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vol VII: Notes

2017

Notes

Sunday 27 August 2017 - Saturday 2 September 2017

[Notebook: DB 81: Scientific theology]

[page 118]

Sunday 27 August 2017

Zurek: Decoherence: This looks like an unnaturally long and complex attempt to explain the transition between 'quantum' and 'classical' states, ie states represented by a complex number or function ψ [and a real number]. The equivalence between vectors and functions [is shown] by the fact that a vector is a mapping from the natural numbers, which index the components of the vector, to the complex numbers, the value of the probability amplitude represented by each [element of the] vector. The mapping from the natural numbers to the complex numbers is dynamic, changing (in the Schrödinger picture that we assume here, one view of the relativity of vectors and operators) in a way determined by the wave equation, so we see no problem in principle to modelling eigenvectors as Turing machines, ie computers. This suggests that the cardinal of the set of eigenvectors is equivalent to the cardinality of the set of computers, ie 0. Wojciech H Zurek: Decoherence, Einselection, and the Existential Interpretation (the Rough Guide), Schroedinger picture - Wikipedia

[page 119]

We close the gap between continuous and discrete by recognising that the discrete, ie the logical, is much more powerful than the continuous since all the properties of the continuum are established by discrete arguments (theorems) which can be represented by turing machines. Every valid deterministic computation is a proof. The eigenvectors are the computer that evaluate the eigenvalues, and there is little empirical doubt that these values are computed by deterministic processes. It may be claimed, through the doctrine that continuous arithmetic is just as deterministic as digital arithmetic, but this is not possible since we cannot make a deterministic continuous (ie analogue) computer precise because of the uncertainty introduced into mathematics by Gödel and Turing. Getting there, a bit like sex, looks like there might be an orgasm (halted computation emitting an eigenvalue) to come.

As we lay out the mathematics of the transfinite computer network we model it with the results of quantum field theory, based on the idea that quantum mechanics describes a communication network. We describe this first in the transfinite world of Gödel and Turing and then bring it back to earth beginning with the assumption that 0 = 0, 1, 2, 3, . . . in succession as the world complexifies.

einselection Einselection - Wikipedia

My writing is conformal to wrestling for orgasm, ie struggling to bring a computation to a halt, yielding observable output as a consequence of the hidden [but felt] process generating fixed points.

Each dimension in a Hilbert space may be considered as a source represented by a basis vector. Each of them progresses at its own phase velocity [frequency].

The mapping of computers onto wave functions has something to do

[page 120]

with the Born rule.

The rotation of an orthonormal base must proceed by infinitesimal breaks of orthonormality in the basis vectors, and the whole rotation group is then constructed by integration, but can this be physically realized? Lie Group - Wikipedia

The geometry of orthogonality and rotation is built around the Pythagorean theorem [a fixed point in any Euclidean space].

How do we logically - computationally represent the various group operations that play a role in physics? We may think of an algorithm as a vector in a space which the process follows element by element, or as a box in which everything has to find its natural eigenfunctions, so that they can all live together in harmony. The best known family is the vibrating string. String vibration - Wikipedia

Clebsch-Gordan coefficients for SU(3). Special Unitary Group. Clebsch-Gordan coefficients - Wikipedia, Special unitary group - Wikipedia

Monday 28 August 2017

Is this work or self indulgence? What is the difference? In effect we work to indulge ourselves, the purpose of work being directly or indirectly to improve our physical and spiritual condition. Somewhere in my upbringing [or my evolution] I was oriented toward doing good [cooperating] or trying to make the world a better place as an alternative to solipsistic self indulgence, and I still feel this and feel that my theoretical quest is a work in this direction, giving us a scientific understanding or our nature and role in the world and bringing to light the peacemaking power of divine creativity. The challenge, in terms of effective propagation, is to write something that inspires readers to develop and propagate the ideas expressed, that is to create a field of study and action. I like to think I am onto something and want to keep the little flame going until it finds suitable fuel, or potential (in the minds of readers) that will be released by the ideas proposed.

[page 121]

Libertarian solipsism versus cooperative parallel processing of the human state, rotating the state vector of humanity toward peace, ie complete human symmetry [and consequent harmony?].

Feynman III:3: 'When a particle goes by a particular route the amplitude for that route can be written as a product of the amplitude to go part of the way with the amplitude to go the rest of the way. So [if the ampliitude] for a particle to go from a to b is ψ, to go from b to a is ψ*, then the probability of the round trip is ψψ*, ie |ψ|2 = p. Feynman, Leighton & Sands FLP III:03: Chapter 3: Probability Amplitudes

<r2|r1> = eipr12/h / r12 where p is the momentum which is related to the energy by the relativistic equation p2c2 = E2 - (m0c2)2 or the non-relativistic equation KE = p2/2m.

'Provided that the particles do not interact, the amplitude that one particle will do one thing and the other something else is the product of the two amplitudes that the two particles would do the two things separately.'

'Suppose we didn't know where the particles [approaching the holes] came from before arriving at holes 1 and 2 of the first wall. We can still make a prediction of what will happen beyond the wall . . . provided that we are given two numbers: the amplitude to have arrived at 1 and the amplitude to have arrived at 2. In other words, because of the fact that the amplitude for successive events multiplies, . . . , all you need to know to continue the analysis is two numbers — in this case < 1| s > and < 2| s >. These two complex numbers are enough to predict all the future. That is really what makes quantum mechanics so easy.

[page 122]

'You must never add amplitudes for different and distinct final states. . . . by "final" we mean at that moment tje probability is desired—that is when the experiment is "finished".

