I tried to explain it as some of you will be aware & even show it's existence.

I have described some things really bad, I didn't have the words or knowledge.

My current view is this, I didn't have any sort of idea at all. I haven't discovered anything.

I wonder if I've merely 'seen' something/s physics already has a theory or theories for & it is just extremely strange.

I don't mean everything in the physics world, just an angstrom snippet if you will.

For back up, I refer to my very first post in another thread: https://scienceforums.net/topic/134685-1-sub-quantum-echo-particlessqeps-sub-quantum-echo-particle-kinetic-resonance-flux/

On 9/24/2024 at 7:05 PM, Imagine Everything said:

In it's very basic form, I see an edge of one item meeting the edge of another item and inbetween these 2 edges is a resonation flux formed from SQEP kinetic energy.

I see SQEP's as the very very smallest anything can be before it tries to become 'nothing'.

On 9/24/2024 at 7:05 PM, Imagine Everything said:

I see these SQEPKRF's in the same way people shed their skin. Always happening, all the time items are next to each other.

The space between to 2 edges is now phased or merged with each others SQEP's at all times while these 2 items are next to each other.

As soon as one is moved, the SQEPKPRF would change to fit the new 'double' or 'pairing' of whatever they then ended up next to edge to edge.

Disregarding completely the particle I tried to see, at the very least, could my bad description not be thought of as having loosely described

Boundary Conditions, States, Systems, Quantum Tunneling, Zero Point Energy & maybe at a stretch something loosely similar to the https://en.wikipedia.org/wiki/Casimir_effect

There are 2 ways of perceiving what I'm saying I guess

.

I ended up referring to something in that thread, that I thought of as everything, everywhere, always has been, always will be.

Then I found about this https://en.wikipedia.org/wiki/Zero-point_energy

The Zero Point Energy Field

Have you, the experts here, encountered other people who have seen scientific theories, explained in their own odd way of describing it.

Descriptions that were close enough for you to see a little substance in them.

Have you, yourselves had an insight into something in your own lives that was a little surreal?

A poor photocopy of photocopies with degraded readability; can A.I. in some sort of optical character recognition renew/retype text to a very readable condition ?

What would be the "instruction/request/text" to ask A.I. to

• perform such on a image with text, or;

• giving A.I. a .pdf document ?

Would it be something like "retype/reconstruct this document" attached ? (xxxxxxx.pdf)

Example with NO interest in the context but on its reconstruction and readability:

---> Can anyone teach me how to do it ?

How does this work in practice?

Is the universe expanding "in" to something?

Or is the universe itself perpetually pushing a "boundary" ?

The lower part of the shoulders of humans and animals is called the 'trunk'. It includes the female vagina, uterus, hands, feet, lungs.

'Mercury' means the 'trunk'.

'Venus' means the male sex organ. In man's body, 'trunk' means hands, feet, lungs, male sex organ..

'Guru' (Jupiter ) means the part above the shoulders of humans. It includes the head, throat, neck, five sense organs (eyes, ears, nose, tongue and mouth).

'Mars' means the blood in the body of humans and animals.

'Saturn 1 ' means Ghost, the sleep and death-sleep.

'Moon' means the mind of humans.

'Earth' means the stomach of humans, animals and birds.

Saturn 2 is associated with death and is called 'Maruti' or 'Hanuman' in Hindu religion. He is the god of rebirth and health.

The human body is formed by these 'nine planets '

I'm posting this to spark discussion – has anyone seen similar geometric approaches? Students, if you're learning relativity and frustrated with the math, try these derivations and let me know if they click. Test the code, replicate the algebra for other cases (like Mercury's orbit etc), and share your thoughts/results. Could this simplify teaching GR?

All equations are purely algebraic and reproduce known results of Special and General Relativity exactly.

Feedback on mathematical structure, reproducibility, and numerical testing is welcome.

---

Abstract

I’m an independent researcher working on a framework called WILL Relational Geometry, which reproduces the main results of SR and GR using only simple algebraic projections on circles and spheres — no tensors, metrics, or differential equations.

The model is based on one principle:

Spacetime ≡ Energy — meaning geometry and dynamics are not separate but mutually defined.

Paper: https://doi.org/10.5281/zenodo.17115270 (October 2025)

Full text (PDF): https://github.com/AntonRize/WILL/blob/46ed9a336bd99607033a811cd3160088a07d3851/documents/WILL_PART_I_SR_GR.pdf

---

Core Summary

- Everything emerges from normalized projections on S¹ and S²:

β → kinematic (v/c)

κ → potential (√(Rₛ / r))

- Closure rule: κ² = 2β² — a purely geometric relation similar to the virial condition but derived geometrically.

- SR and GR factors appear as projections of the same conserved energy relation.

- Spacetime and energy transformations are two faces of one invariant.

(Full symbolic table attached as image for clarity.)

---

Test 1: Photon Sphere Radius

GR:

Derived via geodesics → r = 1.5 Rₛ.

WILL:

Set equilibrium θ₁ = θ₂ ⇒ β² + κ² = 1 ⇒ κ² = 2β² ⇒ κ² = 2/3 ⇒

r = Rₛ / κ² = 1.5 Rₛ.

