What causes the gravitational constant? Is it truly a constant? What makes gravity universal?

Within Newtonian theory and General relativity, it is a fundamental constant. In more speculative theories like Supergravity or string theory, it is a derived quantity from other fundamental constants. In these theories, it can change its value in time, but there are rather strong experimental bounds on it.

I didn't read the question to end. G sets the scale in general relativity. With another fundamental constant C, it sets how much spacetime should be curved given a quantity of energy. Role of any fundamental constants are this. For example, Planck constant sets the scale of energy in quantum theory.

The axiom of choice.

Hey Prakash - how did you calculate this? The dimensions of the gravitational constant are not consistent with a mass divided by a length squared.

Like Prakash, I think that the mass of the universe and space are involved in determining G but I also think that time must be included. In other words, I believe G is determined by values of mass and space-time. I also think Demian is right to mention the role of curved space-time. I look at it this way: At the deepest level of reality the only real things are energy and space-time and they're in a dance with each other curving space-time. This curvature causes gravitational fields and those fields accelerate the quantum particles we observe at a higher level of reality. Einstein's key insight that being in a gravitational field is equivalent to being accelerated means that the energy fluctuations are accelerated and anything that's accelerated, according to special relativity, acquires mass. The slower an energy fluctuation (which we observe as a particle) moves the more it can be accelerated and the more mass it has. Thus, at the deepest level of reality, mass is caused by gravity. If this makes sense, then it's illuminating to explore the consequences of viewing E=mc^2 as a constraint on the evolution of space-time in the universe as well as in any gravitationally bound portion of space-time in the universe. It appears to require augmenting the gravitational fields predicted by general relativity thus providing an explanation of dark energy and dark matter.

Thanks for the feedback! There are some thought provoking responses here. Any suggestions on how to investigate this matter further?

There are two experiments going on right now, David that will shed light on my conjectures. If the OPERA experiment that seems to show neutrinos moving faster than the speed of light is confirmed, the most logical explanation will be that the speed of light itself is increasing. Otherwise special relativity would have been shown to be wrong and the very foundation of physics would be undermined. If the experiment is confirmed it would be strong evidence that my conjecture about the applicability of E=mc^2 to all space-time scales might be right because it requires the speed of light to change. The other experiment is the LHC search for the Higgs boson. If it's found, my conjecture about gravity being the cause of particle mass could still be right because the Higgs could be seen at the level we can observe with gravity being the underlying cause of mass at the deepest level of reality. But, if it's not found, physicists will be faced with the question of what else causes mass. They will certainly start to consider a gravitational answer to that question.

Dear David,

Yip, a pretty difficult question. Usually one would say, well G just is. In fact an equally difficult question would be: "why is the Sun in the one focal polnt of the ellips that the Earth follows, and not in the other".

Seriously, recently Eric Verlinde has caused some unrest by suggesting that Gravity is not really a fundamental force but rather an 'emergent' force stemming from differences in 'information' over and through horizons. The situation there is a bit unclear still.

Kindest regards, Henk Smid

Hi Prakash,

Interesting idea. But isn't the radius of the universe changing as it expands? Also, how does your theory account for dark matter/dark energy?

Prakash,

I don't get the idea, why should the escape velocity of the universe be equal to c?

Thinking about the universe as a analogous to a black hole is a bite awkward to me. Can you show the link of some paper (or something) that use this concept?

Prakash, I've written a paper called "A Theory of Everything" that I've just sent to David for his review. It details the conjecture that I mentioned in an earlier comment about the constraint on the evolution of spacetime imposed by the requirement that E must equal mc^2 in the universe and all gravitationally bound entities in it. It seems that the consequences of this constraint explain a lot of things; like dark energy, dark mass and what caused inflation.

Solo he encontrado un a respuesta a lo que es la gravitacion,,y es que es un a diferencia de energia temporales,,,,acabo de introducir el tiempo como energia....l

No se ingles,sr prakash

If somebody writes something in another language, you can attempt to translate it into English using an online translator, like translate.google.com.

