vol VII: Notes
2018
Notes
Sunday 5 August 2018 - Saturday 11 August 2018
[Notebook: DB 82: Life and Death]
[page 227]
Sunday 5 August 2018
We say that the uncertainty principe is what prevents atoms from collapsing to a point since the more closely we confine an electron the greater its momentum must be. But this is not really due to uncertainty but to the finite size of the quantum of action so ΔxΔp ≈ ℏ is a simple arithmetic relationship [arising from the dimensions of x, p and ℏ], not an 'uncertainty' relationship.
Auyang page 51: 'Being quantum fields φ(x)
[page 228]
and π(x) are quantum dynamical variables represented not by numerical functions but by operators in Hilbert space which is the space of the entire continuous system.' And which therefore has a basis vector for every point in the universe? Auyang: How is Quantum Field Theory Possible?
'Operators are [linear] transformations of the states of the field, for instance excite it in a particular mode at a particular point x.' How does this work?'Spacelike separated field operators commute.' How is spacelike separation represented in the Hilbert space of the universe [if the whole universe is represented in one Hilbert space. They must operate only on subspaces.]?
'Particles are normal modes or quanta of excitations of the field.' Normal modes have fixed frequencies like overtones in a string and are a complete set of solutions of the wave equation governing the system.
Auyang page 52: 'Quanta of interaction fields have names, eg photon, gluon.'
Ground state = no mode excited. Field operator = creation and annihilation operators, a†(kj) excites quantum in mode kj.
page 53: Creation and annihilation operators are dynamical variables but not observables.
Bose particles, any number per mode; fermion one per mode.
Ground state |0> - zero expectation of finding a field quantum in any mode. <Ψ>i ≡ <0|Ψ|0> = 0, but the square of the field operator has non-zero average - vacuum fluctuations which lead (eg) to the Lamb shift.
[page 229]
Auyang page 54: spontaneous symmetry breaking, Higgs field, Higgs particle, changes the masses of fields with which it interacts.
Interacting fields and gauge field theories.
'Systems of interacting fields constitute the most fundamental structure of the world as we know it today.' So why are they so horrendously complex?
page 55: 'In quantum mechanics non spatio-temporal features are generally called phases which are defined in a phase space or state space appropriate to the natural system under study.'
Isospin orientation occupies 3D isospin space: protons and neutron axes of isospin space.
'The relaxation of global symmetry is the starting point of gauge field theories.'
QED
Monday 6 August
Auyang page 57: ψ(x) → ψ'(x) = eiθψ(x), where eiθψ = U(1).
We can localize transformation to x ψ(x) → ψ'(x) = eiθ(x)ψ
Electromagnetic potential (photon) Aμ(x) can overcome the effect of a local phase change.
[page 229]
Auyang page 57: If a term [which represents the interaction between the electron and the electromagnetic field] -φ(x)γμAμφ(x) is added to the free electron Lagangian, then the resultig Lagrangian is invariant under the joint local trsnsformation of θ(x) and Aμ(x).
page 58: Logic of gauge theories
'We start with the free electron filed and end up with an interacting electron - electromagnetic field system'. Where the electromagnetic field is embodied as photons.
So: We start with a free matter field and derive the interacting field in the following steps:
1. 'an individual state space is set up for the local field φ(x) for each x
page 59:
2. A term is found to preserve global invariance in the face of local invariance.
3. This term is interpreted as the coupling between the phase of the matter field and the potential of the interaction fields.
In QED phase transformations involve a parameter θ and the phase exponent contains only numbers which commute. In nuclear interactions transformations involve several parameters and the phase exponent contains matrices which [may] commute.
Fibre Bundle Formulation of Dynamical Theories.
[page 231]
Auyang page 60: t'Hooft: 'All four forces are now described by means of theories that have the same general form. Thus if physicists have not yet found a single key that fits all known locks, at least all the needed keys can be cut from the same blank.
Auyang page 214: Fibre Bundle and Interaction Dynamics.
