Notes
Sunday 20 March 2022 - Saturday 26 March 2022
[Notebook: DB 88: Salvation]
[page 37]
Sunday 20 March 2022
So we align all the basis vectors of the quantum Hilbert space of which there are ℵ0 distinct species (like angels) in different sequences to achieve certain transformations.
Now read Many Worlds, Everett III and Deutsch and suggest that some of these ideas are absurd and therefore untranslatable, since no reversible codec exists. Hugh Everett III et al (1973): The Many Worlds Interpretation of Quantum Mechanics, David Deutsch (1997): The Fabric of Reality: The Science of Parallel Universes - and its Implications
De Witt page v: Preface: 'In 1957 in his Princeton doctoral dissertation, Hugh Everett III proposed a new interpretation of quantum mechanics that denies the existence of a separate classical realm and asserts that it makes sense to talk about the state vector for the whole universe. This state vector never collapses, and hence reality as a whole is rigorously deterministic.'
[De Witt page 141 in Everett III: "Relative State" Formulation of quantum mechanics].
[pagination from Weylmann.com. Hugh Everett III (1957): "Relative State" Formulation of Quantum Mechanics]
Wheeler on Weyl: ' Weyl invented the gauge concept in 1918. By 1928 he had reformulated and restated the idea in the way it is still understood: "gauge invariance corresponds to the conservation of charge as a coordinate invariance corresponds to the conservation of energy and momentum."
'the most elementary statement of algebraic geometry: that the boundary of a boundary is zero'. Misner, Thorne & Wheeler (1973): Gravitation chapter 15.
Back to Weylmann.com/relative_state.pdf
Everett page 2: "The special postulates of the old theory which deal with observation are omitted in the new theory. The altered theory thereby acquires a new character. It has to be analysed in and for itself before any identification becomes possible between qualities of the new theory and the properties of the world of experience.'
ie he seems to follow the idea that quantum theory exists independently of space-time. So far so good. "External observation" formulation of quantum mechanics:
Two processes change state function φ: 1. Observation; 2. deterministic evolution of wave function ∂φ = Aφ, A a linear operator.
[page 39]
Everett page 3: 'von Neumann showed how to treat a special class of approximate measurements by the method of projection operators. However a general treatment of all approximate measurements by the method of projection operators can be shown (sec 4) to be impossible.'
page 4: ' No way is evident to apply the conventional formulation of quantum mechanics to a system that is not subject to External observation' Because there is no external observation. The system is conscious, observes itself.
So ' This paper proposes to regard pure quantum mechanics (process 2) only as a complete theory. It postulates that a wave function that follows a linear wave equation everywhere [?] at all times [?] supplies a complete mathematical model for every isolated physical system without exception. [It further postulates that every system that is subject to external observation can be regarded as part of a larger isolated system.] '
page 5; Section 4 investigates the states of composite systems in terms of the states of constituent systems. The mathematics leads one to recognize the concept of relativity of states in the following sense: a constituent system cannot be said to be in any single well defined state independently of the remainder of the composite system [introducing the role of a network of communication which we represent with a matrix operator].' In the present formulation all measurement and observation processes are to be regarded simply as interactions between the physical systems involved—interactions which produce strong correlations.'
page 8: 'The discontinuous "jump" into an eigenstate is thus only a relative proposition dependent on the decomposition of the total wave function into a superposition and relative to a particularly chosen apparatus / coordinate value.'
page 9: In order to say that observer O has observed event α it is necessary that the state of O has become changed from its former state to a new state which is dependent upon α [lot of instantaneous communication throughout the universe required here - entanglement?].
Observers therefore need memories [where can they store them?]
page 13: ' These two rules, which follow directly from the superposition principle, give a convenient method for determining the total states for any number of observation processes in any combination. We now seek an interpretation of such final states.
page 15; ' We now arrive at the following picture: Through all the sequence of observation processes there is only one physical system representing the observer but there is no singe state
[page 40]
of the observer. What we are trying to say is that in some way the superposition of the state of the observer and the state of the observed system = 0. Perhaps this is a way of saying Wheeler's boundary of a boundary is zero.