For the Sun (M ≈ 1.989×10³⁰ kg, Rₛ ≈ 2.95 km) → r ≈ 4.425 km.

Matches GR exactly.

---

Test 2: GPS Time Dilation Offset

Known value: net +38.5 μs/day (satellite runs faster).

WILL: Unified equation for both effects:

τ = √(1 – κ²) × √(1 – β²)

where κ² = 2GM/(c²r), β = v/c.

Python verification (if python not your thing - down below there's link to Desmos projects ready to go):

import numpy as np

# Constants

G = 6.67430e-11

c = 2.99792458e8

# Earth / GPS parameters (SI)

M_earth = 5.972e24 # kg

R_earth = 6.37e6 # m (mean radius)

r_gps = 2.6571e7 # m (GPS orbital radius)

# Orbital speed (circular)

v_gps = np.sqrt(G * M_earth / r_gps)

# Dimensionless parameters

beta = v_gps / c

kappa_gps = np.sqrt(2 G M_earth / (c**2 * r_gps))

kappa_earth = np.sqrt(2 G M_earth / (c**2 * R_earth))

# Proper-time factors (WILL unified form)

tau_gps = np.sqrt(1 - kappa_gps**2) np.sqrt(1 - beta*2)

tau_earth = np.sqrt(1 - kappa_earth**2)

# Net daily offset (satellite clock faster => positive)

offset_us_per_day = (1 - tau_earth / tau_gps) 86400 1e6

print(f"beta = {beta:.9e}")

print(f"kappa_gps = {kappa_gps:.9e}, kappa_earth = {kappa_earth:.9e}")

print(f"tau_gps = {tau_gps:.12f}, tau_earth = {tau_earth:.12f}")

print(f"Offset ≈ {offset_us_per_day:.2f} μs/day")

Result: 38.52 μs/day — perfect match.

---

Discussion

The same framework reproduces:

- Lorentz factor and energy–momentum relation.

- Schwarzschild potential without curvature formalism.

- ISCO (3 Rₛ) and Kerr limits algebraically.

- Natural singularity removal without extra assumptions.

Interactive demonstrations with ready desmos projects:

https://antonrize.github.io/WILL/relativistic-foundations/

https://antonrize.github.io/WILL/

https://antonrize.github.io/WILL/predictions/

https://antonrize.github.io/WILL/results/

---

Invitation

This post invites independent testing of a fully algebraic approach to SR and GR that replaces tensor formalism with geometric projections

If you reproduce the above results — or find where it fails — please share your numbers.

Constructive criticism and falsification proposals are very welcome.

---

License: CC BY-NC 4.0 — free for scientific use and replication.

© 2025 Anton Rize

I sort of understand the reasons for this, but it simply isn't accurate. The peak of the pressure wave is hotter and the trough cooler due to compression/expansion and this does affect sonic velocity. I believe it's significant enough to be a major factor in eg. developing the characteristic timbres of wind instruments which nobody seems to have got a proper theoretical handle on yet.

I've made a start on developing a mathematical system modelling a spherical wave accommodating a variable sonic velocity and attached a brief summary. I'd be most grateful if someone would  give it a quick once over to see if I've made any blunders along the way.

The pair of simultaneous ODEs I've come up with are beyond my skills to solve analytically, but they're quite amenable to numerical integration. Any hints from the more mathematically gifted would also be much appreciated.

Spherical Adiabatic Acoustics.pdf

Passing through the Kuiper Belt, Planet 9 chaotically interacts with TNOs, leading to alignment, anti-alignment, and scattering and a decrease in the period of their orbits. But at the same time, alignment creates a closer interaction, which ultimately accelerates scattering.

Thus, TNOs whose arguments of perihelion as a result of scattering are grouped in an area at ~180° opposite to Planet 9 have more stable orbits due to a shorter interaction time. And the most stable orbits of TNOs are those located closer to its perihelion, reaching the region of the planets of the Solar System.

This is confirmed by improvised computer modeling in Sace Flight Simulator. Unfortunately, you can't see all the orbits at once, but some stages of evolution are screened separately. TNOs are initially given arbitrary circular orbits, then they become elliptical and disperse. Due to the limitations of the model, the dispersed objects exceed the escape velocity, but under certain conditions this would lead to the appearance of very elongated orbits.

Based on observations, it was assumed that the period of Planet 9 does not exceed the minimum for extreme TNOs of 4274 (2012 VP113), which can be formed as a result of alignment or anti-alignment.

In the image, the orbits of the UTOs are aligned in the plane of the ecliptic coordinate system. For Planet 9, the perihelion longitude is set at 146°, in accordance with the maximum value of 138+-8° (anti-alignment with the common argument of perihelion for clusters of 318+-8°) in the hypothesis of M. Brown and K. Batygin. This ensures the overlap of all orbits.

