Natural Theology

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Notes DB 93 Theological Genocide - 2025

Sunday 28 December 2025 - Saturday 3 January 2025

[page 210]

Sunday 28 December 2025

Long conversation with JC. Catching up on last week notes

[page 211]

Monday 29 December 2025

Books for Profs:

Gerard O’Brien
Jonathan Opie
Philip Gerrans
Antony Eagle
Garrett Cullity

Physics article: An alternative to QFT [CC_QFT_alt_Jan2026]
Abstract: From Minkowski space to initial singularity
1. Initial symmetry
2. Initial aingularity Aquinas + Einstein
2a. Zero energy - Stationary Lagrangian
3. Fixed point theory and Hilbert space
4. Superosition, quantum mechanics and hermitian operators
5. A qubit ψ = α|fermion⟩ + β|boson
[go to page 213]

Letter to Fellow search: John D. and Catherine T. MacArthur Foundation Office of Grants Management 140 S. Dearborn Street Chicago, IL 60603-5285 To: 4answers@macfound.org

I would be surprised if your search for potential fellows would ever encounter me so, following Martin Luther’s initiative for theological and religious reformation, I have decided to knock on your door.

I am 81. In my 20s I was a solemnly professed monk in the Australian Province of the Dominican order and a keen student of Thomas Aquinas (1225-1274). Aquinas \ radically revised Christian theology by introducing the newly translated work of Aristotle.

At the time of [the] work of the Second Vatican Council there was a call for ideas to assist the work of the Council. I suggested to my superiors that the time had come to convert theology from poetry to science by repeating Aquinas’s Ansatz with the hypothesis that the universe is divine. We could approach the mind of God in the same way that we approach human minds, through body language, where God’s body is the physical universe. In effect our experience of the universe and ourselcves would became a living “Bible".

From a Roman Catholic point of view, this idea is heretical and I was ejected from the Order and my vows annulled.

Now, 60 years later, I have published a book: Cognitive Cosmogenesis: a systematic integration of physics and theology. The core idea is that the statistical structure of the communication we receive from the physical universe is identical to the statistical structure of all human communication as defined in Claude Shannon’s Mathematical Theory of Communication. The divine world tells us what “God” is thinking. Jeffrey Nicholls (2025): Cognitive Cosmogenesis: A systematic integration of physics and theology

Doctors no longer have borders because scientific biology has unified our understanding of human physiology. My work can create a similar unity in care of the human soul by emphasizing our spiritual unity in a divine universe. This will reduce the incidence of misunderstanding and conflict at human theological and religious interfaces.

In the last chapter of my book I note the political consequences of gravitation and quantum mechanics when extrapolated through symmetry with respect to complexity from elementary particles to human affairs. A draft of an essay suggesting this possibility is available at Essay l4l01: Quantocracy: The universal quantum mechanical foundations of democracy and freedom

I see my current book as analogous to the First Part of Aquinas’s Summa of Theology, and I am currently engaged in following this analogy into the areas of politics, ethics, spirituality and care for our only divine planet.

Yours sincerely,

Jeffrey Nicholls (BA (hons) Adelaide.

Tuesday 30 December 2025

Developing CC_QFT_alt_Jan2026 and Commentary cl4l05_particles in parallel. My developments are exciting but also rather tentative but I am bouyed by a combination of the heuristic of simplicity and Feynman’s doctrine “a physical understanding is completely unmathematical.” The gigantic hiatus in my life is that I am completely alone with no collaborators in my quest for a divine unverse symbolized by Cognitive Consciousness, but perhaps my book will bring me someone. Now to the market, 08:17

[page 212]

Everything is gorgeous and progressing beautifully but lonely, a partner and a collaborator would be good, but $1000 days are heartening. Putting everything on the icloud, cheaper than local storage [and rediscovering my old subscription to Clean my Mac]

Tweet: In our divine universe the physical world is the living “Bible” speaking to us through our own senses and imaginations. I have a new view of the creative and inspired scribes and priests who wrote traditional sacred texts for their old masters. I want to rewrite their old books [280 char, posted with book image]

Chaitin’s version of Gödel’s proof tells us that there are limits in universal information density ie no matter how we look at a photon or any other qubit we only get one bit of information and the quantum computation people who think we can treat quantum mechanics as a continuous (complex) analogue machine are barking up the wrong tree. The entropic content of a quantum process is the log of the dimension of the Hilbert space and determines the number of eigenvectors that we can extract. We have to carefully distinguish between the frequency of events in a probabilistic sense and the actual details of the events (like which side of the coin is showing) which eventuate. Gregory J. Chaitin (1982): Gödel's Theorem and Information

Posted a copy of CC to Editor: Conversation Media Group Ltd Tenancy B level 5 700 Swanson St, Carlton 3053.

