What is the Fine-Structure Constant and its Relation to Gravity?

[rubi32]

Hi, I'm new posting to these forums, so I'm not sure if this is in the right place. Anyway, here it goes:

I've done a lot of research (on my own and in college; academic articles, educational videos, etc.) about astrophysics, and I've always been fascinated by the concept of gravity. Gravity is what makes life flow; it is the causation of all macro-events (so we think), and is still one of the greatest mysteries to puzzle mankind. As we know, the Newtonian view of gravity doesn't really work. Right now, though, we think that Einstein's general relativity model does. However, after spending hours looking over it, it doesn't quite seem to fit to me(or at least it's not polished). I certainly agree that the general concept is sound (with rifts in space-time being the causation for gravity, force, perception of time etc.), and that there is something out there that mass alters, but I've always wondered about space-time's mechanical properties.

Space-time is often assimilated to a fabric that can be folded and dimpled by a mass--but I think that this is a very narrow view. In order to make an indentation, would the mass not have to make an impact in space-time, thus already exhibiting the properties that space-time supposedly gives it? In essence, how is a mass--let's say a planet--supposed to warp this fabric in a way that implies a force, if it's force is inherent in the warp in space time? Even further, why is space-time represented as a single fabric, a two-dimensional entity? What tells an object to travel along this indented, two-dimensional path in a three-dimensional world?

Does anyone with more knowledge on this subject have any input? I am aware that I have no foundation on which to assert my argument, but I've always found these questions/observations puzzling.

 

[strangerep]

However, after spending hours looking over [GR], it doesn't quite seem to fit to me(or at least it's not polished).

"Hours", huh? You think you can acquire an understanding of GR in a matter of hours?? It takes a lot longer than that to achieve even a basic understanding.

how is a mass--let's say a planet--supposed to warp this fabric in a way that implies a force, if it's force is inherent in the warp in space time?

The curvature of 4D spacetime is determined by the energy-momentum tensor of matter fields, via Einstein's field equations.

why is space-time represented as a single fabric, a two-dimensional entity?

It's not. Spacetime is 4-dimensional (3 space and 1 time).

What tells an object to travel along this indented, two-dimensional path in a three-dimensional world?

Small test particles travel along geodesics in the curved spacetime, just as they follow a straight line in a flat spacetime. (A geodesic is a path of shortest length.) This can be derived from the Einstein's field equations.

Does anyone with more knowledge on this subject have any input?

Input? Well, yes -- you really need to try and study some proper textbooks. This forum is intended for discussions at graduate-level and higher. Also, questions on General Relativity should be asked in the Relativity Forum (surprise!).

 

[HallsofIvy]

Hi, I'm new posting to these forums, so I'm not sure if this is in the right place. Anyway, here it goes:

I've done a lot of research (on my own and in college; academic articles, educational videos, etc.) about astrophysics, and I've always been fascinated by the concept of gravity. Gravity is what makes life flow;

I don't know what you mean by this. There are four "fundamental forces", gravity, electro-magnetism, the strong nuclear force, and the weak nuclear force. They are equally important to life or any other property of the universe. (Actually gravity is the weakest of them.)

it is the causation of all macro-events (so we think), and is still one of the greatest mysteries to puzzle mankind. As we know, the Newtonian view of gravity doesn't really work. Right now, though, we think that Einstein's general relativity model does. However, after spending hours looking over it, it doesn't quite seem to fit to me(or at least it's not polished). I certainly agree that the general concept is sound (with rifts in space-time being the causation for gravity, force, perception of time etc.), and that there is something out there that mass alters, but I've always wondered about space-time's mechanical properties.

Space-time is often assimilated to a fabric that can be folded and dimpled by a mass--but I think that this is a very narrow view. In order to make an indentation, would the mass not have to make an impact in space-time, thus already exhibiting the properties that space-time supposedly gives it? In essence, how is a mass--let's say a planet--supposed to warp this fabric in a way that implies a force, if it's force is inherent in the warp in space time? Even further, why is space-time represented as a single fabric, a two-dimensional entity? What tells an object to travel along this indented, two-dimensional path in a three-dimensional world?

