, despite these existing approaches to quantum chemistry, often times they still fall short of being theoretically correct, since the Hamiltonian is still approximate. For example, most approaches to solving the electronic structure problem utilize the Born-Oppenheimer approximation, which assumes that the nuclear wavefunction is uncoupled from the electronic wave function. While this approximation has received substantial attention in recent quantum simulation work, comparably less progress has been made to properly treat relativistic effects in electronic structure simulations , which give rise to orbital contractions/expansions, spin-orbit coupling, modification of electron-electron repulsion and more. The absence of relativity from the majority of existing quantum simulation algorithms raises both practical and a theoretical questions. First, relativistic effects are significant for the ground states of some molecules. For example, atomic gold and uranium dimers both have significant relativistic effects that need need to be considered to accurately model their ground state. ' back |
Tedros Adhanom Ghebreyesus, A 'me first' approach to vaccination won't defeat Covid , ' The future is ours to write. Let’s not be held back by politics, business as usual or those who say we can’t. This is the biggest crisis of our lifetimes, but seeing vaccines rolling out in Ghana should only buoy our collective enthusiasm to make sure that no country is left behind. While the virus has taken advantage of our interconnectedness, we can also turn the tables by using it to spread life-saving vaccines further and faster than ever before.
If not now, when?' back |
The Book of Joshua, Joshua 18:10-14, '10 Joshua then cast lots for them in Shiloh in the presence of the LORD, and there he distributed the land to the Israelites according to their tribal divisions. 11 The lot came up for the tribe of Benjamin, clan by clan. Their allotted territory lay between the tribes of Judah and Joseph:' back |
The Imaginarium of Doctor Parnassus - Wikipedia, The Imaginarium of Doctor Parnassus - Wikipedia - the free encyclopedia, ' The Imaginarium of Doctor Parnassus is a 2009 fantasy film directed by Terry Gilliam and written by Gilliam and Charles McKeown. The film follows a travelling theatre troupe whose leader, having made a bet with the Devil, takes audience members through a magical mirror to explore their imaginations and present them with a choice between self-fulfilling enlightenment or gratifying ignorance. . . . Outside a London pub, an elderly bearded sage named Doctor Parnassus runs a nearly-bankrupt traveling theatre troupe, which includes his teenaged daughter Valentina, a sleight-of-hand expert and barker Anton, and a dwarf assistant Percy. The troupe's main attraction is a portal to a magical "Imaginarium", a surreal dream world that transforms according to its participants' own desires and offers them a choice between difficult self-fulfillment or easy ignorance.' 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 |
Timothy W Jones, For whom the Pell tolls: what did we learn from George Pell's royal commission appearance?, 'It is evident that Archbishop Frank Little and Bishop Ronald Mulkearns neglected their responsibilities and even contravened canon law in their dealings with sexually offending clergy. But Pell’s claims to have fulfilled his moral responsibility in the face of this dysfunction ring hollow.
Pell chose to keep knowledge of his fellow priests' offending at bay and allowed his superiors' neglect and malpractice to continue. After the exposure of this legal dysfunction and moral cowardice, we can expect the royal commission’s recommendations will include changes to Roman Catholic governance and canon law.' back |
United States District Court, Central District of California, Eastern Division, In the matter of the search of an Apple iphone seized during the execution of a search warrant on a black Lexus IS300, California license plate 35KGD203, Apple Inc's motion to vacate order compelling Apple Inc to assist agents in search, and opposition to Governmnent's motion to compel assistance back |
Unmoved mover - Wikipedia, Unmoved mover - Wikipedia, the free encyclopedia, ' The unmoved mover (Ancient Greek: ὃ οὐ κινούμενον κινεῖ, romanized: ho ou kinoúmenon kineî, lit. 'that which moves without being moved'] or prime mover (Latin: primum movens) is a concept advanced by Aristotle as a primary cause (or first uncaused cause) or "mover" of all the motion in the universe. As is implicit in the name, the unmoved mover moves other things, but is not itself moved by any prior action. In Book 12 (Greek: Λ) of his Metaphysics, Aristotle describes the unmoved mover as being perfectly beautiful, indivisible, and contemplating only the perfect contemplation: self-contemplation. He equates this concept also with the active intellect. This Aristotelian concept had its roots in cosmological speculations of the earliest Greek pre-Socratic philosophers and became highly influential and widely drawn upon in medieval philosophy and theology. St. Thomas Aquinas, for example, elaborated on the unmoved mover in the Quinque viae. ' back |
Waren Buffet, Berkshire HsthawayInc, Shareholder Letters, back |
Wojciech Hubert Zurek, Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical, 'Submitted on 17 Mar 2007 (v1), last revised 18 Mar 2008 (this version, v3))
Measurements transfer information about a system to the apparatus, and then further on – to
observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide framework
for the “wavepacket collapse”, designating terminal points of quantum jumps, and defining the
measured observable by specifying its eigenstates.' back |
Zero-energy universe - Wikipedia, Zero-energy universe - Wikipedia, the free encyclopedia, 'The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly canceled out by its negative energy in the form of gravity. . . . The zero-energy universe theory originated in 1973, when Edward Tryon proposed in the journal Nature that the universe emerged from a large-scale quantum fluctuation of vacuum energy, resulting in its positive mass-energy being exactly balanced by its negative gravitational potential energy.' back |
Zipf-Mandelbrot law - Wikipedia, Zipf-Mandelbrot law - Wikipedia, the free encyclopedia, 'In probability theory and statistics, the Zipf–Mandelbrot law is a discrete probability distribution. Also known as the Pareto-Zipf law, it is a power-law distribution on ranked data, named after the linguist George Kingsley Zipf who suggested a simpler distribution called Zipf's law, and the mathematician Benoît Mandelbrot, who subsequently generalized it.' back |
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