The answer would require use of three fields each describing a specified order of relations

Linear acceleration and stress

math]f(r) = 4\pi r^2[/math] can be plotted on a 2D graph does not make the expression itself "graphical coordinates

Thats a 2 dimensional graph using the double cover of the SO(3) group under SU(2)

1 hour ago, Mordred said:

The answer would require use of three fields each describing a specified order of relations

Linear acceleration and stress

math]f(r) = 4\pi r^2[/math] can be plotted on a 2D graph does not make the expression itself "graphical coordinates

Thats a 2 dimensional graph using the double cover of the SO(3) group under SU(2)

Why are you here? You not reading my answers you ignoring my derivations after 20+ comments posted you cant even answer the basic question about model under critic. So why are you here? Are you that desperate for self validation that you hanging out in speculations subforum in order to school armatures? And here you got the armature that publicly schooling you... Must be hard for your fragile ego to accept it... I feel sad for you man...

From now on I will ignore all your messages. I wish you to find reasons to love and respect yourself.

9 hours ago, Anton Rize said:

It is the physical manifestation of the star hitting the energetic floor (the Fundamental Tone) supported by the global resonance of the Universe

How? and why?

1 hour ago, Anton Rize said:

Why are you here? You not reading my answers you ignoring my derivations after 20+ comments posted you cant even answer the basic question about model under critic. So why are you here? Are you that desperate for self validation that you hanging out in speculations subforum in order to school armatures? And here you got the armature that publicly schooling you... Must be hard for your fragile ego to accept it... I feel sad for you man...

From now on I will ignore all your messages. I wish you to find reasons to love and respect yourself.

Its too bad you do not understand linearization.

However your right I'm done trying to help you improve the quality of your articles. I can quarantee without linearization applied to specific sets such as S^2 vs S^1 vs SO ( 3.1) aka (spacetime) Lorentz or Poincare group relations none of your articles will ever gain any weight in any peer review publication standard.

Llinearizarion also involves specific equations such as your use of the Beta function.

However that's obviously too much for you.

Good luck

Obviously any adherence to math relations beyond simple scalar quantities is too much math for you.

For other readers 3P is the spatial sum of Pressures in all three spatial directions.

\[P_x, P_y, P_z\]

Edited February 27Feb 27 by Mordred

On 2/26/2026 at 1:21 AM, Anton Rize said:

In RG, this isn't a "coincidence" - it is derived. The density still has 3DOF:

ρ=Rsc28πGr3=κ2c28πGr2

ρmax=c28⋅π⋅G⋅r2

Who derived the above relation you or AI

https://www.google.com/search?q=%5Crho+%3D+%5Cfrac%7BR_s+c%5E2%7D%7B8%5Cpi+G+r%5E3%7D+%3D+%5Cfrac%7B%5Ckappa%5E%7B2%7Dc%5E%7B2%7D%7D%7B8%5Cpi+Gr%5E%7B2%7D%7D&rlz=1C1VDKB_enCA1142CA1142&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCDEzNjlqMGo3qAIIsAIB&sourceid=chrome&ie=UTF-8&udm=50&fbs=ADc_l-aN0CWEZBOHjofHoaMMDiKp9lEhFAN_4ain3HSNQWw-mMGVXS0bCMe2eDZOQ2MOTwnMa06_-qUutYsIv5lB1HqB7Pf6gcWqPaZz5tPxChciWAvSSkt6iwnm8RS5iDIeKXMcHR4MMz-Y7wrd2kVxuyN5L5Fi49WMc2CLg4H9YMVUU0sdAvw8c5baTg2adLWst0WJE16c5OvP6B3zpkfcIBdQb4Nxtg&ved=2ahUKEwit6pODlvuSAxUcMDQIHV7TJmkQ0NsOegQIAxAB&aep=10&ntc=1&mstk=AUtExfDA6k-pGEJLfvT-Whh9mpJ8Rv55s-ylm6OHEw-LdTIhitRcSlJP6q0VkARNCS10P7oiM5UFDIQCgw3pu7W5spbj2k80JtUZWU387TL06i_YVqZZoyHKohJizCDlMyWJW76LDOBR95gnlS3L8VhPEMCAtec-seV7vQVCLTko71y0TPrVW0OU4U7s6vopeyp_1j6LnHTvS9J6OuVZBL1-NkV05P5P0KDg5eAfLSoyY58uwWEAp_KG20Jb5-2YJXbjZc6Y5JTUmN1PQjBqwnrD_WpW66SDm5YK-eFff3v_1WdMsidKY-TWO3qUKfl4RYrtqNvRH6xQDFaofg&csuir=1&mtid=gVeiabTpJuzb0PEP_vGJgA4

\[H_{0}=\sqrt{8\pi G\frac{4\sigma_{SB}T_{CMB}^{4}}{3\alpha^{2}c^{3}}}\]

what about this equation which I noticed also in the Allen app.

https://www.google.com/search?q=H_%7B0%7D%3D%5Csqrt%7B8%5Cpi+G%5Cfrac%7B4%5Csigma_%7BSB%7DT_%7BCMB%7D%5E%7B4%7D%7D%7B3%5Calpha%5E%7B2%7Dc%5E%7B3%7D%7D%7D&rlz=1C1VDKB_enCA1142CA1142&oq=H_%7B0%7D%3D%5Csqrt%7B8%5Cpi+G%5Cfrac%7B4%5Csigma_%7BSB%7DT_%7BCMB%7D%5E%7B4%7D%7D%7B3%5Calpha%5E%7B2%7Dc%5E%7B3%7D%7D%7D&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCDQ4MTRqMGo5qAIAsAIB&sourceid=chrome&ie=UTF-8

3 hours ago, Mordred said:

Who derived the above relation you or AI

https://www.google.com/search?q=%5Crho+%3D+%5Cfrac%7BR_s+c%5E2%7D%7B8%5Cpi+G+r%5E3%7D+%3D+%5Cfrac%7B%5Ckappa%5E%7B2%7Dc%5E%7B2%7D%7D%7B8%5Cpi+Gr%5E%7B2%7D%7D&rlz=1C1VDKB_enCA1142CA1142&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCDEzNjlqMGo3qAIIsAIB&sourceid=chrome&ie=UTF-8&udm=50&fbs=ADc_l-aN0CWEZBOHjofHoaMMDiKp9lEhFAN_4ain3HSNQWw-mMGVXS0bCMe2eDZOQ2MOTwnMa06_-qUutYsIv5lB1HqB7Pf6gcWqPaZz5tPxChciWAvSSkt6iwnm8RS5iDIeKXMcHR4MMz-Y7wrd2kVxuyN5L5Fi49WMc2CLg4H9YMVUU0sdAvw8c5baTg2adLWst0WJE16c5OvP6B3zpkfcIBdQb4Nxtg&ved=2ahUKEwit6pODlvuSAxUcMDQIHV7TJmkQ0NsOegQIAxAB&aep=10&ntc=1&mstk=AUtExfDA6k-pGEJLfvT-Whh9mpJ8Rv55s-ylm6OHEw-LdTIhitRcSlJP6q0VkARNCS10P7oiM5UFDIQCgw3pu7W5spbj2k80JtUZWU387TL06i_YVqZZoyHKohJizCDlMyWJW76LDOBR95gnlS3L8VhPEMCAtec-seV7vQVCLTko71y0TPrVW0OU4U7s6vopeyp_1j6LnHTvS9J6OuVZBL1-NkV05P5P0KDg5eAfLSoyY58uwWEAp_KG20Jb5-2YJXbjZc6Y5JTUmN1PQjBqwnrD_WpW66SDm5YK-eFff3v_1WdMsidKY-TWO3qUKfl4RYrtqNvRH6xQDFaofg&csuir=1&mtid=gVeiabTpJuzb0PEP_vGJgA4

3 hours ago, Mordred said:

Who derived the above relation you or AI

https://www.google.com/search?q=%5Crho+%3D+%5Cfrac%7BR_s+c%5E2%7D%7B8%5Cpi+G+r%5E3%7D+%3D+%5Cfrac%7B%5Ckappa%5E%7B2%7Dc%5E%7B2%7D%7D%7B8%5Cpi+Gr%5E%7B2%7D%7D&rlz=1C1VDKB_enCA1142CA1142&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCDEzNjlqMGo3qAIIsAIB&sourceid=chrome&ie=UTF-8&udm=50&fbs=ADc_l-aN0CWEZBOHjofHoaMMDiKp9lEhFAN_4ain3HSNQWw-mMGVXS0bCMe2eDZOQ2MOTwnMa06_-qUutYsIv5lB1HqB7Pf6gcWqPaZz5tPxChciWAvSSkt6iwnm8RS5iDIeKXMcHR4MMz-Y7wrd2kVxuyN5L5Fi49WMc2CLg4H9YMVUU0sdAvw8c5baTg2adLWst0WJE16c5OvP6B3zpkfcIBdQb4Nxtg&ved=2ahUKEwit6pODlvuSAxUcMDQIHV7TJmkQ0NsOegQIAxAB&aep=10&ntc=1&mstk=AUtExfDA6k-pGEJLfvT-Whh9mpJ8Rv55s-ylm6OHEw-LdTIhitRcSlJP6q0VkARNCS10P7oiM5UFDIQCgw3pu7W5spbj2k80JtUZWU387TL06i_YVqZZoyHKohJizCDlMyWJW76LDOBR95gnlS3L8VhPEMCAtec-seV7vQVCLTko71y0TPrVW0OU4U7s6vopeyp_1j6LnHTvS9J6OuVZBL1-NkV05P5P0KDg5eAfLSoyY58uwWEAp_KG20Jb5-2YJXbjZc6Y5JTUmN1PQjBqwnrD_WpW66SDm5YK-eFff3v_1WdMsidKY-TWO3qUKfl4RYrtqNvRH6xQDFaofg&csuir=1&mtid=gVeiabTpJuzb0PEP_vGJgA4

H0=8πG4σSBT4CMB3α2c3−−−−−−−−−−−−−√

what about this equation which I noticed also in the Allen app.

https://www.google.com/search?q=H_%7B0%7D%3D%5Csqrt%7B8%5Cpi+G%5Cfrac%7B4%5Csigma_%7BSB%7DT_%7BCMB%7D%5E%7B4%7D%7D%7B3%5Calpha%5E%7B2%7Dc%5E%7B3%7D%7D%7D&rlz=1C1VDKB_enCA1142CA1142&oq=H_%7B0%7D%3D%5Csqrt%7B8%5Cpi+G%5Cfrac%7B4%5Csigma_%7BSB%7DT_%7BCMB%7D%5E%7B4%7D%7D%7B3%5Calpha%5E%7B2%7Dc%5E%7B3%7D%7D%7D&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCDQ4MTRqMGo5qAIAsAIB&sourceid=chrome&ie=UTF-8

I wish he could arrange what he saying in that manner...AI is just challenging our ways in a substantial way....I could just perceive prior knowledge from his explanations.