Such a comet-like orbit is explained by the fact that Planet 9 may be a rogue planet, attracted by the Solar System in the distant past and influencing its evolution.

https://arxiv.org/abs/2008.02110

here is a breakdown into singlets and doublets

SU(2)

\[{\small\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline Field & \ell_L& \ell_R &v_L&U_L&d_L&U_R &D_R&\phi^+&\phi^0\\\hline T_3&- \frac{1}{2}&0&\frac{1}{2}&\frac{1}{2}&-\frac{1}{2}&0&0&\frac{1}{2}&-\frac{1}{2} \\\hline Y&-\frac{1}{2}&-1&-\frac{1}{2}&\frac{1}{6}&\frac{1}{6}& \frac{2}{3}&-\frac{1}{3}&\frac{1}{2}&\frac{1}{2}\\\hline Q&-1&-1&0&\frac{2}{3}&-\frac{1}{3}&\frac{2}{3}&-\frac{1}{3}&1&0\\\hline\end{array}}\]

\(\psi_L\) doublet

\[D_\mu\psi_L=[\partial_\mu-i\frac{g}{\sqrt{2}}(\tau^+W_\mu^+\tau^-W_\mu^-)-i\frac{g}{2}\tau^3W^3_\mu+i\acute{g}YB_\mu]\psi_L=\]\[\partial_\mu-i\frac{g}{\sqrt{2}}(\tau^+W_\mu^-)+ieQA_\mu-i\frac{g}{cos\theta_W}(\frac{t_3}{2}-Qsin^2\theta_W)Z_\mu]\psi_L\]

\(\psi_R\) singlet

\[D_\mu\psi_R=[\partial\mu+i\acute{g}YB_\mu]\psi_R=\partial_\mu+ieQA_\mu+i\frac{g}{cos\theta_W}Qsin^2\theta_WZ_\mu]\psi_W\]

 with \[\tau\pm=i\frac{\tau_1\pm\tau_2}{2}\] and charge operator defined as

\[Q=\begin{pmatrix}\frac{1}{2}+Y&0\\0&-\frac{1}{2}+Y\end{pmatrix}\]

\[e=g.sin\theta_W=g.cos\theta_W\]

\[W_\mu\pm=\frac{W^1_\mu\pm iW_\mu^2}{\sqrt{2}}\]

\[V_{ckm}=V^\dagger_{\mu L} V_{dL}\]

The gauge group of electroweak interactions is 

\[SU(2)_L\otimes U(1)_Y\] where left handed quarks are in doublets of \[ SU(2)_L\] while right handed quarks are in singlets

the electroweak interaction is given by the Langrangian

\[\mathcal{L}=-\frac{1}{4}W^a_{\mu\nu}W^{\mu\nu}_a-\frac{1}{4}B_{\mu\nu}B^{\mu\nu}+\overline{\Psi}i\gamma_\mu D^\mu \Psi\]

where \[W^{1,2,3},B_\mu\] are the four spin 1 boson fields associated to the generators of the gauge transformation \[\Psi\]

The 3 generators of the \[SU(2)_L\] transformation are the three isospin operator components \[t^a=\frac{1}{2} \tau^a \] with \[\tau^a \] being the Pauli matrix and the generator of \[U(1)_\gamma\] being the weak hypercharge operator. The weak isospin "I" and hyper charge \[\gamma\] are related to the electric charge Q and given as

\[Q+I^3+\frac{\gamma}{2}\]

with quarks and lepton fields organized in left-handed doublets and right-handed singlets: 

For neutrinos involving Majorana mass an overview of the related mathematics is below including links to relevant papers

\[m\overline{\Psi}\Psi=(m\overline{\Psi_l}\Psi_r+\overline{\Psi_r}\Psi)\]

\[\mathcal{L}=(D_\mu\Phi^\dagger)(D_\mu\Phi)-V(\Phi^\dagger\Phi)\]

4 effective degrees of freedom doublet complex scalar field.

with 

\[D_\mu\Phi=(\partial_\mu+igW_\mu-\frac{i}{2}\acute{g}B_\mu)\Phi\]\

\[V(\Phi^\dagger\Phi)=-\mu^2\Phi^\dagger\Phi+\frac{1}{2}\lambda(\Phi^\dagger\Phi)^2,\mu^2>0\]

in Unitary gauge

\[\mathcal{L}=\frac{\lambda}{4}v^4\]

\[+\frac{1}{2}\partial_\mu H \partial^\mu H-\lambda v^2H^2+\frac{\lambda}{\sqrt{2}}vH^3+\frac{\lambda}{8}H^4\]

\[+\frac{1}{4}(v+(\frac{1}{2}H)^2(W_mu^1W_\mu^2W_\mu^3B_\mu)\begin{pmatrix}g^2&0&0&0\\0&g^2&0&0\\0&0&g^2&g\acute{g}\\0&0&\acute{g}g&\acute{g}^2 \end{pmatrix}\begin{pmatrix}W^{1\mu}\\W^{2\mu}\\W^{3\mu}\\B^\mu\end{pmatrix}\]

Right hand neutrino singlet needs charge conjugate for Majorana mass term (singlet requirement)

\[\Psi^c=C\overline{\Psi}^T\]

charge conjugate spinor

\[C=i\gamma^2\gamma^0\] 