'. . . we must be careful not to attribute too much reality to the waves in space. They are useful for certain problems but not for all.'

FLP Chapter 4: Identical particles: 'If a process involves two particles that are identical, reversing which one arrives at a counter is an alternative that cannot be distinguished [not revealed] and—like all cases of alternatives that cannot be distinguished interferes with the original unexchanged case. The amplitude for an event is then the sum of the two interfering amplitudes; but, interestingly enough, the interference is in some cases with the same phase, and in other with the opposite phase.' Feynman, Leighton & Sands FLP III:04: Chapter 4: Identical Particles

'Why is it that particles with half-integral spin are Fermi particles whose amplitudes add with a minus sign, whereas particles with integral spin are Bose particles whose amplitudes add with a positive sign? An explanation has been worked out by Pauli . . . The explanation is deep down in relativistic quantum mechanics. That probably means that we do not have a complete understanding of the fundamental principle involved.' Spin-statistics theorem - Wikipedia, Ian Duck and E.C.G. Sudarshan: Toward an understanding of the spin-statistics theorem

'It is generally true in quantum mechanics that the amplitude to get from any condition φ to any condition χ is the complex conjugate of the amplitude to get from χ to φ, < φ | χ > = < χ | φ >*.

Any state can be decribed in a set of base states by giving the amplitudes to be in each of the base states.'

[page 123]

FLP Chapter 7: 'Why does an atom radiate light? The answer has to do with entropy. When the energy is in the electromagnetic field there are so many different ways is could be—so many different places where it can wander—that if we look for the equilibrium condition, we find it in the most probable situation the field is excited with a photon and the atom is de-excited.' Feynman, Leighton & Sands FLP III:07: Chapter 7: The Dependence of Amplitudes Upon Time

'You may be thinking that it is strange to think of a "particle" which has equal amplitudes to be found throughout all space [perhaps because quantum mechanics dates from an epoch before space]. After all, we usually think of a "particle" as a small object located "somewhere". But don't forget the uncertainty principle. If a particle has definite energy it also has definite momentum. If the uncertainty of momentum is zero, the uncertainty relation ΔtΔx = ℏ tells us that the uncertainty in position must be infinite, and that is just what we are saying when we say that there is the same amplitude to find the particle at all points in space.

'Although the amplitudes vary with time, if the energy is definite they vary as an imaginary exponential, and the absolute value does not change.'

'. . . we can measure energy from any zero we want.'

Chapter 8 The Hamiltonian Matrix

'The complete description of an electron, so far as we know, requires only that the base states be described by momentum and spin. Feynman, Leighton & Sands FLP III:08: Chapter 8: The Hamiltonian Marix

'Because the operation of waiting is especially important, we call it U instead of A.

'. . . we can analyze any time interval if we can analyze a series of short time intervals in between.' Provided calculus applies.

To apply calculus we imagine some plausible behaviour at an infinitesimal level, perhaps defined by a function and then integrate this to arrive at the big picture. Perhaps the most audacious application

[page 124]

of this idea is Feynman's path integral. But where does this get us? Is there any [more] information in the integral than there was already in the infinitesimal? So why not (on the logical paradigm) simply apply a logical function directly (if you can find it) to the situation in hand as a software engineer would do if she wanted to transform the state of the machine from a> to b. Feynman & Hibbs: Quantum Mechanics and Path Integrals

Feynman lecture 8: [In accelerator experiments] there is no experimental evidence on the details of the process, only what goes in and what goes out.' Feynman, Leighton & Sands FLP III:08: Chapter 8: The Hamiltonian Matrix

Chapter 10: '. . . s "virtual exchange" means that the phenomenon involves a quantum mechanical interference between and exchanged and a nonexchanged state. Feynman, Leighton & Sands FLP III:10: Chapter 10: Other Two=State Systems

In the "particle" theory of electromagnetism, the process of a virtual photon exchange gives rise to all the phenomena of electrostatics.

Tuesday 29 August 2017

The outputs of a [classical] communication source and a quantum source have the same characteristics. Now compare mechanisms — every [measurement] operator is a codec. Codec - Wikipedia

A message is vector; a function is vector, in function space

A computer is a vector in function space mapping from a program counter to a string of logical operations.

Feynman chapter 8: 'We have discovered that any state in the world can be represented as a superposition—a linear combination with suitable coefficients—of base states.

Fields devised to avoid action at a distance which the network does

[page 125]

using particles to carry messages through spacetime. The messages exist and travel by logical processes that antecede the space-time metric.

'Prepare a state' - put a system through a filter, eg Stern-Gerlach. Stern-Gerlach experiment - Wikipedia

The basis vectors of an operator are orthogonal and (we guess) it takes a quantum of action to transform one into another.

In the Shannon word noise is controlled by packaging information into lumps. In the physical world where information is physical this packaging is achieved by bonding which is explained in quantum mechanics by energy (physics) and entropy (psychology).

I look at all the structures I have build and appreciate the power of just plodding along realizing a design, gradually dealing with all the devilish details encountered in the realization. Now that I have given up building for writing, similar algorithms apply. These notes are intended to serve as a log of the process of building natural theology and using it as a set of principles to design a natural religion, seeking the perfect balance between fermionic behaviour (solipsism, libertarianism) and bosonic behaviour (totalitarianism, cloning into one state.

Is Hilbert space compact and convex?

Identical particles - identical messages, but at different points in spacetime.

Phase change distinguishing fermions from bosons is a sort of square wave, π difference, ψ + ψ vs ψ − ψ.