55 minutes ago, MJ kihara said:

I wish he could arrange what he saying in that manner...AI is just challenging our ways in a substantial way....I could just perceive prior knowledge from his explanations.

If it was I would have had zero issues following it. Lol brings to mind a rule I tend to follow. Look at the math applied and adherence to math rigor and ignore verbal explanations except to identify the labels.

Lol though I do that with professional peer review articles as well

Edited February 28Feb 28 by Mordred

On 2/28/2026 at 1:40 AM, MJ kihara said:

How? and why?

Both hard questions and in order to unswear them properly you will need to read:
https://willrg.com/documents/WILL_RG_I.pdf
https://willrg.com/documents/WILL_RG_II.pdf
and at least the firs half of https://willrg.com/documents/WILL_RG_III.pdf
In total its about 150+ pages and I can imagine what a gatekeeper it might be.

So I made you a nice and easy interactive chart: https://willrg.com/LOGOS2 the logical and philosophical core is on the chart it self, and if one wants to see the math - every logical step is clickable and will direct you to the precise section.
A more detailed version of the LOGOS chart you can find here https://willrg.com/LOGOS_MAP/ but this one is still in development. For now it covering only https://willrg.com/documents/WILL_RG_I.pdf
Please let me know how the LOGOS2 chart communicates the idea.

6 hours ago, Anton Rize said:

Both hard questions and in order to unswear them properly you will need to read:
https://willrg.com/documents/WILL_RG_I.pdf
https://willrg.com/documents/WILL_RG_II.pdf
and at least the firs half of https://willrg.com/documents/WILL_RG_III.pdf
In total its about 150+ pages and I can imagine what a gatekeeper it might be.

So I made you a nice and easy interactive chart: https://willrg.com/LOGOS2 the logical and philosophical core is on the chart it self, and if one wants to see the math - every logical step is clickable and will direct you to the precise section.
A more detailed version of the LOGOS chart you can find here https://willrg.com/LOGOS_MAP/ but this one is still in development. For now it covering only https://willrg.com/documents/WILL_RG_I.pdf
Please let me know how the LOGOS2 chart communicates the idea.

You are complicating things...the question is how ? and why ?...why can't you briefly explain...you are even going against your own thread "simplifying SR and GR"...going with your own philosophy of using minimals it should not be hard for you to answer that question.

27 minutes ago, MJ kihara said:

You are complicating things...the question is how ? and why ?...why can't you briefly explain...you are even going against your own thread "simplifying SR and GR"...going with your own philosophy of using minimals it should not be hard for you to answer that question.

That raises a fundamental question " what is a minimal system"

-Define a start point to every location ( how the original distribution is located point by point)

- describe how any changes occur in the starting distribution with minimal conversions and calculations to any given frame of reference.

-identifying the cause and how much the cause of change results in the final distribution from the starting distribution.

Good luck on those criteria without a geometry as that's really what a geometry is used to describe ( distribution)

Edited March 1Mar 1 by Mordred

53 minutes ago, Mordred said:

Good luck on those criteria without a geometry as that's really what a geometry is used to describe ( distribution)

Am having a sense that even himself is not aware of what is going on, on his most basic arguments.

I'll let you judge that for yourself.

Quite frankly in my viewpoint step one of a minimal geometry is the fewest number of variables to uniquely identify each start position.

initial distribution, same applies to the final distribution is the simplest portions. This obviously includes to tool to choose a reference frame.

Describing causation between initial and final distribution is where the real fun is.

Edited March 1Mar 1 by Mordred

When I was developing a theory from the very most basic assumption and incorporating very few mainstream ideas, such as a Feynman diagram...I was surprised to see how things started fitting together ... Terminology like a Lagrangian, Hamiltonian were exotic and alien to me ... however after learning about them i realized i was doing the same thing....however I also realized I was doing a lot of new things in physics...things that have fundamental consequences like the way people view electromagnetic spectrum to me it's no longer the same,to cut the story short...a new arguments should generate mainstream science and if it deviate it should be clear how and why.

My problem is that something that is not intuitive my brain just block it,therefore,I struggle a lot to learn and internalize ideas,to me unless a formula is intuitive my brain has a problem grasping it ..a good example is the photon propagator in another thread I had to take a whole almost two weeks to see how it makes intuition to me.

I seem to recall that a fair while back it not uncommon, took me years to finally try learning string theory for much the same reasons. QFT for me makes far more sense. We all have our preferred mathematics some prefer differentials others prefer integrals etc.

On 2/21/2026 at 8:32 AM, Anton Rize said:

  On 2/20/2026 at 10:21 PM, KJW said:

That is, the observed Doppler effect can be used to establish that the travelling twin returns younger than the stay-at-home twin.

You are overcomplicating my friend. If we strip the problem of any specific details and other additional anthropocentric components we will see the foundation of this phenomena.

let's test the hypothesis that the age difference is manifested by the asymmetric observation of Doppler shifts (the optical delay of the turnaround) by removing the delay entirely.

Consider a modified scenario: Observer A remains at rest. Observer B does not travel to a distant star, but instead orbits Observer A at a negligible, constant distance with a kinematic projection of [math]\beta = 0.8[/math].

No. The explanation I provided was specifically for the twin paradox scenario. If you want to modify the scenario, then the analysis of the scenario has to be modified as well. You can't say my explanation of the twin paradox scenario is incorrect or even overcomplicated because (although it is a thought experiment) my explanation is purely in terms of what is observed. What is observed by each twin is the redshift and blueshift of the other twin's clock, and the amount of time the redshift and blueshift are observed.

As for your modified scenario, I'd like to first point out that you said nothing about how the observer in circular motion observes the observer in the centre. Your discussion of the scenario suggests that you are only concerned with the time dilation of the circularly moving observer that is observed by the central observer, without addressing the question of consistency between the perspectives of the two observers. And it is the question of consistency between the perspectives of the two observers that lies at the heart of the twin paradox, as well as precisely why the twins end up with different ages.

Unfortunately, so far, I have been unable to provide an explanation of your modified scenario in terms I used for the twin paradox scenario. I'm not sure such an explanation even exists. However, I can say that the central observer observes the observer in circular motion as transverse Doppler redshifted, and that the observer in circular motion observes the central observer as accelerationally blueshifted. In the case of the twin paradox scenario, both legs of the travelling twin's journey were inertial, and although the turnaround is an acceleration, it wasn't treated as such and was merely a time and location where the redshift becomes a blueshift. Thus, the explanation I gave for the twin paradox scenario was the natural explanation. I believe (I have a possibly false recollection of doing the maths) that my explanation of the twin paradox scenario can be extended to arbitrary longitudinal motion of the travelling twin. Although such a case has the travelling twin in an accelerated frame of reference, ultimately all redshifts and blueshifts based on time dilation are Doppler effects. Thus, your modified scenario ought to be able to be treated like the generalised twin paradox scenario, although I am presently unable to connect the accelerated frame of reference associated with circular motion to the Doppler effect. That is, I am presently unable to explain the blueshift of the central observer that is observed by the circularly moving observer in terms of the Doppler effect. Nevertheless, the blueshift can be explained by invoking the metric.

A problem I see with your explanation is that it seems to be unconnected to the actual physics of the situation. And by being unconnected to the actual physics, it is difficult to see how it can deal with subtleties present in the actual physics. For example, suppose I am in circular motion at constant speed around some object at the centre. I face the direction of my inward acceleration. Am I looking at the object at the centre?

3 hours ago, MJ kihara said:

You are complicating things...the question is how ? and why ?...why can't you briefly explain...you are even going against your own thread "simplifying SR and GR"...going with your own philosophy of using minimals it should not be hard for you to answer that question.

You make a fair point. I accept the critique. "Simplifying" means extracting the core mechanism, and I owe you a direct conceptual answer without making you dig through the full mathematical derivation.

Here is the "Why" and "How" of the energetic floor, translated from algebra into physical concepts:

The "Why" (The Ccause):

Standard physics treats spacetime as an empty container (a void) where objects move and interact. Remove objects - the container will stay. So it postulate its ontological independency like its real thing. There's no empirical data that force this postulate. Here's what Einstein had to say about it:

---

``There is no such thing as an empty space, i.e., a space without field. . . . Space-time does not claim existence on its own, but only as a structural quality of the field.''

Albert Einstein, \textbf{Relativity: The Special and the General Theory} (Appendix V: ``Relativity and the Problem of Space''), 1952 edition, Methuen (London), p.~155; based on earlier 1920 additions.