Chirality

\[P_L\Psi_R^C=\Psi_R\]

mass term requires

\[\overline\Psi^C\Psi\] grants gauge invariance for singlets only.

\[\mathcal{L}_{v.mass}=hv_{ij}\overline{I}_{Li}V_{Rj}\Phi+\frac{1}{2}M_{ij}\overline{V_{ri}}V_{rj}+h.c\]

Higgs expectation value turns the Higgs coupling matrix into the Dirac mass matrix. Majorana mass matrix eugenvalues can be much higher than the Dirac mass.

diagonal of

\[\Psi^L,\Psi_R\] leads to three light modes v_i with mass matrix

\[m_v=-MD^{-1}M_D^T\]

MajorN mass in typical GUT 

\[M\propto10^{15},,GeV\]

further details on Majorana mass matrix

https://arxiv.org/pdf/1307.0988.pdf

https://arxiv.org/pdf/hep-ph/9702253.pdf

Now in order to account for the mass terms of DM the mass terms must be in or above the Kev range. Below are some related articles involving DESI. The Kev range would readily fall under the mentioned warm dm models. However there is also papers that place right hand neutrinos being in the GeV range through double beta decay.

DESI constraints

https://www.osti.gov/servlets/purl/3011043

Has a particular section to follow up on massive neutrinos behaving as dark matter described in above link.

https://arxiv.org/abs/2507.01380

double beta decay primer

https://arxiv.org/abs/2108.09364

In a nutshell the possibility is there so I started this thread to explore various examinations and starting a discussion on the the pros and cons of such a proposal. Naturally I would be interested in any related papers including counter arguments. This is not my own model proposal but a discussion on models presented by others. It doesn't suit a mainstream forum not yet anyways lol.

As for myself I see the potential but I question whether or not the mass terms will meet the required DM mass distribution. There was a fairly recent study that placed constraints on any simple Dirac mass term for right hand neutrinos in that examinations of the energy sector did not have any relevant findings. Still digging up that study hopefully I can find it however if I recall it constrained 5 KeV or less if memory serves.

other related papers

https://arxiv.org/pdf/1911.05092.pdf

https://arxiv.org/pdf/1901.00151.pdf

https://arxiv.org/pdf/2109.00767v2.pdf

https://arxiv.org/abs/1402.2301

https://arxiv.org/pdf/0708.1033

Located the light neutrino constraint paper via MicroBoone

https://arxiv.org/abs/2512.07159

I give it pdfs and a long instruction, and then ask questions.

Best Service and Local LLM

I use ChatGPT, should I switch to something else or something local ?

Give AI access to screen, able Point-&-Ask while reading ?

I saw video people doing similar things w/ Gemini, Claude.

1. I may use local OCR/CV and send it to LLM as text.

2. and use local Speech to text ?

Should I give ChatGPT access to local files for this purpose

1. LangChain - TechLinked - https://www.youtube.com/watch?v=9AXP7tCI9PI

2. Local LLM Retraining, RAG, Context Docs - https://www.youtube.com/watch?v=fFgyOucIFuk

How else can I use AI to study ?

It is currently a rough framework, however based essentially on standard physics and has been tested at key points for quantitatively correct results. Still many details are missing and I’ll have to omit even more for brevity.

Overview
TK noticed that you can express the equations of EM within the formalism of differential geometry of GR. To get both EM + GR in 1 metric he:
1) added a 5th dimension (scalar [math] \Phi [/math])
2) used the constant of gravitation, G, in his equations.
The resulting disagreement with particle properties is formally due to the constant used, as noted in TK’s original article. The right step to solve this problem is a step back: drop G. This “unifies” EM and particle physics, gravitation can be recovered by series expansion.
To do so requires a set of electromagnetic units adapted to GR, e.g. keeping basic SI: [math]  c_0^2  = (\epsilon_c \mu_c)^{-1} [/math] with  [math]  \epsilon_c = (2.998E+8)^{-1} [J/m], \mu_c = (2.998E+8)^{-1} [s^2/Jm][/math],  
[math] e_c = 3.110E-18 [J][/math]  and [math] e_c/(4π\epsilon_c) = 7.419E-11 [m]  [/math]
I’ll mainly discuss dimensionless & relative values.

I will work with the following basic conditions:
- electrostatic approximation: among the EM potentials entering Kaluza’s metric only the electric potential, [math] e_c /(4π\epsilon_cr) = \rho_0/r  [/math], will be considered
- flat 5D spacetime [math] G_{AB} = 0[/math],  which is identical to curved 4D and a [math] T_{AB} [/math]  consisting of x5-terms of the metric (Wesson)
- Spin 1/2 [math] \hbar [/math]  as boundary condition for particles.

The last point enters the model via providing an integration limit. This is just a remedy in place of a proper metric including Spin. Einstein-Cartan may be an ansatz, there are others. Anyway the (very) approximate ansatz for the metric I use will be sufficient for the following.

