One way to test this is just to change G by G/2. That will affect the value of G and the value of FPl, which is c**4/G

So, G -> G/2 and FPl -> 2c**4/G

If you plug those values into the proposed formula, the proposed formula will give you G/2 because it is a Tautology. The prediction will predict whatever you jot down as G.

The derivation of Newton's gravitational constant, \( G \), from the gravitational force equation \( F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}} \), is not a tautology. Instead, it's based on empirical observations and experimental data. Newton's law of universal gravitation was formulated based on observations of the motion of celestial bodies, and \( G \) was experimentally determined through measurements of gravitational forces between masses. While the equation itself can be derived from more fundamental principles like conservation of energy and momentum, the value of \( G \) is determined experimentally, not tautologically.

The answer to

“Is this derivation of G the result of a Tautology?”

- is as: the fundamental Nature Gravity force G constant by no means can be derived from anything “purely theoretical” that is known in physics now [and in a long time further], since that is just fundamental Force constant, which – as all fundamental constants in Matter, including the strengths constants of all other [Weak, Electric, Strong/Nuclear] Forces, is/are established in Matter aimed at for Matter to be as it is.

Including G cannot be derived from “geometry” , from that “the ratio of gravitational force to electrostatic force equals the ratio of electrostatic force to Planck force”, etc.

All what is possible now is fundamentally only experimentally to measure the constants, and further to use the experimental values at developing – of so really purely phenomenological - theories and models of what exists and happens in Matter in some concrete general cases. So, say, any claimed “derivations” of G really are nothing else than some tautologies from Newton experimental Gravity law.

Though really it is possible to answer the question “why/how G is as it is?” on fundamentally deeper – Planck scale - level, what can be, and is, done only in framework of the Shevchenko-Tokarevsky’s Planck scale informational physical model, 3 main papers are

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics

https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics,

https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force

- more see SS&VT 2007 Planck scale model of Gravity and Electric Forces in section 6 in 2-nd link or in

https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces

At that it is rigorously scientifically shown that on Planck scale at least Gravity, Electric, and Nuclear [that binds nucleons in nuclei, more see the 3-rd link] act by the same one scheme, Matter on Planck scale is rather simple logical system.

Cheers

Harri Shore Sergey Shevchenko

You missed the point. I am analyzing the work iSpace (I provided the paper), where G is calculated by an Ansatz (guessed formula). It turned out that the guessed formula G = F(G) can be reduced (as I showed in the sympy python code) to G=G, a tautology...:)

That should have been clear to the author since he claimed to calculate cosmological constants with infinite precision.

By the way, I derived the value of G from the first principles, and it is epoch-dependent.

You are welcome to see the derivation and criticize my work. It was presented in my earliest publications.

HU Basics

https://www.youtube.com/watch?v=wuGlDECvifc

Recasting Newton's Laws of Dynamics in the Space Stress Strain Paradigm

https://www.youtube.com/watch?v=_w-5u1WAp6o

HU achievements

https://thehypergeometricaluniverseachievements.quora.com/What-are-the-Hypergeometrical-Universe-Theory-accomplishments

Of course, the model for G contains one parameter related to the elasticity of space. That parameter is used to calculate the natural frequency of metric waves.

Sergey Shevchenko

You are a theoretician. You should know that theoreticians will "prove" anything to get a paper published.

So, I disagree with this statement: At that it is rigorously scientifically shown that on Planck scale at least Gravity, Electric, and Nuclear [that binds nucleons in nuclei, more see the 3-rd link] act by the same one scheme, Matter on Planck scale is rather simple logical system.

Sergey Shevchenko Harri Shore Preston Guynn

I created another discussion item

https://www.researchgate.net/post/Is_the_value_of_H0_derived_through_a_tautology_in_iSpace_paper

I cannot understand the underlying model. Perhaps you people do.

Marco Pereira

quite possibly I did miss the point, certainly my wife would support this assertion…

I'm going through the details; probably need to understand the inputs better

Marco Pereira

interesting stuff, I have few questions et al;

1. On the Methodology of Derivation: Could you elaborate on the specific geometric principles and mathematical methodologies you employed to derive the values of the cosmological constants, including the gravitational constant (\(G\)), with claimed infinite precision?

( apologies if I missed it )

2. Self-Consistency and Tautological Concerns: How do you ensure that your derivations of cosmological constants are not merely tautological, where the conclusions are implicitly assumed in the premises? What steps do you take to verify that your results extend beyond the internal logic of the definitions for \(F_g\), \(F_E\), and \(F_{Pl}\)?

3. Epoch-Dependence of Constants: Your theory suggests that constants such as \(G\) are epoch-dependent. Could you discuss the theoretical underpinnings and observational evidence that support this notion? How does this variability manifest across different epochs, and what are its implications for our understanding of the universe's evolution?

4. Observational Support and Predictions: Could you detail the specific astronomical observations that support your interpretation of epoch-dependent cosmological constants? How do these observations align with or diverge from the predictions of current standard models of cosmology?

5. Innovative Aspects of Your Derivation: In what ways does your derivation of the cosmological constants, including \(G\), differ from or advance beyond previous approaches? What novel insights or methodologies does your work introduce?

