Notes
Sunday 19 June 2022 - Saturday 25 June 2022
[Notebook: DB 88: Salvation]
[page 102]
Sunday 19 June 2022
There are strong parallels between the history of the universe and our history of understanding the universe. In the beginning the universe invented itself. Over the last 3000 years or so we have been stumbling toward an understanding of this creation.
So often go to bed in despair, wake in hope.
Prehistory: The Greeks
1. Parmenides;
2. Plato;
3. Aristotle;
4. Aquinas.
The [scientific] sequence:
1. Maxwell - light;
2. Planck - quantum;
3. Einstein - special relativity;
4. Einstein - photon;
5. Einstein - general relativity. Why so long? Learning to abandon metrics Albert Einstein (1949): Norton: Philosophical Significance of the General Theory of Relativity
6. Heisenberg - Matrix mechanics;
7. Schrödinger - Wave mechanics;
Dirac - Dirac equation. Dirac equation - Wikipedia
Waves go back to Aristotle, potency and act, but he did not know about the pendulum.
Quite possibly the key to the zero energy universe is that periodic functions like the pendulum have zero energy because the potential is the inverse of the kinetic. So the quantum world of Hilbert space is purely formal or ideal without [real] energy or momentum.
[page 103]
So having applied the via negativa to gravitation we now apply it to Hilbert space and say that the transition to Minkowski space generates both kinetic and potential energy and Dirac equation has something to do with it. Here we are lining up for a new breakthrough [tunnel] like the quantum creation of Minkowski space.
Monday 20 June 2022
I am trying to work out how the world works without being deluded by physics or theology by trying to find a consistent connection between both of them.
Even when the universe is infinitesimally small it has [gravitation], 4D, bosons and fermions all contained within a boundary of consistency, which is in effect the recipe for the proton, and so we can imagine a universe expanding by creating more protons [applying the proton symmetry in different regions of space?] and other particles which stay the primordial size while the universe inevitably expands remaining a Lie group full of little Lie groups resembling particles. We imagine that for the universe to get going it needs the full suite of [elementary] particles. . . . In particular the initial Minkowski space is already 'logically curved' [by the recursion of the Schrödinger equation] in order to contain the orbits of bosons and fermions rather like the Earth and the Moon. The question is where do all the numbers that we measure in physics come from. In some way they measure of the processes required in quanta of action to maintain the integrity of the relevant particles. We see this being developed by an evolutionary process exactly analogous to the generation and propagation of living cells. Elementary particle - Wikipedia
Things are impossible until one finds a way to do them and many more things are possible in Hilbert space than in Minkowski space which acts as a control on [Hibert] space.
Music is beautiful and exciting because it gives us an insight into the Hilbert space that underlies the rather plain and logical consistency of Minkowski space. Superposition requires memory, and memory is a function of objects like strings and vocal tracts that shape superpositions that create speech and singing and other significant sounds [since modulated sound, although continuous, carries information]. The aim of physics is to expose the processes that shape the realities that we sense, and the shapes of the senses that perform this task, giving us a view of the interior of the divinity. Marvels like movies and television take advantage of these processes to communicate images of themselves by realizing the quantum networks that make these things possible. My task is to explain this divine underlay in language that makes sense on the macroscopic scale.
We might say that the core of quantum theory is expressed in the equation PmQn − QnPm = δmn ℏ/c I, where P, Q, I are infinite matrices,
[page 104]
in other words 1 quantum of action distinguishes QP from its inverse PQ and this non-commutativity represents the heart of the process.
Can it make any sense to say that a state is defined by a vector with an infinite number of components which are nevertheless normalized to one and orthogonal to a vector with ℵ1 − 1 components?
Von Neumann mqfm 11_General considerations page 6 (= page 231 of the document); '. . . the chief weakness of quantum mechanics: the theory is non-relativistic: it distinguishes the time t from the three space coordinates x, y, z and presupposes an objective simultaneity concept. In fact, while all other quantities (especially those x, y, z—so closely related to t by Lorentz transformation) are represented by operators, there corresponds to t not an operator T but an ordinary parameter t just as in classical mechanics' [so we are in effect back to the Newtonian concept of universal time]. John von Neumann (2014): Mathematical Foundations of Quantum Mechanics
This suggests that we must consider Hilbert space to precede Minkowski space and all the operations in Hilbert space when it generates Minkowski space must embody the Lorentz transformation from the start through the mechanism discussed on page 12: The quantum creation of Minkowski space. This further suggests that we bypass Schrödinger etc and go straight to Dirac and speak of the diron as a pixel of spacetime containing both photons and charged particles and antiparticles with spin ±½.
' That measurements cannot in fact be instantaneous but must be of a non-vanishing finite duration has the status of natural law ' [maybe].