Feynman III:7: Amplitudes are dependent upon (aware of) time.

[page 126]

Stern-Gerlach: '. . . only one component of a particle's spin can be measured at one time, meaning that the measurement of the spin along the z axis destroys information about the particle's spin along the x and y axis.' Does this mean sin exists in 2D space-time?

Let us imagine that only one electron exists in the pre-space epoch and it is somehow reproduced to make a vast number of electrons as the space expands and the same for all the other fundamental particles that are essentially points built out of the code implicit in space. So photons and electrons exist in time but are multiplied by the emergence of space. ?

Wednesday 30 August 2017

One of the assumptions of the application of calculus in physics is that infinitesimals are linear, that is very short pieces of curves can be assumed to be straight. This works in the geometric world but not in the logical world where all the functions [except identity] are [discrete] steps [as in a proof].

We might say that there are no things only messages, which, in the form of particles ranging from atoms to galaxies and beyond, are the only things we observe.

I have written the same things many times, always looking for a succinct, comprehensive and stable text [writing is like software for the mind].

Art Hobson: There are no particles only fields Art Hobson: There are no particles, there are only fields

Hobson page 2: 'Based on standard non-relativistic and relativistic quantum physics, do experiment and theory lead us to conclude that the universe is ultimately made of fields, or particles, or both or neither?

[page 127]

Hobson page 2: Wilczek: ' " uniquely (so far as I know) among physicists of high stature, Feynman hoped to remove the field-particle dualism by getting rid of the field." '

page 5: '[Faraday] saw lines of force as space-filling physical entitites that could move, expand and contract. He concluded that magnetic lines of force, in particular, are physical conditions of "mere space" (ie space containing no material substance). Today this description of fields as "conditions of space" is standard.'

'if energy is emitted here and now, and received there later, then where was it in the meantime? Clearly in the field [or just as clearly in a swarm of particles!].

page 6: 'For Einstein, there was no material support ether to support light waves. Instead the "medium" for light was space itself. [Now we are saying that it is a field]

'The implication of special relativity that energy has inertia further reinforces both Einstein's rejection of the ether and the signficance of fields. Since fields have energy they have inertia and so should be considered "substance like" themselves rather than simply states of some substance such as ether.' or space-time?

page : '. . . fields are inherently extended in space and don't have specific positions', ie they exist in a layer 'under' space [somewhere between the initial singularity and space].

'. . . the radiation field's quantum states exist in a Hilbert space of variable N called Fock space. . . . the full state of |ψ> is (in general) a superposition of states having a definite number of quanta [one quantum of action = 1 cycle per second of energy?]. Fock space - Wikipedia

page 11: 'Quantum fields have one particle-like property that classical fields don't have: they are made of countable quanta.'

page 12: 'The superposition principle should have been a dead giveaway: a sum of quantum states is a quantum state. Such superpositions are characteristic of all linear wave theories and at odds with the generally non-linear

[page 128]

nature of Newtonian particle physics.'

Hobson page 12: A benefit of QFT is that all quanta of a given field must be identical because they are all excitations of the same field, . . .. ' How does this field fill all space if it can not grow with the space rather that spilling into it and spreading?

page 12: 'When a field changes its energy by a single quantum it must do so instantaneously, because a non-continuous change would imply that, part way through the change, the field had gained or lost only a fraction of a quantum. . . . a quantum is a unified entity even though its energy might be spread over light years—a feature that raises issues of non-locality intrinsic to the quantum puzzle [also, we presume, the change in the field must propagate superluminally].

page 14: Two slit experiment explained by extended field, not localized particle. Dirac: 'Each photon interferes only with itself '.

page 18: Two slit: 'only spatial fields must be postulated to form the fundamental objects to be quantized . . . while apparent particles are a mere consequence of decoherence [ie localization by the detection process]'. So how does the detection process decide where to localize to give the observed interference pattern?

page 20: 'even under a broadly inclusive definition of "particle" quantum particles conflict with Einstein causality.'

page 20: QFT vacuum phenomena that are difficult to reconcile with particle, ie Casimir effect, Lamb shift, electron [anomalous] magnetic moment. Casimir effect - Wikipedia, Lamb shift - Wikipedia, Anomalous magnetic dipole moment - Wikipedia

We do not yet understand the quantum vacuum. The most telling demonstration of this is that the most plausible theoretical estimate

[page 129]

of the QFT estimate of the energy density of the vacuum implies a value pf the cosmolgical constant that is some 120 orders of magnitude greater than the upper bound placed on this parameter by astronomical observations.' Stephen Weinberg: The Cosmological Constant Problems

So we won't let this worry us, since QFT in QED gives results accurate to one part in 108ish.

The trouble lies in the uncertainty princilpe which is really just telling is that we cannot know what s going on between the natural numbers and our development of real numbers to fill this gap is unphysical. Every measurement is digital, and the least uncertainty is the gap between the least significant digits, eg millimetres in the construction business

page 22: Unruh / Sokolov-Ternov effect. Sokolov-Ternov effect - Wikipedia

'The Unruh effect is counter-intuitive for a particle ontology, as it seems to show that the particle concept isobserver-dependent. Of course it is, a particleis a message.

'Non-locality is pervasive, the characteristic quantum phenomenon.'

E. Lombardi, F. Sciarrino, S. Popescu, and F. De Martini E. Lombardi, F. Sciarrino, S. Popescu, and F. De Martini: Teleportation of a Vacuum-One-Photon Qubit

Our central nervous system is literally a microcosm, a subnet of the universal network.

