Hypothetically, per Equivalence Principle, what would kilograms be for any given mass in a variable G?

Asking it this way may be illustrated as follows:

We are in a region of space where G is much higher than here, say beyond the solar system somewhere. Let's say it's 10G. Then, per equivalence, what would the kilograms measuring mass, or inertia, be in that region? Would kilograms be 10 times greater than here, 10kg? Or perhaps 100 times greater?

Think of this, and why I am bringing up this hypothetical question:

If G is 10 times what we know as the universal Newton's G, and the equivalence requires that inertial mass measured in kg is also 10 times, what happens to the kg in terms of what we know as measurement of mass here? So per equivalence, 10G gives us 10kg, but this may be only a local pehonomenon, meaning that 10kg in our kilograms may be 10 times that, viz. 100kg.

Is there an issue here, or kill the thread now? :roll:

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"As the universe manifests itself as an infinite variety of patterns and forms, the more an individual realizes himself to be one with that universe, the more of an individual he becomes." -- Alan Watts

This should be in the "Against The Mainstream" forum.


The Equivalence Principle says that the gravitational mass equals dynamical (a.k.a. inertial) mass.
It has nothing to do with the value of G.

Newtons' formula for gravitation:
F = G * (m*M) / r^2 (1)

Newton's second law:
F = M * a (2)

Equivalence principle: M in (1) is the same as M in (2).


As I said, 1 kg gravitational mass is 1 kg inertial mass, whatever the value of G.
What would change is the gravitational force on the mass.

Well, I suggest you look up the threads in the "Against The Mainstream" forum where Lunatik and Jerry try to argue in favour of a variable G.

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papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

Thanks papageno for your response. My purpose for entering this hypothetical question on the Equivalence Principle here (rather than Against the Mainstream, per Lunatik & Jerry) is not to argue for a variable G, which would be speculative, but to consider how such a (hypothetical future) discovery would affect our measure of mass in kilograms. Which kilograms would we use, and how would they be affected? Your response addresses how kilograms work at 1 G, which is known, but how would this change if we found a variable G, at 10G for example? Or would it not change at all, and still preserve equivalence?

To my thinking (and I must admit I really do not know the answer to this hypothetical question on measuring mass under a variable G scenario), the kilograms we developed in our 1G universe are in part a function of gravity, mainly Earth's gravity, so we can weigh things in kilograms. The Equivalence is that this same kilograms applies to F = Ma, as you pointed out, so we can measure inertial mass with the same unit. I believe it was Einstein who thus resolved that gravity and inertial mass are linked, which we know as the Equivalence Principle. So the question remains, in a hypothetical variable G, would the kilogram units remain the same, or forced to change?

I would think this is a valid astronomy-physics question, in anticipation of some point in the future that our distant space probes, or other observations, yield a variable G. To date, this has not been observed, to my knowledge. Perhaps this question of measurement in kilograms (at this point a merely philosophical question since we have not confirmed any change in Newton's G from its universal constant) should be explored in the event we find the universal G is something else. We must allow for nature to be a tricky place, so she might throw us a surprise. Would we know what to do with our units of measure of mass at that point if she did? :-?

__________________
"As the universe manifests itself as an infinite variety of patterns and forms, the more an individual realizes himself to be one with that universe, the more of an individual he becomes." -- Alan Watts

Equivalence principle and the value of G are independent from each other.
Do not confound mass and weight.


It would be the same.
The Equivalence principle is based on experimental results. Einstein decided to elevate to the status of postulate.

I explained it to Lunatik.
If G depended on positions, the mass of an object would not be affected, but the gravitational force would be.
A different force would give a different acceleration, because the inertial mass has not changed.
But this problem is no more exotic than a variable dielectric constant in electromagnetism (which gives us refraction, and lenses).

Yes, because the experiments used for the units would not change their outcome if we found something new.

__________________
papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

I see this really as a question referring to our units of measure, what we call kilograms. Can the same kilograms be used if G is different from what we know it to be as a universal constant?

In yours you said: "The Equivalence Principle says that the gravitational mass equals dynamical (a.k.a. inertial) mass. It has nothing to do with the value of G."

