Notes

Sunday 26 June 2022 - Saturday 2 July 2022

[Notebook: DB 88: Salvation]

[page 109]

Sunday 26 June 2022

Complexity requires memory and memory, as in a turing machine, is an instance of formalism, changeable because memory states an be created and annihilated. Momentum is a form of memory . . . which makes inertial motion possible because momentum keeps things moving . . . [and this memory is changed by force, ie writing or communication]. A point in function space carries as much information as the dimension of the space, so Hilbert space is a formal model of memory because it is a function space and in quantum mechanics we mark momentum with a minus sign so it is an analogue of negative energy, a precursor of the real memory and real momentum which makes tunnelling possible, as does momentum in real space.

So we can compare momentum to real memory and in some way similar to potential. We can imagine gravitation and other forms of binding energy as negative energy, so the seeds of the zero energy universe are present in Hilbert space, to become real in Minkowski space where time energy is analogous to the negative dimension. our choice of metric is a choice of the picture we make of potential and kinetic in

[page 110]

the bifurcation of energy into potential and kinetic which is a variable like the transformation implicit in a pendulum or harmonic oscillator, illustrated by the transformations of the real and formal elements of a harmonic oscillator embedded in the wave function in the angular momentum which carrie a system from real to complex and back again. So we refer time and the clock to be complex and we map the oscillations of a wave or a pendulum to the angular momentum implicit in the complex circle group which we can then map to a real function. The zero energy story is embedded in the space-time and momentum-energy four vectors and we see the mass of the massive particles bound in their internal momentum. This is confusing, but the distinction between Hilbert and Minkowski may help us to sort it out.

Particles, in other words, are instances of null geodesics which carry photons and momentum, the momentum in a null geodesic being outside time, formally mass and negative energy, ie potential, binding energy and memory. So particles, like memories, can be created and annihilated, ie forgotten. When we forget a massive particle we get photons and we model all this as a computational / logical process, the beginning of quantum field theory which is built into spacetime by its nature as a new symmetry built on the formalism of a Hilbert space.

The orthogonality of the dimensions in Hilbert space is represented by the orthogonality of the axes of the angular momentum embodied in the quanta which are the formal representation of the basis states constitution the Hilbert function space [a sort of string theory, each quantum of angular momentum has a discrete linear axis of rotation: vector = string? loop = circuit of vectors, rotation of rotations].

What is the role of smoke and therefore fire in mysticism and creativity? Music and incense are at the heart of religious ceremony, not to mention candles. Look at the Indigenes for historical clues.

Could I be doing something better than pursuing my theological dreams? Like what? My fallback is always someone has to do it and I have not found anyone else yet, so plough on.

Quantum phase is important in the Hilbert world when we add amplitudes but it is cancelled in the Minkowski world where we have probabilities which are squared amplitudes [perhaps the more interesting question is 'probabilities of what' ie eigenvectors, ie fixed points in the intersections of operators and vectors].

Monday 27 June 2022

Feynman on quantum mechanics and knowledge:

[page 111]

'In the beginning' is Feynman on quantum behaviour:

1. Probability = |ψ|²
2. Alternatives: ψ = ψ₁ + ψ₂, P = |ψ₁ + ψ₂|²
3. Known path P = |ψ₁|² + |ψ₁|² = P₁ + P₂

Why is this? Feynman says we do not know. I have always wanted to go deeper and am looking for a logical explanation in terms of logic, computation and computer network. So

1. Many computers in network with different clock frequencies
2. Interference: without memory, signal gets through when clocks in sync
3. Classical: memory and buffering, signal gets through 'deliberately.

So where does knowledge of path enter the picture?

Somehow we want to explain the zero-energy state in terms of a logical computer network and my whole story stands or falls on this. Memory = momentum makes complexification possible. This is already implicit in cc18_trans_minkowski.

Another rearrangement. A new order, layered network of symmetries.

Old cc22 → new cc19_ memory: explaining network buffering, complexification
old cc21 → new cc20_fixed-points: expanding on memory, eigenfunctions
old cc20 → new cc21_zero-energy: pendulums and wave equations
old cc19 → new cc22_gravitation: consistency bound universe

cc23_field theory: simple version of field theory, communication
cc24_chromodynamics: the eternal proton
cc25_mathematicians: mind space = cosmic space = ideal + imagination
cc26_principles

Much work, but a glimpse of hope. At last a picture is emerging from the Sunday morning gobbledegook which I wrote in the early hours of Sunday [above]. It is embarrassing to write this but I think of myself as an image of the universe trying to evolve by mental trial and error into an understanding of the physical body that serves as the substrate symmetry of my mind. On the old picture I am a sequence of images of God rooted in the completely simple initial singularity imagined by the more mystical of theologians.

[page 112]

Tuesday 28 June 2022

We might say that quantum mechanics produces kinetic waves which are representatives ['stretched' in time and space] of the complex circle group, whereas classical mechanics produces dynamic waves which like the pendulum or the equations of electromagnetic radiation are the result of an interaction between potential and kinetic energy. The exact equivalence of these two forms of energy is to be explained by zero-sum bifurcation. How does the circle group break into positive kinetic and negative potential energy? Has it got something to do with spin, a sort of there and back again?

What has this got to do with particle wave duality? When we look at quantum phase we see that half the complex dimension is positive and half of it is negative so when we superpose them they cancel out, rather like potential and kinetic energy. In the quantum regime and in the real regime the linearity of superposition is manifest so we get stationary nodes in standing waves like vibrating strings or the air in an organ pipe.