---

I complete agree with this quote. But standard physics does not. It speculate this extra primitive:

So when standard approach has 2 primitives:
1. SPACETIME
2. ENERGY

I have only one:
1. SPACE-TIME-ENERGY and just for convenience of shorter name and a sudle ironic joke I calling it:
WILL ≡ SPACE-TIME-ENERGY ⟹ [math]SPACETIME \equiv ENERGY[/math].

The Universe is not a box; it is a closed relational structure. No background. So there's no such thing as just distance. Distance or period can form only between objects/events. Distance is the tension between potential states.
Because the topology is strictly closed, any energy perturbation (like a star orbiting a galaxy) cannot just dissipate its influence into an infinite emptiness. It must interact with the boundaries of the system itself (the global horizon).

The "How" (The Mechanism):

You are the center of your observable Universe with Hubble horizon (R_H) as a boundary of causality. Energy is change. The rate of change is universal and finite.
Faster change in space ⟹ slower change in time. The value of "change rate" associated with c - stays conserved. Interactions are not instantaneous, causality propagate just like a wave one thing influence another thing energy transforms but stay conserved. So if we have non instant propagation of cause and effect (c) and we have a boundary as Hubble horizon (R_H). This leads to waves of cause and effect propagation to interfere with themselves. Think like a guitar string or even better think like a drum skin (math says drum). Waves can interact in a good way or bad way. All bad ways just dissolves. So constructive interference only can make a stable propagation. And like with any harmonics the lowest posible would be the fundamental Tone. It means 1 oscillation of this tone will have a wavelength of your observable Universe. And we can calculate it: Its just speed of light divided by the circumference of Hubble horizon expressed as a frequency
[math]\frac{c}{2\pi R_{H}}=\frac{H_{0}}{2\pi}=3.5148579278\times10^{-19} 1/s[/math]
for the reference its 1 full oscillation in around 90.1565273986 billions years. So we currently still in the yearly days of fundamental Tone cycle.

OK, now Imagine a star orbiting the center of a galaxy. In the standard model, the only thing keeping it moving is its local kinetic energy fighting local gravity. When it gets far away, gravity drops, so the math says the star should slow down. When it doesn't, they invent "Dark Matter" to pull it.

In RG, the vacuum itself has a structural tension ([math]\rho_{\Lambda}[/math]) between you and R_H. It required to keep the Universe's geometry open against collapse. The star is not moving through an empty void; it is vibrating on a globally tensioned geometric "carrier" (think of a stretched drum skin).

The local orbital frequency of the star and the global frequency of the horizon (the Fundamental Tone) superimpose. This creates a constructive geometric interference.

This interference adds a constant energetic baseline to the star's kinetic state. As the star gets further from the galactic center, its local gravity drops, but it hits that baseline geometric tension. It cannot slow down past this limit, because slowing down would require it to decouple from the global horizon fundamental Tone, which is topologically impossible. That absolute limit is what we observe as the "flat rotation curve." And to test this hypothesis I used equation from wave mechanics where 2 values are multiplied under the square root to model geometric interference:

[math] v_{obs}^2 = \underbrace{v_{N}^2}_{\text{Local Self-Energy}} + \underbrace{\sqrt{v_{N}^2 \cdot (\Omega a_{Mach} r)}}_{\text{Reson. Interference}} [/math]

That absolute limit is what we observe as the "flat rotation curve." To make the mechanics of this geometric interference perfectly clear and dimensionally strict, we can express this exact relation through dimensionless velocity (β = v/c). The interference occurs strictly between the local causal limit (the Schwarzschild radius of the central mass, R_s) and the global causal limit (the Hubble horizon, R_H):

[math]\beta_{Q}=\sqrt{\beta^{2}+\sqrt{\beta^{2}\frac{R_{s}}{3\pi R_{H}}}}[/math]

Here, the term under the inner square root is the direct cross-correlation (interference) between the local kinematic state (β²) and the global structural tension. This tension is expressed as the pure geometric ratio of the two causal horizons: R_s / (3πR_H). It is this exact fundamental resonance that provides the constant energetic baseline and prevents the orbital velocity from dropping.

And when I tested against 10000 + datapoints from 3 different datasets I got precise agreement.

Regarding what constitutes a "minimal system": a true generative geometry does not require an absolute coordinate grid or a "start point to every location." It only requires relative energy differentials. Spacetime is generated by these relations; it does not pre-exist them.

Does this conceptual summary answer your "how and why" more clearly?

On 2/28/2026 at 4:02 PM, MJ kihara said:

I wish he could arrange what he saying in that manner...

And this is exactly why I developed WILL-AI. Its free its open and it trained on all 3 main papers of mine. Don't expect him to preform any complex calculations (he cant use any tools) But he can unswear any questions about the model and provide citations. When I was testing him by comparing mine and his answers to the same questions - it was hard to decide do I prefer mine or he's answers. So yeh have fun: https://willrg.com/WILL-AI/
Feedback on he's performance is required so please do share the feedback at some point

3 hours ago, MJ kihara said:

Am having a sense that even himself is not aware of what is going on, on his most basic arguments.

That is not the sense Id like to propagate.

I can't promise anything about your sense (as its in majority your internal processing), but I can guaranty that direct and sound questions will provide you with direct and sound answers. The hard part is to transform the sense in to direct and sound question.
Actually I think https://willrg.com/WILL-AI/
could help you with this. He can process half-baked questions.

Edited March 1Mar 1 by Anton Rize

Asking questions on public forum about new model with new ontology its like changing pants in the middle of the crowded street.
We never in our history had a chance to ask as many and as dumb questions as we want without being judged or annoying. That's why I think AI will do wanders in education. We living at exiting times.

1 hour ago, Anton Rize said:

You make a fair point. I accept the critique. "Simplifying" means extracting the core mechanism, and I owe you a direct conceptual answer without making you dig through the full mathematical derivation.

Here is the "Why" and "How" of the energetic floor, translated from algebra into physical concepts:

The "Why" (The Ccause):

Standard physics treats spacetime as an empty container (a void) where objects move and interact. Remove objects - the container will stay. So it postulate its ontological independency like its real thing. There's no empirical data that force this postulate. Here's what Einstein had to say about it:

---

``There is no such thing as an empty space, i.e., a space without field. . . . Space-time does not claim existence on its own, but only as a structural quality of the field.''

Albert Einstein, \textbf{Relativity: The Special and the General Theory} (Appendix V: ``Relativity and the Problem of Space''), 1952 edition, Methuen (London), p.~155; based on earlier 1920 additions.

---

I complete agree with this quote. But standard physics does not. It speculate this extra primitive:

So when standard approach has 2 primitives:
1. SPACETIME
2. ENERGY

I have only one:
1. SPACE-TIME-ENERGY and just for convenience of shorter name and a sudle ironic joke I calling it:
WILL ≡ SPACE-TIME-ENERGY ⟹ SPACETIME≡ENERGY.

The Universe is not a box; it is a closed relational structure. No background. So there's no such thing as just distance. Distance or period can form only between objects/events. Distance is the tension between potential states.
Because the topology is strictly closed, any energy perturbation (like a star orbiting a galaxy) cannot just dissipate its influence into an infinite emptiness. It must interact with the boundaries of the system itself (the global horizon).

The "How" (The Mechanism):

You are the center of your observable Universe with Hubble horizon (R_H) as a boundary of causality. Energy is change. The rate of change is universal and finite.
Faster change in space ⟹ slower change in time. The value of "change rate" associated with c - stays conserved. Interactions are not instantaneous, causality propagate just like a wave one thing influence another thing energy transforms but stay conserved. So if we have non instant propagation of cause and effect (c) and we have a boundary as Hubble horizon (R_H). This leads to waves of cause and effect propagation to interfere with themselves. Think like a guitar string or even better think like a drum skin (math says drum). Waves can interact in a good way or bad way. All bad ways just dissolves. So constructive interference only can make a stable propagation. And like with any harmonics the lowest posible would be the fundamental Tone. It means 1 oscillation of this tone will have a wavelength of your observable Universe. And we can calculate it: Its just speed of light divided by the circumference of Hubble horizon expressed as a frequency
c2πRH=H02π=3.5148579278×10−191/s
for the reference its 1 full oscillation in around 90.1565273986 billions years. So we currently still in the yearly days of fundamental Tone cycle.

OK, now Imagine a star orbiting the center of a galaxy. In the standard model, the only thing keeping it moving is its local kinetic energy fighting local gravity. When it gets far away, gravity drops, so the math says the star should slow down. When it doesn't, they invent "Dark Matter" to pull it.

In RG, the vacuum itself has a structural tension (ρΛ) between you and R_H. It required to keep the Universe's geometry open against collapse. The star is not moving through an empty void; it is vibrating on a globally tensioned geometric "carrier" (think of a stretched drum skin).

The local orbital frequency of the star and the global frequency of the horizon (the Fundamental Tone) superimpose. This creates a constructive geometric interference.

This interference adds a constant energetic baseline to the star's kinetic state. As the star gets further from the galactic center, its local gravity drops, but it hits that baseline geometric tension. It cannot slow down past this limit, because slowing down would require it to decouple from the global horizon fundamental Tone, which is topologically impossible. That absolute limit is what we observe as the "flat rotation curve." And to test this hypothesis I used equation from wave mechanics where 2 values are multiplied under the square root to model geometric interference:

v2obs=v2NLocal Self-Energy+v2N⋅(ΩaMachr)−−−−−−−−−−−−√Reson. Interference

That absolute limit is what we observe as the "flat rotation curve." To make the mechanics of this geometric interference perfectly clear and dimensionally strict, we can express this exact relation through dimensionless velocity (β = v/c). The interference occurs strictly between the local causal limit (the Schwarzschild radius of the central mass, R_s) and the global causal limit (the Hubble horizon, R_H):

βQ=β2+β2Rs3πRH−−−−−−√−−−−−−−−−−−−√

Here, the term under the inner square root is the direct cross-correlation (interference) between the local kinematic state (β²) and the global structural tension. This tension is expressed as the pure geometric ratio of the two causal horizons: R_s / (3πR_H). It is this exact fundamental resonance that provides the constant energetic baseline and prevents the orbital velocity from dropping.