Kaluza’s ansatz gives a) EFE, b) Maxwell equations c) a wave-like equation connecting the scalar  [math] \Phi [/math] with the electromagnetic tensor.
I solve for  [math] \Phi [/math] and put it back in a 4D metric. The solution I use will be [math]  \Phi ≈ (\frac{\rho_0}{r})^2 exp(-((\rho_0/r)^3)) = (\frac{\rho_0}{r})^2 \phi_0(r) [/math]. (Euler-) Integrals over this will feature the incomplete [math] \Gamma  [/math]-functions. Of particular importance will be the limits of [math] \Gamma(+1/3) ≈ 2.679  [/math] appearing in the integral over a point charge, [math] \frac{ \phi(r)}{r^2}  [/math] and [math]  \Gamma(-1/3) ≈ 4.062 [/math] appearing in the integral for a (wave-) length,  [math] \phi(r)dr[/math].
A semi-classical approach for angular momentum will be used to recalculate an integration limit, [math]\sigma [/math]:
[math] J_z = r[/math] x [math]p =  rW/c_0 = \int{}\phi(r) \frac {e_c^2} {(4π\epsilon_c r)} dr ≡ 1/2 [\hbar]   [/math]    (*1)
this gives as limit (of the Euler integral) [math]\sigma_0 [/math] for spherical symmetry:
[math] \sigma_0  ≈ 8 (\frac{4 \pi \Gamma(-1/3)^3} {3})^3  [/math] = 1.77E+8[-]    (*2)
(*1 This relation will be the reason for the fine-structure constant,  [math] \alpha [/math], entering the equations.)
For a particle the equation for [math]\Phi [/math] given above will include 2 more coefficients.
- It can be shown that [math]\sigma_0 [/math] has to be included due to the existence of a limit implying the exponential to be an approximation for a solution of a quadratic equation and the properties of the Euler integral.
- A constant referring to a ground state, which turns out to be the lightest charged particle, the electron. This constant my be recalculated from the electron energy but it can be given as a function of [math] \alpha [/math] as well
[non-sph.sym.part] *[math]\alpha^9 =  [9/8\alpha]*\alpha^9 = \alpha_{Pl}[/math]
Its value is identical with the ratio of the electron and the Planck energy, denoted [math]\alpha_{Pl}[/math]. ([math]\frac {e_c^2}{(4\pi\epsilon_c)}  = \frac {G W_{Pl}^2}{c_0^4} [/math] as definition for Planck)
This gives:
[math] \Phi = (\rho_0/r)^2 exp(-(\sigma_0 \alpha_{Pl}(\rho_0/r)^3)) = (\rho_0/r)^2 \phi(r)  [/math] in
[math]  g_{µµ} = (\frac {\rho_0} {r})^2 \phi(r), - (\frac {\rho_0} {r} )^2 \phi(r),  −  r^2,   −  r^2 sin^2 \theta [/math].
You may see where you will get gravitation back from, the expansion of [math]\phi(r)[/math]. Due to its origin from a quadratic equation, r in the exponential is limited to particle radius [math]\lambda_c ≈ \rho_0[/math]. For [math] r > \rho_0[/math] the terms related to spin should vanish (i.e. [math]\sigma [/math] and the difference between [math]\lambda_c[/math]  and [math]\rho_0  [/math]) giving  [math]\Phi ≈ [/math]  electromagnetic term  * [math] (1- \alpha_{Pl}) [/math].
(The same reasoning will give correct values for ≈ critical, vacuum density originating from minor terms of the metric.)

Particle energies
Solving the EFE and integrating for energy, W, gives:
[math] W_n ≈ 8\pi \Gamma(+1/3)/3 \epsilon_c \rho_0^2 (\sigma_0 \alpha_{Pl} \alpha(n)(\rho_0/r)^3)^{(-1/3)}  [/math]  with [math] (\alpha(n)) [/math] being a particle specific coefficient.
Solutions for different particles will not be orthogonal, I guess they shouldn’t since in general mass is a continuous property. However, there will be a distinguished set of solutions if you relax the condition of orthogonality to “solution not being dependent on parameters of other particles (except ground state)”. Factor [math]  \alpha^9 [/math] for spherical symmetry in [math]  \phi [/math] will give (relative to the electron, We):
[math]  W_n /W_e  ≈  \frac {3} {2} \Pi_{k=1}^{n} \alpha[/math]^[math](-3/3^k) [/math]   n={1;2;...}
a convergent series (giving a range of [math]  \alpha^{-1.5} [/math]) from the electron to the Delta-baryon.
The ratio proton/electron will be: [math] 1.5 \alpha^{(-1-1/3-1/9)} = 1.5 \alpha^{-1.444} [/math] = 1831 = 0.997 [exp. value].
Symmetry is encoded in [math]\sigma [/math], for an approximation of the next spherical harmonic, y1, there will be an additional factor 3^1/3, giving a second series from the pion to the tauon.  At this point the model is to primitive to give more solutions, with one important exception:
The Euler formalism defines a minimum for [math] \sigma: \sigma_{min} = (2\Gamma(-1/3) /3)^3  [/math]. Inserting the ratio [math] ((\sigma_{0} / \sigma_{min})^{(1/3)} = 4\pi\Gamma(-1/3)^2) ≈ 1.5 \alpha^{-1}[/math] in [math]W_n /W_e [/math] will give as maximum value for energy [math] 1.5^2 \alpha^{-2.5} W_e[/math]) ≈ 254.5 GeV = 1.04 [exp. Value (Higgs VEV)]).
(While (*2) for spherical symmetry can be given as a term describing the volume of a sphere, the limit case for Higgs corresponds to a 1D element. This will be important in a more detailed modeling of the fermions in a following post.)