'In the 1960s . . . physicists . . . recognised that interaction potentials can be represented by connections on principal fibre bundles. . . . In 1975 Wu and Yang used the fibre bundle method to solve a long-standing probem on magnetic monopoles. . . . fibre bundle provides a unified conceptual framework for all our physical theories.
page 216: Principal Fibre Bundles
Auyang page 72; 'The philosophical task of this work is to articulate a sense of the objective world that accounts for the working understanding and the success of quantum theories . . . My concern is how we have managed to understand the quantum world to the extent that we do without a satisfactory quantum measurement theory. Ie avoiding the real issue.
Bohr: 'Atomic systems should not even be thought of as possessing definite properties in the absence of a specific experimental setup designed to measure these properties.' The 'experimental setup' is a reference frame (a measurement operator) which we use to measure the quantum system and arrive at definite results, like a track in a cloud chamber.
R. I. G Hughes ' "quantum systems do not have definite properties" ': tell that to an atomic clock.
[page 232]
Auyang page 65: Object is a symmetry of a state space which does not change with a change of state in the state space.
page 68; Penrose: ' "It seems to me to be perfectly clear that there is (if we accept standard quantum mechanics) a completely objective meaning to
|φ> [= eiθ|φ>].
The weak spot in physics is that it thinks that continuous mathematics is a valid representation of the world and deterministic, whereas the world must be quantized to be deterministic. Make the argument at the beginning. We are taking the Kronecker view here. Mathematical analysis is a logical creation that may serve as a symmetry but ma not reflect the real world. Have said this before, and will probably say it again, but it s important since it invalidates the whole of classical and quantum physics. We have to replace it with something digital, but how? The perennial question which can be solved by continuously chipping away. Leopold Kronecker - Wikipedia
page 69: 'As the classical positional value is defined relative to a coordinate system, so the quantum amplitude is defined relative to a basis associated with an observable [like the eigenvalues of an observable].'
page 70; 'In this section I make a clear distinction between the meaning of being physical and being empirical.'
page 72: 'In stipulating that quantities admissable as measured results must be real numbers, quantum theories made explicit a general limit to human empirical capabilities. The general form of our sensible capability is representedby real numbers.' ie counts or ratios of counts.
[page 233]
Numbers are a form of representation.
Auyang page 72: 'The paradigm entity represented by the real numbers is the continuous line.' Which I think does not exist. We can only observe quanta, ie natural numbers.
page 73: All visualisation involves continua? What about counting sheep? Everything we can see is quantized, down to grains of sand.
'Classical characteristics are represented by real numbers.'
Quantum characteritics are irreducibly complex — ie they are periodical. It all comes down to phase, which is an angle [a two dimensional object].
page 74: 'The relative phases are somehow destroyed in experiments, exactly how we do not know . . . it is due to the fundamental limitation of our form of observation.' If there was anything to see there in the first place [perhaps, as we can only observe whole quanta, we can only observe 'full cycles' of phase, not partial (relative) circuits].
Tuesday 7 August 2018
It is easy to argue against the details of quantum field theory on the grounds of the non-existence of mathematical infinity in the world and some of the inconsistencies noted by Veltman, but we have to face the fact that it gets results and any reasonable replacement seems very distant but necessary if we are to be thoroughgoing panpsychologists. Veltman: Diagrammatica
We understand both the constraints and the freedoms on people to arise from "society" and we think similar forces are at work in physics, where the relationships between particles determine what they are.
[page 234]
Auyang page 75: "kickable = responds to stimulus. This requires a theory.
page 76: 'The deeper physical significance of the coupling between phases and potentials will be discussed in §27 (pp 183 sqq [this notebook pp 248 sqq])
'To determine a quantum state |φ> we need to find out its amplitude in [each element] of one set of bases.'
page 77: 'The utility of quantum phases in real life engineering systems is the ultimate proof of their physicality [but this does not prove that they are continuous].
page 78: 'Many studies have shown the impossibility of systematically and consistently assigning definite eigenvalues to quantum systems under certain reasonable constraints.' What about laser? What about spectroscopic observations of atoms? [the eigenvalues we read are the eigenvalues of the operator we use for our measurement].
page 80: 'The property of the quantum system is its wavefunction in the position representation and momentum amplitude in the momentum representation.'