And when I tested against 10000 + datapoints from 3 different datasets I got precise agreement.

Regarding what constitutes a "minimal system": a true generative geometry does not require an absolute coordinate grid or a "start point to every location." It only requires relative energy differentials. Spacetime is generated by these relations; it does not pre-exist them.

Does this conceptual summary answer your "how and why" more clearly?

And this is exactly why I developed WILL-AI. Its free its open and it trained on all 3 main papers of mine. Don't expect him to preform any complex calculations (he cant use any tools) But he can unswear any questions about the model and provide citations. When I was testing him by comparing mine and his answers to the same questions - it was hard to decide do I prefer mine or he's answers. So yeh have fun: https://willrg.com/WILL-AI/
Feedback on he's performance is required so please do share the feedback at some point

Thanks for your explanations,it's clear....first I should state that SPACETIME≡ENERGY ....to me it's not a new idea ..I have been advocating the same since i entered this forum, tho for me I don't throw away spacetime,it's just an emergent phenomenon that is appropriately modelled by a coordinate system.

How does your stated fundamental tone change as the universe expand? In your formulation is there any force carriers? ...how will the star get coupled to the fundamental tone.

1 hour ago, Anton Rize said:

Energy is change

Meaning without change this is no energy?

1 hour ago, Anton Rize said:

It is this exact fundamental resonance that provides the constant energetic baseline and prevents the orbital velocity from dropping.

Is this not a form of curve fitting?

3 hours ago, KJW said:

No. The explanation I provided was specifically for the twin paradox scenario. If you want to modify the scenario, then the analysis of the scenario has to be modified as well. You can't say my explanation of the twin paradox scenario is incorrect or even overcomplicated because (although it is a thought experiment) my explanation is purely in terms of what is observed. What is observed by each twin is the redshift and blueshift of the other twin's clock, and the amount of time the redshift and blueshift are observed.

As for your modified scenario, I'd like to first point out that you said nothing about how the observer in circular motion observes the observer in the centre. Your discussion of the scenario suggests that you are only concerned with the time dilation of the circularly moving observer that is observed by the central observer, without addressing the question of consistency between the perspectives of the two observers. And it is the question of consistency between the perspectives of the two observers that lies at the heart of the twin paradox, as well as precisely why the twins end up with different ages.

Unfortunately, so far, I have been unable to provide an explanation of your modified scenario in terms I used for the twin paradox scenario. I'm not sure such an explanation even exists. However, I can say that the central observer observes the observer in circular motion as transverse Doppler redshifted, and that the observer in circular motion observes the central observer as accelerationally blueshifted. In the case of the twin paradox scenario, both legs of the travelling twin's journey were inertial, and although the turnaround is an acceleration, it wasn't treated as such and was merely a time and location where the redshift becomes a blueshift. Thus, the explanation I gave for the twin paradox scenario was the natural explanation. I believe (I have a possibly false recollection of doing the maths) that my explanation of the twin paradox scenario can be extended to arbitrary longitudinal motion of the travelling twin. Although such a case has the travelling twin in an accelerated frame of reference, ultimately all redshifts and blueshifts based on time dilation are Doppler effects. Thus, your modified scenario ought to be able to be treated like the generalised twin paradox scenario, although I am presently unable to connect the accelerated frame of reference associated with circular motion to the Doppler effect. That is, I am presently unable to explain the blueshift of the central observer that is observed by the circularly moving observer in terms of the Doppler effect. Nevertheless, the blueshift can be explained by invoking the metric.

A problem I see with your explanation is that it seems to be unconnected to the actual physics of the situation. And by being unconnected to the actual physics, it is difficult to see how it can deal with subtleties present in the actual physics. For example, suppose I am in circular motion at constant speed around some object at the centre. I face the direction of my inward acceleration. Am I looking at the object at the centre?

Thank you for pushing me on this. Your critique forced me to look deeper into how my own equations handle the observable light signals, and I have to concede a major point to you: you are absolutely right that we cannot ignore the frequency shift of light. In fact, it holds the exact mathematical answer.

I think the friction between our perspectives comes down to the fact that we are looking at two different layers of the Doppler effect.

In my Relational Orbital Mechanics (R.O.M.) framework, I strictly separate the observed frequency shift into two components:
1. Observer dependant: the raw optical signal ([math]Z_{raw}[/math])
2. Systems intrinsic: the invariant systemic state ([math]Z_{sys}[/math]).

When you analyze the standard linear Twin Paradox, you are tracking the raw line-of-sight signal ([math]Z_{raw}[/math]). This includes the optical signal delay and the longitudinal Doppler shift (the red/blue shifts you mentioned). It absolutely works for calculating the end result, but the optical delay masks the underlying geometric engine.

In R.O.M., the true proper time projection of the system ([math]\tau_{Wo}[/math]) is literally the exact inverse of the systemic frequency shift:

[math]\tau_{Wo}(o) = \sqrt{1-\frac{R_{s}}{r(o)}}\cdot\sqrt{1-\beta(o)^{2}} = \kappa_{Xo}(o) \cdot \beta_{Yo}(o) = (Z_{sys}(o))^{-1}[/math]

Here, [math]Z_{sys}[/math] is strictly the product of the gravitational redshift ([math]z_k = \frac{1}{\kappa_{X}}-1 [/math]) and the transverse Doppler shift
([math]z_b = \frac{1}{\beta_{Y}}-1[/math]). It dictates the algebraic aging difference instantly and continuously, without relying on signal travel times.

[math]Z_{sys}(o) = (1+z_{ko}(o))(1+z_{bo}(o))[/math]

This is why I brought up the circular orbit scenario. In a circular orbit, the distance is constant, so the longitudinal line-of-sight Doppler effect drops to zero. The "optical noise" of [math]Z_{raw} = (1+\beta_{int}(\cos(o+\omega_{i})+e \cos(\omega_{i}))\sin(i)) Z_{sys}(o)[/math] strips away, and we are left staring purely at [math]Z_{sys}[/math]. The central observer and the orbiting observer age differently not because a signal takes time to flip from red to blue, but because the continuous, invariant structural tension ([math]Z_{sys}[/math]) geometrically restricts their internal proper time ([math]\tau_{Wo}[/math]). The light just transmits this underlying state.

I realize this is much easier to see when you can interact with the math directly. I've built a full Desmos project that contains the closed algebraic system of R.O.M., showing exactly how these invariants generate the orbits and frequency shifts natively:

I also have the formal documentation and a massive dataset test explaining how this system rigorously separates the geometric reality from the line-of-sight optical shadow ([math]M \sin(i)[/math]):

1. The complete closed algebraic system R.O.M.: https://willrg.com/documents/WILL_RG_I.pdf#eq:rom

2. Documentation: https://willrg.com/documents/WILL_RG_I.pdf#sec:M_sin(i)

3. Blind Data Test Results: https://willrg.com/msini_test

4. R.O.M Desmos Project: https://www.desmos.com/calculator/n4lmkpsebx

I'd love for you to play around with the Desmos graph. When you look at it through the lens of separating [math]Z_{sys}[/math] (the geometric state) from [math]Z_{raw}[/math] (the optical shadow), does this bridge the gap between our two explanations?

Edited March 1Mar 1 by Anton Rize

Decided not to bother

Edited March 1Mar 1 by Mordred

22 hours ago, MJ kihara said:

Thanks for your explanations,it's clear....first I should state that SPACETIME≡ENERGY ....to me it's not a new idea ..I have been advocating the same since i entered this forum, tho for me I don't throw away spacetime,it's just an emergent phenomenon that is appropriately modelled by a coordinate system.

How does your stated fundamental tone change as the universe expand? In your formulation is there any force carriers? ...how will the star get coupled to the fundamental tone.

You welcome! And yes this idea is not new. Leibniz, Mach, Einstein, you, me... I like this gang!
The Tone depends on Hubble parameter (H_0) and I derived it from alpha and T_CMB. I can't say for sure yet but so far my bet is on the temperature. But its probably wrong to refer to a single parameter... Its all connected. But for intuitive one-liner its fair to say that it might be what we interpret as expansion could be more like cooling down...

22 hours ago, MJ kihara said:

In your formulation is there any force carriers? ...how will the star get coupled to the fundamental tone.

This is brilliant! You just said yourself that SPACETIME≡ENERGY. The concept force carrier assumes that there's a void through which, one has to "carry" the "force". Can you see the problem?

---

22 hours ago, MJ kihara said:

Meaning without change this is no energy?

What your intuition tells you?

22 hours ago, MJ kihara said:

Is this not a form of curve fitting?

Is this an accusation or misunderstanding? Im not taking lightly calling my research "curve fitting". You have to present the argument properly or take it back.

---

In my humble opinion the best way to develop intuitive and deep understanding is engage with equations. Just play around with them. So I made a desmos project for you https://www.desmos.com/calculator/s9gvcuttqm
It calculates H_0 and then using it to predict the rotation speed of the solar system.
Also I think Im getting better at it. This one is pretty.

5 hours ago, Anton Rize said:

You welcome!

Not soo quick....for me I extend that further....mmmm....

5 hours ago, Anton Rize said:

This is brilliant! You just said yourself that SPACETIME≡ENERGY. The concept force carrier assumes that there's a void through which, one has to "carry" the "force". Can you see the problem?

In my case everything is energy,therefore, no void...there is no "carrying"

5 hours ago, Anton Rize said:

  On 3/1/2026 at 12:29 PM, MJ kihara said:

Meaning without change this is no energy?

What your intuition tells you?