So ' Thus with each suceeding observation (or interaction) the observer state "branches" into a number of different states. Each branch represents a different outcome of the measurement, and the corresponding eigenstate for the object-system state.
Everett page 15 (cont): ' The trajectory of the memory configuration of an observer performing a sequence of measurements is thus not a linear sequence of memory configurations, but a branching tree, with all possible outcomes existing simultaneously in a final superposition with various coefficients in the mathematical model.'
Now that my energy is going I have to look for faster algorithms for my success and I remain wedded to the idea that what I have got to say makes some impact on our expectations of both theology and physics.
How do we reconcile the transfinite expansion of the real numbers with quantum mechanics?
Everett overcomes the problem of the relationship of the Hilbert world and the Minkowski world by deleting the Minkowski world, saying that it tells us nothing because we cannot see the changing superposition of a [system] infinitely branching into trees with infinite branches [with] no real way of representing or observing them.
All he really seems to be saying that it is the Hilbert world interacting within itself that brings to us the variety we observe in our classical world.
I agree with Everett on the point implied by his treatment of observation that it is the universe interacting with itself. The real issue for engineers and experimentalists is the nature and appearance of a particular interaction which we set up and observe with our machinery, but there is a mystical boundary between our world and all the others.
[page 41]
Everett III page 18: 'There is direct correspondence between our measure structure to the probability theory of random sequences.'
page 19: ' This prescription for the calculation of averages over memory sequences by probabilities assigned to individual events is precisely that of conventional "external observation theory" (Process 1).'
page 21; '. . . pure process 2 wave mechanics without any initial probability assertions leads to all the probability concepts of the familiar formalism.'
'Discussion: The theory based on pure wave mechanics is a conceptually simple, causal theory which gives predictions in accord with experience. It constitutes a framework in which one could investigate in detail, mathematically and in a logically consistent manner a number of sometimes puzzling subjects such as the measurement process itself and the interrelationship of several observers.'
And in real life we have to recognise that every particle is observing every other according to various protocols (forces, languages, codes) all sharing in gravitation which means we need to deal with the interactions of two infinite sets, {observables} and {observers}, subject to the constraint that observation is bidirectional observer &ident; observable.
Next Wheeler's crit; But before that Jeffrey Barrett Stanford Jeffrey Barrett (Standord Encyclopedia of Philosophy): Everett’s Relative-State Formulation of Quantum Mechanics
' So the standard theory has two dynamical laws: the deterministic continuous linear rule (4a) describes hw a system evolves when it is not being measured, and the random, discontinuous non-linear rule (4b) describes how a system evolves when it is measured.'
'. . . if observers and their measuring devices are understood as being constructed of simpler system each behaving as quantum mechanics requires each obeying rule 4a, then the standard formulation of quantum mechanics is logically inconsistent, since it says that the two systems must obey rule 4b.'
De Witt: ' "The trajectory of the memory configuration of a real observer . . . does not branch. I can testify to this from my own introspection, as can you. I simply do not branch".' Wrong. You just not see all our other branches [and they cannot see you]. Otherwise the theory would be justified in observational grounds,
'5.1 Experience is found in the relative memory records of observers.' [What if the observer is a photon, annihilated on contact?]
[page 42]
'5,2 Pure wave mechanics predicts that one would not ordinarily notice that there are alternative relative records.'
'5.3 The surplus structure of pure wave mechanics is in principle detectable and hence not surplus at all . . . all branches, in any basis, are in principle detectable.'
'5.4 One should expect to find in standard quantum statistics a typical relative sequence of measurement records.'