Coupling constants
Equating the energy of a point charge with the energy of a photon will give
[math] \int{}\phi(r) \frac {e_c^2}{(4π \epsilon_c r^2 )} dr = hc_0/(\int{}\phi(r) dr) [/math]
which can be solved for the fine-structure constant [math]  \alpha^{-1} = 4π\Gamma(+1/3)\Gamma(-1/3)  [/math]  = 0.998 [exp. Value].
Doing the equivalent in 4D-space allows to give both weak coupling constant and [math] \alpha[/math]  in 1 equation
[math] \alpha_N^{-1}≈ \frac {S_N\Gamma(+N-2/N)\Gamma(-N-2/N) } {(N-2)^2} [/math]   (SN = N-D-surface area, N={3;4})
This gives a Weinberg angle [math] sin^2\Theta_W [/math]= 0.227.
tbc

1. The Axiom of Time:
Time is not a dimension, but a Processing Rate (Φ).
Formula:
dt=1/Φ

In this view, 'time dilation' is a local reduction in the vacuum's update frequency due to high informational density (mass-energy).

2. The Invariance of c:
The speed of light is the Maximum Processing Speed of the medium. An observer measures c as constant because the observer's own 'perception cycles' (biological or mechanical) are throttled by the same local Φ.
Logic Check: Does this 'internal observer' logic hold up against the Lorentz transformations?

3. Mass-Energy Conservation (The Engineering Link):
In a closed computational system, 'double-counting' (redundancy) is impossible. Mass-energy conservation is the conservation of System Bandwidth.

Conclusion & Request:
If this model contradicts the FLRW metric or the Equivalence Principle in a way that cannot be reconciled, I am prepared to discard it. If not, how can we mathematically define the 'update frequency' of the vacuum to match observed gravitational redshift?"

What do you think about that?

— On the one hand, it derives the classical Newton–Maxwell–Einstein (GR) equations from a single "noisy" Hamiltonian on a discrete quantum graph, so it is essentially a candidate for a theory of quantum gravity.

— On the other hand, it also incorporates the symmetries of the Standard Model (U(1)×SU(2)×SU(3)), the spontaneous breaking of these symmetries, and even predictions about the "shor anomaly" and microwave resonances in cryogenic qubits.

Thus, this is not just "yet another" model of gravity, but a genuine attempt at a unified description of:

• quantum dynamics (via the σ-Hamiltonian),

• SM symmetries (via graph automorphisms),

• gravity (via discrete curvature and its continuous limit).

In this sense, the author claims a "theory of everything" on a discrete graph. But the key distinguishing feature is that it is constructed to yield specific laboratory predictions already at energies ≲10⁻⁴ eV and can therefore be quickly refuted or confirmed in cryogenic qubits and microwave experiments.

The theory itself is described in detail here: A Testable Quantum Graph Theory of Spacetime: Predictions for Cryogenic Qubits and Colliders

https://gizmodo.com/no-earth-wont-lose-gravity-for-7-seconds-on-august-12-nasa-says-2000711970?fbclid=IwdGRjcAPcpGNleHRuA2FlbQIxMQBzcnRjBmFwcF9pZAo2NjI4NTY4Mzc5AAEehrTBUqGLZGFofgeantDjZutdIdMMTgKc9DcSJiTWwr-FCBs1DLQvLpEOmE0_aem_HrwYsNQzUCA1gDyknQ6IGg

The claim:

“In November 2024, a secret NASA document titled “Project Anchor” leaked online. The project’s budget is $89 billion, and its goal is to survive a 7-second gravitational anomaly expected on August 12, 2026, at 14:33 UTC [10:33 a.m. ET].”

“The text went on to claim that the anomaly would result from the intersection of two gravitational waves from black holes, predicted by NASA in 2019 with a probability of 94.7%. It also claimed the agency is “building underground bunkers” to provide refuge for government leaders, scientists, military personnel, and “selected citizens with genetic diversity” during the event.”

“When Snopes contacted NASA about the rumor, a spokesperson said exactly what we’re all thinking: That’s not how gravity works.”