Does anyone with more knowledge on this subject have any input? I am aware that I have no foundation on which to assert my argument, but I've always found these questions/observations puzzling.

 

[Nugatory]

Even further, why is space-time represented as a single fabric, a two-dimensional entity? What tells an object to travel along this indented, two-dimensional path in a three-dimensional world?

It sounds very much as if you've been misled by the so-called "rubber sheet" pictures in the popular press, which shows a two-dimensional surface with an indented dimple and the mass at the bottom of the dimple.

That's not a good starting point for understanding GR. You might try searching this forum for the really excellent animation done by user A.T. to explain how curvature really works.

 

[rubi32]

Thanks. Sorry, I definitely put this in the wrong forum. I have very little knowledge of high-level astrophysics, and was just putting out a few things I questioned. Wasn't trying to rewrite the laws of physics lol.

 

[gabriel.dac]

You don't seem to know much about relativity, and there is nothing wrong with that.

Space and time are related. They are the two sides of the same coin. A massive object like a planet curves the space time and objects just follow a straight line. Technically gravity isn't a force. Objects in orbit are just following a straight line. They can't know that the space is curved

 

[Naty1]

John Wheeler said

"Matter tells spacetime how to curve, and spacetime tells matter how to move."

Spacetime curvature IS gravity...three dimensions of space and one of time.

Try reading here for a bit more of an introduction:

http://en.wikipedia.org/wiki/Gravity

and try here for some background on spacetime

http://en.wikipedia.org/wiki/Spacetime

You should note that while relativity is focused on three dimensions of space and one of time, other theories include many more dimensions...

 

[A.T.]

Even further, why is space-time represented as a single fabric, a two-dimensional entity?

Because humans can't even visualize flat 4-dimensional manifolds, yet alone curved ones. You reduce the dimensions of the manifold, to visualize its curvature by embedding it in a higher dimensional flat manifold. Since flat 3D is the limit for intuitive human understanding, 2D is the intuitive limit for curved manifolds.

What tells an object to travel along this indented, two-dimensional path in a three-dimensional world?

When no forces act on the object, it follows a straight line in distorted space-time. This animation shows this better than the indented rubber sheet you are referring to.

https://www.youtube.com/watch?v=DdC0QN6f3G4

 

[Dale]

What tells an object to travel along this indented, two-dimensional path in a three-dimensional world?

Inertia. Inertial means that in the absence of an external force an object travels along a geodesic. In flat spacetime this means traveling in a straight line at a constant velocity, but when the spacetime is curved these "straight" lines (geodesics) become more complicated.

One of the great theoretical accomplishments of GR is to unify inertia and gravity. Prior to Einstein it was recognized that the passive gravitational mass was equal to inertial mass, but it was not known why. Afterwards, it became clear that they must be equal since gravitation is inertia in curved spacetime.

 

[yogi]

Hi rubi 32. Its ok to be apprehensive about any theory - If Einstein were alive today, he would likely agree - historically, Einstein's thinking changed over the years. In 1916 he was convinced the universe was static and closed. As first published the theory couldn't work because a static universe would collapse due to gravity. Moreover, the theory is incomplete even today as it does predict the gravitational constant - G is inserted from the measured value, and it is G that tells space and time how to obey. In spite of these shortcomings, the theory is considered an epic of theoretical physics, it makes predictions that have been verified and could not be understood or even appreciated prior to General Relativity. Over the years other theories of gravity have been proposed based upon Mach's principle, scalar-tensor and like. A good book that ties history and physics together at an undergrad level is Ed Harrison's book, "Cosmology, the Science of the Universe.

 

[Naty1]

yogia:

Moreover, the theory is incomplete even today as it does predict the gravitational constant - G is inserted from the measured value, and it is G that tells space and time how to obey.