Granted, given that G is universally the same, it has nothing to do with it, though G is part of the function describing Newton's formula for gravitation, as per yours above:

F = G * (m*M) / r^2 , which is related to Newton's second law:

F = M * a

Now, this equivalence can be also shown as:

F = M * a = M * (G*m) / r^2, where by default a = (G*m) / r^2

which also means: G = (r^2 * a) / m

Now assume that both a and r^2 are fixed, same values, but G is greater, viz. G1 = 10G. So we have:

G1 = (r^2 * a) / m1, except now of necessity, m1 = 1/10th of m, if G1 = 10G.

However the mass had not changed, same mass (same atomic composition and volume), so the mass did not suddenly shrink to a tenth of its original form. What changed instead was that the measures in kilograms had changed, to where now the kilograms are 10 times greater than the kilograms used earlier, to match up with G ten times Newton's G.

Can you see how this could be a problem? Though for now, given that G is universal, we don't have a problem. But if it were discovered that G is different, something might have to be adjusted in the measure of our (Earth derived) kilograms.

(That said, I still think that the answer above, kg1 = 10kg is wrong, but I'm not sure of what the right answer is. I suspect a is in fact not fixed as assumed, for a variable G. Hypothetically, the real answer may be more like kg1 = 100 kg, if G1 = 10G, or its squared. It may take 10 times as much acceleration to move the same mass in 10G, so a is not fixed, but rather a1 = 10X a. But I don't know this.)

So you can see why I am frustrated, and I don't like my own answers! There must be a better way to see this.

Interesting if this might not apply as well to a " variable dielectric constant in electromagnetism", since it might impact how light bends around stars, which would impact gravitational lensing. :-?

Actually, now that I re-read this, I can almost begin to appreciate the frustration Galileo must have had trying to prove why the Earth is not standing still with the heavens going around, but instead it is spinning.

__________________
"As the universe manifests itself as an infinite variety of patterns and forms, the more an individual realizes himself to be one with that universe, the more of an individual he becomes." -- Alan Watts

The definition of the unit kilogram has nothing to do with G.

No, it has nothing to do with G, whether it is constant or not.

As you can see, G does not affect M, which is the mass the Equivalence has been applied to, but affects the acceleration a the mass M is subjected to.


But we applied the Equivalence principle to M.
By changing the value of G, you changed the force M and m are subjected to.

If the only mean we had to measure the mass m, was from the acceleration of M due to its gravitational interaction with m, then changing G would affect our measured m because the acceleration is different (assuming that we did not know that G has a different value).

No. What changed is the gravitational force between the two masses, and hence the acceleration changed.

This has nothing to do with the units.

No. The units would not need to be adjusted.

We don't need to change the unit of electric charge because the dielectric constant is not universal in materials.

This is the point.

You just need to realize that the value of the constant G does not affect the mass of an object.

Refraction is very common phenomenon, which is due to a change in dielectric constant: this is why lenses work.
A G dependent on position would not be more exotic than refraction.

__________________
papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

Let's see if this anecdotal illustration better explains how I see it:

I live on planet X (not a real planet we know) where gravity's proportional G is ten times what we know here as G, so Xian's gravity is 10G (in Earth terms). I very carefully measure this Gx, set up my weights of measure in kilograms per this Gx, then work out the Equivalence Principle per F = Ma = G*(Mm)/ r^2 (everyone knows gravity and inertial mass are related), so my mass Mx (and mx) is measured in the kilograms I developed. Now I am content, since I worked it all out, where my units of measure for weight on X are measured in kilograms, for which I then established an equivalence with F = Ma, where Mx is measured in kgx. Confident, I now teach at a prominent Xian university and (since I never traveled off world) merrily accept that my Gx and kilograms kgx are universal.

Four hundred years go by and in a very fancy space ship arrive people (to every Xian's surprise) who say they're from some far off place called Earth. Now these Earthians (all descendents of a prominent university where physics had been taught with confidence for the past 400 years) are very eager to impress their newfound Xians, so they too go and measure G and kilograms. To their surprise, they discover that the Xians are using a different unit of measure for kilograms than the Earthian measure. So they carefully explain to the Xians that G is not what they thought it is (since it is universal), but it is 10 times less, and that only the "acceleration" derived from the greater gravity of their planet is 10 times greater. Kilograms cannot change. They further explain that what they had done wrong was make a tenfold mistake (or hundredfold?) in estimating their kilograms. They made the error of thinking that their Gx (which is 10G in Earthian terms) is the correct G, so the kilograms they developed was based on this error. Since, as your Earthian student descendents take great pains to explain, only "aceleration" is ten times what it should be, so mass measured in kilograms has to be the same, so their Xian kilograms are obviously wrong. The Xians challenge this, saying no, that the Earthian kilograms are wrong, because they are only a tenth of what they should be for G, as everyone who studied at the Xian universsity can tell you, and that their kilograms are correct, since the acceleration works out exactly for their equivalence principle F = Ma. In fact, they (barely) tolerantly explain, the Earthians had got it wrong. In thinking that G is only a tenth of Gx (everyone knows this is a universal constant), it is the Earthians who should adjust their kilograms to reflect the correct G. And that correct measure of mass is tenfold Earthian kilograms, so obviously Xian kilograms are the correct measure for mass.