Wednesday 31 December 2025
Dear Conversationalists,

I am not an academic but would like to bring your attention to my book which is aimed at reducing religious conflict around the planet.

[page 213]

Reading Dirac for insight to put into CC_QFT_alt_Jan2026, looking for a pure statement of quantum mechanics to put in the initial singularity in QFT_alt. What we need is superposition and self adjoint operators with real diagonals — this is the mathematical core of QM, “selective pressure” from QM to real, but how did we get complex in the beginning? Why waves? [the only source can be randomness, positive events occurring at intervals, the pendulum again]. Paul A M Dirac (1983): The Principles of Quantum Mechanics (4th ed)

Dirac’s error, and that of most pundits, is the concentration on the probability of quantum events rather than the concentrating of precision of events which QFT defines through diagrams adding the possibilities of particular hermitian operators which Feynman finds by his path integral. Here we assume that the path integral is always stationary on one quantum of action = one logical operator in the domain of elementary particles [assuming that energy is released one quantum at a time by the zero-sum bifurcation of gravitation (reference to appear in Lust–4–Life in 2026).

Hamiltonian operators and global stability. These operators embrace the exclusion principle and all the other stable states on the basis that only real numbers are real, but where do the waves come from? Randomness controlled. [I had an idea at the beginning of the paragaph which I refrained from writing in and now it has escaped me, damn]. It relates to the stationarity of the combined Lagrangian of a fermion and the associated boson, either emitted or absorbed [see comment on gravitation above].

From page 211 re CC_QFT_alt_Jan2026:

6. Gödel, Chaitin and the entropy of explanation, including the heuristic of simplicity and the principle of symmetry w.r.t. complexity.

[page 214]

Tomonaga and Feynman on the ‘incomptence’ of QED. Sin-Itiro Tomonaga (1965): Nobel Lecture: Development of Quantum Electrodynamics

Summing up, the mechanism of quantum mechanics working in the complex domain creates and feeds into Minkowski space in the real domain and the operational perfection of this transition is measured by hermitian operators which arrange the superposition of complex vectors to yield real numbers.

The first appearance of the complex domain in theological history is in the treatment of the Trinity by Augustine of Hippo. Augustine (419, 1991): The Trinity

Dirac Mathematics: in quantum mechanics causality is implemented by linear superposition with adjustment of phase.

Thursday 1 January 2026

A new year and back to cl4l05_particles, announcing my discovery that the inertial symmetry of Minkowski space shows that it is the result of pure quantum theory in Hilbert space with no reference to spacetime so that every point in Minkowski space is equivalent, and the speed of light, rooted in quantum electro dynamics [beneath Minkowski space] is a local phenomenon, identical for every observer as Einstein found and so demands the Lorentz transformation and the Minkowski infinitesimal metric to connect distant events in Minkowski space, so establishing the [classical] spacetime light cone.

[page 215]

Love is the cosmic boson. In a physical universe inspiration is the direct work of the divinity, manifest in this sentence while listening to Kpop NewJeans ETA. Kpop: NewJeans: ETA

Gross: Yang: “Symmetry dictates interaction. The first example of this was general relativity where Einstein employed the symmetry of space-time [a consequence of quantum theory] under local changes of coordinates to determine the laws of gravity.” [listen to what Einstein said:

The postulate of relativity in its most general formulation (which makes space-time coordinates into physically meaningless parameters) leads with compelling necessity to a very specific theory of gravitation that also explains the movement of the perihelion of Mercury. However, the postulate of general relativity cannot reveal to us anything new and different about the essence of the various processes in nature than what the special theory of relativity taught us already.
Chen Ning Yang (1957): Nobel Lecture: December 11, 1957: The Law of Parity Conservation and Other Symmetry Laws of Physics, David J Gross (1996_05_11): The role of symmetry in fundamental physics, Albert Einstein (1915): The Field Equations of Gravitation

Here we are getting to the proof of the divinity of the universe to be incorporated in L4L via the ten steps to the divine world.