I think this is supposed to say .." as it does NOT predict the gravitational constant"
which is a common occurrence in many of our theories.

GR also seems to be incomplete , to fail, at points of extreme gravity, extreme curvature, such as the center of black holes at at the Big Bang. At these places, infinities are predicted yet noinfinites have ever been observed.

 

[ZapperZ]

Moreover, the theory is incomplete even today as it does predict the gravitational constant - G is inserted from the measured value, and it is G that tells space and time how to obey.

Do you know of ANY theory in physics that's "complete"?

Zz.

 

[Dale]

Moreover, the theory is incomplete even today as it does predict the gravitational constant - G is inserted from the measured value, and it is G that tells space and time how to obey.

This isn't a limitation of the theory (although there are limitations such as that mentioned by Naty1). It is an artifact of our system of units. We can set G to any value we like by simple choice of units, and frequently we choose to set it to 1.

See: http://math.ucr.edu/home/baez/constants.html

 

[yogi]

Do you know of ANY theory in physics that's "complete"?

Zz.

Good point Zapper - no theory is ever complete - I recall a statement from Hawking years back. We have two theories of gravity and neither can predict its strength, nor do we as yet have a theory to explain the magnitude of the electron charge.

I guess I will have to get to work on it

 

[ZapperZ]

Good point Zapper - no theory is ever complete - I recall a statement from Hawking years back. We have two theories of gravity and neither can predict its strength, nor do we as yet have a theory to explain the magnitude of the electron charge.

I guess I will have to get to work on it

Then please note that the "incompleteness" of GR is NOT a "problem" here, the way you had written earlier, since every theory in physics can be considered as incomplete. Practically every single theory in physics have to use values that are experimentally derived, and not from First Principle calculations.

Zz.

 

[yogi]

Then please note that the "incompleteness" of GR is NOT a "problem" here, the way you had written earlier, since every theory in physics can be considered as incomplete. Practically every single theory in physics have to use values that are experimentally derived, and not from First Principle calculations.

Zz.

That is true - there are no "first principle calculations" and that is the basis for my observation - the so called constants have dimensional units that relate their properties to one another. General Relativity is descriptive at the point where functionality is needed. Einstein did the best that was possible with the knowledge of the day. As in Special Relativity, He turned the problem into a postulate - a century later there is still no satisfactory explanation as to how inert matter can distort static space.

"What I cannot create, I do not understand" Written by Richard Feynman in the corner of his office blackboard at Caltech where it remained for more than 8 years

My object in commenting to this o.p. and others who have ventured to inquire with a criticism of a standard theory that nobody really understands (Like why G has the value we measure in relation to the value of something else we also measure) is to blunt some of the harsh criticism heaped upon new posters ... I sometimes get into trouble for this.

 

[Dale]

That is true - there are no "first principle calculations" and that is the basis for my observation - the so called constants have dimensional units that relate their properties to one another.

Again, dimensionful universal constants like G do not represent any limitation of any theory. They are simply artifacts of our system of units. There can never be any "first principle calculations" because they don't come from physics at all. They come from our chosen system of units. That is all.

a criticism of a standard theory that nobody really understands (Like why G has the value we measure in relation to the value of something else we also measure)

That simply isn't correct. It isn't a criticism of any theory, and we understand completely. G has the value it does because we use the units we use.

 

[yuiop]

That simply isn't correct. It isn't a criticism of any theory, and we understand completely. G has the value it does because we use the units we use.

What about when we compare the force of gravity to something like the strong nuclear force at short range. The ratio is then independent of the units used and as far as I know there is no way to predict why the dimensionless constants have the values they have.

 

[Dale]

What about when we compare the force of gravity to something like the strong nuclear force at short range. The ratio is then independent of the units used and as far as I know there is no way to predict why the dimensionless constants have the values they have.

