Gravity Septet

 The two quartets mentioned in the previous post "Four Forces";

(Energy, Time, Mass, Gravity) ... (Gravity, U(1), SU(2), SU(3))

are linked by Gravity. This suggests a septet centered around Gravity,

(Energy, Time, Mass, Gravity, U(1), SU(2), SU(3))

The three couplings implied by this stack of 7 (Details from Gemini);

(Mass, U(1));

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There is a fundamental and tightly woven connection between mass and the U(1) symmetry group, primarily operating through the mechanics of the Higgs mechanism and the definition of physical particles in quantum field theory.

Here is how mass and U(1) interact across the fabric of physics:

1. The Higgs Mechanism and Mass Generation

• Spontaneous Symmetry Breaking: In the Standard Model, the electromagnetic U(1) symmetry we see today is actually born from a larger group: group: SU(2)_L × U(1)_Y (the electroweak symmetry).

• The Massless Phase: At incredibly high energies, all quarks, leptons, and gauge bosons are completely massless because this joint symmetry forbids them from having rest mass.

• The U(1) Survivor: When the universe cooled, the Higgs field acquired a vacuum expectation value, breaking the electroweak symmetry. Only one specific, unbroken \(U(1)_{em}\) symmetry (electromagnetism) survived.

• Acquiring Mass: The particles that coupled to the Higgs field slowed down and acquired rest mass, while the photon—the gauge boson of the surviving \(U(1)_{em}\) symmetry—remained strictly massless.

2. The Masslessness of the Photon

• Gauge Invariance protects Mass: The algebraic structure of a U(1) gauge theory mathematically forbids the force-carrier (the photon) from having a mass.

• If the photon had even a tiny resting mass, it would explicitly violate U(1) gauge invariance, destroying the renormalizability and mathematical consistency of quantum electrodynamics (QED). Therefore, U(1) symmetry ensures the photon's mass is exactly zero.

3. Mass Splitting and Charge-to-Mass Ratios

• Breaking Isospin: In nuclear physics, particles with different U(1) electric charges (like the proton and the neutron) have slightly different masses.

• This mass splitting occurs because the electromagnetic U(1) field energy contributes differently to the self-energy of charged vs. neutral particles, directly linking a particle's U(1) quantum number (charge) to its total inertial mass.

4. Space-Time vs. Internal Symmetries

• Mass as a Spacetime Casimir: Mathematically, mass is defined by the Poincaré group (the symmetries of spacetime), where mass squared (m²) is a Casimir invariant.

• U(1) as an Internal Phase: U(1) is an internal phase symmetry. The connection between the two means that while spacetime symmetries define what mass is, internal U(1) gauge dynamics dictate how much mass a particle is allowed to dynamically acquire.

(Time, SU(2));

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There is a deep mathematical and physical connection between Time and SU(2) (the special unitary group in 2 dimensions), primarily through how time evolution is structured in quantum mechanics, relativistic spinors, and gravity. [1] (https://trappedflux.substack.com/p/the-shape-of-su2)

1. Quantum Evolution and Qubit Dynamics (SU(2) as Time-Evolution)

• Time-dependent Hamiltonians: In quantum mechanics, the time evolution of a two-state system (a qubit or spin-1/2 particle) is governed by the Schrödinger equation, yielding a unitary evolution operator U(t). [1] (https://www.mdpi.com/1099-4300/25/1/96)

• SU(2) group structure: Because these evolution operators are 2 × 2 unitary matrices with a determinant of 1, the set of all possible pure quantum time-evolutions for a two-level system locally or globally belongs to SU(2). [1] (https://www.mdpi.com/1099-4300/25/1/96), [2] (https://trappedflux.substack.com/p/the-shape-of-su2)

• Geometric representation: The time-dependent evolution of an SU(2) system can be mapped directly onto a rotation in a 3D abstract space (like a magnetic field or Bloch sphere trajectory) controlled by time-dependent parameters. [1] (https://www.academia.edu/100167235/SU_1_1_SU_2_and_SU_3_coherence_preserving_Hamiltonians_and_time_ordering_techniques), [2] (https://www.mdpi.com/1099-4300/25/1/96)

2. Spacetime, Lorentz Group, and \(SL(2, \mathbb{C})\) / SU(2)

• Spinors and Time: In special and general relativity, the Lorentz group of spacetime transformations SO(1,3) is locally isomorphic to \(SL(2, \mathbb{C})\) (the group of 2 × 2 complex matrices with determinant 1). [1] (https://physics.stackexchange.com/questions/108212/whats-the-relationship-between-sl2-mathbbc-su2-times-su2-and-so)