When you say energy is change...change in relation to what?....You have to av a point of reference to know there is change.

5 hours ago, Anton Rize said:

Is this an accusation or misunderstanding? Im not taking lightly calling my research "curve fitting". You have to present the argument properly or take it back.

Am not accusing you of anything...what am saying is that by stating existence of ''a baseline,a fundamental tone or a floor" it's given if you work out math in that direction the curve will fit to the expected value...if you don't say what that fundamental tone is and it's working mechanism(coupling) that is tantamount to calling it dark matter.

Expansion is largely a thermodynamic process.

Here to check your numbers

\[{\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&Scale (a)&S&T (Gyr)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&V_{now}/c&V_{then}/c&H(t)&Temp(K)&rho(kg/m^3)&OmegaM&OmegaL&OmegaR&OmegaT \\ \hline 1.09e+3&9.17e-4&1.09e+3&3.71e-4&6.25e-4&4.53e+1&4.15e-2&5.67e-2&8.38e-4&3.13e+0&6.64e+1&1.56e+6&4.59e-18&2.97e+3&7.56e-1&1.29e-9&2.44e-1&1.00e+0\\ \hline 9.70e+2&1.03e-3&9.71e+2&4.52e-4&7.55e-4&4.52e+1&4.65e-2&6.36e-2&1.03e-3&3.13e+0&6.16e+1&1.29e+6&3.15e-18&2.65e+3&7.77e-1&1.88e-9&2.23e-1&1.00e+0\\ \hline 8.63e+2&1.16e-3&8.64e+2&5.48e-4&9.11e-4&4.51e+1&5.22e-2&7.14e-2&1.26e-3&3.12e+0&5.73e+1&1.07e+6&2.17e-18&2.36e+3&7.97e-1&2.74e-9&2.03e-1&1.00e+0\\ \hline 7.68e+2&1.30e-3&7.69e+2&6.65e-4&1.10e-3&4.50e+1&5.85e-2&8.01e-2&1.53e-3&3.11e+0&5.34e+1&8.91e+5&1.49e-18&2.10e+3&8.15e-1&3.97e-9&1.85e-1&1.00e+0\\ \hline 6.83e+2&1.46e-3&6.84e+2&8.06e-4&1.32e-3&4.49e+1&6.56e-2&8.98e-2&1.87e-3&3.11e+0&4.97e+1&7.41e+5&1.03e-18&1.87e+3&8.32e-1&5.75e-9&1.68e-1&1.00e+0\\ \hline 6.08e+2&1.64e-3&6.09e+2&9.75e-4&1.59e-3&4.48e+1&7.36e-2&1.01e-1&2.28e-3&3.10e+0&4.63e+1&6.16e+5&7.13e-19&1.66e+3&8.48e-1&8.31e-9&1.52e-1&1.00e+0\\ \hline 5.41e+2&1.84e-3&5.42e+2&1.18e-3&1.91e-3&4.47e+1&8.24e-2&1.13e-1&2.78e-3&3.09e+0&4.32e+1&5.13e+5&4.94e-19&1.48e+3&8.62e-1&1.20e-8&1.38e-1&1.00e+0\\ \hline 4.81e+2&2.07e-3&4.82e+2&1.42e-3&2.29e-3&4.46e+1&9.24e-2&1.27e-1&3.38e-3&3.08e+0&4.04e+1&4.27e+5&3.43e-19&1.31e+3&8.75e-1&1.73e-8&1.25e-1&1.00e+0\\ \hline 4.28e+2&2.33e-3&4.29e+2&1.71e-3&2.74e-3&4.44e+1&1.03e-1&1.42e-1&4.11e-3&3.07e+0&3.77e+1&3.56e+5&2.38e-19&1.17e+3&8.88e-1&2.48e-8&1.12e-1&1.00e+0\\ \hline 3.81e+2&2.62e-3&3.82e+2&2.06e-3&3.29e-3&4.43e+1&1.16e-1&1.59e-1&4.99e-3&3.06e+0&3.52e+1&2.97e+5&1.66e-19&1.04e+3&8.99e-1&3.57e-8&1.01e-1&1.00e+0\\ \hline 3.39e+2&2.94e-3&3.40e+2&2.49e-3&3.94e-3&4.41e+1&1.30e-1&1.79e-1&6.05e-3&3.05e+0&3.29e+1&2.48e+5&1.16e-19&9.27e+2&9.09e-1&5.12e-8&9.12e-2&1.00e+0\\ \hline 3.02e+2&3.30e-3&3.03e+2&2.99e-3&4.72e-3&4.40e+1&1.45e-1&2.00e-1&7.33e-3&3.04e+0&3.08e+1&2.07e+5&8.07e-20&8.25e+2&9.18e-1&7.34e-8&8.20e-2&1.00e+0\\ \hline 2.68e+2&3.71e-3&2.69e+2&3.59e-3&5.64e-3&4.38e+1&1.63e-1&2.24e-1&8.88e-3&3.03e+0&2.88e+1&1.73e+5&5.64e-20&7.34e+2&9.26e-1&1.05e-7&7.36e-2&1.00e+0\\ \hline 2.39e+2&4.17e-3&2.40e+2&4.31e-3&6.75e-3&4.36e+1&1.82e-1&2.51e-1&1.07e-2&3.02e+0&2.70e+1&1.45e+5&3.94e-20&6.53e+2&9.34e-1&1.50e-7&6.61e-2&1.00e+0\\ \hline 2.12e+2&4.69e-3&2.13e+2&5.17e-3&8.07e-3&4.34e+1&2.04e-1&2.81e-1&1.30e-2&3.00e+0&2.52e+1&1.21e+5&2.76e-20&5.81e+2&9.41e-1&2.15e-7&5.92e-2&1.00e+0\\ \hline 1.89e+2&5.27e-3&1.90e+2&6.20e-3&9.64e-3&4.32e+1&2.28e-1&3.15e-1&1.57e-2&2.99e+0&2.36e+1&1.01e+5&1.93e-20&5.17e+2&9.47e-1&3.07e-7&5.31e-2&1.00e+0\\ \hline 1.68e+2&5.92e-3&1.69e+2&7.43e-3&1.15e-2&4.30e+1&2.54e-1&3.53e-1&1.89e-2&2.98e+0&2.21e+1&8.49e+4&1.35e-20&4.60e+2&9.53e-1&4.38e-7&4.75e-2&1.00e+0\\ \hline 1.49e+2&6.65e-3&1.50e+2&8.90e-3&1.38e-2&4.28e+1&2.84e-1&3.95e-1&2.28e-2&2.96e+0&2.07e+1&7.11e+4&9.49e-21&4.10e+2&9.58e-1&6.24e-7&4.25e-2&1.00e+0\\ \hline 1.33e+2&7.47e-3&1.34e+2&1.07e-2&1.64e-2&4.25e+1&3.18e-1&4.42e-1&2.75e-2&2.94e+0&1.93e+1&5.95e+4&6.66e-21&3.65e+2&9.62e-1&8.89e-7&3.80e-2&1.00e+0\\ \hline 1.18e+2&8.40e-3&1.19e+2&1.28e-2&1.96e-2&4.22e+1&3.55e-1&4.94e-1&3.31e-2&2.92e+0&1.81e+1&4.99e+4&4.67e-21&3.25e+2&9.66e-1&1.27e-6&3.40e-2&1.00e+0\\ \hline 1.05e+2&9.44e-3&1.06e+2&1.52e-2&2.34e-2&4.20e+1&3.96e-1&5.52e-1&3.98e-2&2.90e+0&1.69e+1&4.18e+4&3.28e-21&2.89e+2&9.70e-1&1.80e-6&3.03e-2&1.00e+0\\ \hline 9.33e+1&1.06e-2&9.43e+1&1.82e-2&2.79e-2&4.17e+1&4.42e-1&6.18e-1&4.79e-2&2.88e+0&1.58e+1&3.50e+4&2.31e-21&2.57e+2&9.73e-1&2.57e-6&2.71e-2&1.00e+0\\ \hline 8.29e+1&1.19e-2&8.39e+1&2.18e-2&3.33e-2&4.14e+1&4.93e-1&6.90e-1&5.76e-2&2.86e+0&1.48e+1&2.94e+4&1.62e-21&2.29e+2&9.76e-1&3.65e-6&2.42e-2&1.00e+0\\ \hline 7.37e+1&1.34e-2&7.47e+1&2.60e-2&3.97e-2&4.10e+1&5.49e-1&7.71e-1&6.92e-2&2.84e+0&1.38e+1&2.46e+4&1.14e-21&2.04e+2&9.78e-1&5.20e-6&2.16e-2&1.00e+0\\ \hline 6.55e+1&1.50e-2&6.65e+1&3.11e-2&4.73e-2&4.07e+1&6.12e-1&8.61e-1&8.32e-2&2.81e+0&1.29e+1&2.07e+4&8.01e-22&1.81e+2&9.81e-1&7.39e-6&1.92e-2&1.00e+0\\ \hline 5.82e+1&1.69e-2&5.92e+1&3.71e-2&5.65e-2&4.03e+1&6.81e-1&9.61e-1&9.98e-2&2.79e+0&1.21e+1&1.73e+4&5.64e-22&1.61e+2&9.83e-1&1.05e-5&1.72e-2&1.00e+0\\ \hline 5.17e+1&1.90e-2&5.27e+1&4.43e-2&6.73e-2&3.99e+1&7.57e-1&1.07e+0&1.20e-1&2.76e+0&1.13e+1&1.45e+4&3.96e-22&1.44e+2&9.85e-1&1.49e-5&1.53e-2&1.00e+0\\ \hline 4.59e+1&2.13e-2&4.69e+1&5.29e-2&8.02e-2&3.95e+1&8.42e-1&1.20e+0&1.44e-1&2.73e+0&1.05e+1&1.22e+4&2.79e-22&1.28e+2&9.86e-1&2.12e-5&1.36e-2&1.00e+0\\ \hline 4.07e+1&2.40e-2&4.17e+1&6.31e-2&9.56e-2&3.90e+1&9.35e-1&1.33e+0&1.72e-1&2.70e+0&9.78e+0&1.02e+4&1.96e-22&1.14e+2&9.88e-1&3.02e-5&1.22e-2&1.00e+0\\ \hline 3.61e+1&2.69e-2&3.71e+1&7.53e-2&1.14e-1&3.85e+1&1.04e+0&1.48e+0&2.06e-1&2.67e+0&9.11e+0&8.58e+3&1.38e-22&1.01e+2&9.89e-1&4.29e-5&1.08e-2&1.00e+0\\ \hline 3.20e+1&3.03e-2&3.30e+1&8.98e-2&1.36e-1&3.80e+1&1.15e+0&1.65e+0&2.47e-1&2.63e+0&8.47e+0&7.20e+3&9.73e-23&9.00e+1&9.90e-1&6.09e-5&9.65e-3&1.00e+0\\ \hline 2.84e+1&3.40e-2&2.94e+1&1.07e-1&1.62e-1&3.75e+1&1.28e+0&1.84e+0&2.96e-1&2.59e+0&7.88e+0&6.04e+3&6.85e-23&8.01e+1&9.91e-1&8.64e-5&8.60e-3&1.00e+0\\ \hline 2.52e+1&3.82e-2&2.62e+1&1.28e-1&1.93e-1&3.69e+1&1.41e+0&2.04e+0&3.55e-1&2.55e+0&7.31e+0&5.07e+3&4.83e-23&7.13e+1&9.92e-1&1.23e-4&7.66e-3&1.00e+0\\ \hline 2.23e+1&4.30e-2&2.33e+1&1.52e-1&2.30e-1&3.63e+1&1.56e+0&2.27e+0&4.25e-1&2.51e+0&6.78e+0&4.25e+3&3.40e-23&6.35e+1&9.93e-1&1.74e-4&6.82e-3&1.00e+0\\ \hline 1.97e+1&4.83e-2&2.07e+1&1.82e-1&2.74e-1&3.57e+1&1.72e+0&2.52e+0&5.08e-1&2.47e+0&6.28e+0&3.57e+3&2.39e-23&5.65e+1&9.94e-1&2.47e-4&6.08e-3&1.00e+0\\ \hline 1.74e+1&5.42e-2&1.84e+1&2.17e-1&3.26e-1&3.50e+1&1.90e+0&2.80e+0&6.08e-1&2.42e+0&5.81e+0&3.00e+3&1.69e-23&5.03e+1&9.94e-1&3.51e-4&5.41e-3&1.00e+0\\ \hline 1.54e+1&6.09e-2&1.64e+1&2.58e-1&3.89e-1&3.43e+1&2.09e+0&3.10e+0&7.27e-1&2.37e+0&5.37e+0&2.52e+3&1.19e-23&4.47e+1&9.95e-1&4.99e-4&4.82e-3&1.00e+0\\ \hline 1.36e+1&6.85e-2&1.46e+1&3.08e-1&4.63e-1&3.35e+1&2.29e+0&3.43e+0&8.70e-1&2.32e+0&4.95e+0&2.11e+3&8.37e-24&3.98e+1&9.95e-1&7.07e-4&4.29e-3&1.00e+0\\ \hline 1.20e+1&7.69e-2&1.30e+1&3.67e-1&5.52e-1&3.27e+1&2.51e+0&3.79e+0&1.04e+0&2.26e+0&4.56e+0&1.77e+3&5.90e-24&3.54e+1&9.95e-1&1.00e-3&3.82e-3&1.00e+0\\ \hline 1.06e+1&8.64e-2&1.16e+1&4.37e-1&6.57e-1&3.18e+1&2.75e+0&4.18e+0&1.24e+0&2.20e+0&4.19e+0&1.49e+3&4.16e-24&3.15e+1&9.95e-1&1.42e-3&3.40e-3&1.00e+0\\ \hline 9.29e+0&9.71e-2&1.03e+1&5.21e-1&7.83e-1&3.09e+1&3.00e+0&4.61e+0&1.48e+0&2.14e+0&3.84e+0&1.25e+3&2.93e-24&2.81e+1&9.95e-1&2.02e-3&3.02e-3&1.00e+0\\ \hline 8.16e+0&1.09e-1&9.16e+0&6.20e-1&9.32e-1&2.99e+1&3.27e+0&5.08e+0&1.77e+0&2.07e+0&3.51e+0&1.05e+3&2.07e-24&2.50e+1&9.94e-1&2.86e-3&2.69e-3&1.00e+0\\ \hline 7.15e+0&1.23e-1&8.15e+0&7.39e-1&1.11e+0&2.89e+1&3.55e+0&5.58e+0&2.12e+0&2.00e+0&3.20e+0&8.81e+2&1.46e-24&2.22e+1&9.94e-1&4.06e-3&2.39e-3&1.00e+0\\ \hline 6.26e+0&1.38e-1&7.26e+0&8.80e-1&1.32e+0&2.78e+1&3.83e+0&6.12e+0&2.53e+0&1.93e+0&2.90e+0&7.40e+2&1.03e-24&1.98e+1&9.92e-1&5.75e-3&2.12e-3&1.00e+0\\ \hline 5.46e+0&1.55e-1&6.46e+0&1.05e+0&1.57e+0&2.67e+1&4.13e+0&6.70e+0&3.02e+0&1.85e+0&2.63e+0&6.22e+2&7.28e-25&1.76e+1&9.90e-1&8.14e-3&1.89e-3&1.00e+0\\ \hline 4.75e+0&1.74e-1&5.75e+0&1.25e+0&1.87e+0&2.55e+1&4.43e+0&7.32e+0&3.61e+0&1.76e+0&2.37e+0&5.23e+2&5.14e-25&1.57e+1&9.87e-1&1.15e-2&1.67e-3&1.00e+0\\ \hline 4.11e+0&1.96e-1&5.11e+0&1.49e+0&2.22e+0&2.42e+1&4.73e+0&7.97e+0&4.30e+0&1.67e+0&2.13e+0&4.40e+2&3.64e-25&1.39e+1&9.82e-1&1.63e-2&1.48e-3&1.00e+0\\ \hline 3.55e+0&2.20e-1&4.55e+0&1.77e+0&2.64e+0&2.28e+1&5.01e+0&8.65e+0&5.14e+0&1.58e+0&1.90e+0&3.71e+2&2.58e-25&1.24e+1&9.76e-1&2.29e-2&1.31e-3&1.00e+0\\ \hline 3.05e+0&2.47e-1&4.05e+0&2.10e+0&3.12e+0&2.14e+1&5.28e+0&9.37e+0&6.13e+0&1.48e+0&1.69e+0&3.13e+2&1.84e-25&1.10e+1&9.67e-1&3.22e-2&1.16e-3&1.00e+0\\ \hline 2.61e+0&2.77e-1&3.61e+0&2.50e+0&3.70e+0&1.99e+1&5.51e+0&1.01e+1&7.30e+0&1.37e+0&1.49e+0&2.64e+2&1.31e-25&9.83e+0&9.54e-1&4.51e-2&1.02e-3&1.00e+0\\ \hline 2.21e+0&3.12e-1&3.21e+0&2.97e+0&4.36e+0&1.83e+1&5.69e+0&1.09e+1&8.70e+0&1.26e+0&1.30e+0&2.24e+2&9.43e-26&8.74e+0&9.36e-1&6.28e-2&8.87e-4&1.00e+0\\ \hline 1.86e+0&3.50e-1&2.86e+0&3.52e+0&5.13e+0&1.66e+1&5.81e+0&1.16e+1&1.04e+1&1.15e+0&1.13e+0&1.91e+2&6.82e-26&7.78e+0&9.12e-1&8.68e-2&7.69e-4&1.00e+0\\ \hline 1.54e+0&3.94e-1&2.54e+0&4.17e+0&6.00e+0&1.49e+1&5.84e+0&1.24e+1&1.23e+1&1.03e+0&9.74e-1&1.63e+2&4.98e-26&6.93e+0&8.80e-1&1.19e-1&6.60e-4&1.00e+0\\ \hline 1.26e+0&4.42e-1&2.26e+0&4.93e+0&6.98e+0&1.30e+1&5.77e+0&1.31e+1&1.47e+1&9.03e-1&8.26e-1&1.40e+2&3.69e-26&6.16e+0&8.39e-1&1.61e-1&5.60e-4&1.00e+0\\ \hline 1.01e+0&4.97e-1&2.01e+0&5.80e+0&8.05e+0&1.12e+1&5.55e+0&1.38e+1&1.74e+1&7.73e-1&6.90e-1&1.22e+2&2.77e-26&5.49e+0&7.86e-1&2.14e-1&4.67e-4&1.00e+0\\ \hline 7.91e-1&5.58e-1&1.79e+0&6.80e+0&9.18e+0&9.27e+0&5.18e+0&1.44e+1&2.06e+1&6.42e-1&5.64e-1&1.06e+2&2.13e-26&4.88e+0&7.22e-1&2.78e-1&3.81e-4&1.00e+0\\ \hline 5.94e-1&6.27e-1&1.59e+0&7.94e+0&1.04e+1&7.35e+0&4.61e+0&1.50e+1&2.44e+1&5.09e-1&4.46e-1&9.45e+1&1.68e-26&4.34e+0&6.46e-1&3.53e-1&3.04e-4&1.00e+0\\ \hline 4.19e-1&7.05e-1&1.42e+0&9.22e+0&1.15e+1&5.44e+0&3.83e+0&1.55e+1&2.87e+1&3.76e-1&3.33e-1&8.50e+1&1.36e-26&3.87e+0&5.63e-1&4.37e-1&2.36e-4&1.00e+0\\ \hline 2.63e-1&7.92e-1&1.26e+0&1.06e+1&1.26e+1&3.55e+0&2.81e+0&1.59e+1&3.38e+1&2.46e-1&2.23e-1&7.76e+1&1.13e-26&3.44e+0&4.76e-1&5.24e-1&1.77e-4&1.00e+0\\ \hline 1.24e-1&8.90e-1&1.12e+0&1.22e+1&1.36e+1&1.73e+0&1.54e+0&1.63e+1&3.96e+1&1.20e-1&1.14e-1&7.19e+1&9.72e-27&3.06e+0&3.90e-1&6.09e-1&1.29e-4&1.00e+0\\ \hline 0.00e+0&1.00e+0&1.00e+0&1.38e+1&1.45e+1&0.00e+0&0.00e+0&1.66e+1&4.62e+1&0.00e+0&0.00e+0&6.77e+1&8.60e-27&2.73e+0&3.11e-1&6.89e-1&9.18e-5&1.00e+0\\ \hline -1.09e-1&1.12e+0&8.91e-1&1.55e+1&1.52e+1&1.61e+0&1.81e+0&1.68e+1&5.36e+1&1.11e-1&1.19e-1&6.45e+1&7.82e-27&2.43e+0&2.42e-1&7.58e-1&6.37e-5&1.00e+0\\ \hline -2.06e-1&1.26e+0&7.94e-1&1.73e+1&1.57e+1&3.11e+0&3.91e+0&1.70e+1&6.21e+1&2.15e-1&2.49e-1&6.22e+1&7.26e-27&2.16e+0&1.85e-1&8.15e-1&4.33e-5&1.00e+0\\ \hline -2.92e-1&1.41e+0&7.08e-1&1.91e+1&1.62e+1&4.49e+0&6.34e+0&1.71e+1&7.16e+1&3.10e-1&3.92e-1&6.05e+1&6.87e-27&1.93e+0&1.38e-1&8.62e-1&2.88e-5&1.00e+0\\ \hline -3.69e-1&1.58e+0&6.31e-1&2.10e+1&1.65e+1&5.74e+0&9.10e+0&1.72e+1&8.23e+1&3.97e-1&5.52e-1&5.93e+1&6.60e-27&1.72e+0&1.02e-1&8.98e-1&1.90e-5&1.00e+0\\ \hline -4.38e-1&1.78e+0&5.62e-1&2.29e+1&1.68e+1&6.88e+0&1.22e+1&1.72e+1&9.44e+1&4.76e-1&7.31e-1&5.84e+1&6.40e-27&1.53e+0&7.43e-2&9.26e-1&1.23e-5&1.00e+0\\ \hline -4.99e-1&2.00e+0&5.01e-1&2.48e+1&1.69e+1&7.91e+0&1.58e+1&1.73e+1&1.08e+2&5.48e-1&9.32e-1&5.77e+1&6.26e-27&1.37e+0&5.38e-2&9.46e-1&7.96e-6&1.00e+0\\ \hline -5.53e-1&2.24e+0&4.47e-1&2.68e+1&1.71e+1&8.84e+0&1.98e+1&1.73e+1&1.23e+2&6.12e-1&1.16e+0&5.73e+1&6.16e-27&1.22e+0&3.87e-2&9.61e-1&5.10e-6&1.00e+0\\ \hline -6.02e-1&2.51e+0&3.98e-1&2.88e+1&1.72e+1&9.67e+0&2.43e+1&1.74e+1&1.40e+2&6.69e-1&1.42e+0&5.70e+1&6.09e-27&1.09e+0&2.77e-2&9.72e-1&3.25e-6&1.00e+0\\ \hline -6.45e-1&2.82e+0&3.55e-1&3.08e+1&1.72e+1&1.04e+1&2.94e+1&1.74e+1&1.60e+2&7.21e-1&1.70e+0&5.67e+1&6.04e-27&9.67e-1&1.98e-2&9.80e-1&2.07e-6&1.00e+0\\ \hline -6.84e-1&3.16e+0&3.16e-1&3.27e+1&1.73e+1&1.11e+1&3.51e+1&1.74e+1&1.81e+2&7.67e-1&2.03e+0&5.66e+1&6.01e-27&8.62e-1&1.41e-2&9.86e-1&1.31e-6&1.00e+0\\ \hline -7.18e-1&3.55e+0&2.82e-1&3.47e+1&1.73e+1&1.17e+1&4.14e+1&1.74e+1&2.05e+2&8.08e-1&2.39e+0&5.64e+1&5.98e-27&7.68e-1&1.00e-2&9.90e-1&8.32e-7&1.00e+0\\ \hline -7.49e-1&3.98e+0&2.51e-1&3.67e+1&1.73e+1&1.22e+1&4.86e+1&1.74e+1&2.32e+2&8.45e-1&2.80e+0&5.64e+1&5.97e-27&6.85e-1&7.10e-3&9.93e-1&5.27e-7&1.00e+0\\ \hline -7.76e-1&4.47e+0&2.24e-1&3.87e+1&1.74e+1&1.27e+1&5.67e+1&1.74e+1&2.63e+2&8.78e-1&3.26e+0&5.63e+1&5.95e-27&6.10e-1&5.04e-3&9.95e-1&3.33e-7&1.00e+0\\ \hline -8.00e-1&5.01e+0&2.00e-1&4.07e+1&1.74e+1&1.31e+1&6.57e+1&1.74e+1&2.97e+2&9.07e-1&3.78e+0&5.63e+1&5.94e-27&5.44e-1&3.57e-3&9.96e-1&2.10e-7&1.00e+0\\ \hline -8.22e-1&5.62e+0&1.78e-1&4.27e+1&1.74e+1&1.35e+1&7.58e+1&1.74e+1&3.36e+2&9.33e-1&4.36e+0&5.62e+1&5.94e-27&4.85e-1&2.53e-3&9.97e-1&1.33e-7&1.00e+0\\ \hline -8.42e-1&6.31e+0&1.58e-1&4.47e+1&1.74e+1&1.38e+1&8.72e+1&1.74e+1&3.79e+2&9.56e-1&5.01e+0&5.62e+1&5.93e-27&4.32e-1&1.79e-3&9.98e-1&8.39e-8&1.00e+0\\ \hline -8.59e-1&7.08e+0&1.41e-1&4.67e+1&1.74e+1&1.41e+1&1.00e+2&1.74e+1&4.27e+2&9.77e-1&5.75e+0&5.62e+1&5.93e-27&3.85e-1&1.27e-3&9.99e-1&5.30e-8&1.00e+0\\ \hline -8.74e-1&7.94e+0&1.26e-1&4.87e+1&1.74e+1&1.44e+1&1.14e+2&1.74e+1&4.81e+2&9.96e-1&6.57e+0&5.62e+1&5.93e-27&3.43e-1&9.00e-4&9.99e-1&3.34e-8&1.00e+0\\ \hline -8.88e-1&8.91e+0&1.12e-1&5.07e+1&1.74e+1&1.46e+1&1.30e+2&1.74e+1&5.42e+2&1.01e+0&7.49e+0&5.62e+1&5.93e-27&3.06e-1&6.37e-4&9.99e-1&2.11e-8&1.00e+0\\ \hline -9.00e-1&1.00e+1&1.00e-1&5.27e+1&1.74e+1&1.48e+1&1.48e+2&1.74e+1&6.10e+2&1.03e+0&8.52e+0&5.62e+1&5.93e-27&2.73e-1&4.51e-4&1.00e+0&1.33e-8&1.00e+0\\ \hline -9.11e-1&1.12e+1&8.91e-2&5.48e+1&1.74e+1&1.50e+1&1.69e+2&1.74e+1&6.87e+2&1.04e+0&9.69e+0&5.62e+1&5.93e-27&2.43e-1&3.20e-4&1.00e+0&8.40e-9&1.00e+0\\ \hline -9.21e-1&1.26e+1&7.94e-2&5.68e+1&1.74e+1&1.52e+1&1.91e+2&1.74e+1&7.73e+2&1.05e+0&1.10e+1&5.62e+1&5.93e-27&2.16e-1&2.26e-4&1.00e+0&5.30e-9&1.00e+0\\ \hline -9.29e-1&1.41e+1&7.08e-2&5.88e+1&1.74e+1&1.53e+1&2.17e+2&1.74e+1&8.69e+2&1.06e+0&1.25e+1&5.62e+1&5.92e-27&1.93e-1&1.60e-4&1.00e+0&3.35e-9&1.00e+0\\ \hline -9.37e-1&1.58e+1&6.31e-2&6.08e+1&1.74e+1&1.55e+1&2.45e+2&1.74e+1&9.77e+2&1.07e+0&1.41e+1&5.62e+1&5.92e-27&1.72e-1&1.13e-4&1.00e+0&2.11e-9&1.00e+0\\ \hline -9.44e-1&1.78e+1&5.62e-2&6.28e+1&1.74e+1&1.56e+1&2.77e+2&1.74e+1&1.10e+3&1.08e+0&1.59e+1&5.62e+1&5.92e-27&1.53e-1&8.03e-5&1.00e+0&1.33e-9&1.00e+0\\ \hline -9.50e-1&2.00e+1&5.01e-2&6.48e+1&1.74e+1&1.57e+1&3.13e+2&1.74e+1&1.24e+3&1.09e+0&1.80e+1&5.62e+1&5.92e-27&1.37e-1&5.68e-5&1.00e+0&8.41e-10&1.00e+0\\ \hline -9.55e-1&2.24e+1&4.47e-2&6.68e+1&1.74e+1&1.58e+1&3.54e+2&1.74e+1&1.39e+3&1.09e+0&2.03e+1&5.62e+1&5.92e-27&1.22e-1&4.02e-5&1.00e+0&5.30e-10&1.00e+0\\ \hline -9.60e-1&2.51e+1&3.98e-2&6.88e+1&1.74e+1&1.59e+1&3.99e+2&1.74e+1&1.56e+3&1.10e+0&2.29e+1&5.62e+1&5.92e-27&1.09e-1&2.85e-5&1.00e+0&3.35e-10&1.00e+0\\ \hline -9.65e-1&2.82e+1&3.55e-2&7.08e+1&1.74e+1&1.60e+1&4.50e+2&1.74e+1&1.75e+3&1.10e+0&2.58e+1&5.62e+1&5.92e-27&9.67e-2&2.02e-5&1.00e+0&2.11e-10&1.00e+0\\ \hline -9.68e-1&3.16e+1&3.16e-2&7.28e+1&1.74e+1&1.60e+1&5.07e+2&1.74e+1&1.97e+3&1.11e+0&2.91e+1&5.62e+1&5.92e-27&8.62e-2&1.43e-5&1.00e+0&1.33e-10&1.00e+0\\ \hline -9.72e-1&3.55e+1&2.82e-2&7.48e+1&1.74e+1&1.61e+1&5.71e+2&1.74e+1&2.21e+3&1.11e+0&3.28e+1&5.62e+1&5.92e-27&7.68e-2&1.01e-5&1.00e+0&8.41e-11&1.00e+0\\ \hline -9.75e-1&3.98e+1&2.51e-2&7.68e+1&1.74e+1&1.61e+1&6.43e+2&1.74e+1&2.48e+3&1.12e+0&3.69e+1&5.62e+1&5.92e-27&6.85e-2&7.16e-6&1.00e+0&5.30e-11&1.00e+0\\ \hline -9.78e-1&4.47e+1&2.24e-2&7.88e+1&1.74e+1&1.62e+1&7.23e+2&1.74e+1&2.79e+3&1.12e+0&4.15e+1&5.62e+1&5.92e-27&6.10e-2&5.07e-6&1.00e+0&3.35e-11&1.00e+0\\ \hline -9.80e-1&5.01e+1&2.00e-2&8.08e+1&1.74e+1&1.62e+1&8.14e+2&1.74e+1&3.13e+3&1.12e+0&4.67e+1&5.62e+1&5.92e-27&5.44e-2&3.59e-6&1.00e+0&2.11e-11&1.00e+0\\ \hline -9.82e-1&5.62e+1&1.78e-2&8.28e+1&1.74e+1&1.63e+1&9.15e+2&1.74e+1&3.51e+3&1.13e+0&5.25e+1&5.62e+1&5.92e-27&4.85e-2&2.54e-6&1.00e+0&1.33e-11&1.00e+0\\ \hline -9.84e-1&6.31e+1&1.58e-2&8.48e+1&1.74e+1&1.63e+1&1.03e+3&1.74e+1&3.94e+3&1.13e+0&5.91e+1&5.62e+1&5.92e-27&4.32e-2&1.80e-6&1.00e+0&8.41e-12&1.00e+0\\ \hline -9.86e-1&7.08e+1&1.41e-2&8.68e+1&1.74e+1&1.63e+1&1.16e+3&1.74e+1&4.43e+3&1.13e+0&6.64e+1&5.62e+1&5.92e-27&3.85e-2&1.27e-6&1.00e+0&5.30e-12&1.00e+0\\ \hline -9.87e-1&7.94e+1&1.26e-2&8.88e+1&1.74e+1&1.64e+1&1.30e+3&1.74e+1&4.97e+3&1.13e+0&7.46e+1&5.62e+1&5.92e-27&3.43e-2&9.01e-7&1.00e+0&3.35e-12&1.00e+0\\ \hline -9.89e-1&8.91e+1&1.12e-2&9.08e+1&1.74e+1&1.64e+1&1.46e+3&1.74e+1&5.58e+3&1.13e+0&8.39e+1&5.62e+1&5.92e-27&3.06e-2&6.38e-7&1.00e+0&2.11e-12&1.00e+0\\ \hline -9.90e-1&1.00e+2&1.00e-2&9.28e+1&1.74e+1&1.64e+1&1.64e+3&1.74e+1&6.26e+3&1.14e+0&9.42e+1&5.62e+1&5.92e-27&2.73e-2&4.51e-7&1.00e+0&1.33e-12&1.00e+0\\ \hline \end{array}}\]