Prior to symmetry  Break Relevant equations

 The FLRW metric of the LCDM universe is used by the LCDM model of the Big bang to describe the evolution history of our Observable universe. The model starts at 10^{-43} seconds forward from a low entropy, hot dense state. One plausible explanation of how our universe began prior to that include quantum fluctuations.  The model only describes our Observable portion as we do not know what occurs beyond the Cosmological event horizon. The FLRW metric is given as follows

\[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\]

\[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\]

where k is the curvature term, a is the scale factor both being dimensionless quantities. The contributions of each particle species via their corresponding equations of state is determines how our universe expands. The evolution history can be determines as a function of Cosmological redshift via the following equation

\[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\]

where the standard model may be represented by the covariant derivative form of the Langrangian 

\[\mathcal{L}=\underbrace{\mathbb{R}}_{GR}-\overbrace{\underbrace{\frac{1}{4}F_{\mu\nu}F^{\mu\nu}}_{Yang-Mills}}^{Maxwell}+\underbrace{i\overline{\psi}\gamma^\mu D_\mu \psi}_{Dirac}+\underbrace{|D_\mu h|^2-V(|h|)}_{Higgs}+\underbrace{h\overline{\psi}\psi}_{Yukawa}\]

\[V_{ckm}=V^\dagger_{\mu L} V_{dL}\]

The gauge group of electroweak interactions is 

\[SU(2)_L\otimes U(1)_Y\] where left handed quarks are in doublets of \[ SU(2)_L\] while right handed quarks are in singlets

the electroweak interaction is given by the Langrangian

\[\mathcal{L}=-\frac{1}{4}W^a_{\mu\nu}W^{\mu\nu}_a-\frac{1}{4}B_{\mu\nu}B^{\mu\nu}+\overline{\Psi}i\gamma_\mu D^\mu \Psi\]

where \[W^{1,2,3},B_\mu\] are the four spin 1 boson fields associated to the generators of the gauge transformation \[\Psi\]

The 3 generators of the \[SU(2)_L\] transformation are the three isospin operator components \[t^a=\frac{1}{2} \tau^a \] with \[\tau^a \] being the Pauli matrix and the generator of \[U(1)_\gamma\] being the weak hypercharge operator. The weak isospin "I" and hyper charge \[\gamma\] are related to the electric charge Q and given as

\[Q+I^3+\frac{\gamma}{2}\]

with quarks and lepton fields organized in left-handed doublets and right-handed singlets: 

the covariant derivative is given as

\[D^\mu=\partial_\mu+igW_\mu\frac{\tau}{2}-\frac{i\acute{g}}{2}B_\mu\]

\[\begin{pmatrix}V_\ell\\\ell\end{pmatrix}_L,\ell_R,\begin{pmatrix}u\\d\end{pmatrix}_,u_R,d_R\]

The mass eugenstates given by the Weinberg angles are

\[W\pm_\mu=\sqrt{\frac{1}{2}}(W^1_\mu\mp i W_\mu^2)\]

with the photon and Z boson given as

\[A_\mu=B\mu cos\theta_W+W^3_\mu sin\theta_W\]

\[Z_\mu=B\mu sin\theta_W+W^3_\mu cos\theta_W\]

the mass mixings are given by the CKM matrix below

\[\begin{pmatrix}\acute{d}\\\acute{s}\\\acute{b}\end{pmatrix}\begin{pmatrix}V_{ud}&V_{us}&V_{ub}\\V_{cd}&V_{cs}&V_{cb}\\V_{td}&V_{ts}&V_{tb}\end{pmatrix}\begin{pmatrix}d\\s\\b\end{pmatrix}\]

Bose Einstein Statistics

\[n_i = \frac {g_i} {e^{(\varepsilon_i-\mu)/kT} - 1}\]

Fermi-Dirac statistics

\[ n_i = \frac{g_i}{e^{(\epsilon_i-\mu) / k T} + 1}\]

Maxwell Boltzmann

\[\frac{N_i}{N} = \frac {g_i} {e^{(\epsilon_i-\mu)/kT}} = \frac{g_i e^{-\epsilon_i/kT}}{Z}\]

Saha Boltzmann equation (calculate hydrogen decoupling

\[\frac{n_i+n_e}{n_i}=\frac{2}{\omega^3}\frac{g_i+1}{g_i}exp[-\frac{(\epsilon_i+1-\epsilon_i)}{k_BT}\]

I’m wondering in 20 years from now what will medicine be like?

I read some thing about gene editing?

Using a and b positions on a length as base with density condensation power as exponentiation along with division to determine number of times a length can be proportionally divided into smaller parts toward position a (i.e. 0) from position b. This kind of creates a case of uniform density condensation.

I connected this formula to gravity because of the way gravity of this Earth gravitates things toward it - meaning mass and energy surely could be dense deep into the core or something like that if so. The formula visualizes that in a simple way, 1-dimension only.

Formula

1. L / 2^x = PL

2. PL * 2^x = L (to double-check #1, I called it density inflation)

Formula Definition

L = length

/ = division

* = multiplication

2^x = a and b position on length (beginning and ending) as objects (i.e. 2) with density condensation power as exponentiation.

PL = Part of length

Equation Examples

I have attached a picture I developed to this post, illustrating what I'm talking about.

Question

How to make formula more useful in understanding areas of gravity if it is applicable, that is?

I’m not claiming new energy is created, only that mechanical advantage can be harnessed in a novel way. Could principles like this have been used in ancient construction methods at sites such as Cusco, Baalbek, or Puma Punku? I’d like to open this up for discussion — do these mechanics resonate with known physics, or might they point toward overlooked applications?

Note to moderator: Please move this thread to the most appropriate section if needed.