• Compact vs. Non-compact: \(SL(2, \mathbb{C})\) can be decomposed or related to compact subgroup structures like SU(2) × SU(2) (which double-covers 4-dimensional Euclidean/spatial rotations SO(4)). While time introduces a non-compact "boost" direction (making full Lorentz symmetry non-compact), the spatial rotation parts are fundamentally anchored by SU(2). [1] (https://ivganev.github.io/notes/files/cover.pdf), [2] (https://physics.stackexchange.com/questions/108212/whats-the-relationship-between-sl2-mathbbc-su2-times-su2-and-so)

3. Loop Quantum Gravity and Ashtekar Variables

• Time as a Dynamical Variable: In canonical general relativity and Loop Quantum Gravity (specifically using Ashtekar variables), the gravitational field is recast using SU(2) gauge fields (connections and triads) rather than metric tensors of spacetime.

• Tied to Evolution: In this formulation, the choice of time and the Hamiltonian constraint of general relativity are deeply intertwined with SU(2) gauge transformations on spatial slices of the universe.

(Energy, SU(3));

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Yes, there is an incredibly profound connection between energy and SU(3), which lies at the very heart of the Standard Model of particle physics, specifically within Quantum Chromodynamics (QCD) and the behavior of the strong nuclear force.

In physics, energy dictates how fields change, how particles interact, and where mass comes from. Here is how SU(3) and energy are deeply intertwined:

1. The Energy-Scale and Asymptotic Freedom

• The Running Coupling Constant: In SU(3) gauge theory (which governs gluons and quarks), the strength of the interaction changes drastically depending on the energy scale at which you probe it.

• High Energy (Asymptotic Freedom): At extremely high energies (or very short distances, like inside a particle accelerator), the SU(3) coupling strength drops toward zero. Quarks behave like free, non-interacting particles.

• Low Energy (Confinement): At low energies (or larger distances), the SU(3) force becomes incredibly strong. This binds quarks permanently inside hadrons (like protons and neutrons), a phenomenon known as color confinement.

2. Mass Generation (Where 99% of Proton Energy Comes From)

• Energy-Mass Equivalence: The rest masses of individual quarks account for only about 1% of a proton's mass.

• SU(3) Field Energy: The remaining 99% of the mass (and therefore the rest energy, via \(E=mc^2\)) is dynamically generated by the kinetic energy of the quarks moving at near-light speed and the massive binding energy of the SU(3) gluon fields.

3. SU(3) Flavor Symmetry and Energy Degeneracy

• Approximate Degeneracy: Historically, Murray Gell-Mann used a global SU(3) flavor symmetry (Up, Down, and Strange quarks) to classify hadrons (the "Eightfold Way").

• Mass/Energy Splitting: Because the Up, Down, and Strange quarks have different masses, this SU(3) symmetry is broken. The degree to which particles in the same SU(3) multiplet differ in rest energy (mass) directly measures how badly the symmetry is broken.

4. Gauge Generators and the Hamiltonian

• Color Charge Conservation: The SU(3) gauge symmetry is generated by 8 Gell-Mann matrices. In quantum field theory, because the Hamiltonian (the operator representing total energy) commutes with these SU(3) generators, color charge is a strictly conserved quantity during any high-energy interaction.

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The symmetry of the septet and it's three couplings are represented by two ancient cultural and religious symbols; Shatkona and Menorah. Both belong to many ancient cultures. The number 7 also has significance in many ancient cultures. I think this is quite interesting.

Four Forces

 There are four fundamental forces of Physics;

(Gravity, Electromagnetism, Weak, Strong)

The study of these and their charges are at the foundation of Physics. The (Charge, Field) duality is the governing duality since these forces are fields. The numbers that correspond to the forces are;

(?, 1, 2, 3)

The last three are obvious because the corresponding groups are;

(?, U(1), SU(2), SU(3))

The group numbers refer to the entry numbers of the complex matrices that govern the corresponding interactions.

The obvious number that corresponds to Gravity is Zero, but there is no group called ?(0). I will call it G(0). Quantum Gravity studies the symmetry of Gravity but apparently "QG can not tolerate global symmetry groups". Since QG is not a mature theory, this remains a mystery. According to Gemini, "the primary mathematical field that studies the structure of "the very small" is Noncommutative Geometry. 