Mr. Soto Colpiante said something to the effect of, "I've only found one to answer to what is gravitation, and that is that unlike a temporary power,,,, just enter the time and energy .... l"

His second response was something like "I don't know English."

My studies in gravitation only used G as a constant, so any theoretical calculations using G as a variable is not something I am familiar with. If it helps my work with G allowed me to mathematically calculate the Hubble constant very accurately and eliminates the need for dark energy/matter. Admittedly, the majority of cosmologists believe that dark matter/energy is in fact real. You can obtain my calculations as an appendix to the book, "The Permutanomicon", which is actually a study in Physics and AI.

It would be interesting to see a side by side of calculations using G as both a constant and a variable and see what the math turns up.

el traductor de google no me ayuda demasiado,,,lo que intente explicar fue:El tiempo es energia,luego esta energia se disipa con la distancia.Un cuerpo cualquiera tiende a moverse hacia donde la energia es mayor.

Ricardo say's is

"google translator doesn't help me a lot, what i wanted to explain is: time is energy, then this energy dissipates with distance. Every body tends to move towards where energy is greatest. "

In Newton's theory of gravity, the gravitational constant is a constant of proportionality which is determined by experiments. Einsteins general relativity (GR) is is also a generalized relativistic theory of gravitation in which Newton's is a limit in the case of a weak fields, and here that the gravitational constant took place on GR.

David Alexander: in F=G(m1.m2)/r², you can understand G as the value of the force when the value of the masses is 1 and the distance is 1, in the units you choose. You can also choose G=1 without dimension, then you will have a relation between masses and distance, frequently used in GR.

If it is truly constant may have two interpretations: 1- if it is constant at this cosmic time in the whole Universe (if we accept the universality of Newton's law then, the answer is yes). 2- if it have got the same values from the beginning of the times. Here there are models that consider a variable G. A beatiful book is that "Six numbers" by Sir Martin Rees.

I agree with Prakash that your answer is beautiful, Horacio Dottori. The approach you described of setting the value of something in an equation to 1 is a powerful way to understand things. If you're a mathematician think of choosing the right units of measure to do that; or, if you like to think abstractly, think of viewing the system described by the equation from the perspective of the thing you want to give the value of 1 to. For example, consider the equation E=mc^2. If E=1 you have a relation between mass and the speed of light; if m=1 you have a relation between energy and the speed of light; if c^2=1 you have a relation between energy and mass. Thanks again, Horacio Dottori for sharing your insight with us.

Ernesto Ulloa's comment is correct.

There is a related article: Wun-Yi Shu, Cosmological Models with No Big Bang.

Why should G be an universal constant? It kind of sounds another example of Earth centric thinking. Here's functional model with calculable G (based on object's spin frequency) http://toebi.com/documents/ToEbi.pdf

As a bonus, the model covers all interactions based on spin frequency (paradigm).

In these questions what must be specified is what is understood and known to be true (Feynman) and what is being sought. The gravitational constant is the coupling constant of the gravitational force, which is one of the fundamental interactions. That has turned out to be the most useful way of considering it. Gravity is ``universal'' in the sense that, in the Newtonian approximation, all masses attract each other with a force proportional to the gravitational constant, independently of the composition of the masses and, in the relativistic case, the metric tensor, that specifies spacetime, couples to the energy-momentum tensor, which specifies the right hand side of Einstein's equations and, thereby, determines the metric. Universality means here that matter enters Einstein's equations *exclusively* through the energy-momentum tensor.

As far as we can tell, based on experiments and theory, the gravitational interaction, like the electromagnetic, weak and strong interactions, cannot be expressed in terms of other interactions, therefore starting from it and the other three, we can perform calculations and do experiments, i.e. do physics.

In particular, we know, since the the work of de Sitter and Friedmann in the 1920s that Einstein's equations do have solutions that describe an expanding Universe, even though the gravitational constant is constant. This is, by now, described in all textbooks on general relativity.