Demonstration video: Unlimited Power: A Breakthrough That Explains Ancient Secrets Ep.1

Another example is a wheel. When you rotate the axil the outside of the wheel moves instantly. It does not wait for an speed of light information signal, it moves instantly.

So consider when you move the outside of a wheel from one end, the other side of the wheel moves at the same time. Not later, but at the same time. You are pulling one side of the wheel toward you and the other side away and the opposite end of the wheel moves exactly at the same time as the section you have just moved.

Now imagine a carousel 100 ft in diameter. you move it from one end and you are moving the other end without delay. It is actually moving simultaneously as you move your end. An observer at the other end is separated from you by a femtosecond or whatever but the action is so, .

So take the outside of a wheel and turn it into a loop and stretch the loop out into a giant ellipse. and put a CCD target attached to the far end of the loop and fire a laser at the target at the same instant you fire a solenoid that shifts the loop on your end.

Will you hit the target? Or will it have already shifted by the time the light signal reached it?

Regards, TAR

Sort of like that row of steel balls hanging from a beam. You swing a ball into one end of the row and the last ball in the chain pops out.

Axel

I thought mRNA vaccines tell your cells to make protein and these protein make large molecules and they fight the virus the virus spike that locks onto the virus spike molecules.

Is this what people are afraid of? Because the mRNA vaccines tell your cells to make protein that these molecules bind to the virus spike? And that the conspiracy saying it not natural and not safe and your cells to make is making this protein?

So you could build a manifold at each level that seamlessly fits with the next level up.

I propose starting with 38 Planck diameter spheres packed around a center void, first an octahedral 6 at the core surrounded by 32 as shown forming around the central 6 making a Truncated Octagon envelope and use the TO to build space at the Atomic level. The Truncated Octagon shells build out into the shape of a Rhombic Dodecahedron and my suggestion is when the shells of Truncated Octagons reach the size of a Carbon Atom, we flatten out the faces of the emergent Rhombic Dodecahedron and build out shells of the RD which are shaped like a Cuboctahedron Envelope to any size Cuboctahedron we need up to the size of the observable universe. I don't see why we would need anymore space than that.

The beauty of using TARSpace is the elements progress as actual reality may have been built. Allowing perhaps new insights into quantum physics and sub atomic interactions. And the switch over to the Rhombic Dodecahedron allows studies into crystal growth and maybe even abiogenesis. AND having a direct Volume/Geometric link between the tiny and the huge, may provide pathways to mathematically tie General and Special Relativity together into a TOE.

Volume Math has some good characteristics. Discrete volumes with an integer radius that fill space with no calculus or spherical approximations required, yet the Rhombic Dodecahedrons pack EXACTLY as inscribed spheres would WITHOUT the voids.

. Copyright Thomas A. Roth January 10th 2026 10:36 AM Eastern

notice the 13 axes shown by the toothpicks in the white Rhombic Dodecahedron are the exact same 13 axes shown with the green Truncated Octagon with the pearls embedded on the edges of the marked Rhombic Dodecahedron on the surface of the Truncated Octagon. The pearls form 4 8 pearl rings, exactly describing an electron shell Notice the red tipped toothpicks show the 6 axes of the Rhombic Dodecahedron going through the center of the faces and the unmarked toothpicks show the 7 axes of the Truncated Octagon going through the 8 hex faces and 6 square faces. For alignment with the Cartesian Space the Cuboctahedron shell of clay balls with black red and green hexagonal planes shown has toothpicks aligned with the xyz axes of Cartesian Space.

Interestingly the two figures occupy the same space each completely. The RD showing the balls. The TO showing the voids.

Note the key polyhedron in this scheme are the Octagon, the Truncated Octagon, the Rhombic Dodecahedra and the Cuboctahedron. Only Truncated Octagon the Rhombic Dodecahedra and the related Cube tesselate space. And you can only build the shells tn one direction. Spheres>Truncated Octagon Shells to Rhombic Dodecahedral shells to Cuboctahedral shell or spheres to Cuboctahedral shells. Rhombic Dodecahedron can be substituted for Spheres at any level.

Regards TAR

PS I have great hopes for this scheme but need some human feedback to know if I have something solid here.

warning the Dodecahedron with the pentagonal faces looks like it would tesselate space but it does not, it leaves spaces. Must use the Rhombic Dodecahedron with the diamond shaped faces for this scheme.

In the same manner we can define a physical, conformal age of the universe. That's the duration of a certain number of the extending CMB radiation periods proportional to the extending peak wavelength of this radiation that passed through a point at which the CMB is isotropic, since its emission. Proportionality factor is the speed of light, because c=λ/T where λ is the extending peak wavelength, and T is the extending wave period.

Conformal time η=∫dη=∫dt/a(t)=47Gy is the conformal age of the universe and I don't question it. I'm proposing a physical definition for it. The inverse of the scale factor 1/a(t) is increasing with time counted backwards, because 0<a(t)≤1 and a(t₀)=1, where t₀ is the present, proper age of the universe. That makes dt/a(t) the equivalent of the wave period extending over time counted backwards. We're integrating over it to sum it up.

Is there something wrong with the proposed, physical definition?