page 81: 'It appears that the world requires two general classes of predicates, quantum and classical, for description [maybe classical is a view of the quantum made symmetrical by the assumption of macroscopic continuity in the place of microscopic quantization].
page 82: '. . . a substantial account of the relation between amplitudes and eigenvalues is not required for a working understanding of quantum theories. My philosophical task is to find the categorical framework that is responsible for both the working understanding and the recognition of deficiency in understanding [what is a categorical framework?]. Paul Studtmann (Stanford Encyclopedia of Philosophy): Aritotle's Categories
[page 235]
page 83: 'There is no universally unified theory that accounts for a levels of complexity.' I think there is, modelled by communication networks that hold for the parts of atoms, birds, nations and galaxies.'
A network is a dynamic structure. The connections only exist as long as they exist and many of them are wireless, depending on photons or phonons or some other bosonic particle representing some 'field' ie communication medium.
If we think of a particular quantum measurement as a source we can use the Born rule to compute the source entropy given a set of eigenvalues si. From a physicists point of view we cannot predict which eigenvalue will be emitted each time we make the identical measurement, but the sequence of measurement will look like a random string emitted by a source, but the string may nevertheless have meaning like the string of letters in this paragraph, if the reader knows how to decode it, as you do since you are reading this. We know that a perfectly coded message has maximum entropy, and is therefore indistinguishable from a random string, despite its meaning. So, we might ask is a quantum source repeatedly measured conveying a message if only we knew how to decode it? We guess not because we think quantum sources are too simple to make complicated speeches, but is this true particularly in the wild, outside the laboratory? It is certainly possible.
page 84: There is no random mechanics in the kinetics of gases because we think classical processes are deterministic. Nevertheless it looks random and statistical methods give credible answers.
[page 236]
Auyang page 86: 'An observable [matrix] introduces a representation of the quantum state space by coordinatizing it.' in terms of the eigenvectors of the observable.
page 89: 'A microscopic object cannot be specified without an account of the entire measuring apparatus because of the unavoidable and inexplicable interaction between them.' "Unavoidable" makes no sense, because it is necessary for the measurement interaction or event. "Inexplicable" — why? We are simply forming the product space of the interacting systems and getting a readout corresponding to the eigenvectors of the measurement operator. Zurek. The "independent reality: is the conversation between system and measurement operator just as the independent reality of a conversation between two people is the encoding, transmission and decoding by the measurement operators in the minds of the conversants. We may think of the visual processing system as a layered measuring operator which extracts a certain set of eigenvalues out of the data presented by the retinas. Wojciech Hubert Zurek: Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
Heisenberg: 'We can no longer talk of the behaviour of particles apart from the process of observation.' We could never talk about the behaviour of anything part from the process of observation. Classical ideas of objectivity are somewhat fallacious.
page 90: 'primitive' - unanalysable
[page 237]
Auyang page 90: 'We see images . . . impressed on the passive receptive mind.' Totally wrong. The conscious images are the output of a long processing pipeline which has ben adapted by evolution to provide a visual system which contributes to our fitness, the modern analogue of Kant's a priori's.
page 91: 'A common Primitive Structure of Physical Theories' which, if true, should reflect the common structure of the physical world.
page 92: symmetry: 'invariance under transformations of representations'.
Wednesday 8 August 2018
page 92: Symmetry: invariance under transformations of representations tells us nothing about reality, only about representations. We are looking for real symmetries, embedded in reality, like the human symmetry expressed by the Universal Declaration of Human Rights etc. United Nations: Official UN Universal Declaration of Human Rights Home Page
page 93: Weyl: ' "All a priori [ie vacuous] statements on physics have their origins in symmetry." '
page 96: I myself am the reference body for my sensual empirical knowledge.
page 97: There are no theory free observations. M observation of you is built within the tacit dimension of everything abut human nature, known and unknown, which sets us both on the same human frame and gives meaning to the raw data we exchange.
[page 238]
Auyang page 97: Hilary Putnam: ' "On [the perspective of metaphysical realism] the world consists of some fixed totality of mind independent objects. There is exactly one true and complete description of the way the world is." ' Which is the world itself, including all the minds within it [most of our knowledge is abstract, ie capturing symmetries rather than detailed instances].
page 99: 'The multiplicity of representations of the same object forces us to recognize the idiosyncracies of particular representations; hence it clarifies the meaning of conventionality.'