Thursday 31 August 2017

Can I really establish that the universe is digital, ie

[page 130]

logic driven, and what is the point if I do? This development seems essential of we are to consider the Universe to be divine so that we replace physics based on the notion of continuity which can be seen to be essentially meaningless, since a continuum carries no information, with the notions of logic and psychology, which break the symmetry of the continuum with events. Energy is a measure of the rate of events, the time frequency of quanta of action.

Friday 1 Septembrt 2017

Feynman maintains that we get the same results on the wave and particle picture, they are duals. Hobson, Weinberg and co want to go all the way with fields but it looks a bit problematic to me but I have yet to have the vision that enables me to see digital to the core enabling calculations. It is clear, however, that we can consider things like the Lamb shift to be the work of channels with relatively low energy / frequency.

The one thing we know is that every event involves a quantum of action. The problem is to map from quanta of action to energy levels which we measure by establishing harmonies with known frequencies. Because we have no fixed zero of energy all these frequencies are expressed as energy differences. The wave functions are a set of potentials which control the motions (including creation and annihilation) of the particles as the gravitational potentials control the motions of the planets and every other thing.

We start with de Broglie who proposed that periodic potentials apply to all forms of energy, so the frequency of the potential determined the energy of the event. Harmonic computation. The clock in a computer controls the superposition of the potentials that drive the execution of computations. The potentials are invisible and manifest themselves in the behaviour of the particles. Quantum field theory is in effect quantum potential theory and the particles and potentials are duals, two representations of the same

[page 131]

information, one is not the other. How does this fit with bosons and fermions? The layering of the software beginning with the initial singularity seems to be a good paradigm and is perhaps the central point of e19_gravitation, inspired by the ancient idea of the Trinity which need not be mentioned in the physical paper but is central to the theology in e17_scientific_theology. We might se gravitation and particles as fixed points in a differentiable manifold that describes gravitation. Louis de Broglie - Wikipedia

Invisibility. What is going on inside god? Model: page 6 Invisibility

In a photon each cycle of the wave is a quantum of action to the energy of the photon is proportional to its frequency.

I have a headful of bits and pieces of quantum mechanics, information processing, etc etc but have yet to boil all these down to a consistent picture that deals with all the problems I see in our current theological and physical pictures of the world. All the time I am looking for a logical or psycho-logical picture of the world because it seems more consistent with my own mind and the mind of god.

How do we explain the linear superposition of potentials? Vector sum of potentials from a distribution of masses / 'charged' particles.

FLP III:1 Heisenberg ' "It is impossible to design an apparatus to determine which hole electron passes through that will not at the same time disturb the electron enough to destroy the interference pattern.

'One might still ask: "How does it work? What is the machinery behind the law?" No one has found any machinery behind the law. No one can "explain" any more than we have "explained". No one will give you any deeper representation of the situation. We have no ideas about a more basic mechanism from which these results can be deduced.' Feynman, Leighton & Sands FLP III:01: Chapter 1: Quantum behaviour, §7

[page 132]

Feynman III 1-8 The uncertainty principle: 'This is the way Heisenberg stated the uncertainty principle originally: If you make the measurement of any object and you can determine the x component of its momentum with an uncertainty Δp, you cannot, at the same time, know its x-position more accurately that Δx ≥ ℏ/2Δp, where is a definite fixed number given by nature. . . . the more general startement was that one cannot design equipment in any way to determine which os two alternatives is taken without, at the same time, destroying the pattern of interference.

'The uncertainty principle "protects" quantum mechanics. Heisenberg recognised that if it is possible to measure momentum and position simultaneously with greater accuracy, the quantum mechanics would collapse. So he proposed it must be impossible. Then . . . nobody could figure out a way to measure the position and momentum of anything . . . with any greater accuracy. Quantum mechanics maintains its perilous but still correct existence.' Werner Heisenberg: Über den anschauclichen Inhalt der quantentheoretischen Kinematik und Mechanik

So we try to measure the diagonal of a unit square with a tape graduated in units. The best we can do is say that it is between 1 and 2, so let us guess [one and a] half. When the unit is the best we can do with the accuracy of ΔxΔp is half a Planck. This is a measure of the product of errors. People say that if we know the momentum exactly we have no idea of the position, but perhaps this is taking it a bit too far. On the whole all we can say is that our calculations are accurate to ±.

A Schrödinger [moving] eigenvector is a computer in action

Quantum jump (from orbit a to orbit b is logical, not continuous.

[page 133]

Farmelo: Dirac page 87: xp - px = iℏ/2π

page 88: Eddington: ' "The fascinating point is that as the development of the process proceeds, actual numbers are exuded from the symbols.

page 89: Dirac: The fundamental equations of quantum mechanics Paul Dirac

page 94: 'Stoppard: "A door like this has cracked open five or six times since we gt up on our hind legs. It is the best possible time to be alive, when almost everything you know is wrong." '

page 109: The interpretation problem is classical quantum mechanics was solved by Born. How do we solve the parallel problem in logical mechanics? Psychological mechanics is based on [abstract, transfinite] computer networks.

Saturday 2 September 2017

Logical tunnelling annihilate the input, create the [output]. Instead of a continuous field, we have a logical field implemented by a network [a channel is not a continuous 'wire' but a computation].

We see the interface between logic and arithmetic in the binary digital computer, first revealed in Russell and Whitehead's Principia. The simplest process we have is the 'half adder'. How does this idea manifest itself in quantum mechanics? Mapping, eg 0 = false, 1 = true. Whitehead & Russell: Principia Mathematica, Adder (elecronics) - Wikipedia

Farmelo page 129: 'The great majority of [physicists] still thought like engineers and were mathematically weak by the standards of Dirac and his peers. So most physicists were still trying to visualise the atom as if it were a mechanical device.' Rather than a logical device, a network exchanging quanta of information as understood by Shannon.

