Notes
Sunday 17 September 2023 - Saturday 23 September 2023
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Sunday 17 September 2023
Algorithmic information theory and diophantine arithmetic. Gregory Chaitin (1987): Algorithmic Information Theory
First memory is the photon created by charged particles
[page 248]
like electrons and positrons. See Feynman and seek another explanation based on software function encoded as a musical Hilbert sound as a superposition of frequencies. What language will we use? Ask Chaitin. We would imagine the universe to be inegral numbers and rings. Ring (mathematics) - Wikipedia
Monday 18 September 2023
cc20_memory cc20.3 physical evolution II: Selection—quantum mechanics. My idea of making Hilbert space prior to and independent of Minkowski space gives free reign to the operators of quantum mechanics while freeing it from the implications of classical special relativity. This makes the Schrödinger equation meaningful and enables both it and the matrix approach preferred by the quantum information and communication theory to operate independently of special relativity. What I really need to understand is how the advent of null geodesics made possible by the Minkowski metric facilitates the operation of quantum theory in classical space through the massless bosons. So today I read von Neumanns unification of quantum theory again and hope for some insight.
Old quantum theory and adiabatic invariants. Adiabatic invariant - Wikipedia
Einstein on specific heat. Albert Einstein (1907): Planck's theory of radiation and the theory of specific heats
I have so much to learn, but it all helps. Bruce: going
[page 249]
like the hammers of hell. Really I am just a silly kid trying to change the world. My process is analogous to the work of the Universe. Physical processes in Minkowski space (eg this writing) feed into my mind (Hilbert space) eliciting new states from which quantum theory extracts stationary points (insights) which feed into the next bit of text I write which is just another step in an endless theory which may yield change in my world at least.
Von Neumann page 7: The classical mechanical problem expressed as a Hamiltonian H(q1 . . . qk, p1 . . . pk). The initial state is determined by q1 . . . qk.
' We must determine the possible energy levels and find out the corresponding "stationary states" and calculate the transition probabilities, etc.'
Matrix Theory
. . .
Only Hermitian matrices permitted.
page 10: Directions for wave mechanics.
Start with the same Hamiltonian
[page 250]
page 11: Schrödinger equation
. . .
page 12: This "wave equation" has the character of an eigenvalue problem in which λ is to be interpreted as an eigenvalue parameter. The eigenvalues λ are the allowed energy levels and the eigenfunctions are the corresponding states of the system.
Wave equation can make observations of systems which are not in Bohr stationary states. ψ can be given for an arbitrary t = t0 and then it is determined uniquely for all t ie t appears as a factor of absolute value 1 so that the evolution of ψ in time is essentially unobservable. The eigenvalues of the differential equation form a complete orthogonal set so that ψ(q1 . . . qk) = Σi aiψi(qi).
Matrix and wave mechanics always yield the same results.
page 14: Transformation theory Schrödinger proved the mathematical equivalence of the two theories. What does this mathematics mean? Nature solves the same equations as physicists have to solve to get the actual answers in terms of stationary states [???].
[page 251]
Von Neumann page 18: Eigenvalue problems → integral equations, integral operator.
page 19: Dirac delta enables differential operators to represent integral operators.
page 21: Von N does not like the Dirac delta and goes to the Schrödinger method of unification of the two theories.
page 22: Discrete values of Z vs continuous state space Ω
The core of the unification is the normalization requirement that Σν |xν|2 = 1
or ∫Ω . . . ∫Ω |φ(q1 . . . qk)|2 dq1 . . . dqk = 1.
page 23: FZ and FΩ are isomorphic even though Z and Ω are very different. FZ = Hilbert space.
page 24: Describe Hilbert space and prove that its properties belong to FZ and FΩ.'
Information is physical / memory is reality. Creation and annihilation, rewriting.
Tuesday 19 September 2023
I am having the same sort of problematic feelings about cc20_memory as I had about cc17_gravitation. The only answer seems to be to wait and think. The role of massless bosons in communicating and memory seems to be very clear and as memories they are created on writing and annihilated on reading. They instantiate "information is physical". More complex particles like atoms can remember and
[page 252]
by internal changes like the annihilation of an electron in one energy level and its recreation in another by communicating a photon. Perhaps the harder bit is characterizing spacetime and dynamic particles as "operating systems", in control of the invisible Hilbert space that underlies all observable changes [Hilbert spaces lie between dynamic systems, beginning with the initial singularity and the first generation of particles, then between the first and next generations of particles and so on].