Yes, that is correct. The dimensionless fundamental constants of a theory do reflect a limitation of the theory. I don't expect that there will ever be a complete theory of everything without any dimensionless constants, so I think it is a limitation that we will have to just accept. But nonetheless, it is an actual limitation of the theory.

 

[Bill_K]

What about when we compare the force of gravity to something like the strong nuclear force at short range. The ratio is then independent of the units used and as far as I know there is no way to predict why the dimensionless constants have the values they have.

All the other forces have dimensionless coupling constants. Gravity does not. You can use G to form the Planck units, but nothing that is dimensionless.

Ratios such as the above that seem to characterize the strength of gravity actually do not. For example, comparison of the electrostatic force between two particles to the gravitational force between them only tells you about the particles themselves, namely their charge to mass ratio.

 

[yuiop]

All the other forces have dimensionless coupling constants. Gravity does not. You can use G to form the Planck units, but nothing that is dimensionless.

I suspected I might of chosen a bad example :). Does the lack of a dimensionless coupling constant for gravity, have anything to do with the problems of forming a GUT?

 

[yogi]

Again, dimensionful universal constants like G do not represent any limitation of any theory. They are simply artifacts of our system of units. There can never be any "first principle calculations" because they don't come from physics at all. They come from our chosen system of units. That is all.

That simply isn't correct. It isn't a criticism of any theory, and we understand completely. G has the value it does because we use the units we use.

You miss the point of that observation - of course the numerical value of G depends upon the units - but in the context of my statement it makes no difference if you express c in units of meters per second or furlongs per fortnight - the statement that G has certain a certain value refers to its relation to other things we measure - as the post above (#18) points out.

 

[Dale]

You miss the point of that observation - of course the numerical value of G depends upon the units - but in the context of my statement it makes no difference if you express c in units of meters per second or furlongs per fortnight - the statement that G has certain a certain value refers to its relation to other things we measure - as the post above (#18) points out.

No, it doesn't, as this points out:
http://math.ucr.edu/home/baez/constants.html

G and c and h have no meaning beyond the system of units chosen. They are entirely dependent on the system of units chosen and provide no information whatsoever as to the properties of the universe itself or the outcomes of any physical measurements. Here is an interesting exercise that I went through and posted on the topic:
https://www.physicsforums.com/showpost.php?p=2011753&postcount=55
https://www.physicsforums.com/showpost.php?p=2015734&postcount=68

G is only one piece of information, one parameter. Because it depends on your system of units it clearly tells you about your system of units. Since it is only one piece of information, once you have used that information to tell you about your units there is no additional information left over to tell you anything about the universe or physics.

 

[Bill_K]

the statement that G has certain a certain value refers to its relation to other things we measure - as the post above (#18) points out.

And as #20 above points out, these relationships don't tell you anything at all about G.

 

[yogi]

This is a response to post 13 and 17. First, I do not read the John Baez paper the way you have interpreted it...IT covers a lot of subjects very briefly - and some of the statements can be taken in ways that might appear to be something different that what John is saying -

In order to avoid going too far astray for the issue raised by the OP, its worth clarifying what is meant by the gravitational constant. It is simply a coefficient - it could be a long term variable as many have suspected including Robert Dicke and P Dirac and other notables. For the purpose of discussing the significance of the dimensionality - whether it changes or not is not a critical shortcoming of GR. But the dimensionality itself is a big clue to the nature of G. Whatever units you choose - G boils down to volumetric acceleration per unit mass. If you use mks units this is expressed as meters^3 per sec^2 per kgm. Once you know the volumetric accel you can calculate G. One way to estimate the volumetric acceleration is to use the relationship which Robert Dicke claimed to be the ratio between inertial and gravitational mass, namely GM/Rc^2 = 1 within the limits of experimental error. From this calculate G based upon R, the mass of the universe M, and the velocity of light.

The dimensionality of G is revealing - it tells us something about the universe. In fact it tells us a lot more than what I have illustrated here - but that is neither proper or necessary to make my point. This is lost by equating c = 1, G = 1 ect ... it throws away valuable information which can be is useful in these types of puzzles. Of course, one can argue all this is a coincidence -

 

[Dale]

The dimensionality of G is revealing - it tells us something about the universe.