' "The representations are united in the object" ' Kant.
We are inclined to give ourselves a special position in the world as observers, but insofar as the world is a communication network, everything is observing everything else and reacting to the messages it receives.
page 105: 'The observer has no place in the working understanding of quantum mechanics.' Wrong. Observer is a term that applies equivalently to each of the entities involved in a quantum (communication) event.
page 106: 'We have no satisfactory theory of perception.' ?
'a corpse is no observer'. It certainly is from a quantum mechanical point of view. It is observing all the photons that fall on it [and responding with other photons].
Everything is a subject.
[page 239]
Auyang page 107: physical interactions represented by |φ> ⊗ |ψ>. In quantum mechanics a observes b implies b observes a. The relation of observation is a communication.
page 109: 'In quantum mechanics there is a symmetry between observer and observed.'
Thursday 9 August 2018
Maybe the time has come to devise a random boolean device to explore the logical evolution of a layered universe. Step 1: choose a language. Python: Python Language Home Page
Shannon's theory is worked out in real function space with a metric. What do we get if we work it out in complex Hilbert space? Claude Shannon: Communication in the Presence of Noise
Auyang page 113: 'The arguments of Hume and Kant have been confirmed by quantum mechanics. The observer or instrument qua observer is never found in the content of quantum mechanics.' ? ? So how come what we observe are eigenvaues of the observable?
Transformation: lossless processing pipeline.
page 118: Saul Kripke: ' " There is no mathematical substitution for philosophy." '
page 119: Einstein: ' " There is no such thing as empty space, ie a space without a field. Space-time does not claim existence on its own but only as a structural quality of the field." ' Mathematically, space-time is the domain of the field and so perhaps logically prior to it [ie a layer of processing underlying the field]. Or maybe the field is its own domain, insofar as it is coordinate free.
[page 240]
Auyang page 119: 'Going from classical mechanics to quantum field theory, the focus of physics changes from locomotion to dynamical interaction.' What I would call communication [which flows across space and time].
'The primary form of matter changes from discrete mass points in empty space to continuous fields comprising discrete events.' Measured by the quantum of action.
'The primary dynamical concepts change from action-at-a-distance to coupling-on-the-spot, from external forces to interactions generated by the interactants themselves.' Which are what? Particles, events, fields? Network again, maybe logic, encoding, decoding, messages embodied in particles. What embodies fields?
Unlike classical and non-relativistic quantum mechanics, where spatial position is a dynamical variable and time is the lone parameter, position is now a parameter on equal footing with time.' Which means?
page 121: 'entities are not individuated without spatial and temporal concepts' [so how are the many different particles fields, which presumable exist in superposition, individuated]. But prior to this individuation is the logical individuation p is not not-p, and we take this to be fundamental ('primitive') in our panpsychic psychophysical world.
'A field is a genuine whole comprising individuals, a continuous world with discrete and concrete entities, technically called events.' In other words a self contradictory setup like a continuum of points.
[page 241]
'Sacrifice' is a theological terms, a loss intended to please God, in effect a political donation with expectation of recompense.
Auyang page 129: 'All local fields with the same parameter x and their products comprise an event. A event is an entity in an interacting field system. An event is extensionless [null?] in four dimension; hence it is spatially and temporally invisible. However it is analysable into idealized free local fields and their interaction. The indivisibility and analysability are compatible with he non-spatial characteristic of quantum possibilities.' So how does all this happen in reality [we are faced with just as many mysteries as in Christianity!] ?
'An event is the transformation of the state of a field system at a given point.' Why? I would prefer it to be the meeting of two or more entities through communication, not just a random fluctuation of the vacuum but something actually happening, a meeting [communication reduces the interval between entities to zero when we take into account the velocity of communication].
page 130: Fibre bundle: 'partition of unity'. Fiber bundle - Wikipedia, Partition of unity - Wikipedia
page 135: 'The implicit relation obtains among events, not between events and spacetime. There is no relation such as embedding or occupation between events and spacetime, for there is no spacetime apart from the system of events.' So you say, but this seems to be the source of most of the problems in physics, overlooking the dynamic role of space embodied in the quantum relationships ΔpΔx ≈ ΔEΔt ≈ ℏ. Space is not a continuum, it is a low level logical foundation of the universal network (he keeps saying this, but what does it mean?). Logical individuation, x is not y and so on.