Kinematic perpetual motion is possible if we have an eternal divine dynamic driver [formal Hilbert space has no "momentum"]. So Hilbert space can be forever new but is selected by quantum mechanics and observation. We say that observation changes conscious entities as our meetings change us. Conscious means input and output change internal states, ie change memory.
Waiting for clarity to come, like Descartes or a quantum mechanical observation. How long does it take a U238 nucleus to decay? Slow thinker! It is interesting to feel that I cannot write without clarity. Instead I feel frustration and usually suspect some sort of "mental block" which is holding fire until all its conditions are met.
Part of this reluctance arises because I have my doubts about my whole story and I have not gone so deeply into detail in the past. Although I have doubts about my story, I have few doubts
[page 253]
about the fact that Western theology and physics are on the wrong track and in all cases of apparent error it seems that the trouble arises from either ancient mythology or the acceptance of mathematical ideals as true representations of reality. These qualifications should be included in cc20_memory. What I am really looking for, to take me to the end, is a deeper and more convincing story about the creation of Minkowski space out of Hilbert space [a job for the fermions?] . I think the bit about massless bosons and null geodesics is very significant, but there is another shoe waiting to drop in my mind, and I feel that this is where the blockage lies. Orgasm is easy to achieve by oriented action but insight is more mysterious and very difficult to organize, which may be why the universe took 14 billion years to get to here [whereas most living things can breed at an exponential rate when conditions are optimal].
I have no doubt that my story is valuable and I motivate myself by setting deadlines but then I remember that us taken me 60 years to get to here and when it is finally published it needs to be as perfect as possible so that its input is maximized and criticism will run off it like the water off the duck's back. So I say on days like this relax and it will come. Although I was a depressed tabula rasa when I woke up this morning, the few pages I have written here so far have cheered me up. What I need most is a new version of QCD because I have quite a few ideas about QFT already. The Hilbert to Minkowski path seems to be the key. Time is ok, but what about space?
[page 254]
New version of cc07_network_brain to become part of cc19_network. Photons carry phase information in quantum mechanics and also energy. Action potentials in the brain also carry energy and phase information as inverse frequency and a large number of phased inputs from synapses [superpose to] determine when the neuron will fire. The brain works as a quantum network realized in real physical times. The internet is a Minkowski network operating logically in real physical times [assisted by a lot of quasi null (electrical) connections]. What we have here is a sort of parallel with Einstein's use of Planck's statistics to explain low temperature behaviour of specific heats and the germ of a coupling between the brain and quantum mechanics to connect eigenvalues and eigenfunctions with ideas and mental processes, ie the foundation of cognitive cosmology and the principle of symmetry with respect to complexity.
So back to Dirac: Need for quantum theory:
1. Stability of atoms, etc
2. Inner motions of atom do not contribute to specific heat
3. Ultraviolet catastrophe
4. Wave / particle
5. Absolute meaning to size [this in effect applies to all of the above] - in Hilbert space there is as minimum symbol, ie minimum action [normalized to 1], quantum
6. Observation is interaction - where Einstein fell off - observation disturbs - whenever you observe something you see it in a definite state [eigenvector]
7. Conservation of alphabet = normalization
8. Every photon interferes with itself, not other photons [maybe representing the two hilbert space vectors that formed the photon in the first place.
[page 255]
Wednesday 20 September 2023
If I had a mental block I may have found it. I have followed the initial singularity evolving to photons and Minkowski space and made the point in cc20_memory that science is the study of memory since reality is memory. Now many of my memories are of the horrendous evils that began with the perfection of war and imperialism. Just as engineering is the study of disasters with a view to preventing them, the principal role of memory is to see where we went wrong and correct it. So this is to become the second part of the page on memory, which is to be about the disastrous effects of imperial delusion. A new direction but it will present material for a further study of the history of cosmic evolution as it has brought us to the present level of intelligence and then to use the principle of symmetry with respect to complexity to understand how the spacetime operating system controlled the creativity of Hilbert space by the conservation of energy [by the gravitational realization of kinetic into dynamic entities] and see what lessons that that has for our own control of our delusions that have arisen with our creative cognition. So we see how cognitive cosmogenesis feeds into ethical behaviour.