It only tells us something about our units. Did you read the links to the PF posts that I provided in post 23? I worked through several examples showing that only the dimensionless constants have any measurable significance. You can change dimensionful constants in a way to keep the dimensionless constants unchanged and you get no physically measurable difference.

Consider Newton's 2nd law in its original form: f=kma. Suppose that you had a system of units where force was measured by a standard elastic band stretched a standard length and mass, length, and time with their respective prototypes or standards. In that system of units k would be a dimensionful universal constant with dimensions of FT²/(ML). This is, in fact, how Newton and several generations of scientists afterwards thought of force and Newton's second law. They also believed that measurements of k were telling them something about the universe.

Eventually, the accuracy of measurements of k would be limited by the reproducibility of the standard elastic bands. We would come to realize that instead of telling us anything about the universe, k would merely be telling us about our elastic band manufacturing process. To remedy that, scientists could define k as an exact number, similarly to how c is defined in SI units. Then the unit of force would be defined in terms of standard accelerations and standard masses.

Now, it is clear that k is only telling us about our system of units, since it is a defined constant in that system of units. And the fact that we had the option to do that shows that we were never, in fact, measuring anything other than a piece of information about our system of units. It is only a small step from that to replacing k by the dimensionless number 1, dropping it from our equations, and using a system of units which is consistent with Newton's 2nd law.

The fact that k=1 (dimensionless) in SI units shows that the SI system of units is consistent with Newton's 2nd law. The fact that G is not a dimensionless 1 merely tells us that the SI system of units is not consistent with the EFE. It tells us nothing about the universe, any more than Newton's k did.

 

[yogi]

It only tells us something about our units. Did you read the links to the PF posts that I provided in post 23? I worked through several examples showing that only the dimensionless constants have any measurable significance. You can change dimensionful constants in a way to keep the dimensionless constants unchanged and you get no physically measurable difference.

Consider Newton's 2nd law in its original form: f=kma. Suppose that you had a system of units where force was measured by a standard elastic band stretched a standard length and mass, length, and time with their respective prototypes or standards. In that system of units k would be a dimensionful universal constant with dimensions of FT²/(ML). This is, in fact, how Newton and several generations of scientists afterwards thought of force and Newton's second law. They also believed that measurements of k were telling them something about the universe.

Eventually, the accuracy of measurements of k would be limited by the reproducibility of the standard elastic bands. We would come to realize that instead of telling us anything about the universe, k would merely be telling us about our elastic band manufacturing process. To remedy that, scientists could define k as an exact number, similarly to how c is defined in SI units. Then the unit of force would be defined in terms of standard accelerations and standard masses.

Now, it is clear that k is only telling us about our system of units, since it is a defined constant in that system of units. And the fact that we had the option to do that shows that we were never, in fact, measuring anything other than a piece of information about our system of units. It is only a small step from that to replacing k by the dimensionless number 1, dropping it from our equations, and using a system of units which is consistent with Newton's 2nd law.

The fact that k=1 (dimensionless) in SI units shows that the SI system of units is consistent with Newton's 2nd law. The fact that G is not a dimensionless 1 merely tells us that the SI system of units is not consistent with the EFE. It tells us nothing about the universe, any more than Newton's k did.

AS we are getting further from the OP's concerns re GR to a general discussion of units - this should probably be revived as separate a new thread - but since you have taken the time to write a post that deserves a reply, I will oblige.