On the other hand, we understand the gravitational interaction only semi-classically-we do not have a quantum theory of it, like we do for the other interactions. We do not know how to take into account spacetime geometries, that are not solutions to the Einstein equations, in full generality. So we do not know how to calculate ``quantum backreaction'', for example.This is the major obstacle in describing Hawking radiation from black holes in detail, for instance.

Open letter.

Dear Prof. Matts Roos,

I use an opportunity given by the ResearchGate site organizers to address this letter to you as to one of the most experienced if not the most experienced in the cosmology ResearchGate member and author of the book “Introduction to cosmology”.

This my action is induced by the opinion that astrophysicists, as scientists of no other specialty, are responsible vis-a-vis the population for its naturalistic world outlook and by the believe that, in sciences, truth is always better than notorious invention.

The present astrophysics, including all its conclusions on the allegedly actual occurrence of such celestial objects as the dark matter and dark energy, black holes and different colored dwarfs, etc., on their sizes, ages, and distances between them, on the Universe age and size, and on the nature and transformations of the celestial objects and the Universe as a whole, is based on four assumptions which, being taken together, represent the basis for all subsequent calculations and conclusions. These assumptions are made about 90 years ago and, thus, are bases on the level of knowledge of those times and were intended for the explanations of the observations then available. The assumptions are as follows.

(i) Stars exist and transform as a result of three-dimensional fusion reactions in their interiors, and just these reactions are the source of the stellar luminosity, heat emission, and other forms of radiation (Eddington);

(ii) The parameters of the stellar state can be calculated on the basis of the ideal-gas laws (Eddington);

(iii) The gravitation coefficient value inherent in the Solar System is applicable to the entire Universe (Einstein, Special Relativity and General Relativity);

(iv) The speed of light is constant and identical everywhere over the Universe (Einstein, SR and GR).

None of these assumptions was proved.

The acceptance of the assumptions (i) and (ii) can be explained only by the absence in the 1920s of any alternative explanation for the solar luminosity and energy and neutrino emission. Indeed, it is unthinkable that a fusion reaction could proceed stationary over giant volumes of a pressed substance with liberation of so small specific energy amount as it is observable for the Sun and that the behavior of a hot highly-concentrated plasma might be assimilated to the ideal gas. Of course, “explanations” for these imaginary phenomena were invented, but they look like a square peg in a round hole. Just these assumptions were put in the basis of this so-called standard solar model which, in turn, represented first floor for the building of fantasies, including the structure and history of the stars, origination of chemical elements, etc.

Today, we have an alternative explanation for the solar luminosity and energy and neutrino emission, this explanation in its common form being apparently applicable to other stars independently of their age and sizes. Isn’t it time to look critically at the fundamental assumptions of almost 100-year age and at the entire building constructed over them?

As for the assumption (iii), it is, as least, questionable, because it is quite unconditioned and nothing counts in its favor, although there are no proved objections against it.

The assumption (iv) is, in our opinion, completely unacceptable as a ground for any earnest conclusions on the Universe as a whole. However, this statement requires a rather detailed substantiation.

We see three factors that force us to doubt in the constancy of the light speed and direction (We think that it is clear that the variations in the direction are equipollent to variations in the speed) over the Universe. Moreover, we think that the speed of light should be dependent on the distance and, there is very likelihood, on the time by the following reasons:

(x) The gravitation coefficient might be different in different stellar systems or, all the more, in different galaxies. It is observationally shown that light deviates in gravitation field (just such an observation was taken as a confirmation of Einstein’s earlier theory). If the gravitation coefficient is different over the Universe and changes in an unknown manner, the light speed out of the Solar System is unpredictable.