Gross: “Gauge theories have assumed a central position in the fundamental theories of nature . . . Gauge invariance forced the existence of special particles, gauge bosons, . . . massless spin one particles that are associated with vector potential and mediate the forces.” And we think they are a consequence of the zero-sum bifurcation of gravitation which builds on the equivalence principle that in pure gravitation pure energy is both fermion and boson, so we have ψ = |fermion⟩ + |boson⟩> at all scales (see Yang above).

Fibre bundle . . .’ a sophisticated geometrical concept [which] has provided a deep and beautiful geometrical foundation for gauge symmetry’ (and, I imagine in violation of the heuristic of simplicity at this level of complexity [the 64$ question is how all these fancy ideas are physically realized]).

[page 216]

Gross: ‘ It has also been understood, a century after Maxwell discovered his equations that the vector potential is not just an artificial construct but has a direct observational meaning, This is most evident on the Bohm-Aharanov effect where an electron beam propagates in a region where there is no EM field yet due to the geometry the vector potential is non-vanishing [once again an inappropriate introduction of geometry before it actually exists?] Due to the change of phase that accompanies a charged particle moving in a background vector potential one can observe interference effects directly. The vector potential [ie photons] is primary ‘ a co-creator of Minkowski space. Akira Tonomura (2006_04): The Aharonov-Bohm effect and its applications to electron phase microscopy

‘ Indeed today we believe that global symmetries are unnatural. They smell of action at a distance. We now suspect that all fundamental symmetries are local gauge symmetries. Either all broken or approximate.’ [This means that they arise from local interactions of fermions and bosons].

This Poincare invariance can be regarded as a residual symmetry of the Minkowski vacuum under changes of coordinates. [My much better (?) explanation at the bottom of page 214]

Gross: The origin of symmetry; Obviously implicit in the structureless simplicity of the initial singularity, the first quantum of action, which is a closed system acting on itself as Augustine realized. Obviously the first symmetry is right before our minds, as Aquinas realized.

As we explore physics at higher and higher energy, revealing the structure at shorter and shorter distances we discover more and more

[page 217]

symmetry. The symmetry is usually broken or hidden at low energies. [This may just be an excuse to build bigger accelerators. Becasue the quantum of action is so small, the real place to see things in Minkowski space where we live is small distances which imply high momentum, but there is nithig more fundaemntal that the quantum of action ≡ initial singularity]

Copy of book to Adelaide U prof of Physics Copy to David J Gross - email and print ready PDF posted.

Gross: ‘Foremost among these is supersymmetry that has the ability to unify bosons And fermions into a single pattern, to unify matter and force [as we see already in gravitation] and to help explain the mysterious fact that the mass scale of atomic and nuclear physics is so much smaller than the scale determined by gravity (the hierarchy problem) . . . [looks like another renormalization problem]. Hierarchy Problem - Wikipedia

String theory is the most ambitious candidate for a unified theory of all the interactions that naturally embodies in a consistent fashion quantum gravity. String theory - Wikipedia

Gross: “Thus once again we are embarked on a new stage of exploration of fundamental laws of nature, a voyage guided largely by the search for and the discovery of new symmetries.

I would like to do everything by symmetry, but I will stick with trying to express Maxwell’s equations in quantum mechanics without using fields in spacetime. The ‘vector potential’ is a spacetime thing but the Bohm-Aharanov effect suggests that is is a pure quantum thing, a superposition of abstract ‘waves’ ie periodic functions, something to do with hermitian operators.

[page 218]

Behel: In Minkowski space where Lagrangian operates fermions [and bosons] come in mating pairs probably with zero energy, like a pendulum, massive fermions made of kinetic, massless bosons made of potential, so Lagrangian L = T − V remains stationary at zero,the basic symmetry is in effect equivalence. We see this in gravitation where mass is both fermion and boson, ie essence ≡ existence, form ≡ energy. So we decide energy is like substance / matter, but mass and energy are also equivalence, massive fermions, massless bosons (mostly)? Non mathematical dreaming. What are the real quantities in quantum mechanics. [at the quantum level the vector potential does not involve mass, energy or momentum]. Photon energy = Δ orbital energy. Keep shifting the bits until they fit. Its got to be far simpler than the field theorists think. I have to look at Behiel’s derivation of the Maxwell’s equations, mixing up quantum mechanics and classical mechanics as though there is feedback rather than quantum control. Part of the problem of QFT is that it is premissed on the assumption that classical controls quantum but quantum is too real for that via random basis states and hermitian operators [and one suspects that the quantum computers are mistaken when they think they can isolate individual quantum eigenfunctions]. This is the speculation that will lead to a conclusion, the difficult point of making the real world out of quantum mechanics, bit like making life out of genes but in this case quantum mechanics does both the randoms and the selection [and as I have manged to accidentally discover, the route from quantum mechanics to Minkowski space is via particles. Richard Behiel: Electromagnetism as a Gauge Theory