Adams, horrendous evils and the goodness of god. Marilyn McCord Adams (1999): Horrendous Evils and the Goodness of God
The inability to deal with gravitation and the impact of infinities and renormalization means to me that we really do not
[page 256]
understand our world. Only cognitive cosmology can do the job, and we need to know how natural selection keeps us on the straight and narrow [ie it deletes the things that do not work, or they delete themselves]. Always depending on symmetry with respect to complexity to give us the global picture. Time to run though the principles again.
Ballet is the perfect illustration of the relationship between Hilbert space and physical motion transformed through the human audio-motor system. Another vision from the principle of symmetry with respect to complexity built into Hilbert space. This is the work of transfinite (ie layered) operators. The first layer after gravitation and quantum mechanics is the massless bosons and photons. How do we make an electron and a positron out of a photon? See Feynman and Weinberg. Richard Feynman & Steven Weinberg (1986): Elementary Particles and the Laws of Physics: The 1986 Dirac Memorial Lectures
Is ballet reversible, ie is the entropy of the music equal to the entropy of the dance? Yes and no. The network duplicates the music in each dancer so all their entropies are equal and roles are reversible but the entropy of the dance is the entropy of the music multiplied by the number of the dancers, very much like the specific heat and entropy content of a particulate medium as studied by Planck and Einstein. Every move in a dance and every phase in the music is an eigenvector in the dance operator. Trying to
[page 257]
capture the music / scientific spirit of Oppenheimer / Aquinas / Einstein. Albert Einstein (1907): Planck's theory of radiation and the theory of specific heats
Water waves can superpose on each other because they are fluid. Rigid vehicles like electrons cannot superpose (exclusion principle). Intrinsic to quantum superposition is normalization of all vectors even if they are a countable sum of components.
Thursday 21 September 2023
Why the reluctance to imaginbe direct creation of photon? I have been feeling that we need electrons and positrons to create photons but maybe it is the other way around and zero sum bifurcation of photons creates electrons and positrons and also serves to make spacetime electric on the large scale necessary to propagate Maxwell's photons. Just because I do not have a theory to explain it does not mean that it does not happen (although this idea is a sort of theory) because we have to take the Universe as we find it and it may take a little courage to accept this.
Evolutionary [events] happen at all scales. Symmetry with respect to complexity again.
three issues:
1. The constraints placed on the world by Hilbert space
2. The constraints placed on Hilbert space by quantum theory [hermitian operators]
3. The constraints placed on quantum theory by Minkowski space, that is the constraints placed on reality and therefore memory.
[page 258]
In this hierarchy we distinguish between kinematic and dynamic entropy and each new layer of the system is in effect a replica of the initial singularity, based on the ideal mathematics of Hilbert space.
Jennan Ismael: Observable ≡ physical quantity. Jennan Ismael (Standord Encyclopedia of Philosophy): Quantum Mechanics
' The heart and soul of quantum mechanics is contained in the Hilbert spaces that represent the state spaces of quantum mechanical systems.'
' Know your way around Hilbert space and become familiar with the dynamic [kinetic?] laws that describe the paths of the vectors travel through it and you know everything there is to know, in the terms provided by the theory about the system which it describes.'
' It turns out that the state of a complex system is not uniquely determined by those of its components . . . It means that there are facts about systems as whole that don't supervene on the way these parts are arranged in space.'
' Operator maps space onto itself.'
' Eigenvalue / operator relation is invariant under change of basis.'
'Quantum mechanics: Four principles:
1. physical states every physical [kinematic, formal] state is associated with a Hilbert space. Every unit in the space corresponds to a pure state of the system and every possible pure state corresponds to some vector.
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Pure states are vectors of norm 1, unit sphere in hilbert space.
Relative phase factors are physical; global phase factors are unphysical.
2: Physical quantities: Hermitian operators.
3. Composition : Hilbert space of a complex system is the tensor product of simple systems.4. Dynamics [maybe kinematics, since this equation cannot be realized physically]: Schr&0uml;dinger equation is deterministic, unitary, and linear. Collapse: Born rule.'