(y) Even if the gravitation coefficient is the same over the Universe (We have grounds to think that this is improbable; see below), it is possible that light propagates through the inter-galaxy space, in preference, along the between-galaxy channels and through the intra-galaxy space, in preference, along the between-star channels , where gravitation to the adjacent objects is compensated; thus, it can propagate in a straight line along great but limited distances and, when propagating through multi-galaxy distances, choose the directions of minimum resistance; in this case, its direction is also unpredictable.

(z) In the 20th century, after development of the quantum field theory (1934), an opinion existed that gravitation is a property of each atom as such and that this property is caused by the existence of gravitons, i.e., massless spin-2 boson particles that represent carriers of this property. However, no gravitons were discovered within nuclei, in spite of their 80-year searches over the world. Eighty years is a rather long period; today, it is necessary to be rather obstinate optimists to wait the discovery of such particles and there are no scientific ground to believe that the gravitation constant is the same over the Universe; the recent LHC experiment is the source of optimism for some physicists, however no consensus exists even among its participants. It must not be ruled out (although we do not undertake to state) that gravitation is an integral feature of the space/celestial-body system but not the feature of each atom and that this feature depends on the size and, may be, age of the star that forms the stellar system.

We wrote earlier about a wide criticism relative to the present calculations of the masses and distances for the celestial bodies. Eddington’s assumptions are arbitrary, like the assumption on the over-Universe constancy of the gravitation coefficient and on the light speed constancy over the Universe, and the miracles, to which this set of assumptions has led the astrophysics, show that these assumptions should be turned down. Therefore, we state that not only the Universe expansion is questionable. The opinions on the natures of the so-called standard solar model, all dark things, black holes, variegated dwarfs, etc. should be reconsidered. At the ResearchGate site, a number of researchers had tried to make objections against this our conclusion but nobody of them presented scientific proofs counting in favor of these products of hypnotizing imagination. We are sure that the half-hearted hypotheses are scarcely acceptable. If a pseudo-science is build on sandy dunes, it is necessary to be ready that the sand may begin to move in any day. And, please, demonstrate your magic wand, if you have it. The today astrophysics includes the entire set of the four assumptions listed in the beginning of this letter; rejection of any one of them would lead to its full dismounting. Meanwhile, three first of them are not proved and the fourth one is practically disproved by the occurrence of the so-called Einstein’s rings and other figures obtained as a result of not-direct light incidence on an object. It is difficult to ignore that light is capable of changing at any boundary, where the space density varies.

The occurrence of the so-called Einstein’s rings in their ideal or deformed variants shows that the time of light propagation from any object to the Earth can’t be used to determine the object-Earth distance even if the gravitation coefficient is constant. (Really, there is quite likelihood that it is non-constant.) Einstein’s mistake who took in the SR and GR that the light speed is constant and identical everywhere over the Universe is explainable: he can’t know that, 50 years after his death, Hubble will discover on the vault of heaven a great number of rings and similar figures and so many “glowworms” that, even if 99.99% of them represent mirages, the real quantity of the stars is immeasurably greater than it was known in his time. May be, in the Universe, which was known to Einstein, it was possible to take approximately that light propagates in straight lines, but in the Universe, which is known to us after studies by Hubble, light propagates by more complicated routes.

Apparently, only one explanation of these phenomena occurs: if an illuminating object, the center of a half-way galaxy, and an observer are along the light stream (the conventional wisdom that these three objects should be along a straight line is not quite correct, because light deviates in gravitation fields) and if no other galaxies exist along this line, the observer sees a dark disk and a light ring around it (very random situation); if the light direction from the illuminating object is somewhat shifted from the center of the half-way galaxy, the observer sees any other more complicated figure instead of the ring (not so random situation). Thus, Einstein’s figures are observable as the result of rounding the half-way galaxies by light. However, it is clear that not the entire outer radiation rounds the half-way galaxy and the excluded light streams not necessarily interlock after it. Depending on the light pitch angle, on the galaxy size, and on other causes, some portions of the primary light stream pass through the galaxy and are being absorbed, reflected, and scattered by it. Apparently, just the scattered and reflected light is the cause of the observable space background radiation.