My first comment would be that in matters of global significance, rate of change of momentum as force is IMO perhaps the most fundamental transform of physics - it is stellar example of the holistic continuity of the universe - as valid in its complete form (d/dt)(mv) as it was prior to the discovery of SR. That said, the application of the F = ma half of the relationship to a spring would be incomplete and not generally observed as a statement about the universe - it is a description of the spring - how its cut, treated and the matter it is made of. If the analogy is upgraded to a uniform steel bar a much better model is created in that we can find a stretching modulus and a bulk modulus that tells us something about the material - the connection to the universe however is still very oblique - if one had sufficient information about how much heat was created during compression or lost during distension you might begin to find some relationships that could be extended to the universe [As Sagan once said if you want to make an apple Pie from scratch,you must first create the Universe]- in fact it might lead to you to the conclusion that the energy of expansion and distension is actually supplied via space - and with great imagination you could tie the modulus of the bar to some global property. Richard Feynman in Volume II of his lectures on physics briefly ponders these ideas in connection with the heating of an electrical resistor and the charging energy of a capacitor - very fascinating implications...all this brings me to my third comment

The gravitational constant as a dynamic inertial modulus. Depending upon the expansion model one selects, the volumetric acceleration of the universe per unit area defines a characteristic of the expanding space - 3(c^2)/R. This simple expression leads to many surprising relationships - for example the propagation velocity in free space.

These are interesting subjects - but as I said we are far from the subject - if you would like to chat more I would be happy to do so - send me a personal email

Happy Thanksgiving

Yogi

 

[Dale]

That said, the application of the F = ma half of the relationship to a spring would be incomplete and not generally observed as a statement about the universe - it is a description of the spring - how its cut, treated and the matter it is made of.

No, it isn't. The k in F=kma is a universal constant for a given set of units. E.g. in US customary units $k=0.031 \; lb_f s^2/lb_m ft$. It doesn't matter if the net force is provided by springs or by electrostatic repulsion or by a pneumatic actuator or what. In all cases a given amount of force will provide the same amount of acceleration.

The only place where the manufacturing details are important is in terms of reproducibility. How it is made influences how reproducible your force prototype is, but k itself is the same regardless of what experimental set up you use. All net forces would have the same k.

Here is another example. You consider G to be a property of the universe. Its first appearance is in Newton's law of gravitation: $f = G m_1 m_2/r^2$. There is another very similar law called Coulomb's law: $f = k_e q_1 q_2/r^2$. If you consider the gravitational constant, G, to be a property of the universe then I would suspect that you would also consider the Coulomb constant, $k_e$, to be a property of the universe.

In SI units $k_e=8.99\;10^9\;Nm^2/C^2$, but in Gaussian units $k_e=1$ which is dimensionless. Clearly $k_e$ tells us about our units, not the universe. So why do you think G is different?

 

[yogi]

In the case of the electric force between two charged particles - we have the same inverse square form of action - So let us write the electric force as F = K(q^2)/d^2. K in this formulization tells us about the universe just as G does
in f = G(m^2)/d^2. Take the ratio of F/f and use the measured value of the electron mass m_e for m. What is revealed is that these things called q are about 10^42 times more effective in producing forces at a separation distance d than can be explained by the matter content acted upon by acceleration. This express the essence of the charge/mass force efficacy which would seem to be, by any reckoning, an important attribute of the universe.

I am not sure how you are applying acceleration to springs - when I think of springs in tension or compression I imagine F as dE/dS and not (d/dt)(mv) - I suppose you can equate this to an acceleration of the spring once you know the spring constant in a special situation - I don't know how it applies to the universe unless you are considering space as some sort of elastic, which it is not.

 

[Dale]

K in this formulization tells us about the universe just as G does

Then how can K be set to a dimensionless value of 1 by choice of units?

 

[yogi]

When you form a dimensionless ratio, such as alpha, you cannot let everything = 1. If you let K = 1, you have to scale q to get the correct force ratio (10^42). If G and K are both set equal to l you would have to express q in terms of mass units which is a contradiction of logic because we already know the electron mass unit is m_e.

