I think, we cannot (at least not in the macrocosm) experimentally verify separately any force law or inertia force, we can only verify the validity of the equation of motion, which contains both laws. Each equation of motion can probably be re-wtitten in the dimensionless form (I did so for a trivial case of Newton and Coulomb laws in: arXiv:1206.0405), in which the gravitational constant, permitivity of vacuum, and Planck constant disappear.

Consequently, I think that if all physical laws were expressed in the natural physical quantities, there would not be any physical constants (with dimensions). In other words, we can ask: does nature know such the physical quantities, which were established by man, as e.g. "mass", or "electric charge"? It may not. So, the fundamental constants seems to be only the conversion constants between the quantities established by us (human beings) and natural quantities. Hence, I am afraid that the asked question may not be meaningful, in principle.

No, How the fundamental constants could be function of a variable (i.e. gravitational potential) ?! As you know, gravity potential depends on other variables.However we can imagine relations of other fundamental constants with gravitational constant G .

Dear Manouchehr,

Mach’s principle: Local physical laws are determined by the large-scale structure of the universe, or in our words by functions of the gravitational potential.

Dear Guoliang , I can not find out from many version of Mach's principle, a notion similar to your notion of this conjecture which nominated by Einstein as "principle". see for example this link of arXiv : http://arxiv.org/abs/gr-qc/9607009. Moreover this conjecture (say principle) as you can trace it out in first paragraph of this link of wikipedia: http://en.wikipedia.org/wiki/Mach%27s_principle is an imprecise "conjecture". However it was an attempt for description of "inertia" by distribution of all masses of the world. In this "principle" there is not any place for "gravitational potential" which carries a precise definition through GR based on metric tensor and space-time Ricci curvature in a Riemannian manifold. It can easily be deduced that this potential varies from one point to another point of this manifold and hence could not be attributed to "fundamental constants".                

Dear Manouchehr,

This is from the link of Wikipedia you provided:

A very general statement of Mach's principle is "Local physical laws are determined by the large-scale structure of the universe."

That is a quotation from Stephen W. Hawking & George Francis Rayner Ellis (1973). The Large Scale Structure of Space–Time. Cambridge University Press. p. 1. ISBN 0-521-09906-4.

The background gravitational potential should be a reasonable candidate to represent the large-scale structure of the universe.

Dear Guoliang: the mentioned statement from wikipedia is an imprecise one at all, because you can not find any example of this claim, it is just a "conjecture" used mostly by philosophers not physicists, on the other hand in the same statement there can not be found any trace of "gravitational potential" which calculated simply by Newton gravity law as -Km/r and in GR by some additional term of higher orders.So gravitational potential "is not" a candidate for this very unspecified conjecture. this conjecture is a concept closer to philosophical view rather physical view.  

Dear Manouchehr,

Mach indeed was a philosopher, that's why he could not define the so-called large scale structure of the universe in terms of physics.

Functions of the gravitational potential are derived by myself, so you will not be able to find them except from my paper.

One way to present Mach´s Principle is to say that the relativistic energy mc^2 of a particle of mass m, m gravitational/inertial mass, is due to the gravitational potential energy of this mass with respect to de rest of the universe, seeable universe of size R and mass M. Then one may say

                                        mc^2 = GMm/R

or waht is the same          GM/c^2 = R , which is close to the Swarzschild gravitational radius of M, or the size of a black hole of mass M. If R is the size of the universe and if it is expanding then it depends on time and some of the "constants" G,M,c or a combination of some of them must be time varying. Unless the object of size R has R constant, there must be other properties time varying.

Dear Antonio,

I indeed have derived M/R=c^2/2G as formula (6.75) in section 6 of my paper, so I conclude that Mach's principle is consistent with functions of the gravitational potential. The universe has to be stable at its critical rest mass density in order to satisfy this formula. 

The question of what is dependent from what is always a difficult question, even in Econometrics a Nobel Prize was given for the so called Granger causality. Thus the answer is not an obvious one. Even if we find relations about fundamental constants, it is necessary to have a tested theory 'on hand' in order to accept the causality scheme that we have found. So, my answer is: Maybe.

I think it is an ill-posed question.

Guoliang,

I have just published research that will more or less answer your question. I have proven the inferred accelerated metric expansion is indeed an illusion due to local geodesics deflecting into a cosmological-scale gravitational potential, i.e. distant objects are accelerating into it (preprint is attached). Thus we see that observations such as distant SNIa provide a strict test for the evolution of G with respect to gravitational potential. For example, there have been many tests for the evolution of G, some of which can be combined with my recent discovery:

http://adsabs.harvard.edu/abs/2010HiA....15..311I

http://cds.cern.ch/record/520422/files/0109299.pdf

http://arxiv.org/pdf/1108.0859.pdf

Although some variation of fundamental constants cannot be ruled out with current constraints, any evolution at this point would be insignificant.

Скорость света не имеет отношения к гравитации. Гравитационное поле влияет на направление спина (константы Планка) атомов и молекул.

Hello Guoliang,

Thank you for sharing your efforts to find a self-defining cosmological model. I see that you are applying a standard engineering approach, normalization. I have seen a number of applications, the best known being the Reynolds Number. It only is meaningful if the factors are related to each other. Unfortunately, this is not known about your starting set.