This means that a major portion of light doesn’t go through galaxies but chooses the way around them, where there is no gravity, and may go down and bifurcate. The way of each portion of a primary light stream from a radiating celestial object is much longer than the straight distance. The light from any remote star may round many galaxies. Therewith, it may separate, may walk over the Universe, and may come to the Earth even from a direction that is opposite to the real direction to the real remote star. Moreover, a portion of the light should be reflected and dissipated over the space.

We address ourselves to you as to one of the main advocates of the widely distributed understanding of the Universe with the following concrete questions and we are waiting unambiguous answers to them.

(1) Is there any scientific proof that stars exist as a result of fusion reactions within them, or is this assumption taken only because there is no other idea to explain the stellar emission of light, heat, and neutrinos and the mechanism of formation of chemical elements?

(2) Is there any scientific proof that stars can be assimilated to balls of ideal gas to calculate their state independently of fulfillment the previous assumption, and is there the confidence in correctness of such calculations if the previous assumption is fulfilled and stars represent highly-pressed concentrate plasma?

(3) The independence of the gravitation coefficient over the Universe and time, can it really be obviously true and are there any scientific proofs that the gravitation coefficient is constant over the Universe?

(4) Are there any scientific proofs that the speed of light is constant over the Universe?

We contend that all these assumptions are artificial, wrong, and smell of the lamp, and their application had led to nothing but secondary fantasies, such as dark matter and energy, black holes, expansion of the Universe etc.; the masses, speeds, and distances of the celestial bodies are obtained just on the basis of these four fantastic assumptions supplemented with different other no more grounded fabrications. And I think that any attempts to save the widely distributed views on the Universe are today in the Internet epoch senseless.

The available notion of the way of formation of the chemical elements is too complicated and requires several meets of several objects and rather questionable processes, such as many-parsec collapses, their initiations, supernova, etc. Too many of unknown and questionable things are used to explain the incomprehensible things. Meanwhile, Nature is simple and doesn’t luxuriate in excesses. Such a complicated way of formation of the chemical elements is of low probability for one realization and is scarcely possible for billions realizations in any one galaxy. The explanations for such phenomena as the solar corona high temperature, high planetary moment, periodicity of the protuberances and of the variability of the magnetic moments, isotopic anomalies, cold Bok globules, and many others are obscure and can be easily subjected to criticism.

The following group of our questions to you relates to the understanding of the Origin. In our opinion, when discussing Origin, scientists should keep in mind that Origin, according to the content of the term, should be absolute, i.e., the questions about the events and phenomena, which had been occurring before Origin, should not arise at all and that there are no grounds to ignore the physical laws of conservation and the laws of thermodynamics. Meanwhile, the notion of the so-called Big Bang fulfils none these conditions. In the philosophical plane, it cannot be considered as the Origin. The notion of it has no physical ground because the expansion of the Universe is no more than a myth, put new unreciprocated questions about the pre-explosion events, previous history of the "neutron egg" and “energetic field”, time and events before it, etc., and assumes its appearance outside physical laws. This notion solves no problems but initiates a number of new problems and has no scientific grounds. In this connection, we ask you for answering the following question:

(5) Do you have any opinion about the appearance of those materials that were the subject of the so-called Big Bang?

Meanwhile, apparently, there is a unique solution that leads to no additional problems. Only one solution is irreproachable from the scientific point of view, can be proved from the contrary and leaves no additional questions; it is given by Friedrich Engels (“Natural dialectics”, Papers, any edition: the last page of the Introduction) in his discussion with Eugen Dührings: “universe is eternal and infinite”. Not all agree to this, but, unfortunately, there is no absolutely closed question over the world. We put you one more question:

(6) Do you object to this Engels’s solution, and, if so, can you formulate your principal objections?

I use, may be, too undisguised expressions. I ask you and all readers of this open letter to excuse me for the intransigence. The fact is that the many-decade scientific activity has taught me that science has no intermediate solutions and that efforts of accommodation of conflicting interests are non-productive.