Well, this heated discussion goes on for some time, and as their appears no solution to this problem, with both Earthians and Xians convinced their measures for mass are correct, it appears the two worlds are in danger of declaring war. Knowing that we really don't know, my (long descendent) student politely (diplomatically) reminds his friends at the Xian academy that it was smart Earthians who came to Xian, and not the otherway around, so perhaps Earthian measured kilograms of mass should be adopted (though they are different from Xian kilograms), just to keep the peace. But he gets shouted down because they say the Earthians are on X now, so must use Xian kilograms instead. :-?

Who is right?

__________________
"As the universe manifests itself as an infinite variety of patterns and forms, the more an individual realizes himself to be one with that universe, the more of an individual he becomes." -- Alan Watts

DISCLAIMER

Let it be know to all who post here and read, that "Lunatik" had been retired, put into permanent "safing" with post # 555, and that my lame attempt to revive him with "Luna2uno" had been in violation of BA rules (prior unbeknownst to me, but Phil made the point), so neither name shall henceforth be shown. All future posts will now default to my other (unwitting alias), from here on in my legitimate handle: "nutant gene 71".

I fully accept any and all criticisms, scorn, ridicule, shunning, or wisecracks, for I am truly repentant.

And I would not be here were it not the high level with which I hold the participants of this board, myself excepted.

Mea culpa. ops:

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Credibility is simply incredible... sometimes even to me.
disclaimer

Luna2uno, I still don't understand your question. I'm pretty confused about what you're asking right now. I've only skimmed the last half of the thread, but let me attempt a response.

As papageno said, don't confuse mass and weight. Mass is an intrinsic property to matter, where as weight is force caused by gravity and determined by mass, distance, and the value of G. (The equivalence principle does not apply here, as a = G*M/R^2 [your mass, m, remains the same].) The amount of mass here where G=G would be the same amount where G'=2G.

Now, different systems of units are a completely different beast. Your story seems to discuss different systems of units. The amount of mass is the amount of mass is the amount of mass, no matter how it is defined. A mass of 10 kg is the same amount of mass whether measured in kg, g, slugs, or whatever. 10 miles is the same distance if measured in miles, feet, meters, or parsecs, in just the same way as above. It's also true that G has different numerical values in units of kg,m,s, or g,cm,s, or slugs,feet,fortnights, but these are all the same value.

Mass doesn't change if G does.

So, Luna2uno, you were Lunatik.
And you still don't get the distinction between mass as physical quantity and the unit of measurement to express that quantity in numbers.

Exactly my point.

Whether G is a universal constant or not, it has absolutely no bearing on the unit kilogram.

__________________
papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

Yes, I agree with you and Tobin Dax, that it doesn't matter what units of measuring mass are used (it could be stones), since mass is mass, always the same. Nothing changed as far as the physical properties of the object of mass is concerned, whether weighed or accelerated. What I had been trying to show, why this is a problem for me, is that a unit of measure for mass derived in one G is going to be different for the same unit of measure in another G. In other words, 1 kg doesn not equal 10 kg for the same mass. So this unit of measure chosen is dependent on G where it is derived.

Let me show it another way. As shown above, G can be defined as G = r^2 * a/ m. But then it must also be: 10G = r^2 * 10a/ m, so mass is still the same, only G' is ten times what we know. Now, if the Xians (per illustration above) think their 10G is merely Gx (one unit of G'), then of necessity their equation would be: Gx = r^2 * 10a/ (?m). This is the problem I'm trying to show. Should (?m) now not be, in Xian kilograms, 10m? So per "their" equivalence, kgx = 10kg in ours.