So we get to zero energy via the notion of the Minkowski metric which means that the energy of a photon is the inverse of its momentum when it in on a null geodesic and [massive] particles that travel at less that the c on geodesics have no energy, ie their kinetic energy is in some way equal and opposite to the potential energy that binds them together [and both these forms of energy exist in the ideal complex quantum mechanical world where E = ∂φ/∂t].
I have been depressed today by my difficulties with my project but now I see some new light.
von Neumann page 232: von Neumann escapes the problem above by measuring quasi-stationary states, ie we can only measure stationary states, stopped particles or reactions [cc26_principles §13; Only fixed points are observable].
page 230: Fundamentally different interactions:
1. measurement
2. dynamical evolution - time independent energy operator
[page 105]
Why do we need the special process 1 for measurement? 'The reason is this: In a measurement we cannot observe the system S by itself but must rather investigate S + M, in order to obtain (numerically) its interaction with the measuring apparatus M.'
2: simple unitary, transforming states into states. 1 can transform states into mixtures.
von Neumann page 234: 2 is reversible.Chapter V.2: Observation creates entropy.
Tuesday 21 June 2022
What I need to feel confident is a clear understanding of the mechanism of the world which I would expect to be supplied by settled processes arising from evolution. The only thing I have to go on is unlimited action controlled by consistency. The problem is to derive self-sustaining processes, expressed as algorithms or groups, to explain this situation. At the moment my big problem is to explain the zero-energy universe through the bifurcation of energy into negative potential and positive kinetic, and I would like to see it in the relationship between the spinors predicted by the Dirac equation. Spinor - Wikipedia
My basic project is to couple logic and reality via Landauer's idea that information is physical, expanded by the idea that information processing is physical (as it is) and that the quantum of action is a thing, the basic hardware of information processing, able, like the traditional god, to reproduce itself ad infinitum. The rate of reproduction we perceive as energy, but the big problem here is to see that the total energy of the universe is a dynamic version of zero sum bifurcation to be understood by a modern version of Aristotle's potential and act which says that potential + act = 0, as we see in harmonic oscillators like the pendulum and quantum harmonic oscillators which work at the simplest level by creation and annihilation of states (situations, particles) whose sum, like particles and antiparticles, is zero. Feynman's idea that time runs backwards in antiparticles is equivalent dynamically to an antiparticle dismantling the structure created by a particle. One day maybe something will come of all this. The basic problem is to see how periodic functions (waves as in Hilbert space) can get anywhere and the clue lies in the fact that observation creates entropy, that is fixed points, ie eigenvectors and eigenvalues.
The perennial problem with quantum mechanics has been
[page 106]
how to interpret it, ie what does it mean? What do complex numbers mean? It feels good to write passages like this, but they have to find a place in an overall structure and I am still in the disassembled jigsaw stage with a 60 year collection of pieces from Plato to Piketty which have still to be fitted together. Thomas Piketty (2022): A Brief History of Equality
Theological pleasure, rooted in god, offsets the financial pain of the plunging stock marked upon which I am relying to propagate my ideas if ever I manage to cast them in a legitimately preachable form.
Quantum of action ≡ spinor?
Von Neumann page 127: ;. . . quantum mechanics makes possible the determination of one particular physical quantity—energy.
Energy is what we measure as a count per time and what we are counting is the number of quanta of action in a time interval. Timing appears to be of the essence in all activity as we see in sports, complicated information processing like computation and complicated mechanical processes like weaving, printing newspapers or filling and capping bottles of beer. What counts in an atom is the energy difference between different states which we measure with a spectrometer and then try to compute using quanta of action [and unitarity] as the fundamental constraint.
One suspects that all the spinor continuous belt trick stuff is fictitious because at that scale there is no continuity, only quantization, creation and annihilation. The continuous element, if any, is in the probability distributions and their evolution as circumstances represented by relatively fixed points change.
Feynman on symmetry. Operator changes state. We want to map quantum operators onto logical operators: Nielsen & Chuang. Nielsen & Chuang (2000); Quantum Computation and Quantum Information
'17.1 A physical system is symmetric with respect to the operation Q when Q commutes with U, the operation of passage of time.
17.11: QH = HQ defines a symmetry, H = Hamiltonian
Conservation of momentum: Dx (a) | ψ0 > = eika | ψ0 >.
Conservation of energy Dt (τ) | ψ0 > = e− iωt | ψ0 >. [' It is conventional to use the negative sign in defining ω; with this convention ω ℏ is the energy of the system, and it is conserved.'] Feynman Lectures on Physics III: Chapter 17: Symmetry and Conservation Laws
Note the negative exponent - does this mean zero energy
[page 107]
ie momentum − energy = 0. Displacement in time conserves energy. Displacement in place conserves momentum. Can we get zero energy out of this via the [spacetime and momentum-energy] 4 vectors in Minkowski space analogous to the null geodesic? Calculate!