' the problem here is more fundamental: insofar as a probability is a measure over possibilities where precisely one is in fact realized and insofar as all the possibilities are represented in pure wave mechanics there simply can be no probabilities associated with alternative relative sequences of measurement records,'
' In his description of the may words interpretation, De Witt (1970) emphasized the fact that the central feature was the metaphysical commitment to a potentially splitting world.'
De Witt: ' ". . . However Everett, Wheeler and Graham's interpretation of quantum mechanics pictures the [Schrödinger's] cats as inhabiting two simultaneous non-intersecting but equally real worlds".'
Monday 21 March 2022
Deutsch page 32: the waffle about parallel universes starts here. David Deutsch (1997): The Fabric of Reality: The Science of Parallel Universes - and its Implications (ref link above)
Light is invisible unless the sensor annihilates it [dying to be seen]
page 34: Light is particulate. Is this quantization?
[Deutsch first mentioned in notes 2003 m05d04. DB 25]. Book records not dated until #626, 16 April 1999]
[The dimensions of h are ML2T-1] the same as angular momentum [in Minkowski space], suggestive of the fact that the fundamental processes if the universe appear to be cyclic. [Although we think of a quantum logically as a not operator, it is physical and has a unit of angular momentum, ie it is real].
[page 43]
The difference between action and energy is time: energy = h / t.
So in Minkowski space we have ΔE.Δt ≈ h a fundamental limit on the precision of measurement in spacetime. We can only measure it with units of h so there are uncertainties associated with every quantum step.
The fact that h has built in angular momentum means that nothing can stop it from spinning without annihilating it, which happens with photons.
Tuesday 22 March 2022
Deutsch page 44; ' Thus we have inferred the existence of a seething prodigiously complicated, hidden world of shadow photons.'
page 45: 'It follows that reality is much bigger thing than [it seems and most of it is invisible]' if we consider possibility to be real, but it is in fact half real, a potential not yet actuated, the core of Aristotle's hylomorphism : matter is the possibility that form makes actual. Hylomorphism - Wikipedia
Then the fantasy continues that there is another load of extrascientific invisible universe like this one. He is going in the wrong direction - the invisible universe of unrealized possibility [potential energy?] lies beneath, and not on top of spacetime.
page 47: 'Thus we have reached the conclusion of the chain of reasoning thst begins with strangely shaped shadows and ends with parallel universes.' Just as improbable and and unprovable as the old Christian God.
page 49: '. . . interference is observed only in special situations where the paths of a particle and its shadow counterparts separate and reconverge (as when a photon and a shadow photon are heading toward the same point in the screen' [ie moving through real spacetime].
He has got a glimpse of two factor authentication here but it normally happens in the Hilbert regime where a vector and its complex conjugate interact as eigenvectors to produce a real particle with an eigenvalue. This idea gives us a clearer picture of quantum / inertial interaction, the mechanism that creates real particles (bosons) and space (fermions).
page 50: Did Everett invent the multiverse with his branching or was this step taken by De Witt?
page 52: ' Tangibility is relative to a given observer' [a fundamental theorem of quantum mechanics - action occurs only when there is harmony. Dissonance does nothing, so photons go straight through glass, nothing will talk to them].
[page 44]
Action is a mark in time, it has a before and an after and may be numbered to give us numerus motus secundum prius et posterius. Aristotle (Time): Aquinas' Commentary on Aristotle's Physics 219b sqq
Mathematicians think a set whose cardinal is ℵ1 is continuous and use this idea in proofs such as fixed point theory and Noether's theorem. But this is not really true because no information is passed along this channel because the points in a continuum (so called) are not by definition continuous because they are not welded tgether. They do not have ends in common [point set theoretical proofs by continuity may be therefore considered suspect or circular, like the epsilon-delta argument that assumes that epsilon and delta are themselves continuous quantities.] (ε, δ)-definition of limit - Wikipedia
One can fourier transform from a string of symbols into a file of frequencies and phases that carries the same information. In this way one packages a whole musical concert in the frequency / phase domain.