I think that the notions of fusion reactions within stars, gravitation coefficient and light speed constancy over the Universe, and stars as balls of ideal gas are the viruses of the terrible disease. No one of these assumptions is confirmed with independent measurements, and they led to ideas fix on the dark matter, dark energy, black holes, Universe extension, and Big Bang as the consequence of this entire devilry and just the shock therapy is the unique medicine for this disease. In any other science, any one of similar results would be sufficient to set aside the system of the initial assumptions and to start the construction of the scientific building on a new fundament. For 90 years, there was no new fundament. Today, such a fundament occurs. The rejection of the notion of fusion reactions is necessary because it was possible only at the dawn of discovery of such reactions to believe that they can be localized by Nature within giant volumes with no explosion, because the notion of fusion reactions gives no possibility of going to a realistic notion of the mechanism of formation of chemical elements, and because of other causes about which we wrote above and in our published works.

Until no new hypothesis was available, the criticism against the old one was non-productive because it could create a vacuum zone and because each vacuum zone in the system of knowledges is dangerous as different superstitions rush there.

The times have changed after formulation of the PFO-CFO Hypothesis by me together with Elena Kadyshevich, and its ignoring under Internet is senseless. Its first version was published in the Advances in Plasma Astrophysics, 2011; and, at present, we propose for discussion the works of 2013. The PFO-CFO Hypothesis is presented at the ResearchGate in its development including its finish state of 2013; it includes our version of the mechanism of formation of stars.

The main principles of the hypothesis are as follows.

The Universe is eternal and infinite, and the space consists of energy/mass of a low concentration and has infinite rotational moment. The stars are the knots in the energy/mass space. No fusion reactions proceed within stars. Just radiochemical decays over the stellar vicinities represent the unique alternative to fusion reactions. The energy/mass transformation into matter starts within stars and finishes in their surroundings. In each stellar system, all chemical elements originate over the star vicinity from radioactive and non-radioactive pico-drops of the stellar substance and just the radiochemical decays are the source of the stellar luminosity and heat-emission, the neutrinos resulting from the beta-decays of the pico-drops. The planetary systems around stars are formed on the basis of the stellar substance emitted by protuberances and as results of explosive destructions of the stellar radiation zones, after which stars return to their initial state. The hypothetical mechanisms of all processes are described in the available publications.

I am waiting for unambiguous answers to questions (1) – (6). And I think that not only I am waiting for your answers.

The point is that the conclusions on astrophysical problems are of great public importance; they propagate over the world by the mass media, writers, etc., get into the scholar books, and are taken by the population as the reality. Therefore, I think that, at least, the degree of validity of each statement should be strictly determined by the most experienced scientists and the assumptions underlying these statements should be clearly outlined. It is an open secret that the results in the field of astrophysics are of ideological importance. Thus, the responsibility of each researcher who works in the field of ideology is too high vis-a-vis the population to be ignored.

Sincerely,

Victor

Viktor, this is not the appropriate language for a scientific discussion. If you use phrases like "pseudo-science build on sandy dunes", "magic wand" for mainstream science, it cannot be expected that you will be taken seriously. If you, after this, use Friedrich Engels in a role of scientific authority, you are out.

Then, it seems you have no idea about modern scientific methodology. Scientific theories are hypotheses, they cannot be proven. They can be corroborated by evidence, if predictions derived from these hypotheses are confirmed by observation, that's all.

About your main idea: Ok, light is curved by gravity, so we cannot be sure if light which arrives here from direction A really comes from direction A. But how often this happens, and how much the direction will be changed? This is something which can be computed. You haven't. Then, such a change of direction by heavy matter does not lead to a redshift. But the background radiation is highly redshifted.

In my works, G is derived from G-L theory applied to nucleon substructure and is related to Planck lenght and quarks string force, so to paricles. I have demonstred a firmly connection between Gravitation and Quantum Mechanics-QCD.