I have always been a critic of Planck units as standing for something fundamental - nothing has ever really come out of it that makes any predictions about the real world - in that regard I liked John Baez comments re the difficulty of handling Planck units in the classical world in the paper you cited - what I don't understand is why one set of units formed from one set of so called constants is any better than any other - e.g., Stoney Constants, or Weinberg's mass constant - the physics communities thinking is that G must be a contributor to the derivation of a set of fundamental units because it has global significance - but so does q since it is a long range ... and of much greater strength. If you like G as a fundamental constant entity ( I don't) it is easy to create a set of dimensions from G, c and M_u where the latter represents the mass of the universe which most feel is constant (not I, however). But in any event, my point is that using these three so called constants of nature you arrive at GMu/c^2 as a unit of length commensurate with the Hubble scale whereas GMu/c^3 corresponds to the Hubble time and the third constant for mass is already decided upon (i.e., Mu).
If you don't like Mu as a constant, try m_e and get a length 10^-57. You may recognize that length
as significant, but my point is, its easy to generate a set of dimensional units from the many items now considered constant. IMO there may actually be only one constant c since it represent the coupling between space and time. All the rest is numerology. Modern physics tries to make sense out of the Planck scale, while at the same time tacitly dismissing the Planck mass and Planck time as having no known significance. This is inconsistent. `

 

[Dale]

When you form a dimensionless ratio, such as alpha,

You seem to be dodging the question. I agree that the fine structure constant is a dimensionless constant and it actually does tell us something meaningful about physics. That is not relevant to the question at hand which is regarding dimensionful constants such as G and K.

Again, K can be made to completely drop out of Coulomb's law simply by using Gaussian units. Thus, its value and even its existence depends entirely on the system of units. So how can it possibly tell you anything about the universe?

 

[yogi]

Back to you Dale

If you let K= 1, then you can use values for q such that the ratio of F/f is a dimensionless magnitude = 10^42. There is nothing magic about K per se. The ratio of F/f is what is significant - the magnitude of the one with respect to the other. Once you know the ratio, you can turn your attention to why the ratio has the value of 10^42.

But here is what is lost by dropping the units or using cumbersome units. Taking the example of gravity again - usually expressed as ntn-meters squared per kgm squared. To me, that doesn't translate to anything obvious - but when converted to meters cubed per second squared per kgm - something may come to mind - can you think of anything that has an accelerating volume to which the constant might be applicable?

 

[Dale]

There is nothing magic about K per se. The ratio of F/f is what is significant - the magnitude of the one with respect to the other.

Exactly my point. Same with G. There is also nothing magic about G per se, nor any other universal dimensionful constant. Only dimensionless quantities like your F/f tell us anything about physics.

Taking the example of gravity again - usually expressed as ntn-meters squared per kgm squared. To me, that doesn't translate to anything obvious - but when converted to meters cubed per second squared per kgm - something may come to mind - can you think of anything that has an accelerating volume to which the constant might be applicable?

Regardless of what you might want to apply the constant to, you can always choose units such that its value is a dimensionless 1 and it drops out of the equations entirely. Once you do that, then you look at the equations and any dimensionless constants to provide the meaning that you might erroneously want to attribute to G.

 

[yogi]

If i write a statement f = Gmm'/r^2 and let G = 1, then to get get a meaningful answer in terms of ntn, all the information must be encoded into the masses because kgm squared over meters squared does not equal force. You would have to write each mass in terms of an effective acceleration to the 1/2 power.

I recall reading some years ago, that in his original formulation, Newton treated the coefficient as a combination which incorporated the Sun - so the equation reduced to a constant and one mass divided by the distance squared. The information is retained either way - Newton's relationship between acceleration and mass is not lost.

When a constant such as alpha shows up in physics as dimensional-less - it is not always easy to unravel what meaning should be given to the factors that lead to the loss of dimension-ality We know alpha is the ratio of the velocity of an electron in the first Bohr orbit to c, but why should it have this value and not some other? No doubt there is some theory yet to be revealed that will explain this - it became an obsession for Eddington. My point is that alpha is consternation - we really don't know what has been canceled out to form the ratio. Alpha is a prime example of information lost