10 hours ago, MJ kihara said:

When you say energy is change...change in relation to what?....You have to av a point of reference to know there is change.

This is the most important question you could possibly ask. In physics, to measure change, you have exactly two options for a reference point:

Option 1: The Standard Method (The Ghost Reference)

Standard physics tries to establish a universal background grid. To do this, they invent a mathematical concept called the "Observer at Infinity" (asymptotic flatness). They pretend there is a magical observer infinitely far away, where gravity is zero and space is perfectly flat, and they measure everything relative to that ghost. It has no physical reality, but it makes correct approximations.

Option 2: WILL Relational Geometry (The Real Reference)

In RG, there is no background grid and no observer at infinity. The observer is always the origin point. Every observer places themselves at the exact center of their own relational coordinate system: [math](\beta, \kappa) = (0,0)[/math]. (its not space and time its state difference)

When you observe a star, you are not locating it on a universal 3D grid (x, y, z). You are measuring the energy differential between your state and the star's state. You measure two projections:

1. Its kinematic shift relative to you (Velocity/Direction): [math]\beta[/math]

2. Its gravitational shift relative to you (Potential/Depth): [math]\kappa[/math]

Here is the geometric representation of how these two projections define the system's state on their respective relational carriers:

The total change - Total Relational Shift - between you and the star is just the sum of squares of these two projections:

[math]Q^2 = \beta^2 + \kappa^2[/math] (don't confuse with simple right triangle, [math]Q^2[/math] is NOT constant)

Now, here is the beauty of Relational Reciprocity. If that star has an observer looking back at you, they do not see themselves at some coordinate
[math](x,y,z)[/math]. They place themselves at [math](0,0)[/math]. They measure your speed and your potential relative to them, and they calculate the exact same total shift: [math]Q^2 = \beta^2 + \kappa^2[/math].

This reciprocity can be visualized on the [math]\beta-\kappa[/math] plane. The observer is always at the center, and the observed object is at the end of the [math]Q[/math] vector:

There is no common background arena. There are only mutual total shift magnitudes [math]Q[/math] computed from each observer's own relational origin. This is what I mean by Ontological Minimalism: we do not need to invent an empty box for the universe to exist in. The relationships are the geometry.

And this way all extremely complex GR surfaces emerge as simple and beautiful ratios:

If you want to interact with this geometrically, I made a very simple interactive graph showing how the Observer, the Object, and the Total Shift Q relate to each other:

Desmos

Q as Total Relational Shift

To dive a bit deeper and see the derivations you can read this section https://willrg.com/documents/WILL_RG_I.pdf#sec:DisQ

Does this clarify what the "point of reference" is?

10 hours ago, MJ kihara said:

Am not accusing you of anything...what am saying is that by stating existence of ''a baseline,a fundamental tone or a floor" it's given if you work out math in that direction the curve will fit to the expected value...if you don't say what that fundamental tone is and it's working mechanism(coupling) that is tantamount to calling it dark matter.

You are describing "curve fitting" - the process of inventing a free parameter and tuning its value to match the data. If I did that, you would be absolutely right. It would just be Dark Matter under a new name.

But WILL Relational Geometry has zero adjustable parameters. I cannot "tune" the Fundamental Tone to make the curves fit. It is strictly derived.

Here is exactly what the Fundamental Tone is:

1. The Hubble parameter ([math]H_0[/math]) is not a fitted cosmological parameter in RG. It is derived algebraically from the Fine Structure Constant ([math]\alpha[/math]) and the Cosmic Microwave Background temperature ([math]T_{CMB}[/math]):

[math]H_{0}=\frac{T_{CMB}^{2}}{\alpha}\sqrt{\frac{32\pi G\sigma_{SB}}{3c^{3}}}[/math]

There is absolutely nothing to adjust here. It relies only on fundamental constants and the single most precisely measured temperature in cosmology.

2. The Fundamental Tone is simply the geometric frequency of the observable universe. It is the speed of causality ([math]c[/math]) divided by the circumference of the Hubble horizon ([math]2\pi\frac{c}{H_{0}}=2\pi R_H[/math]):

[math]\text{Fundamental Tone} = \frac{H_{0}}{2\pi}=\frac{c}{2\pi R_{H}}[/math]

The Mechanism (Coupling):

Because [math]\text{SPACETIME} \equiv \text{ENERGY}[/math], there is no empty void. Therefore, "coupling" is not a mechanical force carried by a particle through space. They was never decoupled in the firs place. No object exists in isolation. Space is determent by relations within.

The structural tension of the global horizon (the Tone) geometrically superimposes with the local kinetic state of the star.

[math]\beta_{Q}=\sqrt{\beta^{2}+\sqrt{\beta^{2}\frac{R_{s}}{3\pi R_{H}}}}[/math]

You can interact with this derivation and confirm it yourself using this pretty Desmos project:
https://www.desmos.com/calculator/s9gvcuttqm

Because I have zero free parameters, this specific geometric constraint either predicts the exact rotation curves of 10,000+ datapoints of hundreds of galaxies perfectly, or it completely fails. You cannot "curve fit" thousands of different galaxies using a single, rigid equation unless that equation represents the actual structural constraint of the universe.

So using the words "curve fitting" towards my research makes no f*** sense.

Does this clear's out the misunderstanding for you?

@MJ kihara Forgot to mention: you can test this predictions yourself against 175 galaxies from SPARC database: https://willrg.com/galactic_dynamics/