My ideas need a matrix, and are given context by the

[page 134]

theory of everything we call theology.

Dirac (Farmelo 130) ' "[Projective geometry] was most useful for research but I did not mention it in my published work . . . because I felt most physicists were unfamiliar with it. When I had obtained a particular result, I translated it into analytic form ad put down the argument in terms of equations.

In a 'full' unverse, all motion is permutation. I go north the air I occupy goes south. Wave motion is rather like this, swapping one thing for another and back again At the bottom level of the universe, permutation of bosons produces on new phenomena but permutation of fermions produces structure through the exclusion principle.

Fixed point theory picks structure out of completely simple divine dnamic continuum, which is functionally identical to the initial singularity or the vacuum. How many times hae I said this? Each time slightly coloured by a new context, feeling a sort of Lamb shift.

page 181: [Dirac] was convinced that [his equation] was correct—what was needed was a correct interpretation of the mathematics.

page 204: ' "No progress without paradox." '

Cosmological constant problem: the lowest energy states of the vacuum harmonic oscillatorsare ½ℏω, and there are so many of them, and theor frequencies o high that their energy appears t be 10 times greaterthan observation suggests. So how do we deal with this? reduce the number of states? Reduce the frequencies: get rid of the notion of zero point energy? In general the trouble seems to arise from the quantum mechanical application of continuous mathematics and we would do better to think digitally. Feynman's notion that the total energy of the Universe is zero might apply locally

[page 135]

to deal with this problem.

Vacuum - fundamental information free energy network from which all else is built, quantum mechanics, relativity . . . Vacuum is the region where pure action bifurcates into kinetic and potential energy, whose total is zero . . .

From a logical point of view an electron is not a pint of zero size and infinite self energy but a symbol with two spin states and mass which means a 'private' process and momentum which is relative to an observer in a certain reference frame (as is the direction of spin)). Make sen of this. A photon has spin 1, but the frequency of the quanta in its process is proportional to its momentum which is fixed by its energy, since its velocity is fixed, so its time frequency and spatial frequency are deterministically related.

pag 330: J S Mill: "What are the first general propositions from which all the uniformities existing in nature could be derived?' We say computer network theory, NAND.