Nevertheless (one of my favourite words) the quantum interpretation of momentum as a wave and the change of phase by the permutation of massive fermions brings about the exclusion principle by the superposition of opposite phases. This means that the probability of fermions occupying the same position in space is zero, something reminiscent of the zero energy of the superposition of the phases of a pendulum where the sum of the kinetic and potential energy is zero, giving us a clue to the zero energy of the universe of massive particles. This relates in some way to the fact that real momentum has the quality of memory, a feature of inertial momentum which remains constant as required by Newton's first law.

Wednesday 29 June 2022

How do we connect logic to energy? It has nothing to do with the actual content of the logical process but with the rate of processing of logical transformations according to E = hf. All that we know abut the electronic structure of atoms comes from spectroscopic measurements which yield energy and polarization at most, so the link from spectroscopy is tenuous, first discerned by Balmer and Rydeberg and Rydeberg's discernment of the functional relationships between these lines / energies. How do we couple processing rate to electronic structure? Is there any point in doing so? Perhaps we should think in inverse terms not about frequency but about the [length] of the time interval taken by an electronic event.

All interactions are quantum mechanical but we read the results

[page 113]

in Minkowski space.

Thursday 30 June 2022

Friday 1 July 2022

Another principle: Symmetry, Noether and Neuenschwander. Dwight Neuenschwander (2011): Emmy Noether's Wonderful Theorem

We can map the whole of Sleeping Beauty onto one angel with a vector of sufficient complexity, well within the range 1 . . . ℵ₀. The Australian Ballet: Sleeping Beauty

cc20_fixed points page 20: Fixed points and particles = observables = eigenfunctions.

Saturday 2 July 2022

Pais page 241: 'But local gauge transformations survived not in the original meaning of regauging lenths and times [given to them by Weyl]. In the late 1920s Weyl introduced the modern version of these transformations: local phase transformations of matter wave functions. This new concept, suitably amplified, has become one of the most powerful tools in modern theoretical physics.'

Weyl, page 138: ' The underlying general feature that determines the metrical structure of a point P is the group of rotations.' Herman Weyl (1985); Space, Time, Matter

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Further reading

Books

Neuenschwander (2011), Dwight E, Emmy Noether's Wonderful Theorem, Johns Hopkins University Press 2011 Jacket: A beautiful piece of mathematics, Noether's theorem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space or rotation will obey the laws of conservation of energy, linear momentum or angular momentum respectively. This exciting result offers a rich unifying principle for all of physics.'  Amazon   back

Weyl (1985), Hermann, and Henry L. Brose (translator), Space Time Matter , Dover 1985 Amazon customer review: ' The birth of gauge theory by its author: This book bewitched several generations of physicists and students. Hermann Weyl was one of the very great mathematicians of this century. He was also a great physicist and an artist with ideas and words. In this book you will find, at a deep level, the philosophy, mathematics and physics of space-time. It appeared soon after Einstein's famous paper on General Relativity, and is, in fact, a magnificent exposition of it, or, rather, of a tentative generalization of it. The mathematical part is of the highest class, striving to put geometry to the forefront. Actually, the book introduced a far-reaching generalization of the theory of connections, with respect to the Levi-Civita theory. It was not a generalization for itself, but motivated by the dream (Einstein's) of including gravitation and electromagnetism in the same (geometrical) theory. The result was gauge theory, which, slightly modified and applied to quantum mechanics resulted in the theory which dominates present particle physics. Weyl's unified theory was proved wrong by Einstein, and his criticism alone, accepted by Weyl and included in the book, would justify the reading. Though wrong, Weyl's theory is so beautiful that Paul Dirac stated that nature could not afford neglecting such perfection, and that the theory was probably only misplaced. Prophetic words! . . . ' Henrique Fleming  Amazon   back

Links

Andrew Court, Inventor of world’s first cellphone: Put down your devices and ‘get a life’ , ' Cooper wanted each person to have their own phone number — which he now calls his “greatest accomplishment.” Until that time, phone numbers had been associated with places, such as a home, car or desk. Motorola subsequently poured millions into Cooper’s project and it took the engineer and his team just three months to make the phone, given they had used similar technology to previously put together police radios. . . . On April 3, 1973, Cooper made the first-ever cellphone call using the device, deciding to ring his competitor, Joel Engel, who was working as a head engineer at AT&T. . . . The phone didn’t hit the market for a further decade, finally released to the public in 1983. It cost a whopping $3,995.' back

Andrew Sheng, Whose world? What order? Time has passed for the West to call the shots, ' To cut a complex story short, the Nato military alliance, comprising nearly 1 billion people and some 47 per cent of world GDP, assumes its status quo role of final arbiter of the “rules-based order”. The problem is that the economies of BRICS (Brazil, Russia, India, China and South Africa), plus Indonesia, account for 3.5 billion people and one-quarter of world GDP in market terms. But on GDP based on purchasing power parity, they are nearly equal with Nato and so may have their own views on the international order. What if the larger non-Western countries want their own version of the Monroe Doctrine? The moral principle that we all should live peacefully on one planet should override sovereign nations’ fighting over power, especially when this means humanity could go up in flames, either from climate change or nuclear war. For the nomos (or order) of the planet, we should all cooperate rationally. If we truly believe in democracy, can all 8 billion people in the world vote on the rules-based order, or do we still leave it to the Group of 7? No order is stable without true legitimacy on democratic principles. How to achieve that order remains a truly open question.' back

Hugh White, Friday essay: if growing US-China rivalry leads to ‘the worst war ever’, what should Australia do?, back

The Australian Ballet, Sleeping Beauty, ' The Australian Ballet presents Sleeping Beauty, in a production by David McAllister. With lavish sets and costumes, this ballet casts a spell of delight all the way to true love's kiss. Music performed by Orchestra Victoria.' back