The key to the computational power of quantum mechanics is the continuous deterministic transformation created by a unitary operator which is understood to operate on the state function in an entropy preserving and reversible manner. By a suitable choice of operators one can maintain the integrity of a multidimensional piece of Hilbert space into any other orthogonal basis. This we might see as a permutation of the order of execution of the operators we are applying to the state function : we are looking at something here as the computer network operating inside a Lie group, logically continuous rather than point set continuous. We may look upon this process as a sequence of superpositions whose complex expression is a countably infinite permutation group of coupled processes. It all comes down to the codec, and here we can deal with gravitation as the "null" codec.
Then we come to the digital face of quantum mechanics [which] is what we observe, the interactions of particles, ie messaging between particles. Gravitation works through the zero code, readable and writeable by energy. In a sense each gravitational channel is simply a string of bits, quanta of action, marks in time. The quantum of action is the graviton? Which carries no information. Just current.
So we introduce no-cloning and Zurek. Relativistic quantum mechanics is the interface that joins the two versions io quantum mechanics. Two different processes - perpetual motion and change. Why is there change? Uncertainty. No cloning theorem - Wikipedia, Wojciech Hubert Zurek (2008): Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
[page 45]
The total energy, potential + kinetic of a quantum harmonic oscillator is zero, thereby taking care of the cosmological constant problem.
Many of the effects in the universe are very faint.
The existence of 3D is the solution to a practical problem of interaction [interference] free communication [thus taking some interaction out of the Hilbert domain].
Unitary processing is equivalent to the rotation of a multidimensional sphere. It permutes all the bases in the vector, leaving the length of the vector normalized to 1.
We may imagine that everything that can be said about quantum observation follows from the application of statistics and cybernetics.
We've got a lot of mathematics, but we are missing some physical intuition. This is where the heuristic of simplicity pays off.
I feel that I am approaching a coherent physical theology [coming in through the trinity and the qubit].
Wednesday 23 March 2022
The world of quantum mechanics contains both halves of the half real in the form of complex conjugates. We may think of the complex conjugate as a static thing but in the dynamic situation the state is rotating between the conjugates, spending half its time in each. Realty is formed when the conjugates meet on the real axis and (a mathematical miracle here) become real, a real particle. The theory tells us this is what happens. It is the natural selection process that cuts down the cloud of half reality to a real event achieved by contact, since x + i y + x − iy = x2. This little creation story deals with observation, but how does it work? It is an application of superposition closely related to no-cloning and the differentiation of particles into fermions and bosons which we explain by relativistic transformation of the wave function but which in fact arises at the lower quantum level when the entropy of the universe is 1, because at this resolution a superposition has only two equally probable states, 1 = boson, 0 = fermionic exclusion.
This process must be the first step after the emergence of wave functions. The simplest wave function has two logically distinct states connected by the angular momentum of the cyclic transformation 1 → 0 → 1 &raddr; 0 . . .
[page 46]
Deutsch page 132: 'As I shall explain in chapter 9 quantum computers can perform computations which no (human) mathematician will ever be capable [of?].'
page 141: '. . . there is an opposing theory – common sense which reason requires we refute in detail whenever it seems to conflict with what i am asserting,'
page 195: 'Quantum computation is therefore nothing less than a distinctly new way of harnessing nature. . . . A quantum computer would be capable of distributing components of a complex task among vast numbers of parallel universes and then sharing the results.' Dream on.
page 197: 'The fabric of reality must be, as it were layered for easy access.'
What is the conclusion of cc18_trans_hilbert? The creativity of the Hilbert space drives it into the next level, continuity containing all the quantum structures. This continuity is established by a Cantor transformation from ℵ0 to ℵ1. The particles projected into Minkowski space are surrounded by a measure of uncertainty.