The gravitational situation demands a zero Lagrangian for every qubit, and so we expect all the fermions and bosons appearing in Minkowski space to have a Lagrangian stable at zero and so a balance between fermion and boson.

Friday 2 January 2026

My manifesto for scientific theology, finally bring the most ancient and mystical science out of the hands of imperial autocratic popes and all those mystical pseudoscientists who use their power to get us to believe that they have an infallible connection to a non-existent [invisible] God which entitles them to override all our art and science for their [own] benefit.

In many places these people still enforce their control by claiming the power to imprison, torture and murder heretics, make war and deny the spiritual power of women.

Squish this into a tweet with passion.

All that gauge (ie phase) theories are telling us is that in nature information is encoded in the phase of quanta of action. I do not really understand this but my hunch is that the multidimensional phase encapsulated in a vector in Hilbert space is a logical operator [ie software] which serves as a message which, when uttered by a natural authority, is in infallible command.

It is interesting to me how my understanding of the world has increased incrementally over a lifetime of study and trade to finally arrive that the theory of everything is theology, the universe is divine and the only way to understand it is as a mind — a sheet of corrugated steel is a logical operator in the construction of a dwelling [both an operator and a thing, boson and fermion]. This is where my spiritual manifesto meets technology and my old deceased work mates Bruce Wilson and Graham Ellis.

Saturday 3 January 2026

[page 220]

The Aharanov-Bohm thing is the clincher [demonstrating the foundational role of quantum mechanics]. Electrons are flipped by π by the quantum vector potential in the absence of E and M fields in Minkowski space. [see Tonomura above]

I begin to see why Einstein worked alone. A feeling is a personal thing, a quantum thing that cannot be shared until it gets the energy to be expressed and then it can be shared. My book is a shared feeling that has taken me 60 years to materialize/energize and now it can be shared and start a movement - a bit of cognitive cosmogenesis ie poetry.

Back to Behiel 1:10:1 (started at page 207): ‘Dirac field per se does not have local phase symmetry’, And we begin to invent the photon field in Minkowski space via the Lagrangian to corrct this lack.Because we are using the Lagrangian in Minkowski space, this is not strictly quantum mechanics. We are discussing the EM 4 potential which is an energy thing, not part of quantum mechanics per se but does seem to be sub-Minkowski thrugh the Aharanov-Bohm effect whicg changs electron phase outside the presence of EM fields in spacetime. Richard Behiel: Electromagnetism as a Gauge Theory

[pages of Behiel notes pp 221 - 225]

[page 225]

So now I have watched the whole video and seen a lot of mathematics about distance and time which have nothing to do with quantum mechanics and wonder if in reality everything is much simpler. And in a way the whole thing comes down to the fine structure constant [the “force”, “coupling” between bosons and fermions]. Fine-structure constant - Wikipedia

At present I am stypied but i feel confident that we can start with the qubit ψ = α|fermion⟩ + β|boson⟩ and magine that the vectors representing fermion and boson are normalized, orthogonal and in EM the simplest possible with U(1) symmetry to be ncreased to higher dmensins as we go to higher energied but all is ?? and my next task is to add to cl4l05_particles to woerk toward an answer.

[page 226]

to be also incorporated in l4l_e02_Justice based on gravitation and zero sum bifurcation after Essay l4l01: Quantocracy: The universal quantum mechanical foundations of democracy and freedom on agency and independence. How does this relate to the interaction between fermions and bosons which requires a stationary Lagrangian.