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Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Feynman, Richard P, and Albert P Hibbs, Quantum Mechanics and Path Integrals, McGraw Hill 1965 Preface: 'The fundamental physical and mathematical concepts which underlie the path integral approach were first developed by R P Feynman in the course of his graduate studies at Princeton, ... . These early inquiries were involved with the problem of the infinte self-energy of the electron. In working on that problem, a "least action" principle was discovered [which] could deal succesfully with the infinity arising in the application of classical electrodynamics.' As described in this book. Feynam, inspired by Dirac, went on the develop this insight into a fruitful source of solutions to many quantum mechanical problems.  
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Heisenberg, Werner , Physical Principles of the Quantum Theory (translated by Carl Eckart and Frank C Hoyt), Dover 1949 Jacket: 'In this classic, based on lectures delivered at the University of Chicago, Heisenberg presents a complete physical picture of quantum theory. He covers not only his own contributions, but also those of Bohr, Dirac, Bose, de Broglie, Fermi, Einstein, Pauli, Schroedinger, Sommerfeld, Rupp, Wilson, Germer and others in a text written for the physical scientist who is not a specialist in quantum theory or in modern mathematics.' 
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Jaynes, Julian, The Origin of Consciousness in the Breakdown of the Bicameral Mind, Mariner Books 2000 Jacket: 'At the heart of this book is the revolutionary idea that human consciousness did not begin far back in animal evolution but is a learned process brought into being out of an earlier hallucinatory mentality by cataclysm and catastrophe only 3000 years ago and still developing.' 
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Kolmogorov, A N, and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. . . . This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be in complete analogy with the corresponding properties of orthogonal functions . . .' 
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Migne, J P , Patrologiae cursus completus. Series graeca. (vols 1-166), 1857-87 The Patrologia Graeca includes the printed works of Greek Christian writers down to the Council of Florence (1438-39back
Migne, J-P, Patrologiae cursus completus. Series latina. (vols 1-221), 1844-82 The Patrologia Latina comprises the works of the Church Fathers from Tertullian in 200 AD to the death of Pope Innocent III in 1216.back
Noble, David F, The Religion of Technology: The Divinity of Man and the Spirit of Invention, Penguin Books 1999 Introduction: 'It is the aim of this book to demonstrate that the present enchantment with things technological ... is rooted in religious myths and ancient imaginings. Although today's technologists, in their sober pursuit of utility, power and profit, seem to set society's standard for rationality ... their true inspiration lies elsewhere, in an enduring, other-worldly quest for transcendence and salvation.'  
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Weyl, Hermann, Space Time Matter (translated by Henry L Brose), Dover 1985 Amazon customer review: ' The birth of gauge theory by its author: This book bewitched several generations of physicists and students. Hermann Weyl was one of the very great mathematicians of this century. He was also a great physicist and an artist with ideas and words. In this book you will find, at a deep level, the philosophy, mathematics and physics of space-time. It appeared soon after Einstein's famous paper on General Relativity, and is, in fact, a magnificent exposition of it, or, rather, of a tentative generalization of it. The mathematical part is of the highest class, striving to put geometry to the forefront. Actually, the book introduced a far-reaching generalization of the theory of connections, with respect to the Levi-Civita theory. It was not a generalization for itself, but motivated by the dream (Einstein's) of including gravitation and electromagnetism in the same (geometrical) theory. The result was gauge theory, which, slightly modified and applied to quantum mechanics resulted in the theory which dominates present particle physics. Weyl's unified theory was proved wrong by Einstein, and his criticism alone, accepted by Weyl and included in the book, would justify the reading. Though wrong, Weyl's theory is so beautiful that Paul Dirac stated that nature could not afford neglecting such perfection, and that the theory was probably only misplaced. Prophetic words! The philosophic parts are, alas, too much for our present cultural level, but you can ignore them. The mathematical and physical parts are perfectly accessible and, of course, of the highest class. The pity is that the number of misprints is immense, particularly in the formulas, so that the reading is made much more difficult than it should. Also, the English edition is not the latest one. If you read German, choose the original, also available here.' Henrique Fleming 
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Whitehead, Alfred North, and Bertrand Arthur Russell, Principia Mathematica (Cambridge Mathematical Library), Cambridge University Press 1962 The great three-volume Principia Mathematica is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premisses and primitive ideas, and so to prove that mathematics is a development of logic. Not long after it was published, Goedel showed that the project could not completely succeed, but that in any system, such as arithmetic, there were true propositions that could not be proved.  
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Adder (elecronics) - Wikipedia, Adder (elecronics) - Wikipedia, the free encyclopedia, 'An adder is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units. They are also utilized in other parts of the processor, where they are used to calculate addresses, table indices, increment and decrement operators, and similar operations.' back
Anomalous magnetic dipole moment - Wikipedia, Anomalous magnetic dipole moment - Wikipedia, the free encyclopedia, 'In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. (The magnetic moment, also called magnetic dipole moment, is a measure of the strength of a magnetic source.)' back
Arijit Sen, The demons within: India's tryst with torture, 'Today, state torture in India is no longer restricted to its northeastern corner. Be it in Manipur or Kashmir or Chhattisgarh, torture has become the norm in counterinsurgency operations or in police custody and successive governments chose to turn a blind eye to this reality.' back
Art Hobson, There are no particles, there are only fields, 'Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows, experiment and theory imply unbounded fields, not bounded particles, are fundamental. This is especially clear for relativistic systems, implying it's also true of non-relativistic systems. Particles are epiphenomena arising from fields. Thus the Schroedinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to occur at that point. The field for an electron is the electron; each electron extends over both slits in the 2-slit experiment and spreads over the entire pattern; and quantum physics is about interactions of microscopic systems with the macroscopic world rather than just about measurements. It's important to clarify this issue because textbooks still teach a particles- and measurement-oriented interpretation that contributes to bewilderment among students and pseudoscience among the public. This article reviews classical and quantum fields, the 2-slit experiment, rigorous theorems showing particles are inconsistent with relativistic quantum theory, and several phenomena showing particles are incompatible with quantum field theories.' back
Casimir effect - Wikipedia, Casimir effect - Wikipedia, the free encyclopedia, 'In physics, the Casimir effect or Casimir-Polder force is a physical force arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, placed a few micrometers apart, without any external electromagnetic field. In a classical description, the lack of an external field also means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using quantum mechanics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. This force has been measured, and is a striking example of an effect purely due to second quantization.' back