Friday 10 August 2018
page 137: Space-time is substantial if it exists independently of material entities.
[page 242]
Perhaps space-time is a 'material' entity, or at least a logical one, since it enables / is the implementation of the not operator, insofar as t1 is not t2 and x1 is not x2.
Space-time behaves just like momentum-energy = matter, ie dynamic structure, energy = dynamic (ie time variant) and momentum = structure (space variant) [so space-time is a dynamic variant of Aristotle's materia prima]. Materia prima - Wikipedia, Thomas Ainsworth (Stanford Encyclopedia of Philosophy): Form v. Matter
Auyang page 138: 'The existence of a filled space-time implies the existence of the past, present and future [simultaneously, as envisaged in the 4D formalism of general relativity] ? Space-time is instantaneously full.
page 141: 'Since [rest] mass and spin, the most basic characteristics of particles, are tied to spatio-temporal concepts, space-time is absolute.' [?]
page 147: 'The concept of fields integrates the concepts of matter, space-time snd dynamical interaction.' As does the concept of network communication, but the network is conceptually more comfortable even if we have yet to learn how to compute with it. Maybe many paths and feynman diagrams ie stationary action, ie completed computation. Statistics does not come from the nature of computation but from the relative frequences of different computations [yielding different results with a corresponding statistical distribution].
'. . . curvatures can all be interpreted as interaction field strengths.' or (which amounts to the same thing) rates of communication.
page 148: Weinberg: ' Separating gravity and interpreting it as substantive space-time has "driven a
[page 243]
wedge between General Relativity and the theory of elementary particles". '
How can a point particle have a personality, eg electron mass, spin and charge [each of which must be infinitely dense]. If we think of this in terms of logic and the quantum of action, size does not matter.
What do we mean by 'categorical difference'? Generic difference, eg mathematics vs physics?
Auyang page 149: 'ontological status of physical entities.' to be or not to b>
We may see space as a subroutine, a lower layer that may be called to perform a certain function to provide a photon with energy and momentum, for instance, as it does also for an electron, so we can have pair production, Is this getting a bit closer to something? - introduces subroutine for lower network layer — which requires passing parameters.
page 150: 'Space-time is a strutural property [component?] of the fields, not the other way around,'
'fields [with their complicated structures] are self sufficient' (by definition). Part of the motivation of the network model is to tie the complex universe back to the classical god via the initial singularity.
page 151 'The fields, which I regard as fundamental ontology, are unobservable and unreal according to positivist standards.' What about permanent magnets?
Evolution requires prior layers to be substantial, ie physical, ie capable of existence without the higher layers, so atoms can exist without molecules, electrons without atoms etc. But what about quarks?
[page 244]
At the speed of light space-time ceases to exist. It only comes into existence when we have particles with rest mass, ie whose internal energy represents internal process [which has to be translocated through space, ie massless particles have no internal process].
We would like to interpret fields as logical entities embodied reason[ing].
Auyang page 152: 'Reference is were ontology, epistemology and semantics meet.'
Ruth Bader Ginsberg had a simple task in a way because it is perfectly obvious that women are equivalent to men, legally and constitutionally identical, the same species, elements of the human symmetry. What is the obvious task I am trying to undertake? that the world is divine. RBG (film) - Wikipedia
'. . . an empirical theory is not complete in coordinate free form, for coordinate systems must be invoked to yield numbers that can be compared to experiments.'
Saturday 11 August 2018
'Coordinate systems . . . constitute an integral part of the structure of physical theory,' Measuring the S matrix: input particles ↔ output particles. question ↔ answer.
In interpret the local symmetry group as the kind of the field . . . and interpret [the space-time group] as the referential structure of the fields theories.' So in LHC accelerator provides spatially located input streams of particles, detection systems determine the nature and distribution of output particles.'
page 153: 'Semantically, the values of coordinates serve as proper names.'