All that QED stuff has shocked me a bit but I still have faith in unrestricted quantum mechanics. Energy makes he photons and electrons/positrons real. Their interactions create Minkowski space but we need to create an analogy of the Dirac equation to get back to the Minkowski track with the spinors — how does a spinor differ from a Hilbert basis state? We have to plot the quantum mechanics behind it and get to the idea that the exclusion principle automatically demands 3D space and the photons add the minus dimension that gives the null geodesics which never get a mention in Behiel. Dirac equation - Wikipedia

We assume that the spinor solutions to the Dirac equation are orthogonal and indistinguishable from Hilbert basis states so we can imagine 4D Hilbert space representing fermions up and down, in the simplest case electrons and positrons. We simply assume that there is enough entropy in each basis to define the associated particle, and there might be much more to each one as Qiu might see. All that is required in a qubit is that the two bases are orthogonal but they could have the entropy of male and female mammals with the occasional [bisexual] superposition. Spinor - Wikipedia, Qiu-Hong Hu (2005_12_29): The nature of the electron

My fondest pleasure is to write something gripping, but it is

[page 227]

not always available. like reading the crime novel, the big question is what is going on in the universe and the problem is the interface between the simplicity of quantum mechanics and the complexity of the world. This is my problem and my way around it is to apply the Gödel Chaitin measure of entropy to the complexity that needs to be explained in Minkowski space which, in the case of QED, is the whole subject of electrical engineering, from power through computation ion to biology. What I can do now is write more about quantum precision and politicd. Quantocracy is good and now I have to get on with the 10 steps and Justice and the big problem with the ten steps is producing analogues of QED and QCD, most of which comes down to explaining the exclusion principle, asymptotic freedom and containment.

The core point if the divine universe is the inspiration that appears in own own minds as we pick up some tool to realize the inspiration with pen, guitar, violin or bulldozer and this brings us into contact wth the people who cooked up the Hebrew Bible, the Dreamtime and all the other human artistic snd industrial constructs with which we have filled and sometimes damaged the world. The root problem with our mental states, which I try to explain in the theory of peace and my book, is to find the psychological space to treat everybody as we would like to be treated in contrast to the widespread notion held by some that they are entitled to more good things and fewer bad things, the effective core of Christianity as opposed to imperialism. The next book, going on from the genetic content of bodies as a source of cooperation must take us back to a quantum mechanical elaboration of justice, as envisaged in l4l_eo3_Justice and the rest of the site.

[page 228]

Behiel’s video was completely about calculus in the relativistic mass shell explaining the work of Faraday and Maxwell and almost nothing about quantum mechanics except phase in space illustrated by arrows.

Copyright:

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Further reading

Books

Augustine (419, 1991), and Edmond Hill (Introduction, translation and notes), and John E Rotelle (editor), The Trinity, New City Press 399-419, 1991 Written 399 - 419: De Trinitate is a radical restatement, defence and development of the Christian doctrine of the Trinity. Augustine's book has served as a foundation for most subsequent work, particularly that of Thomas Aquinas.  
Amazon
  back

Dirac (1983), P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)  
Amazon
  back

Nicholls (2025), Jeffrey, Cognitive Cosmogenesis: A systematic integration of physics and theology, Austin Macauley Publishers 12025 ' This book is a personal narrative of those events and a defense of the belief that the universe itself is divine. The central argument is that by embracing this reality and abandoning notions of supernatural deities, humanity can resolve its problems. The universe, it is argued, is self-creating, and a proper understanding of physics leads to a plausible scientific theology. The natural intelligence inherent in the universe, from cellular organization to ecosystems, far surpasses any artificial intelligence. Comprehending this natural order, the author suggests, would make achieving world peace relatively straightforward. The book contends that modern theologians should recognize the physical world, rather than ancient texts, as the foundation for credible theology. It also addresses the historical entanglement of religion and politics, asserting that the model of creation presented herein fundamentally rejects the imperialistic ambitions that have fueled genocidal holy wars.'  
Amazon
  back

Links

Akira Tonomura (2006_04), The Aharonov-Bohm effect and its applications to electron phase microscop , ' The Aharonov-Bohm effect was conclusively established by a series of our electron interference experiments, with the help of some advanced techniques, such as coherent field-emission electron beams and microlithography. Using this fundamental principle behind the interaction of an electron wave with electromagnetic fields, new observation techniques were developed to directly observe microscopic objects and quantum phenomena previously unobservable.' back