Prakash:

I think that the idea that the universe may be a black hole has been raised quite a few times - it's certainly a staple in science fiction! The problem is how to turn the idea into something that produces testable predictions (or explains some feature that otherwise seems anomalous).

The use of the idea that springs to mind is Lee Smolin's "Fecund Universe" hypothesis.

Smolin's suggestion (as reported) was that our universe's fundamental parameters seem fine-tuned to encourage the creation of black holes, and that this could be explained as the by-product of a sort of Darwinian evolution in which universes could contain black holes whose interiors represented baby universes that in turn could contain more black holes.

The idea was then that if universes inherited fundamental constants that were based on those of their parents, then universes whose constants encouraged a larger number of black holes would have more children, and for a randomly-selected universe, if would be statistically much more likely that this universe would have black-hole-friendly constants than constants that made black hole formation more difficult.

(universes that contained no black holes would be in the minority, because they wouldn't have any offspring and would therefore be badly outnumbered by the offspring of those that did).

Then again, I suppose that it's a difficult hypothesis to test ...

In a discussion that was supposed to be about whether the gravitational constant is really a constant, it's surprising to me that no-one has mentioned the Brans-Dicke theory of the 1960's, which modified Einstein's gravitational theory by replacing the gravitational "constant" by a scalar field.

[Perhaps it's the Higgs field... (-; ]

PS: An interesting curiosity: The Kaluza-Klein theory (GR in 5 spacetime dimensions) gives the usual equations for gravity and electromagnetism in four dimensions. The metric component g55 is presumed to be constant. If that restriction is removed, we get GR + EM + BD.

@David Alexanderand and about the original question.

General Relativity (GR) is the most accurate theory of gravitation we have so far. It predicts the behavior of gravitational phenomena in a large range of scales, from micrometers to pulsars with a remarkable precision. Moreover, if you add a bunch of exotic (dark matter) particles and a cosmological constant (which by the way is allowed by the fundamental principles from which GR is "derived"), the range of its validity has been tested up to scales beyond the cosmological Hubble horizon = 1/H.

In GR the gravitational constant G is a conversion factor and can be defined simply as G = G_mn / 8 pi T_mn , for all m and n fixed. Nevertheless, there is no mathematical reason of why G must be a constant. You can promote G to be a field in spacetime, say a scalar field, but in doing this you must add a dynamical tensorial term for this field, otherwise general covariance is broken. By doing this, you finally will end up with a Scalar Tensor Gravity, as in Jordan-Brans-Dicke theory.

The discussion initiated by Prakash Kumar is very interesting, and the fact that the Scharzchild radius of the Universe coincides with its "size" = 1/H should not be treated as a simply coincidence. This ideas could point in the direction of an evolving gravitational constant.

No, it's not possible to divide by a tensor, so the assertion doesn't make sense. Within general relativity, Newton's constant, defined from the prefactor of the term of the Einstein-Hilbert action that multiplies the Ricci scalar, must be assigned a value-its value cannot be predicted from solutions of the classical equations of motion. If the cosmological constant is taken into account, as it must, since it is, also, consistent with all the symmetries, the solutions depend only on the ratio of the cosmological constant to Newton's constant, multiplied by some scale, to make the ratio dimensionless-and there exist solutions for any value of this ratio.

@Stam Nicolis

The equation I wrote is not tensorial, it is for fixed n and m, and it is valid in any chosen coordinates. But anyway, I agree that it is not the best definition of Newton's constant, because Einstein's equations vacuum solutions, where the above definition does not hold, are not trivial; and although the Ricci tensor is zero, the Riemann and Weyl are not. Of course, one can remove this ambiguity by saying that G is the constant that appears in Einstein's equations in order to the rhs and lhs have the same units. No more nor less at the classical level.

G has origin in density of quantum vacuum. 

see my work :what is gravity...  http://vixra.org/pdf/1507.0207v2.pdf

Although not my primary field, I came across a derivation of G based upon cosmological expansion.