The symmetries of the number 4 may shed some light into this;

((2+2), (2*2), (1+3), (3+1), (1+1+1+1))

This may look trivial but all these exist in the fields. For example;

(2+2); ((Gravity, Electromagnetism), (Weak, Strong))

(1+3); ((Gravity), (Electromagnetism, Weak, Strong))

Electromagnetism enters General Relativity directly, making them a strong duality. The (1+3) symmetry is obvious since Gravity stands apart from the other 3.

The (2*2) symmetry shows itself in the couplings;

((G(0), U(1)) * (SU(2), SU(3))) =

((G(0), SU(2)), (G(0), SU(3)), (U(1), SU(2)), (U(1), SU(3)));

(G(0), SU(2)) coupling; Gravity as SU(2) gauge theory.

(G(0), SU(3)) coupling; A clash.

(U(1), SU(2)) coupling; Electroweak Unification.

(U(1), SU(3)) coupling; QCD.

These second order couplings come after the stronger ones based on the (2+2) symmetry;

(G(0), U(1)) and (SU(2), SU(3)).

...

From another more fundamental view, there are four fundamental categories of Physics;

(Energy, Time, Mass, Gravity)

The (2+2) and (1+3) symmetries are obvious here too. The (2*2) symmetry shows itself in the 4 couplings;

((Energy, Time) * (Mass, Gravity)) = 

((Energy, Mass), (Energy, Gravity), (Time, Mass), (Time, Gravity));

(Energy, Mass) coupling is obvious; E=m*c**2

(Energy, Gravity) coupling; Gravity has negative Energy.

(Time, Mass) coupling; The most obvious is the Compton frequency; f=m*c**2/h.

(Time, Gravity) coupling; Time slows down in Gravity.

These second order couplings come after the stronger ones based on the (2+2) symmetry;

(Energy, Time) and (Mass, Gravity).

0, 1, 2, 3

Numbers and their operations or Arithmetic have emerged out of the need to count and record. So Numbers can be regarded as the starting point of Mathematics from a historical point of view at the least. This point of view puts Number Theory at the foundation of Mathematics. After all, numbers are the purest objects of Mathematics. Lets call this step as One.

Mathematical Logic and Set Theory are closely related yet separate fields. They have always been there in Mathematics but it took time to establish them as distinct fields. Lets call this step as Two.

When One and Two are defined like this, Three becomes obvious; Analysis, Algebra and Geometry. 

This implies an obvious question; What would be the ground that is Zero? It exists in every mathematical field in different forms and as '0' in Number Theory and null set '{}' in Set Theory. It took time to invent the number Zero and it has not been obvious that it simplifies Arithmetic. Even the ancient Greeks and Romans failed to invent or discover it. Counting seems to be the foundational step Zero. Even animals must count. There is Counting Theory also called Combinatorics.

0. Counting,

1. Number Theory,

2. Mathematical Logic, Set Theory,

3. Analysis, Algebra, Geometry.

This (0, 1, 2, 3) classification of Mathematics rings an interesting bell; Hurwitz's (1, 2, 4, 8) theorem. 

12 aspects of economy

In line with the recent 'The Ternary Classification' post, another quartet can be added to the two quartets of the 'Eight Aspects of Economy' post of 2010;

(((Gather, Hunt), (Farm, Manufacture)),

((Information, Intelligence), (Imagine, Create)),

((Barter, Trade), (Commerce, Finance)))

as the Application layer to complete the classification. I renamed the (Spiritual, Artistic) duality to (Imagine, Create). This way, the first quartet becomes the Measure, and the second the Theory of the ternary foundational classification. In the economics context, the first and third element can be called Production and Exchange.

The Ternary Classification

The classifications based on the stack of 12 for various fields I have attempted until now have the dominant symmetry 3*4. The outer aspect is ternary and the inner is quaternary or rather dual binary. For example for Mathematics;

(((Number,Function),(Operation,Equation)),
((Set/Logic,Analysis),(Algebra,Geometry)),
((Probability,Statistics),(Computation,Information)))

and for Physics;

((((Energy,Time),(Momentum,Distance)),((Angular-Momentum,Area),(Spin,Volume))),

(((Mass,Gravity),(Electric-Charge,Electric-Field)),((Weak-Charge,Weak-Field),(Strong-Charge,Strong-Field))),

(((Higgs,Atom),(Boson,Planet)),((Lepton,Star),(Quark,Black-Hole))))

 

The one for Physics has the symmetry of 3*4*2=24, and its outer shape is still 3.

 

If 3 words are assigned for the elements of this ternary symmetry they would probably be;

 

(Measure, Theory, Application) 

Previously I have mentioned the number triplet (0,1,∞) which also has ternary symmetry and this suggests Zero and Infinity have Binary symmetry. They are inversions of each other around unity anyway.