Clebsch-Gordan coefficients - Wikipedia, Clebsch-Gordan coefficients - Wikipedia, the free encyclopedia, 'From a vector calculus perspective, the CG coefficients associated with the SO(3) group can be defined simply in terms of integrals of products of spherical harmonics and their complex conjugates. The addition of spins in quantum-mechanical terms can be read directly from this approach as spherical harmonics are eigenfunctions of total angular momentum and projection thereof onto an axis, and the integrals correspond to the Hilbert space inner product.' back
Codec - Wikipedia, Codec - Wikipedia, the free encyclopedia, 'A codec is a device or computer program capable of encoding or decoding a digital data stream or signal. Codec is a portmanteau of coder-decoder or, less commonly, compressor-decompressor.' back
E. Lombardi, F. Sciarrino, S. Popescu, and F. De Martini, Teleportation of a Vacuum-One-Photon Qubit, 'We report the experimental realization of teleporting a one-particle entangled qubit. The qubit is physically implemented by a two-dimensional subspace of states of a mode of the electromagnetic field, specifically, the space spanned by the vacuum and the one-photon state. Our experiment follows the line suggested by Lee and Kim [Phys. Rev. A 63, 012305 (2000)] and Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)]. An unprecedented large value of the teleportation “fidelity” has been attained: F=(95.3±0.6)%.' Phys. Rev. Lett. 88, 070402 – Published 30 January 2002 back
Einselection - Wikipedia, Einselection - Wikipedia, the free encyclopedia, 'In quantum mechanics, einselection, short for environment-induced superselection, is a name coined by Wojciech H. Zurek[1] for a process which is claimed to explain the appearance of wavefunction collapse and the emergence of classical descriptions of reality from quantum descriptions. In this approach, classicality is described as an emergent property induced in open quantum systems by their environments. Due to the interaction with the environment, the vast majority of states in the Hilbert space of a quantum open system become highly unstable to entangling interaction with the environment, which in effect monitors selected observables of the system.' 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
Feynman, Leighton & Sands FLP III:03, Chapter 3: Probability Amplitudes, 'We will begin in this chapter by dealing with some general quantum mechanical ideas. Some of the statements will be quite precise, others only partially precise. It will be hard to tell you as we go along which is which, but by the time you have finished the rest of the book, you will understand in looking back which parts hold up and which parts were only explained roughly. The chapters which follow this one will not be so imprecise. In fact, one of the reasons we have tried carefully to be precise in the succeeding chapters is so that we can show you one of the most beautiful things about quantum mechanics—how much can be deduced from so little.' back
Feynman, Leighton & Sands FLP III:04, Chapter 4: Identical Particles, 'In the last chapter we began to consider the special rules for the interference that occurs in processes with two identical particles. By identical particles we mean things like electrons which can in no way be distinguished one from another. If a process involves two particles that are identical, reversing which one arrives at a counter is an alternative which cannot be distinguished and—like all cases of alternatives which cannot be distinguished—interferes with the original, unexchanged case. The amplitude for an event is then the sum of the two interfering amplitudes; but, interestingly enough, the interference is in some cases with the same phase and, in others, with the opposite phase.' back
Feynman, Leighton & Sands FLP III:05, Chapter 5: Spin One, 'In this chapter we really begin the quantum mechanics proper—in the sense that we are going to describe a quantum mechanical phenomenon in a completely quantum mechanical way. We will make no apologies and no attempt to find connections to classical mechanics. We want to talk about something new in a new language. The particular situation which we are going to describe is the behavior of the so-called quantization of the angular momentum, for a particle of spin one.' back
Feynman, Leighton & Sands FLP III:06, Chapter 6: Spin One-Half, 'We will show you in this chapter how the transformation coefficients can be derived for spin one-half particles. We pick this case, rather than spin one, because it is somewhat easier. Our problem is to determine the coefficients Rji for a particle—an atomic system—which is split into two beams in a Stern-Gerlach apparatus. We are going to derive all the coefficients for the transformation from one representation to another by pure reasoning—plus a few assumptions. Some assumptions are always necessary in order to use “pure” reasoning!' back
Feynman, Leighton & Sands FLP III:07, Chapter 7: The Dependence of Amplitudes on Time, 'We want now to talk a little bit about the behavior of probability amplitudes in time. We say a “little bit,” because the actual behavior in time necessarily involves the behavior in space as well. Thus, we get immediately into the most complicated possible situation if we are to do it correctly and in detail. We are always in the difficulty that we can either treat something in a logically rigorous but quite abstract way, or we can do something which is not at all rigorous but which gives us some idea of a real situation—postponing until later a more careful treatment. With regard to energy dependence, we are going to take the second course. We will make a number of statements. We will not try to be rigorous—but will just be telling you things that have been found out, to give you some feeling for the behavior of amplitudes as a function of time.' back
Feynman, Leighton & Sands FLP III:08, Chapter 8: The Hamiltonian Matrix, 'The idea, then, is that to describe the quantum mechanical world we need to pick a set of base states i and to write the physical laws by giving the matrix of coefficients Hij. Then we have everything—we can answer any question about what will happen. So we have to learn what the rules are for finding the H’s to go with any physical situation—what corresponds to a magnetic field, or an electric field, and so on. And that’s the hardest part.' back
Feynman, Leighton & Sands FLP III:09, Chapter 9: The Ammonia Maser, 'In this chapter we are going to discuss the application of quantum mechanics to a practical device, the ammonia maser. You may wonder why we stop our formal development of quantum mechanics to do a special problem, but you will find that many of the features of this special problem are quite common in the general theory of quantum mechanics, and you will learn a great deal by considering this one problem in detail. The ammonia maser is a device for generating electromagnetic waves, whose operation is based on the properties of the ammonia molecule which we discussed briefly in the last chapter.' back
Feynman, Leighton & Sands FLP III:10, Chapter 10: Other Two-State Systems, 'In the last chapter we discussed some aspects of the ammonia molecule under the approximation that it can be considered as a two-state system. It is, of course, not really a two-state system—there are many states of rotation, vibration, translation, and so on—but each of these states of motion must be analyzed in terms of two internal states because of the flip-flop of the nitrogen atom. Here we are going to consider other examples of systems which, to some approximation or other, can be considered as two-state systems.' back