' From a mathematical point of view what really distinguishes quantum mechanics from its classical predecessors is that states and quantities have a richer structure [because they are complex!!!].'
' P1: All sums and multiples of vectors in Hilbert space yield another vector [and in cartesian space??].
P2: There are operators on the same Hilbert space that do not necessarily share eigenvectors.'
' the real difficulty in understanding quantum mechanics lies in coming to grips with their implications, physical, metaphysical and epistemological anyone trying to come to an understanding about what quantum mechanics says about the world has to grapple with one remaining fact' ie the measurement problem. He seems to ignore the fact that a measurement of a system is an action on that system.
' Pure and mixed states are represented by density operators.'
[page 260]
There are no basic objects in the quantum world, there are mathematical ideals.
Just as words can have no meaning, mathematics can have no meaning [just be a pure formal construct, obeying the syntax but saying nothing]
Violence is implicit in imperialism as we see in may religions. The minimum level of violence is unconstrained individual interactions. Quantum mechanics, like the natural world, is a mess from the point of view of corporate organization. The imperialist way is to change minds by killing or torturing their physical implementations [thus altering the environment of selection]. The peaceful way is education, kinetic mind to mind interaction.
The fundamental ethical point, which is embedded from the beginning, is the consistency of dynamics which serves as the selector of ethical truth from the creation of Minkowski space throughout the history of the universe. [This] really begins to bite when theology transfers from imperial mythology to creative reality [this is the creative step of gravitation which provides the energy to transform kinesis to dynamis while at the same time maintaining energy conservation by paying for this transformation by deepening gravitational potential].
Friday 22 September 2023
This may be a happy morning that recognizes the principle of conservation of energy (based on the zero energy universe) as not only a fundamental physical principle but also as a fundamental moral [ethical] principle marking the boundary between formal kinetic ideals and
[page 261]
real dynamic entities that can be selected for individual survival This sounds good and develops the heart of cc20_ memory by showing that the operating system in Minkowski space keeps the universe on the straight and narrow at the fundamental level of the creation of photons. This now just needs to be filled out and used to lay the foundation for dynamic transfinity, as countable version of Cantor's proof (dynamic and strictly finite) laying the foundations (c21_transfinity + cc22_trans_minkowski) for a reasonable version of cc23_quantum_field, my fantasy is coming along nicely, emphasize the power of evolution by Bhowmick on photosynthesis. Asmit Bhowmick et al: Structural evidence for intermediates during 02 formation in photosystem II
so the big question is what should we make real by giving it energy. The question should be decided at the formal cognitive level before the input of energy which in minkowski space means work and force, begins. Chanel Contos (2023); Consent Laid Bare
Looking back I see that I have been a total fool but I am always hoping to do good in the end, so I start again, more or less from scratch, so build a theology I can trust, to guide my life to peace, the wealth I have in my beautiful children and my dream would be to pass on a better world to them, which currently looks somewhat improbable, but one hopes for a change of paradigm. The Taming of the Shrew (1967 film) - Wikipedia
I could not have been brought lower by life but I am higher than I have ever been and coming into my cosmic birthright.
[page 262]
I wish; I hope
Saturday 23 September 2023
(equinox)cc25_principles: The power of evolution resides in random variation, memory and incremental development.
Entropy is the measure of simplicity and complexity. Boltzmann began with a simple count. Planck on ultraviolet catastrophe and Einstein on reduction of specific heat with reduction in temperature introduced weighted count like Gibbs and Shannon. Entropy (information theory) - Wikipedia
Gravity is codeless communication. Quantum mechanics is conversation. Universe like Hilbert is making up formal mathematics.
A clearer distinction: A nail is dead and it needs a dynamic driver but within itself it is alive and real.
Living things may move dead things which are real and alive inside and dead formal things which owe their whole lives and existence to being constructed and motivated by living things like the formal hilbert space inside the initial singularity.
Living thing are limited in what they can do but they can use dead things like the Hilbert space inside the initial singularity
[page 263]
which the initial singularity may use to create correlations beyond its capability just as a live hand can use a spanner to undo a tight nut. So gene sequences can occur in a genome which is supported by a cell even though they are sequences that are meaningless in the contact of the cell, ie lethal mutations can exist unless they are transcribed and used.