Why is this important, since it appears a rather mundane problem? I can see it as a problem when it comes to estimating the size and density of a foreign body should G there be different from ours. Back to planet X, if Gx = 10G, and we're using our kilograms, then Gx = r^2 * 10a/ m, but if our kilograms are used, then "mx", planet X's mass, is 10 kg in our terms, but one kgx in theirs. I interpret this as us thinking their planet X should be either 10 times the size of Earth (which it is not) or 10 times the density. Another way is to say that their planet, given its known size parameters, is actually ten times gravity denser than it should be. In fact, if Gx is ten times G, the density of the planet need not be affected, only the results of what things would weigh there, and by equivalence, how things would respond to acceleration (and perhaps also affect their centripetal force, so affect their planetary spin).

Can you see where this is taking me? If, for example, a neutron star (so called) has a great mass equivalent (in our G terms) to several solar masses, we of necessity must think it is very dense for the amount of gravity it displays (hence the resultant spin is very great), that its composition must of necessity be something we do not have here in our vicinity of space, though we know it is very small by comparrison to our Sun. But if it is the G of the neutron star that is so great that it "appears" as if it were several solar masses (I'll skip for now the reasoning why this might be), then its size may be even larger than we estimate (as if made of only neutrons), and density not necessarily so compact. In fact, it may be not too much denser than our own Sun, and perhaps only comparatively smaller if its internal radiation pressure is less, meaning it was a small star to start with.

Take another example. I read somewhere that Jupiter may have a rocky core about two or three Earth masses. Whether or not this is true, I can't confirm since I never saw how this was arrived at, whether through radar probing of Jupiter's interior, or derived from atmospheric occultation, or from ephemeris spin data(?). But if true, given a constant G, how could a small rocky core hold such a vast atmosphere? Unless the G is much greater than supposed, it is virtually impossible as a gas. (This may be another reason why speculations on Jupiter's atmosphere is that it has a liquid core?) I know all the arguments against why this cannot be true, how the springs on Huygens worked properly, etc. (in fact I have no way of knowing whether or not my hypothetical planetary G' calculations are right, as shown earlier), but if mass is measured in Earth's kg, then Jupiter's atmopshere cannot be possible for such a small rocky core. A small rocky core can hold a very large atmopshere only if the acceleration towards the center of mass, the gravity, is much greater for the size and density of the planet would otherwise allow. This is why I think the kilograms used is important, because if they are not adjusted for local G conditions, like in the neutron star example above, we may be overestimating density versus what it really is. A neutron star may not be so dense, only its mass (due to much higher G) acts as if it were.

There is also a practical side to this question (on hypothetical mass in a hypothetical variable G), and that has to do with how space probes will behave near any under-over estimated planetary body. If we can get that right, then we can have a more direct physics to plot flight paths without having to use adjustment tables, and then numerous inflight adjustments. In effect, it cleans up our engineering task for space flight with a better physics. It's not that we fail to get there, since using gravitational assist trajectories are of necessity self correcting (G * M as a product value is still the same, even if G and M are wrong), but that we may be handicapped with a constant G. A better way may be to use local kilograms (as opposed to Earth kilograms) to work out the dynamics of how a spaceprobe will behave in the vicinity of another planet, hypothetically.

So, can a (variable) measure of mass size and density improve on Newton's physics for a variable G? That ultimately is the question. Can we better understand very distant bodies, such as neutron stars with variable kg, adjusted for local G? Would our overall understanding of cosmology be improved, if G is found to be a variable (something we still do not know)? These were my reasons for bringing up this question. (At this point, however, I don't even want to get close to what this means for Einstein's General Relativity theory.) For this reason, I titled this question as "hypothetical" only, until such time that we find G to be otherwise than now postulated.

And I still do not know what the Xian's kilograms should be, ten fold or a hundred fold.

Sorry about the identity mixups, it may be due to a "multiple personality" syndrome. ops: I never like "Lunatik" anyway.

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Credibility is simply incredible... sometimes even to me.
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Can you provide references for these "numerous" presumably unexplained and unplanned "inflight adjustments" you claim are happening? Also, what are "adjustment tables" and can you provide a reference?

Alas, I cannot at this time, so take my statement under advisement. I can only refer you to this "gravity anomaly" page for now, only very indirectly related. This ESA page on trajectory corrections is better, but still not it. If I find different, I'll report. I read something somewhere, but can't put my fingers on it now...

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Credibility is simply incredible... sometimes even to me.
disclaimer

Since you cannot provide any evidence for "numerous inflight adjustments" or "adjustment tables", I will take your statements as if you just made them up for your own benefit.