Auyang seems to be able to make the discussion of field
[page 245]
theories much too complex for something which applies to the simple primordial structure of the world, even though we have to understand that primordial structure through the enormously complex structure that we now inhabit.
Auyang page 155: We would like to say that coordinates are natural fixed points, that is invariants or algorithms that are frequently instantiated. From this point of view an electron, a photon and the conservation of energy snd momentum are all coordinates.
we are looking for forms of words that model the form of reality, a one-to-one corresponding description.
page 157: 'A field is a whole comprising individual elements.' [logical elements?]
page 158: 'A field quantum is a discrete increment in a mode of field excitation and is often called a particle,' How does such a particle (eg photon, electron) move?
'The technical terms "particle" and "field" mean something diametrically opposite to the ordinary meanings of particles and fields' [which is not very helpful!].
One analogy is phonons in a solid, states of motion for the solid atomic lattice.
page 159: 'Are field quanta entities?' Yes and no, she says,
page 165: 'We are intrinsically spatial and temporal beings.' ? Or are we intrinsically logical, interested more in conversation than space-time relationships?
'How to reconcile non-spatial quantum characteristics with spatio-temporal individuation is perhaps the next great problem physics has to overcome.' We are individuated by our personalities, not our positions in space [just like fundamental particles]'.
[page 246]
Auyang page 166: In human affairs, language is the gauge particle.
' events . . . are totally disjointed. There is neither spatio-temporal nor qualitative relation between events.' This looks like rubbish. How can it be if events are meetings of individuals? ' The absence of qualitative relations is rigorously expressed by the fact that the convention of definite description of each event is chosen independently of that of any other.' So what happened to the gauge particles coupling local symmetries?
She cooks up a paper tiger in the form of a world with a lot of discrete individuals and then has to explain how they are connected. In fact the very multiplicity of event as a consequence of their connection. The world does not begin as dust which has to be connected but, like the trinity, the multiplicity emerges from the creative power of the interaction. At least that seems to be a much more reasonable approach. The world, like the tree of life, begins as one and diversifies, rather than it begins diversified and then unifies. Singularity is established by descent. Auyang has no explanation of the source and differentiation of the diverse elements of the world. She proves, in effect that quantum field theory is impossible, and must be replaced with something else. But what?
page 170: 'The number of points in M [the cosmic manifold] and hence the number of events in the world are as permanent as M' Very formalist.
[page 247]
'The permanence of the number of events paves the way for the introduction of conservation laws.' Makes no sense (at lest to me). Conservation laws are more likely to exist because some quantity [initially non-existent arises from ] a split into a duality like equal positive and negative charges, equal kinetic and potential energy, equal momentum in two opposite directions etc.
In the end if we want to explain anything we must explain everything and in order to do this we have to start with something which is simple enough to admit of complete explanation in a relatively complete way which we can then use as a skeleton to deal with more and more complex systems.
Auyang page 173: 'We are relieved from the notion of radical existence-change; all changes are conceived as alterations in the abiding four dimensional framework. The excitation and de-excitation of fields, also known as the creation and annihilation of particles, are understood in this way.' Matter and form again. Perhaps we should bite the bullet, in the name of simplicity, and understand creation at the root as radical changes of existence from which we create space-time and all the things that are executed using the subroutines we call energy and momentum.
page 176: Hume imagines a world of disconnected dust, and Auyang seems to follow him trying to connect thing by the mathematical notion of a differentiable manifold which is just a continuous representation of a discrete network.
Auyang is trying to solve all sorts of philosophical problems by assuming the rather dubious truth of quantum field theory.
page 179: 'How does a memory know that it is a memory?' By coupling itself to a know invariant object like a text or a sculpture.
[page 248]
page 181: 'Our failure to justify consistent predication stems from our having assumed a concept of objects that precludes it.' Ie you deny the ability of all objects to communicate.
For Auyang "gauge principle" is root of communication. It is much easier to understand in terms of network communication rather than differentiable manifold etc.
page 183: Communication modifies 'the concept of individuals [into] that of individuals in the world.'