Albert Einstein (1915), The Field Equations of Gravitation, ' In two recently published papers I have shown how to obtain field equations of gravitation that comply with the postulate of general relativity, i.e., which in their general formulation are covariant under arbitrary substitutions of space-time variables. [. . .] With this, we have finally completed the general theory of relativity as a logical structure. The postulate of relativity in its most general formulation (which makes space-time coordinates into physically meaningless parameters) leads with compelling necessity to a very specific theory of gravitation that also explains the movement of the perihelion of Mercury. However, the postulate of general relativity cannot reveal to us anything new and different about the essence of the various processes in nature than what the special theory of relativity taught us already. The opinions I recently voiced here in this regard have been in error. Every physical theory that complies with the special theory of relativity can, by means of the absolute differential calculus, be integrated into the system of general relativity theory — without the latter providing any criteria about the admissibility of such physical theory' back

Chen Ning Yang (1957), Nobel Lecture: December 11, 1957: The Law of Parity Conservation and Other Symmetry Laws of Physics, ' The existence of symmetry laws is in full accordance with our daily experience. The simplest of these symmetries, the isotropy and homogeneity of space, are concepts that date back to the early history of human thought. The invariance of physical laws under a coordinate transformation of uniform velocity, also known as the invariance under Galilean transformations, is a more sophisticated symmetry that was early recognized, and formed one of the corner-stones of Newtonian mechanics. Consequences of these symmetry principles were greatly exploited by physicists of the past centuries and gave rise to many important results. A good example in this direction is the theorem that in an isotropic solid there are only two elastic constants.' back

David J Gross (1996_05_11), The Role of Symmetry in Fundamwental Physics, ' Until the 20th century principles of symmetry played little conscious role in theoretical physics. The Greeks and others were fascinated by the symmetries of objects and believed that these would be mirrored in the structure of nature. Even Kepler attempted to impose his notions of symmetry on the motion of the planets. Newton’s laws of mechanics embodied symmetry principles, notably the principle of equivalence of inertial frames, or Galilean invariance. These symmetries implied conservation laws. Although these conservation laws, especially those of momentum and energy, were regarded to be of fundamental importance, these were regarded as consequences of the dynamical laws of nature rather than as consequences of the symmetries that underlay these laws. Maxwell’s equations, formulated in 1865, embodied both Lorentz invariance and gauge invariance. But these symmetries of electrodynamics were not fully appreciated for over 40 years or more' back

Dirac equation - Wikipedia, Dirac equation - Wikipedia, the free encyclopedia, 'In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1⁄2 massive particles such as electrons and quarks, for which parity is a symmetry, and is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It accounted for the fine details of the hydrogen spectrum in a completely rigorous way.' back

Fine-structure constant - Wikipedia, Fine-structure constant - Wikipedia, the free encyclopedia, ' In physics, the fine-structure constant, also known as Sommerfeld's constant, commonly denoted by α (the Greek letter alpha), is a fundamental physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles. . . . While there are multiple physical interpretations for α it received its name from Arnold Sommerfeld introducing it (1916) in extending the Bohr model of the atom: α quantifies the gap in the fine structure of the spectral lines of the hydrogen atom, which had been precisely measured by Michelson and Morley' back

Gregory J. Chaitin (1982), Gödel's Theorem and Information, 'Abstract: Gödel's theorem may be demonstrated using arguments having an information-theoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread rather than pathological and unusual.'
International Journal of Theoretical Physics 21 (1982), pp. 941-954 back

Hierarchy Problem - Wikipedia, Hierarchy Problem - Wikipedia, the free encyclopedia, ' In theoretical physics, the hierarchy problem is the problem concerning the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 1024 times stronger than gravity.
Technical definition
A hierarchy problem occurs when the fundamental value of some physical parameter, such as a coupling constant or a mass, in some Lagrangian is vastly different from its effective value, which is the value that gets measured in an experiment. This happens because the effective value is related to the fundamental value by a prescription known as renormalization, which applies corrections to it.
Typically the renormalized value of parameters are close to their fundamental values, but in some cases, it appears that there has been a delicate cancellation between the fundamental quantity and the quantum corrections. Hierarchy problems are related to fine-tuning problems and problems of naturalness.' back

Kpop: NewJeans, ETA, Producer: MIN HEE JIN Music Video Director: Wooseok Shin In collaboration with Apple, this music video was entirely shot on iPhone 14 Pro. back