Wednesday 22 June 2022
Feynman Lectures Main Index. Feynman Lectures: main Index
Looking for inspiration. In cognitive cosmology the physics comes from Feynman and the theology from Aquinas. The current sticking point is cc20_zero-energy. The global problem seems easy [derived from Einstein relativity]. What I am looking for is a local expression of this in my baby Hilbert / Minkowski universe.
Feynman I.15: The special theory of relativity. Relative mass increases with relative velocity.
Lorentz: Invariance of Maxwell's equations under Lorentz transformation.
I.15.7: Four vector x' 2 − c2t' 2 = x2 − c2t2.
15.8: Body acted upon by a force picks up momentum p = mv, m = m0 / √(1 - v2/c2).
15.9: 'The energy of a body always equals mc2. Equivalence of mass and energy.
We still have not found that mass energy is the negative of kinetic energy, the opposite in fact.
Feynman I.16: E2 − p2c2 = m02c4. Iff m0 = 0, E2 = p2c2.
I.40: Statistical mechanics applies to systems in thermal equilibrium. Logical mechanics applies to all systems.
One's ability to be deluded by other people id proportional to one's ability to delude oneself.
The dark night is creeping up. The heuristic simplicity is lost in the midst of 4D gravitation, fermions and bosons and zero energy, unable to find an order of precedence. So just cruise along reading Feynman for a while.
So am I getting drowned in physics or should I keep on trying to find a stable coupling between physics and knowledge? Remember that for many the uncertainty principle is a statement on the limits to knowledge [but it is more accurately a limit on both measurement and the reality to be measured, so no meaning is actually lost; same situation as when we communicate,as here, in discrete letters].
[page 108]
What we are looking for is an ordered set of symmetries. Maybe pitched in the model of building a computer [beginning with the clock = repeated undifferentiated action = energy]. Struggle is good. There are days when a sentence every few hours is good going.
Farmelo Dirac page 137: 'It seemed to me that the foundation of the work of mathematical physicists is to get the correct equations, that the interpretation of these equations is only of secondary importance' Yet to be verified they must be applied. Graham Farmelo (2009): The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom
Perhaps I was so cruel to my mother by leaving home at 17 and not coming back until the end of her life in 2016, 54 years later, but in a way we were religiously incompatible, even though I frequently took her to church near the end.
Thursday 23 June 2022
Wake in delight! A way forward appears. On interpreting Dirac. Dirac says the equation is the thing. I see that what counts is the interpretation so cc20_zero-energy §1; becomes On interpreting Dirac, and we put together the stories of the interpretation of the Dirac equation from Weyl, Kuhlman, Dirac (4th ed) etc and the universe as an information processor, and somehow use his equation to lay the foundation for the computational model of creation. Where there is hope there is faith, where there is faith there is hypothesis.
'Fluid, playful, elaborate pointlessness,' Bruce Isaacs Bruce Isaacs: Baz Luhrmann’s Elvis is super-spangly, explosive, narratively unhinged – and an artistic triumph
Zero-energy isthe interfsce to formalism, ie no motion [eternity], Platonism motivated by Aristotle's unmoved mover. Creation from nothing = formalism. Inflation (cosmology) - Wikipedia
Friday 24 June 2022
Farmelo page 168: the Negative Energy Difficulty (Dirac 1929). P. A M. Dirac (1929): A Theory of Electrons and Protons
On the verge of replacing wuantum mechanics with something better. Zero energy comes from the harmonic oscillator, the pendulum which has motion but no energy [potential + kinetic - 0]. So we can start the world with a grandfather clock.
No-cloning, like every other proof, cannot exist without spatial interaction and memory, like the mind of God which is in fact formalism [possibly real].
[page 109]
Saturday 15 June 2022
Bogged in zero energy. Feynman and co argue that it holds for the whole Einstein Universe but how does it apply locally? It seems to make sense in quantum theory (Wave mechanics) if we see a wave like a pendulum, a periodic function connecting potential and kinetic energy around zero. This makes sense in the linear regime, but when we enter the quadratic regime (−PE)2 becomes +PE. So we might see the interface between quantum and classical as the interface between linear and quadratic via the equation probability = |amplitude|2. So in the complex regime we can have negative energy as we find in the Dirac equation, but in the 'real' regime we have positive definite energies as appear to be demanded by relativity [perhaps another argument for differentiating Hilbert space from Minkowski space]. Nevertheless we have the quantum personality preserved in the 1, -1 signature of the Minkowski metric. Edging toward a solution made possible, I hope, by the independence of Hilbert space whose domain is no longer (?) Minkowski space. There is more here than met my eye when I first hit on this idea on page 12 of cognitive cosmology. Go for a walk in the botanic gardens and think about it and get some flower photos to send to my embattled Ukrainian friends. Metric signature - Wikipedia
Spacetime is made compatible with quantum mechanics by the Minkowski metric.
Zero energy universe, Schwartzchild metric E = Mc2 - GM2 / 2R. M = 0, R = 0, we have Minkowski metric. Berman Marcelo Samuel Berman: On the Zero-Energy Universe