§ Relational Properties: Phase and Potential
page 185: 'In QED . . . the fundamental coupling term eψ(x)γμA(x)μφ(x) involves the potential Aμ . . . For it is the potential, not the force, that couples to the phase factor.'page 186: 'Both relational properties and their coupling belong to a single event designated by the same x [coordinate]. Thus the concept of event is enriched.' (?) - It was already the meeting of two things force and object, [force] = ∂μAμ, event = φ.
'When we do measurements we effectively substitute one partner of the interacting system with out experimental equipment and then discount the equipment.' No, this cannot be done, the measurement is effectively subjective.
Sunday 12 August 2018
[page 249]
Auyang has very little to say about computation and renormalization.
Auyang page 187: '[Tangent vectors] represent all instantaneous variations, including going from one event to another as manifested in an infinitesimal change of identity or position and the infinitesimal differences in the qualities of various events.' Very commonsensical but what if true continua and true infinitesimals do not exist, but everything is locally quantized? Ie we do away with all the ethers and just face quantum steps on the universal process, ie phase is not continuous, but steps like a ticking clock. Harder to imagine than continuity [this might be a reason for complex phase since the imaginary overlaps the real as we go around].
She is heavily dependent on continuous geometric visualizations. So she likes Feynman's contributions from all paths (page 189) which contributes to the demise of empty space, which is in a way Hume's bugbear.
Yet 'we find that the general concept of interactions is inherent in the general concepts of objects.' otherwise we would never see objects. She seems to think that field theories are special to physics, whereas they are to be understood more as a subset of universal communication theory.
page 189: Now to remormalization. Perturbation theory assumes interactions of things are relatively minor, rather than as we find in the case of quarks, constitutive.
An hypothesis is a set of stipulations which are ultimately justified by the observable consequences of the hypothesis, eg wave functions are probability amplitudes. I am pursuing a set of stipulations that might unite the physical world and a concept of divinity. Why am I doing this? Maybe just political pigheadedness like Mr Trump and Mr Abbott.
[page 250]
In e20_paradise we will confine ourselves to the network version of QED, drawing from Zee and Peskin and Schroeder.
QED is worked out as a perturbation theory, but the space-time network approach would prefer the idea that the communication relationships are substantive, as they are in the trinity beginning somehwere in the distinction between bosons and fermions, so we have the layers
action
energy - time
space-time - momentum - energy
fermion - boson - velocity of light
etc etc gravity, quantum chromodynamics, weak force
Auyang page 192:
' There is nothing to prevent an electron from absorbing a photon that it itself creates. In fact the electron cannot escape from interacting with the electromagnetic field it itself generates. The self energy of the electron gives rise to infinities.' By the same token we would expect the Father's interaction with itself to create an infinity of Sons? A bit weird, but why should an electron create an infinity of interactions with itself except in a theory that has completely missed the point whatever that is.
page 193: A truly fundamental theory should be able to specify all the dimensionless parameters,
Glashow: ' "Today the standard theory requires the specification of ninetween fundamental dimensionless parameters.'
[page 251]
4 Problems:
1. Measurement problem
2. Statistical nature of measured data - same as a well coded message
3. Ground state fluctuations - how does uncertainty create energy
4. Spooky action at a distance
Auyang page 194: Epilogue - Intelligibility of the objective world.
Maybe we can only understand the world subjectively [general relativity is subjective, via Gaussian coordinates]? The subjective mind evolved in concert with the world [there is no outside to be objective from, if the universe is divine, God's eye view is subjective, looking into itself rather than outside].
Some more problems with current physics
5. renormalization - infinities do not appear in reality
6. continuity - a false concept given the quantization of action
7. explanation of digitization/quantization - Shannon's theory of error control
8. [QED, QCD] much too complex for a fundamental theory of the universe
9. 19 parameters
10. Infinite energy of initial singularity
11. No explanation of vast number and variety of particles
12. Path integral explores an infinity of paths to get stationary action
13. determinism of continuous mathematics 14. infinite density of point particles [15.why do we square the probability amplitude to get probability
16. Why are the metrics in flat space quadratic
. . . ]