Qiu-Hong Hu (2005_12_29), The nature of the electron, ' Through investigating history, evolution of the concept, and development in the theories of electrons, I am convinced that what was missing in our understanding of the electron is a structure, into which all attributes of the electron could be incorporated in a self-consistent way. It is hereby postulated that the topological structure of the electron is a closed two-turn Helix (a so-called Hubius Helix) that is generated by circulatory motion of a mass-less particle at the speed of light. A formulation is presented to describe an isolated electron at rest and at high speed. It is shown that the formulation is capable of incorporating most (if not all) attributes of the electron, including spin, magnetic moment, fine structure constant, anomalous magnetic moment, and charge quantization into one concrete description of the Hubius Helix. The equations for the description emerge accordingly. Implications elicited by the postulate are elaborated. Inadequacy of the formulation is discussed.' back

Richard Behiel, Electromagnetism as a Gauge Theory, ' "Why is electromagnetism a thing?" That's the question. In this video, we explore the answer given by gauge theory. In a nutshell, electromagnetism arises from local phase symmetry. But what does that mean, and how exactly does that work? That's what this video is all about!
This video is quite long and technical. Think of it as a video textbook, so you can skip around to different parts if you’d like. But I wanted to err on the side of rigor and thoroughness, to show comprehensively how local U(1) symmetry blossoms into electromagnetism. So the ideas are all there for you, but you don’t have to watch this in one sitting! ' back

Simon Lamb (2026_01_02), Ancient African bedrock reveals the violent beginnings of life on our blue planet, ' You have probably seen the images of the surface of Mars, beamed back by NASA’s rovers. What if there were a time machine capable of roaming Earth during its remote geological past, perhaps even going right back to its beginnings, beaming back pictures of similar quality?
This is not science fiction. In remote corners of the world, geologists have found tiny relics of Earth’s very ancient surface.
I have been part of this scientific endeavour, looking at the treasure trove of information in the bedrock of the Makhonjwa Mountains in South Africa and the adjacent small kingdom of Eswatini.
These rocks reach back more than three quarters of the way through our planet’s long history of nearly 4.6 billion years. In my new book, The Oldest Rocks on Earth, I describe the graphic images “beamed back” by this geological time machine. [. . .]
Going back in time beyond the Makhonjwa Mountains, we still find evidence for oceans, life and, I argue, plate tectonics. Earth became blue within the first tenth of its history.
Mars and Venus may have started this way, too. But our planet uniquely lies in the so-called Goldilocks Zone, receiving just the right amount of solar energy to avoid becoming a boiling Venusian hell or freezing Martian world.
It is also big enough to have a magnetic field and pull of gravity sufficient to retain its atmosphere. And right at the start, a dramatic collision with a Mars-sized asteroid spalled off our Moon, stabilising Earth’s spin axis so that day and night were less extreme.
Finally, the biochemistry of living organisms may have played a key role in keeping Earth this way by helping the bedrock absorb greenhouse gases in the face of a steadily warming Sun.
We must not be the first to let Earth lose its distinctive life-giving blue, a colour so wonderfully referred to in the Siswati language of Eswatini as luhlata lwesibhakabhaka, literally “green like the sky”. back

Sin-Itiro Tomonaga (1965), Nobel Lecture: Development of Quantum Electrodynamics: Personal recollections, ' (1) In 1932, when I started my research career as an assistant to Nishina, Dirac published a paper in the Proceedings of the Royal Society, London1. In this paper, he discussed the formulation of relativistic quantum mechanics, especially that of electrons interacting with the electromagnetic field. At that time a comprehensive theory of this interaction had been formally completed by Heisenberg and Pauli, but Dirac was not satisfied with this theory and tried to construct a new theory from a different point of view. Heisenberg and Pauli regarded the (electromagnetic) field itself as a dynamical system amenable to the Hamiltonian treatment; its interaction with particles could be described by an interaction energy, so that the usual method of Hamiltonian quantum mechanics could be applied. On the other hand, Dirac thought that the field and the particles should play essentially different roles. That is to say, according to him, “the role of the field is to provide a means for making observations of a system of particles” and therefore “we cannot suppose the field to be a dynamical system on the same footing as the particles and thus be something to be observed in the same way as the particles” [. . .]' back

Spinor - Wikipedia, Spinor - Wikipedia, the free encyclopedia, 'In geometry and physics, spinors are elements of a (complex) vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation. When a sequence of such small rotations is composed (integrated) to form an overall final rotation, however, the resulting spinor transformation depends on which sequence of small rotations was used: unlike vectors and tensors, a spinor transforms to its negative when the space is rotated through a complete turn from 0° to 360°.' back

String theory - Wikipedia, String theory - Wikipedia, the free encyclopedia, 'In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force. Thus string theory is a theory of quantum gravity. ' back

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