Enough Deutsch. Both Everett and Deutsch make rather extravagant claims and then have to go to considerable lengths to show that although their approach is radical it makes no discernible difference to the results of our measurements. Despite this invisibility, they both insist that other worlds exist. That way madness lies, and I will just plod along with my plot as I slowly work it out, starting with the one bit implementation.
Thursday 24 March 2022
natural numbers ≈ Turing machines ≈linear operators ≈ ℵ0
(linear operators)! ≈ℵ1
Friday 25 March 2022
My construction of the universe is going so well that I dare not touch it lest, like a house of cards when you try to add another card, a touch will make it all fall down. The driving forces are the quantum of action that does the work by adding each card, and the constraint arising from the no-cloning theorem [basically a tautology, since if you create an identical copy in the realm of quantum states, you create nothing, true clones are identical to and indistinguishable from their originals]. This makes the Hilbert space
[page 47]
of the universe. We can, formally, apply the Cantor trick to this and create a new cardinal using the vectors in the Hilbert space as Cantor used the set of natural numbers. Now we bring in another bit of magic to overcome the hurdle embedded in the no-cloning theorem. To create a power set or a permutation of a set of elements we must create new copies of the elements. We need ℵ1 copies of the element 1 to construct the detailed formal representation of ℵ0! or P(ℵ0), snd no-cloning forbids this. The baby universe skips this problem by creating spacetime as a vehicle for storing multiple copies of each state vector in the primordial Hilbert space.
It is all getting to the stage where it writes itself, just as it creates itself. The perpetual motor is action. In the elementary domain quanta of action are major upheavals, basically the creation and annihilation of states represented by vectors and operators in Hilbert space which are in effect the primordial duplicity of agent and material. The material is existing structure. The role of the agent is to devise ways to arrange the elements of existing structure into new realities. The universe has gradually progressed from the primordial hydrogen to produce the planet and the universe that we now see.
Maybe the reason so much creativity emerges from Russia is that the people live in so much pain. Russia has never had a revolution in which the forces of evil were banished. The secret police and the palace guard have inculcated the status quo for centuries acting as enemies of the people exploiting the people for their own benefit. Russia, like many ancient countries, has yet to see much in constitutional development.
Saturday 26 March 2022
Complex numbers are well suited to writing wave equations that encode turing machines [through a Fourier transform?]. Transformations are possible between any two equinumerous sets, in the last resort becoming a static algorithm, a lookup table.Does confidence prove anything? When I was about 20 I confidently argued against the master of studies and had no doubt that my position was and is correct. We should identify the universe as god and build our theology on the god we see. This is still my position but now I am embarking on a description of the creation of the universe.
De Maupertuis suspected that there were sweet spots everywhere in the universe and we suspect it is when forms become groups.
[page 48]
I am in awe of the Einsteins and Plancks who have provided me with quite a large panoramic perspective on modern physics, although I am a bit hazy about the details. In a way this might be good, because I am trying to imagine the universe when its entropy was 1.
Now that I am beginning to understand my model a bit I am beginning to feel a little bit poetic about my work and loosen my language a bit now that I feel that I have a plausible story to interpret quantum mechanics in terms of angels and hylomorphism. We are beginning to see the boundary between the quantum world and the classical world as a natural step and so we need not take the story any further because it is implemented in spacetime. This work is designed to show how realized quantum operators interact to produce outcomes in the network.
The notion that spacetime created a foundation for an explosion of particles and gravitation.
The qubit does the same work as the whole universe in miniature and in a form which can grow by injecting new basis vectors into the space. These bases are the capital of the quantum society which enable the exploration of transfinite possibilities to identify another step forward,
Quantum electrodynamics is the simplest way after gravitation that we can construct a consistent story of the growth of electrodynamics out of quantum mechanics.
The two state universe : boson / fermion. Two ways of superposition, photons and electrons, positrons. Because it is too complex for me I have to boil it down by a renormalization process to something I can [partly] understand, a qubit.