6. Implications for Fundamental Physics and Cosmology: Assuming the validity of your derivations and the epoch-dependence of constants, what are the broader implications for fundamental physics and cosmological theories? How might this change our understanding of key cosmological phenomena, such as the big bang, cosmic inflation, or dark energy?

7. Future Directions and Experimental Verification: What future research directions do you envision based on your findings? Are there specific experiments or observations that could further test or refine the epoch-dependence of cosmological constants?

8. Critiques and Counterarguments: How have the broader scientific and theoretical physics communities responded to your claims? Are there notable critiques or counterarguments that you've had to address, and how have you responded to them?

Harri Shore

You are conflating two projects. Christian G. Wolf's iSpace project is one I cannot understand, and it has tautologies.

I explained and showed the tautology in a Sympy/Python derivation. It wouldn't be a tautology (it would be a different way to measure G) if Fg could be experimentally measured. It cannot, and if it could, it wouldn't produce infinite precision.

My work is the Hypergeometrical Universe Theory (HU). I created a 10-minute video with the basics.

HU Basics

https://www.youtube.com/watch?v=wuGlDECvifc

Recasting Newton's Laws of Dynamics in the Space Stress Strain Paradigm

https://www.youtube.com/watch?v=_w-5u1WAp6o

HU achievements

https://thehypergeometricaluniverseachievements.quora.com/What-are-the-Hypergeometrical-Universe-Theory-accomplishments-1

The Big Pop Cosmogenesis - replacement to the Big Bang

https://www.youtube.com/watch?v=jHK-Lyb7NfM

Big Pop Article

https://www.preprints.org/manuscript/202201.0106/v1

Here, I explained why the Universe has four spatial dimensions by calculating the probability of universes of different dimensionalities.

https://www.quora.com/Can-Dr-Marco-Pereira-explain-WHY-we-live-in-a-3D-Universe/answer/Marco-Pereira-1

HU parameterless prediction of Annular Galaxy Clusters. Not only its existence but also its position in the observable universe.

https://hypergeometricaluniverse.quora.com/Did-Dr-Marco-Pereira-predict-the-existence-of-Annular-Galaxy-Clusters-like-the-one-recently-discovered-1

I am creating slides and a video presentation which I will use to answer your questions.

In the meantime, please, read the links and feel free to ask questions.

Marco Pereira

Harri Shore Sergey Shevchenko

I tried to provide my feedback to Christian. He blocked me, so I wrote my critique here. I intend to review the work of many academicians who have high visibility yet created extremely flawed models.

Of course, I will do the same for crackpots.

You might ask why would anyone criticize someone else's work.

I would love a critique from an academician.

I say that not because I disregard other people's criticism but because a critique from an academician has official value. If I provide a convincing counterargument, the academician would see himself/herself in the position of having to defend my work from the people who have been censoring it for 18 years (e.g., Paul Ginsparg from Los Alamos Archives, Mendola from Physics of the Dark Universe Editor...etc.)

Independent Researchers have no position within the academic hierarchy and carry no weight (unfortunately, they cannot help me). Of course, any critique is always welcomed.

I provided free peer review to Christian G. Wolf. I believe that is what everyone should do. It is a waste of time to pursue a bad idea... or not to become aware of obscure mistakes we all make. In other words, what I did for Christian, I hope other people will do for me.

Science can only improve through criticism. Every hypothesis and derivation should be criticized and independently verified.

He blocked you ?

why ?

Harri Shore

One can never know motivations. I posted my comments in the comments section of his preprints.

There are two issues:

• The issue of claiming to have calculated Cosmological Constants with infinite precision. In particular, having calculated H_0, which is the inverse of the universe's age from cosmological constants. If H_0 is not a constant, one shouldn't be able to calculate it from constants.
• There is an underlying geometrical model which I couldn't understand. I looked around, but I couldn't find the article where the model would be. That said, the formula for H0 has the speed of light divided by 10 (it seems arbitrary and problematic since the formula does not pay attention to units. So, I made an effort but gave up when my interpretation of the model didn't favor it.

So, for the sake of honesty, I have to say that there are things in the information that I couldn't understand or find.

IN SUMMARY

There was no discussion section (that I am aware of) for those papers, so I wrote my comment in the comments section. I mentioned that the idea that one can have infinite precision is a sign of Tautology.

I was told to go away and that I didn't understand the model... etc., which is true.

That said, I could prove the Tautology, so I created this and the other discussion.

Whenever I see some scientific model that doesn't make sense, I write a comment. I believe that is my job or the job of any scientist.

It doesn't take that long.

yes there’s all sorts of problemati/ unsupported items there.

also, how does one get to calculate som with “infinite precision “?

if I can’t techni count to Infinity then how can I calculate something with infinite precision…

H

I suspect he convinced himself that he had found a mapping of observables to integers or rational numbers, which have infinite precision.

If you look at his calculations, they are done in Mathematica with very large integers.

He didn't convince me, and both H0 and G are epoch-dependent in my theory, so I cannot be easily convinced.

This file contains the proof that his derivation of the value of G from factors including Fpl (which contains G)

# Planck mass and Planck length definitions

m_Pl = sp.sqrt(hbar * c / G)

l_Pl = sp.sqrt(hbar * G / c**3)

# Force between two Planck masses at 1 Planck length

F_Pl = G * m_Pl**2 / l_Pl**2

is just a tautology G=G