Feynman, Leighton & Sands FLP III:11, Chapter 10: MoreTwo-State Systems, 'We continue our discussion of two-state systems. At the end of the last chapter we were talking about a spin one-half particle in a magnetic field. We described the spin state by giving the amplitude C1 that the z-component of spin angular momentum is +ℏ/2 and the amplitude C2 that it is −ℏ/2. In earlier chapters we have called these base states |+⟩ and |−⟩. We will now go back to that notation, although we may occasionally find it convenient to use |+⟩ or |1⟩, and |−⟩ or |2⟩, interchangeably.' 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
Ian Duck and E.C.G. Sudarshan, Toward an understanding of the spin-statistics theorem, 'We respond to a request from Neuenschwander for an elementary proof of the Spin-Statistics Theorem. First . . . Then we discuss an argument suggested by Sudarshan, which proves the theorem with a minimal set of requirements. . . . ' back
Lamb shift - Wikipedia, Lamb shift - Wikipedia, the free encyclopedia, 'In physics, the Lamb shift, named after Willis Lamb (1913–2008), is a difference in energy between two energy levels 2S1/2 and 2P1/2 (in term symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy. Interaction between vacuum energy fluctuations and the hydrogen electron in these different orbitals is the cause of the Lamb Shift, as was shown subsequent to its discovery.' back
Lie Group - Wikipedia, Lie Group - Wikipedia, the free encyclopedia, 'In mathematics, a Lie group . . . is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Norwegian mathematician Sophus Lie, who laid the foundations of the theory of continuous transformation groups. Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. . . . One of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its "infinitesimal group" and which has since become known as its Lie algebra.' back
Louis de Broglie - Wikipedia, Louis de Broglie - Wikipedia, the free encyclopedia, 'Louis-Victor-Pierre-Raymond, 7th duc de Broglie . . . 15 August 1892 – 19 March 1987) was a French physicist who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave-particle duality, and forms a central part of the theory of quantum mechanics.' back
Martin H. Redish, A Pardon for Apaio Would Put Trump in Uncharted Territory, 'It has long been recognized that the greatest threat of tyranny derives from the executive branch, where the commander in chief sits, overseeing not just the military but a vast and growing network of law enforcement and regulatory agencies. Indeed, the Articles of Confederation didn’t even provide for an executive, for fear of what dangerous power he might exercise. While the Constitution, in contrast, recognizes the very practical need for an executive, that doesn’t mean its framers feared the growth of tyranny any less. The Fifth Amendment’s guarantee of neutral judicial process before deprivation of liberty cannot function with a weaponized pardon power that enables President Trump, or any president, to circumvent judicial protections of constitutional rights.' back
Nicholas Kristof, The Photos the U.S. and Saudi Arabia Don't Want You to See, 'Human Rights Watch has repeatedly concluded that many Saudi airstrikes were probable war crimes and that the U.S. shares responsibility because it provides the Saudis with air-to-air refueling and intelligence used for airstrikes, as well as with much of the weaponry.' back
Odd Arne Westad, The Cold War and America's Delusion of Victory, 'America’s post-Cold War triumphalism came in two versions. First was the Clinton version, which promoted a prosperity agenda of market values on a global scale. . . . The second was the Bush version. Where President Bill Clinton emphasized prosperity, President George W. Bush emphasized predominance.' back
Paul Dirac, The Fundamental Equations of Quantum Mechanics, It is well known that the experimental facts of atomic physics necessitate a departure from the classical theory of electrodynamics in the description of atomic phenomena. This departure takes the form, in Bohr's theory, of the special assumptions of the existence of stationary stats of an atom, in which it does not radiate, and certain rules, called quantum conditions which fix the stationary states and the frequencies of the radiation emitted during transitions between them.' back
Schroedinger picture - Wikipedia, Schroedinger picture - Wikipedia, the free encyclopedia, 'In physics, the Schrödinger picture (also called the Schrödinger representation) is a formulation of quantum mechanics in which the state vectors evolve in time, but the operators (observables and others) are constant with respect to time.' back
Sokolov-Ternov effect - Wikipedia, Sokolov-Ternov effect - Wikipedia, the free encyclopedia, 'The Sokolov–Ternov effect is the effect of self-polarization of relativistic electrons or positrons moving at high energy in a magnetic field. The self-polarization occurs through the emission of spin-flip synchrotron radiation. The effect was predicted by Igor Ternov and the prediction rigorously justified by Arseny Sokolov using exact solutions to the Dirac equation.' back
Special unitary group - Wikipedia, Special unitary group - Wikipedia, the free encyclopedia, 'In mathematics, the special unitary group of degree n, denoted SU(n), is the group of n×n unitary matrices with determinant 1. The group operation is that of matrix multiplication. The special unitary group is a subgroup of the unitary group U(n), consisting of all n×n unitary matrices, which is itself a subgroup of the general linear group GL(n, C). The SU(n) groups find wide application in the standard model of physics, especially SU(2) in the electroweak interaction and SU(3) in QCD.' 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
Stephen Weinberg, The Cosmological Constant Problems, 'Abstract. The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help with either; anthropic considerations offer a possibility of solving both. In theories with a scalar field that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else.' back
Stern-Gerlach experiment - Wikipedia, Stern-Gerlach experiment - Wikipedia, the free encyclopedia, 'The Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized. It demonstrated that atomic-scale systems have intrinsically quantum properties, and that measurement in quantum mechanics affects the system being measured.' back
String vibration - Wikipedia, String vibration - Wikipedia, the free encyclopedia, 'A vibration in a string is a wave. Resonance causes a vibrating string to produce a sound with constant frequency, i.e. constant pitch. If the length or tension of the string is correctly adjusted, the sound produced is a musical note. Vibrating strings are the basis of string instruments such as guitars, cellos, and pianos.' back
Werner Heisenberg, Über den anschauclichen Inhalt der quantentheoretischen Kinematik und Mechanik, 'Pre-publication proof sheet of the first paper in which Heisenberg advanced his famous uncertainty principle. Includes the Pauling annotation: "Given to me in Göttingen by Born." ; back
Wojciech H Zurek, Decoherence, Einselection, and the Existential Interpretation (the Rough Guide), 'The roles of decoherence and environment-induced superselection in the emergence of the classical from the quantum substrate are described. The stability of correlations between the einselected quantum pointer states and the environment allows them to exist almost as objectively as classical states were once thought to exist: There are ways of finding out what is the pointer state of the system which utilize redundancy of their correlations with the environment, and which leave einselected states essentially unperturbed. This relatively objective existence of certain quantum states facilitates operational definition of probabilities in the quantum setting. Moreover, once there are states that `exist' and can be `found out', a `collapse' in the traditional sense is no longer necessary --- in effect, it has already happened. The records of the observer will contain evidence of an effective collapse. The role of the preferred states in the processing and storage of information is emphasized. The existential interpretation based on the relatively objective existence of stable correlations between the einselected states of observers memory and in the outside Universe is formulated and discussed.' back

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