Why 3 dominates over 2 is open for investigation.

Science fractal

Consider the mapping;

SM0=1 ... Higgs ... Higgs ... Mathematics
SM1=1/2 ... Light ... Atom ... Physics
SM2=1/2 ... Weak ... Cell ... Chemistry
SM3=3/2 ... Quarks ... Planet ... Biology
SM4=18 ... Leptons ... Star ... Psychology
SM5=1080 ... Time ... Galaxy ... Intelligence
SM6=12150 ... Gravity ... Universe ... Aesthetics

Biology corresponds to Planet and sits in the middle. Implying that the universe is a biological form, or that all life obeys M6. Also displaying the analytical/emotional split of a brain. Chemistry/Psychology coupling shows that chemicals make the mood, like Star light make Cell. Physics/Intelligence coupling shows that Physics (electricity or light) make Intelligence, since our chemical and biological brain support the electrical action that make Intelligence. Since light speed is needed to go beyond the chemical reaction speeds to make a hyper-structure like brain. The most interesting is Mathematics/Aesthetics coupling. Aesthetics is beyond intelligence. It is beyond religion, beyond everything, but it needs all of them.

Religion replaces art in broken spirits. Spirits are broken, mostly early in childhood, by power dynamics of society. Spirit of an individual is broken to dominate the person, like breaking horses. But a shepherd is needed to keep the herd, so preachers are invented by the rich and powerful. Revolutionary preachers are eliminated, if not then adopted, like Romans adopted Christianity and Moors adopted Islam. A monotheistic religion naturally reflects the politics of an empire. This is not to say that there are no spirits. Just replace Art with Spirit. But it belongs to the bearer only. When we learn to go beyond the L&S+B&D+S&M+V&M (The Modular Group of monkey culture; Love and Sex, Bondage and Discipline, Sadism and Masochism, Violence and Murder) culture of our monkey past, we will know that a spirit is the most valuable entity of a society, and that it should not be broken by the proxies of the bullies.

 

EDIT 10-6-2026:  First published in 2006. Now some typos corrected. Seeing that the post got some attention lately, I had a reread. It still looks good but the first column of the particle physics classification looks wrong. I had better ones since this post, for example 'Universe in a Box' and '24 Aspects of the Universe'.

Capturability of the mainstream

Why is it that the human mainstream is so easy to capture?

In Cronulla race riots in Australia recently, a large number of youth were captured by a few well organised extreme racists. Since the Iraq invasion and the subsequent bombing in Bali, racial harmony suffered greatly. Racist Anglos were ready to be captured it seemed (most Anglos are decent good people I must add). Many of them were drunken and wrapped in Australian flags. They displayed a disgraceful scene, chasing and beating any dark skinned person who happened to be there, including women. The police chief later explained it as crowds being "captured". The oragnisers of the event would have been happy with the results, but I am sure they were not too happy with being seen as a mob of drunken losers.

Didn't Hitler capture an entire nation? He took so many of them to the grave. It seemed capturing humans was as easy as capturing sheep, maybe easier. Hitler was not alone of course. The Europian aristoctarcy and corporations were desperate to counter the Soviet revolution. They supported despots all over Europe to suppress local revolutions. Franco did not reach the efficiency of Hitler, but he also killed a lot of people. Mussolini was of the same kind. They keep showing docos on how bad were the dictators, but they never mention the fact that they were the ones behind the curtain. Later Hitler went rogue, as they do, and became an embarrasment. But Franco stayed a darling until the end.

Neo-cons also tried to capture the American mainstream and succeeded to a great degree. If they were successful in the invasion and holding of Iraq, we would have quite a different world order now. It was amazing to watch how easily they did it to the Americans. Few low life religious preachers were enough to mesmerise a large section of the society. As happened before in Europe, we all know who was behind the curtain. Greedy and ignorant corporate bully. The story of US is still unfolding. Democrats are putting a show but not too effective. Most democrats are also sponsored puppets.

Humans are easy to capture in all scales, from one person to large crowds. You just use slightly different methods. Controlling the media helps greatly. Internet must be quite a nuisance to these bastards. Falling in love is a consensual capture, supported by chemistry. Finding friends also falls into capturing. In the end it comes to reprogrammability. The mainstream provides a programmable power base for the marginal elements. It is a good representation of the concept of nothingness. It slumbers in the center to provide stability with it's size and power. We should study and understand this fact about ourselves and bring it to attention, if we want a peaceful future.

EDIT: 2-5-2026, I am republishing this as it was 20 years ago.