The origin and formation of Gravity has been totally unknown, for instance, how it is created, how it relates to the other energies. All of the present models that I am aware of, including Einstein’s, start with gravity. Thus in their models, gravity is non-causative and the true property and evolution cannot be derived.

I did apply my knowledge of crystallization to model the formation of particles from energy to the formation of the Universe. Unforeseen, the model led causatively to the discovery that gravity is anti-energy. I just published the manuscript on my site on ResearchGate. The title is:

Here is the link to the manuscript. You can down-load the manuscript and study it for yourself. Maybe, it can help you in your study.

’ Formation of the Universe as a Crystallization Process and the Evolution of Gravity’

https://www.researchgate.net/publication/264339506_Formation_of_the_Universe_as_a_Crystallization_Process_and_the_Evolution_of_Gravity?ev=prf_pub

Much success for you, Ingo

Article Formation of the Universe as a Crystallization Process and t...

Dear Ingo,

Thank you for your comments.

I have discussed the origin of gravity in section 7of my paper: The gravitational force might emerge as a long range quantum entanglement entropic force from the intrinsic magnetic field of fermions. 

I had a peek at the abstract and the introduction of your paper. As you describe it, your work is anchored in the GR model and Einstein's work. Basically, I am supporting efforts to extract the enigma of Gravity from these models.

However, my approach is fundamentally different. I am hoping that you will have a look at my manuscript to see an alternative view. Gravity as anti-energy is a different understanding than bending of space etc. In the standard models gravity is not related to any other energy. Thus, the gravity = anti-energy prediction is a relationship that standard physics has not been able to make. By the way, my model and my research do not attack GR or any other standard physics.

Cheers, Ingo

Dear Ingo,

I have introduced the perfect vacuum full of Higgs field as a preferred flat space-time reference frame in my paper, so not only GR, even SR has to be revised. 

I have introduce the planet erosion process (.planeterosion.blogspot.hu).. which can be happen if the gravity force decreasing to an approximate 0 force onto an rocky planet surface... if the rocky planet has consumed majority of its core energy....  For this my opinion to you question is the funamental constants cannot be function of the gravitational potentional... 

László-Attila Horváth,

I have not found any fundamental constant in your so-called planet erosion theory, not even an equation, so I wonder how you have reached your conclusion. 

If you can point out which assumption in my paper is wrong, or which formula is wrong, it will be much appreciated.

IAs geologist engineer considering the Earth like object of research, the physical laws are onto planetogical scale… Newton interpretation was made such of scale… We know well that in time of Newton’s life, the geology like an independent science did not exist… From this and from the new data obtained (geological scale, solar system scale) exist lot of phenomena which cannot explained even if we are using universal constant of physics… My explanations are so simple that I do not need universal constant… 

I think, we cannot (at least not in the macrocosm) experimentally verify separately any force law or inertia force, we can only verify the validity of the equation of motion, which contains both laws. Each equation of motion can probably be re-wtitten in the dimensionless form (I did so for a trivial case of Newton and Coulomb laws in: arXiv:1206.0405), in which the gravitational constant, permitivity of vacuum, and Planck constant disappear.

Consequently, I think that if all physical laws were expressed in the natural physical quantities, there would not be any physical constants (with dimensions). In other words, we can ask: does nature know such the physical quantities, which were established by man, as e.g. "mass", or "electric charge"? It may not. So, the fundamental constants seems to be only the conversion constants between the quantities established by us (human beings) and natural quantities. Hence, I am afraid that the asked question may not be meaningful, in principle.

If the form of a physics law is changed with energy scale or temperature in microscopic scale because the value of the dimensionless electroweak constant is changed, then the principle of general covariance breaks down in microscopic scale.

When we assume all dimensionless constants will not change, we have to assume the principle of general covariance will never breakdown, but unfortunately it  fails in microscopic scale. Therefore, it is impossible to fit the quantum field theory into the framework of general relativity based on the principle of general covariance.

Dear Guoliang Liu ,

I think the gravitational constant is a function of the gravitational potential. See Model of Gravitational Interaction in the Concept of Gravitons at the link: http://vixra.org/abs/1209.0076

Dear Sergey,

Planck units are defined in terms of five fundamental physical constants; they are the speed of light in vacuum, the reduced Planck constant, the gravitational constant, Coulomb constant, and Boltzmann constant. Even though three out of five fundamental constants have turned into functions of the gravitational potential, Planck length, Planck charge and Planck temperature --three out of five base Planck units -- remain invariant in a gravitational field. Only Planck time and Planck mass turn into functions of the gravitational potential.

Einstein first mentioned a variable speed of light in 1907; he reconsidered the idea more thoroughly in 1911. But Einstein gave up his VSL theory for unknown reasons; it might be because he could not successfully identify all those fundamental constants controlled by the gravitational potential.

Then the constants are not constant, do you realize that? So rename them to functions. Have your functions some other constants inside? If yes, may be "John Smart" says: they are also not constant? Where this all ends? The basic dimensionless constant is 1, e.g. V = k h^3, k = 1. If the final theory has no constants whats or ever, then, in final, we are all dead.